,T 
 
 ^'•T,: . 
 
I53P^MHI 
 
 IF YOU ARE A 
 LANDOWNER . . . 
 
 considering land grading for surface ir- 
 rigation, this circular tells you how to go 
 about it; helps you decide how much of 
 the job you want to do yourself, and how 
 much you want done by professionals. It 
 gives you facts that will make you a better- 
 informed partner in your contracts with 
 the engineers and land-levelers. It tells 
 you about the various pieces of equip- 
 ment and what they can be expected to 
 accomplish. It aids you in writing contracts 
 that will meet your needs and protect you 
 from misunderstanding, injustice, and loss. 
 
 IF YOU ARE A 
 CIVIL ENGINEER . . . 
 
 you may be interested in the land-grading 
 and other pertinent calculations in the ap- 
 pendix, and in the information about con- 
 tracts. 
 
 IF YOU ARE AN 
 EARTH-MOVING 
 CONTRACTOR . . . 
 
 you will find information about grading 
 equipment and about efficiency computa- 
 tions and contracts in the appendix. 
 
GRADING LAND FOR 1 
 
 JAMES C. MARR 
 
 CONTENTS 
 
 Factors to Consider Before Grading 5 
 
 Steps to Take to Prepare Land Grading 8 
 
 What You Should Know About Equipment 20 
 
 Suggestions for Contracts and Specifications 27 
 
 Appendix 32 
 
 I. Methods of Land-Grading Calculations 32 
 
 II. Computation of Cut and Fill Adjustments 40 
 
 III. Earthwork Calculations 41 
 
 IV. Haul Distance Calculations 45 
 
 THE AUTHOR 
 
 James C. Marr is a former Lecturer in Irrigation and Specialist in the Experiment Sta- 
 tion, University of California, Davis. 
 
 REVISED JULY, 1957 
 
SURFACE IRRIGATION 
 
 Factors to Consider Before Grading 
 
 Surface irrigation requires land over 
 which water can flow evenly and without 
 causing erosion. 
 
 Before you take steps to grade your 
 land for that type of irrigation you have 
 to find answers to these two questions: 
 
 1. Is your site suitable for surface irri- 
 gation? 
 
 2. Which method of surface irrigation 
 should you use? 
 
 Is Your Site Suitable? 
 
 There are seven general groups of 
 conditions which may make surface irri- 
 gation unfeasible or uneconomical. 
 
 Excessively permeable soils. Sandy 
 or gravelly soils, and soils consisting 
 largely of organic material, are charac- 
 terized by a high water intake rate. Soils 
 usually absorb water relatively fast at 
 first, and finally at a slower, steady rate. 
 If the final water intake rate exceeds 
 three inches per hour, or less in some 
 cases, it may be assumed that surface 
 irrigation will prove wasteful of water 
 and may cause drainage and salinity 
 problems in most locations due to the 
 excessive use of water required to irri- 
 gate. Hence, unless it has been found 
 economical to do so in a particular case, 
 it may be a mistake to grade such land. 
 
 Insufficient soil depth. A shallow 
 soil may be arable and irrigable and still 
 not have sufficient depth to permit nec- 
 essary grading for surface irrigation. 
 This is particularly the case when the 
 depth of cut required for land grading 
 exceeds the depth of top soil with the 
 
 [ 
 
 result that cobblestones or other unde- 
 sirable material are brought to the sur- 
 face where they permanently reduce crop 
 production. Exposure of the subsoil, how- 
 ever, frequently presents no problem, or 
 may require only the application of nitro- 
 gen fertilizer. Your local farm advisor 
 will know how serious the problem is 
 and can tell you how to deal with it. 
 
 Rough topography. Roughness of 
 topography governs to a large extent the 
 cost of grading. In this sense it is often 
 the limiting factor in the preparation of 
 land for irrigation. Jobs that require 
 moving more than 800 to 1,000 cubic 
 yards of earth per acre are ordinarily 
 considered too expensive to undertake. 
 
 Steep slopes. Slope limitations are 
 necessary for proper control of the irri- 
 gation water. On steep slopes, generally, 
 water directed down the slope tends to 
 channel and cause serious erosion. Fur- 
 thermore, as the slope increases, it be- 
 comes in some cases more difficult to wet 
 the soil without allowing an excessive 
 amount of waste-water runoff. This is 
 especially the case when either the bor- 
 der or furrow method of irrigation is 
 used, and the length of run — the distance 
 the water travels — is short. Specific slope 
 limitations for the different surface meth- 
 ods of irrigation are listed in the table 
 on pages 6 and 7. 
 
 Absence of drainage. A difficult-to- 
 solve drainage problem sometimes pre- 
 cludes the use of surface irrigation and 
 the need to grade land. An example of 
 this condition are areas consisting of 
 very flat land with porous soil and a 
 
 5] 
 
Guide for selecting a method ©J 
 
 Irrigation 
 Method 
 
 Topography Crops 
 
 Remarks 
 
 Ordinary 
 furrows 
 
 Zigzag 
 furrows 
 
 Check back 
 and cross 
 furrows 
 
 Corrugations 
 
 Flat land slopes 
 capable of being 
 graded to 0.15% 
 slope or less 
 
 Land slopes capable 
 of being graded 
 to 1% slope or less 
 but preferably less 
 than 0.4% 
 
 Land slopes capable 
 of being graded to 
 1% slope or less 
 
 Land slopes capable 
 of being graded to 
 0.2% slope or less 
 
 Land slopes capable 
 of being graded to 
 slopes between 0.5% 
 and 12% 
 
 Commercial 
 
 vegetable 
 
 crops 
 
 Row crops 
 and fruit 
 
 Fruit 
 
 Fruit 
 
 Alfalfa, 
 pasture and 
 grain 
 
 Graded 
 
 Variable land 
 
 Row crops 
 
 contour 
 
 slopes of 2% to 
 
 and fruit 
 
 furrows 
 
 25% but preferably 
 less than 8% 
 
 
 This adaptation of the furrow method 
 is especially desirable for truck farm- 
 ing. The land surface should be 
 graded as accurately as possible, so 
 the ridges between adjacent furrows 
 will be wetted through without being 
 overtopped by the irrigation water. 
 This is especially important if vege- 
 table crops are planted in dry soil 
 and irrigated up. 
 
 Surface grading similar to that re- 
 quired for commercial vegetable 
 crops, but less accurate especially 
 for slopes greater than 0.4%. 
 
 This method is designed partially to 
 check the flow of water on steep 
 slopes. It is desirable but not essen- 
 tial that the grade in the direction 
 of irrigation be uniform. Any adverse 
 grade and sharp grade change 
 should at least be leveled out. 
 
 This method is especially designed to 
 obtain adequate distribution and 
 penetration of moisture in soils with 
 low water intake rates. 
 
 This method is especially adapted to 
 steep land and small irrigation 
 streams. An even grade in the direc- 
 tion of irrigation is desirable but not 
 essential. Sharp grade changes and 
 reverse grades should at least be 
 smoothed out. Due to the tendency 
 of corrugations to clog and overflow 
 and cause serious erosion, cross slope 
 should be avoided as much as pos- 
 sible. 
 
 Especially adapted to row crops on 
 steep land, though hazardous due to 
 possible erosion from heavy rainfall. 
 Unsuitable for rodent-infested fields 
 or soils that crack excessively. Actual 
 grade in the direction of irrigation 
 0.5% to 1.5%. No grading required 
 beyond filling gullies and removal of 
 abrupt ridges. 
 
 [6] 
 
jrface irrigation to fit your land 
 
 Irrigation 
 Method 
 
 Topography 
 
 Crops 
 
 Remarks 
 
 Widely spaced 
 borders 
 
 Land slopes capable 
 of being graded to 
 less than 1% slope 
 and preferably 
 0.2% 
 
 Alfalfa and The most desirable surface method 
 
 other deep- for irrigating close-growing crops 
 
 rooted, close- where topographical conditions are 
 growing crops favorable. Even grade in the direc- 
 and orchards tion of irrigation is required on flat 
 land and is desirable but not essen- 
 tial on slopes of more than 0.5%. 
 Grade changes should be slight and 
 reverse grades must be avoided. 
 Cross slope is permissible when con- 
 fined to differences in elevation be- 
 tween border strips of 0.2 to 0.3 foot. 
 
 Closely spaced 
 borders 
 
 Land slopes capable 
 of being graded to 
 4% slope or less 
 and preferably 
 less than 1% 
 
 Pastui 
 
 Especially adapted to shallow soils 
 underlain by clay pan or soils that 
 have a low water intake rate. Even 
 grade in the direction of irrigation is 
 desirable but not essential. Sharp 
 grade changes and reverse grades 
 should be smoothed out. Cross slope 
 is permissible when confined to dif- 
 ference in elevation between borders 
 of 0.2 to 0.3 foot. Since the border 
 strips may have less width, a greater 
 total cross slope is permissible than 
 for border-irrigated alfalfa. 
 
 Rectangular 
 checks 
 
 Land slopes capable 
 of being graded so 
 single or multiple 
 tree basins will 
 be level within 
 0.2 foot 
 
 Orchards Especially adapted to soils that have 
 
 either a relatively high or low water 
 intake rate. May require consider- 
 able grading. 
 
 Contour 
 checks 
 
 Slightly irregular Fruit, rice, Reduces the need to grade land, 
 
 land slopes of grain, and Frequently employed to avoid alto- 
 
 less than 1% forage crops gether the necessity of grading. 
 
 Adapted best to soils that have either 
 a high or low water intake rate. 
 
 Contour 
 
 Irregular slopes 
 
 Hay, pasture 
 
 ditches 
 
 up to 12% 
 
 and grain 
 
 Portable 
 
 Irregular land 
 
 Hay, pasture 
 
 pipes 
 
 surface 
 
 on small 
 scale 
 
 Especially adapted to foothill condi- 
 tions. Requires little or no surface 
 grading. 
 
 Minimum preparation of the land 
 surface required. 
 
 [7] 
 
fairly high water table lying within closed 
 basins or floodways. In order to grow 
 most crops successfully under these con- 
 ditions, it is necessary to apply irrigation 
 water accurately in sufficiently small 
 depths to avoid raising the water table 
 to the surface. This is sometimes impos- 
 sible with surface irrigation and thus the 
 grading of such land may not be advis- 
 able. 
 
 Unstable soil surface. Under some 
 soil or soil profile conditions "sink holes" 
 develop in flood-irrigated fields to such 
 an extent that land and water losses be- 
 come prohibitive. The trouble arises from 
 irrigation water running into gopher 
 holes, cracks or crevices followed by cav- 
 ing of the surrounding ground surface 
 and the loss of very large volumes of soil 
 and water into the subsurface. The ideal 
 remedy for such situations is, of course, 
 
 the use of pipe lines instead of ditches, 
 and overhead instead of surface irriga- 
 tion. Under these conditions, grading the 
 ground surface would be uncalled for. 
 
 Small irrigation streams. When a 
 small stream of water is used to surface- 
 irrigate a fairly porous soil, great in- 
 efficiency may occur due to unequal 
 wetting of the upper and lower ends of 
 furrows or checks. Better use of the water 
 in such cases might be possible by adopt- 
 ing overhead irrigation. 
 
 Which Method of Irrigation? 
 
 There are at least 11 different forms 
 of surface irrigation which have a bear- 
 ing on land grading. The table on pages 
 6 and 7 lists the most important of 
 these methods and the conditions for 
 which the various methods of surface 
 irrigation are suitable. 
 
 Steps to Take to Prepare for Land Grading 
 
 After you have decided that your site 
 is feasible and economical for surface 
 irrigation, and you have chosen the 
 method of irrigation you will use, the 
 time has come to prepare the land for 
 grading. At this point you have three 
 choices. 
 
 1. You can ask a civil engineer to 
 handle the surveying and land-grading 
 calculations, and an earth-moving con- 
 tractor to take care of the grading. 
 
 2. You can find a contracting firm 
 which will handle the engineering as well 
 as the grading. 
 
 3. You can undertake all or part of the 
 work yourself. 
 
 There are good reasons for preferring 
 the first arrangement. The extent of the 
 surveying, the involved nature of the 
 land-grading calculations, the high cost 
 of earth-moving equipment, and the skill 
 required for its efficient operation may 
 make it very difficult — perhaps inadvis- 
 able for landowners without prior ex- 
 perience — to undertake the job alone. 
 
 If you arrange with a single contractor 
 to handle the engineering as well as the 
 grading, you may place him in a position 
 to favor himself by planning a larger job 
 than necessary and by failing to rigidly 
 check and finish his land grading work 
 to the proper degree of tolerance. 
 
 If you hire engineers and contractors 
 to do the work, you should make sure 
 that the work is placed in capable hands, 
 and that the plan to be followed is suit- 
 able and equitable. In general, you stand 
 the best chance of getting a good job 
 done by thoroughly posting yourself on 
 the requirements, and then letting sepa- 
 rate contracts for the engineering and 
 the earth moving. This circular, in the 
 following sections, helps you gain in- 
 formation about the job to be done and 
 offers suggestions concerning the con- 
 tents of the contracts. 
 
 Selecting the time 
 
 It is uneconomical and injurious to the 
 soil to operate earth-moving equipment 
 
 [8] 
 
during wet weather or on muddy ground. 
 In all parts of the State you can depend 
 upon sufficient dry weather during the 
 six months' period from May through 
 October. This should be enough to com- 
 plete any ordinary land-grading job pro- 
 vided the operation is not delayed too 
 long and sufficient equipment is used. 
 Frequently delays are occasioned by use 
 of the land for growing crops and by the 
 men and equipment being engaged in 
 other work. Depending upon the depth 
 of earth to be moved, the length of haul, 
 and the type of equipment used, an ex- 
 perienced operator with one grader of 
 average size will grade land at the rate 
 of one to eight acres per day. If there is 
 more land than can be graded within the 
 expected period of fair weather, either 
 additional units should be put to work 
 or some of the area should be left to be 
 graded at another time. 
 
 Land clearing 
 
 Removal of the native vegetation is 
 sometimes left to be taken care of by the 
 earth-moving contractor. It may consist 
 of roto-beating or railing, windrowing, 
 and burning of small desert brush, or it 
 may include the removal with heavy 
 equipment of trees and large brush. 
 Bulky crop residue should be burned or 
 otherwise reduced or disposed of. In any 
 case, the clearing of the land must be 
 completed before earth moving starts. 
 (Land clearing methods are described in 
 U.S.D.A. Farmers' Bui. 1526.) 
 
 Surveying 
 
 When the time is right and the land is 
 available and cleared, work is usually 
 started by mapping the topography. 
 However, in some cases this operation 
 can be dispensed with and in others it 
 may be impractical unless some prelimi- 
 nary grading is done. It need not be done 
 if the land slopes are relatively steep, 1% 
 or more, and experienced equipment op- 
 erators are available who can grade such 
 steep land satisfactorily by eye. The pre- 
 
 liminary grading is necessary for hum- 
 mocky land which otherwise would re- 
 quire an excessive amount of surveying 
 for topographic mapping. 
 
 Staking 
 
 In order to provide marked spots 
 where the relative elevations of the orig- 
 inal ground surface may be obtained and 
 at which may be indicated the depths of 
 cut and fill for obtaining a graded sur- 
 face, stakes are set according to a pattern 
 similar to the one indicated in the 
 chart on page 10. If two adjacent sides 
 of a field are straight lines which form 
 a 90-degree angle as in the case illus- 
 trated, the staking problem is relatively 
 simple. For crooked-sided fields there is 
 the added problem of establishing the 
 two straight lines and making them con- 
 form as nearly as possible to the bound- 
 aries of the area. The two adjacent sides 
 of either the blocked-out area or the 
 straight-sided field are required to serve 
 as guide lines for the staking. The stakes 
 are set at equal distances (100 feet is the 
 usual station distance) along lines simi- 
 larly spaced and parallel to the two guide 
 lines. The grid pattern thus formed con- 
 sists of squares, though it may be made 
 up of any type of equilateral parallelo- 
 gram that fits a field. If the pattern is 
 other than square, it is necessary for 
 computing purposes to measure and note 
 the angle between the two guide lines. 
 
 The details involved in staking a field 
 with the two adjacent straight sides are 
 as follows: Lath, approximately %" by 
 1%" by 4' are used as stakes. They 
 should be sharpened and driven into the 
 ground far enough to insure that they 
 will withstand strong wind. According 
 to the chart on page 10 the first stake 
 is flagged and permanently set at A, 50 
 feet, or one-half the station distance in- 
 side the field from either guide line. 
 Flagged stakes are also set temporarily 
 at B and D. Starting at A and lining in 
 on B, the distance between A and B is 
 measured and permanently staked at 100- 
 
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 K 
 
 * — *— 2 — *■ — 
 
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 — *f *« * * 
 
 The pattern used for staking a field which is to be graded. 
 
 foot intervals with the stakes fla$ 
 every 400 feet. The stake at B is reset at 
 the last 100-foot station on the line. The 
 distance from A to D is similarly meas- 
 ured, permanently staked, and flagged. 
 The line DC (or — if more convenient — 
 line BC) is then measured off equal in 
 length and approximately parallel to line 
 AB and temporarily staked and flagged 
 
 to correspond with lines AB and AD. 
 The line between B and C and those from 
 the stations marking the 400-foot inter- 
 vals along line AB to the corresponding 
 points on the opposite side of the field 
 are then measured, staked, and flagged to 
 correspond to the staking of line AB. At 
 the same time the flagged stakes which 
 were temporarily set at C and at the 400- 
 
 [10] 
 
foot intervals along DC are reset at the 
 last 100-foot station on these lines. The 
 lines from the 400-foot intervals along 
 AD to the corresponding points on the 
 opposite side of the field along line BC 
 are similarly measured, staked, and 
 flagged. A sufficient number of stakes are 
 then in position to sight in the rest by 
 eye. Essentially the same procedure is fol- 
 lowed for staking an irregularly shaped 
 field. In this case the lines of stakes are 
 extended to cover any area more than 
 100 feet wide lying outside of the blocked 
 out parallelogram. The position of any 
 stake can be located quickly in the field 
 or on a map if the lines of stakes are 
 numbered in one direction and lettered 
 in the other, and each stake is numbered 
 and lettered accordingly. 
 
 Where the topography is unusually 
 irregular and no preliminary leveling is 
 done, more frequent grade stakes may be 
 called for than are provided by the 100- 
 foot spacing. Stakes may be set at 50- 
 foot intervals without seriously obstruct- 
 ing the movement of equipment in the 
 field. However, halving the usual station 
 distance adds greatly to the work of stak- 
 ing a field. On a 40-acre tract of land 
 measuring 1,320 feet to a side, 169 stakes 
 are required to mark points 100 feet 
 apart, while 625 are needed if the inter- 
 val is reduced to 50 feet. 
 
 As landowner you may, by working 
 with or under the direction of an engi- 
 neer, perform at least part of the work 
 of staking your field. 
 
 Mapping the Topography 
 
 If you have had no training or experi- 
 ence in surveying, you may find the dis- 
 cussion on mapping the topography diffi- 
 cult. You also should realize that, unless 
 the mapping is put into competent hands, 
 the investment of possibly $60 to $100 
 per acre for land grading is jeopardized. 
 
 There are several surveying proce- 
 dures for mapping topography, but where 
 land grading is the aim, the usual prac- 
 tice consists of using an engineer's level 
 
 for determining the relative ground sur- 
 face elevations and spotting these eleva- 
 tions directly on a base map. 
 
 Rod reading. The ground surface 
 elevations are obtained with an engi- 
 neer's level as illustrated in the diagrams 
 on page 12. When the instrument is 
 properly leveled, all points which fall 
 in the same plane with the horizontal 
 cross hair are of the same elevation. A 
 leveling rod is used to measure the verti- 
 cal distance from the ground at each 
 stake to the level of the horizontal cross 
 hair in the instrument. This measure- 
 ment is called a rod reading. Differences 
 in rod readings denote changes in eleva- 
 tion. Some engineers simply record the 
 rod readings first at a permanent refer- 
 ence point called a bench mark or B. M. 
 and thence at each grid corner, keeping 
 in mind that elevation increases as rod 
 readings decrease and vice versa. Other 
 engineers start the survey as illustrated 
 on page 12 by obtaining a rod reading 
 on a B. M. of known or assumed eleva- 
 tion, add the rod reading to that elevation 
 to obtain the elevation of the cross hair in 
 the instrument and thereafter subtract the 
 rod readings from the cross hair eleva- 
 tion to obtain ground surface elevation 
 at each stake. In this case elevations as 
 well as the rod readings are recorded at 
 the corresponding points on the base 
 map. 
 
 Resettings of level. One setting 
 of an engineer's level is sufficient to ob- 
 tain a rod reading at each of the 169 
 stakes in a 40-acre tract provided (1) the 
 variation in elevation does not exceed the 
 length of the rod; (2) the view is un- 
 obstructed; and (3) the stability of the 
 instrument is not affected by wind. Other- 
 wise, for larger fields, or when a small 
 farm level is used, it is necessary to reset 
 the instrument and arrange to make the 
 rod readings or elevations comparable 
 with those obtained before the instru- 
 ment was moved. To accomplish this a 
 rod reading is obtained on a point, be- 
 fore moving the instrument, from which 
 
 [ii] 
 
\ Second 
 
 v Position of Rod 
 
 2t 
 
 \ 
 
 N 
 
 \ 
 
 \ 
 N 
 
 Ground Elevation 105.0' 
 
 - 2^5' 
 
 j/ 
 
 — * 
 
 102.5' 
 
 J" 
 2.5' 
 
 Starting a topographic survey from a bench mark. 
 
 102.0' 
 
 Moving instrument while making a topographic survey 
 
 [12] 
 
a second rod reading can be made when 
 the instrument is reset. This point is 
 called a turning point and should be of 
 a semi-permanent nature — a nail driven 
 into a fence post or a 2" x 2" x 12" stake 
 driven flush with the ground surface and 
 plainly marked with a guard stake or 
 stakes so it can be found. If a square 
 160-acre tract is being surveyed and one 
 setting of the instrument for each 40 
 acres is sufficient, a single turning point 
 in the middle of the tract may suffice. If 
 the engineer is recording rod readings 
 only, he arranges either to reset the in- 
 strument at the same elevation as before 
 or at a level which differs from its orig- 
 inal height by a simple figure such as one 
 foot which readily can be added or sub- 
 tracted as required to make the rod read- 
 ings taken from the new instrument set- 
 ting comparable with those obtained be- 
 fore moving the instrument from its first 
 position. If the engineer is recording 
 elevations, he must before moving the 
 instrument determine in the manner al- 
 ready described the elevation of the turn- 
 ing point. Upon resetting the instrument 
 he starts with the rod reading on the 
 turning point and thereafter follows the 
 same procedure as before. This perform- 
 ance is illustrated diagrammatically on 
 page 12 (bottom). Accuracies of ground 
 surface rod readings to the nearest 0.05 
 foot and readings on turning points to 
 the nearest 0.01 foot are required espe- 
 cially when the land slope is 0.2% or less. 
 
 In case the grid stakes are 100 feet 
 apart and the surface elevations at this 
 interval fail to show the surface relief in 
 sufficient detail for accurate determina- 
 tion of the best land grade, the distance 
 between points where rod readings are 
 obtained may be reduced to 50 feet or 
 less by taking additional rod readings 
 between stakes. In many cases this is a 
 satisfactory substitute for a closer spac- 
 ing of grid stakes. 
 
 Rod readings on freshly culti- 
 vated land should be made to conform 
 to the natural ground surface. Frequently 
 
 a tractor is driven along each line of 
 stakes to compress the soil for this pur- 
 pose and the rod readings are taken in 
 the wheel tract next to the stakes. An- 
 other practice consists of tamping the 
 ground at each stake with the rod before 
 the reading is made. As an alternative 
 to such practices, all rod readings may 
 be increased by the estimated amount 
 the ground surface must finally sink to 
 give the soil its original weight per unit 
 volume. 
 
 Selecting the spot for rod read- 
 ing. Judgment and care should be exer- 
 cised in selecting a representative spot 
 for a rod reading. Staking calls for an 
 accurate spacing and alignment of stakes 
 with no allowance for avoiding small 
 surface irregularities. Thus the rod read- 
 ings are not always taken exactly at the 
 stakes, and it may not be always assumed 
 that the amount of cut or fill required for 
 grading can be measured from the 
 ground at the base of the stakes. As will 
 be described on pages 18 and 19 under 
 methods of posting, a reference line or 
 level is marked on each grid stake to 
 serve that purpose. 
 
 Base map. The base map upon which 
 the level notes are recorded, consists of 
 a sheet of cross-section paper laid off in 
 inch squares mounted on a plywood 
 board of convenient size for carrying. 
 The squares printed on this paper repre- 
 sent the staking pattern, the sides of the 
 squares being the interval between stakes, 
 and the corners, the locations of the 
 stakes. Delineation on the cross-section 
 paper of the boundaries of the area with 
 respect to the staked interior completes 
 the base map. 
 
 All survey information is recorded on 
 this map. With one exception the rod 
 reading is always placed in a horizontal 
 position above and to the right of the 
 point on the map representing the grid 
 point where the reading was made. The 
 one exception is a reading at a turning 
 point. In this case the reading is placed 
 in a diagonal position in the middle of 
 
 13 
 
the grid square nearest the turning point 
 and in line with the location of the in- 
 strument. Turning points may be further 
 identified by inscribing them in a small 
 triangle. If elevations are used, they are 
 placed in line with and to the left of the 
 corresponding rod readings. After the 
 land grading calculations, which are de- 
 scribed later, have been completed, the 
 grade and cut or fill figures are tran- 
 scribed on this map in positions beneath 
 the corresponding elevation and rod 
 reading. Convenient forms of entry when 
 rod readings only are recorded and when 
 both rod readings and elevations are 
 noted are shown on page 15. 
 
 Contour lines. To make this survey 
 information more readily understood 
 and studied, lines are drawn connecting 
 points of equal elevation. These lines are 
 called contours. From them it may be 
 seen at a glance where hills and hollows 
 occur and how much and in which direc- 
 tion the ground slopes. It is desirable to 
 have this picture so that a property may 
 be divided into fields that can be graded 
 and irrigated individually to the best ad- 
 vantage. A few simple rules govern the 
 drawing and interpretation of contour 
 lines. 
 
 1. Contour lines are located by an 
 interpolation procedure based on the 
 assumption that the slope of the land sur- 
 face is uniform between adjacent grid 
 corners. See example below. 
 
 2. The difference in elevation between 
 successive contours is called contour in- 
 
 terval. The following intervals are recom- 
 mended for different slopes. 
 
 Recommended Contour Interval 
 
 Slope in feet 
 
 Contour interval 
 
 per 100 feet 
 
 in feet 
 
 0- 1 
 
 0.2-0.5 
 
 1- 2 
 
 0.5-1.0 
 
 2- 5 
 
 1.0-2.0 
 
 5-10 
 
 2.0-5.0 
 
 3. The slope along a contour line is 
 zero. Thus, a contour line connects only 
 points of equal elevation. 
 
 4. On plane surfaces contours are 
 straight lines parallel to each other. 
 
 5. The area within a contour line which 
 closes upon itself is either a summit or a 
 depression. 
 
 6. When completely enclosed within 
 another contour line, a contour must also 
 close upon itself. It never consists of a 
 single line. 
 
 7. Except in such rare cases as over- 
 hanging cliffs and caves, contour lines 
 cannot merge or cross one another. 
 
 8. The direction of steepest slope is 
 always perpendicular to the contour 
 lines. 
 
 9. Closely spaced contours denote 
 steep slopes; widely spaced contours, flat 
 slopes. 
 
 Selection of Areas for 
 Separate Grading 
 
 A step of greatest importance, in some 
 cases, is the division of an area accord- 
 ing to its contours into parcels of land 
 
 Difference in elevation = 9.2 - 8.6 = 0.6, from 9.2 - 9.0 = 0.2; 
 
 0.2 
 
 •52' \ therefore the point on the 9.0' contour line is — ' — = Va of the 
 
 I 
 
 0.6 
 
 total distance from the 9.2' to 8.6' grid corners. 
 
 t Difference in elevation 9.4'- 8.9'= 0.5- 9.0'- 8.9'^ 0.1; therefore 
 • j the point on the 9.0' contour line is Vs of total distance from the 
 94 1 8.9' to 9.4' grid corners. 
 
 14 
 
79' 
 
 2.1 
 
 7.6 
 
 3.0' 
 
 3.2 
 
 4.8' 
 
 6.2 
 70 
 
 /7C. 
 3.6 
 
 e.d 
 
 6.1 
 
 I.O'C. 
 39' 
 
 3.4 o.6r. 
 
 9.5 '0.5' 
 
 61 
 
 C9C. 
 
 3.4 
 
 az'c. 
 
 SJ' 
 
 a+a 
 
 Original 
 Elevation 
 
 Calculated 
 Grade 
 
 Original 
 Rod Reading 
 
 Cut or 
 Fill 
 
 Convenient forms of recording survey data on base map when elevations are used (top) and 
 when rod readings only are used (bottom). 
 
 
 2.1' 
 
 30' 
 
 48' 
 
 3Jd X 
 
 i.rc. 
 
 3.0' 
 
 4.6 
 
 hO'C. 
 3.9' 
 
 4.Z 
 
 o.6f\ 
 
 39 
 
 09C, 
 
 4.1' 
 
 az'c. 
 
 as' 
 
 0.4C. 
 
 Calculated 
 Grade Rod 
 
 Original 
 Rod Reading 
 
 Cut or 
 Fill 
 
 that can be graded separately to the best 
 advantage and at a minimum cost. Here 
 are examples of different contour pat- 
 terns which may warrant separate han- 
 dling and which are illustrated in the 
 diagram on page 16. 
 
 1. Abrupt major difference in contour 
 interval implies a sharp change in slope. 
 Separation may be desirable along the 
 line of slope change as in the case of 
 field A and B. 
 
 2. Sharp bends in otherwise nearly 
 straight contours indicate an important 
 change in the direction of maximum 
 slope. While such an area might be irri- 
 gated as a whole by contour checks, 
 graded contour furrows, or contour 
 ditches, separation into fields at the bend 
 is desirable if either border or furrow 
 irrigation is planned as in the case of 
 fields C and D. 
 
 3. Contour lines either close together 
 or far apart may imply that the average 
 
 natural slope is either too steep or too 
 flat to be satisfactory for the land use 
 intended and that it must be graded to a 
 lesser or greater slope. In such cases the 
 least permissible amount of grading will 
 be required if the length of field in the 
 direction of irrigation is the minimum 
 that can be watered satisfactorily. Such 
 separation into fields is shown in fields 
 E, F, G, and H. 
 
 4. Great irregularity in spacing and 
 direction of contours may show that the 
 topography is nonuniform to the extent 
 that it fails to show where a separation 
 into fields can be made advantageously. 
 Such areas may be set apart to be graded 
 individually as units. 
 
 5. Excessively irregular and/or closely 
 spaced contours indicating land that can 
 be leveled only at great expense and for 
 that, reason may be partitioned off as un- 
 satisfactory for irrigation by surface 
 methods. 
 
 [15] 
 
HIGHEST POINT 
 
 LOWEST POINT 
 
 Division of an area into fields in accordance with different topography. 
 
 While dividing a property in accord- 
 ance with its original contour patterns, 
 an endeavor should be made to keep in- 
 dividual fields rectangular in shape. Ir- 
 regularly shaped fields are difficult to 
 irrigate and cultivate and should be 
 avoided if possible. Also, provision 
 should be made at this time for surface 
 drainage. 
 
 Planning the Irrigation 
 Distribution System 
 
 It is necessary that the design and the 
 map location of the irrigation ditches or 
 pipe lines and the surface drainage 
 ways be adjusted to fit the lay of the 
 land. A full explanation of how this is 
 done is given in California Agricultural 
 Experiment Station Circular 362. In ad- 
 
 dition, if the land has little slope or it is 
 desirable to maintain without the use of 
 structures a high water level in the 
 ditches with respect to the land, special 
 provision is made for extra soil for ditch 
 construction. A "ditch pad" or "ribbon 
 fill" of the proper width and depth serves 
 this purpose. The volume of this fill 
 should be sufficient to form the ditch 
 banks. Usually a fill 10 to 15 feet wide 
 and 1 to 1% feet high is sufficient. Ditch 
 pads are located and marked for depth 
 of fill with stakes set at either edge of 
 the proposed fill at 100-foot intervals. 
 
 Land-Grading Calculations 
 
 The level to which the surface at each 
 grid stake is raised or lowered is termed 
 grade. Many different methods of com- 
 
 [16] 
 
puting grades are used. By using any 
 one of these methods you can delineate 
 a new land surface that will irrigate per- 
 fectly, but you cannot always be sure 
 that the cost will be the minimum. To 
 consider both the cost and suitability for 
 irrigation, the rules for land grading cal- 
 culations that seem best to follow are : 
 
 1. Consider first grading the area to a 
 single plane which is so located as to 
 require moving the minimum amount of 
 earth. 
 
 2. In case the plane which requires the 
 least amount of earth moving is unsuit- 
 able due to its slope, or the elevation at 
 which water must be delivered, adapt a 
 plane as close to it as possible. 
 
 3. If grading to a single plane is too 
 costly, adhere closer to the natural topog- 
 raphy than is possible with a single 
 plane, while staying within the allowable 
 limits of degree and variation of slope, 
 as outlined on pages 6 and 7. 
 
 Three methods of grade calcula- 
 tions are discussed here 
 
 1. Least-squares and average profiles 
 
 2. Cross-section 
 
 3. Two-way profile 
 
 A detailed discussion of the three 
 methods is found in the appendix on 
 pages 32 to 40. 
 
 Cut vs. Fill Requirement 
 
 The depth of soil that must be removed 
 or added to make the original ground 
 surface conform to a prescribed grade is 
 referred to as cut or fill. For example, if 
 the original surface elevation is 10 feet 
 and the land grading plan calls for 8.5 
 feet at that point, a cut of 1.5 feet is re- 
 quired. If these figures are interchanged 
 so that the elevations before and after 
 grading are 8.5 and 10 feet respectively, 
 a fill of 1.5 feet instead of a cut of like 
 amount is indicated. The volume of cut 
 is the area of cut multiplied by the aver- 
 age depth of cut. Likewise, the volume of 
 fill is the product of area and depth of 
 fill. 
 
 Volumes of cut and fill. It is the 
 
 experience in grading land with modern 
 earth-moving equipment that a greater 
 volume of cut than fill must be allowed 
 in order to provide a sufficient volume 
 of cut to take care of the called-for vol- 
 ume of fill. This finding applies to all 
 soils and conditions of soil and thus may 
 not necessarily include the subsidence of 
 freshly cultivated or naturally loose soil 
 previously mentioned as most accurately 
 appraised and allowed for while obtain- 
 ing the rod readings. A common opinion 
 often expressed is that fills made with 
 heavy equipment are compacted to the 
 extent that the extra volume of cut is 
 required to complete them. It would ap- 
 pear more logical to expect compaction 
 of the soil that remains in the areas of 
 cut, since they suffer the most traffic by 
 the earth-moving equipment and besides 
 are exposed to the greater compacting 
 forces owing to the extra power used 
 while loading. It is possible that such un- 
 equal compaction is a factor to be con- 
 sidered in case the necessity arises to 
 grade wet land. No evidence has been 
 found by the author of such an effect on 
 dry mineral soils. Perhaps the most likely 
 and more important explanations are 
 that a tendency exists to crown slightly 
 the ground surface between grade stakes 
 and that loading and transportation 
 losses occur. For the same reason that a 
 pillar of the same diameter throughout 
 its length erroneously appears smaller in 
 the middle than at either the top or bot- 
 tom, level ground surfaces between grade 
 stakes appear to dip in the middle. To 
 the extent that operators of the grading 
 equipment allow this optical illusion to 
 influence their judgment, crowning be- 
 tween grade stakes will occur. The im- 
 portance of this factor is shown by the 
 results obtained from checking the levels 
 on several newly graded fields in the 
 vicinity of Davis. Seventy-five to 90 per 
 cent of the midpoints between grade 
 stakes were found to be 0.05 foot or more 
 above grade, while the remaining middles 
 
 [17] 
 
were approximately at grade. It is to be 
 expected that deviations from the pre- 
 scribed grade in excess of 0.1 foot except 
 when confined to small spots will be dis- 
 covered and corrected, but lesser dis- 
 crepancies are usually allowed. 
 
 Bases for estimates. It is rarely pos- 
 sible to estimate exactly the volume of 
 cut that will be required. Consequently 
 it should be recognized by all concerned 
 that the original posting of grades in the 
 field is somewhat tentative and subject 
 to change after the work of grading the 
 land is under way. The following ob- 
 served performances suggest bases for 
 making the estimate. 
 
 When the depths of cut are uniformly 
 only a few tenths of a foot, it is found 
 necessary to allow up to 100 per cent 
 more cut than fill. This large allowance 
 of cut is undoubtedly due to the rela- 
 tively large proportion that any occur- 
 rence of compaction, crowning, or waste 
 of soil bears to the volume of cut. For 
 example, if cuts range below 0.4 foot, 
 from 70 to 100 per cent cut overage very 
 likely must be used. 
 
 In case the soil is composed principally 
 of organic material such as peat or muck, 
 it is the experience that at least twice as 
 much cut as fill must be provided. Here 
 the major factor without question is com- 
 paction. 
 
 Under some conditions the type and 
 size of earth-moving equipment to be 
 used must be considered. Wheel tractors 
 generally, because of their operating 
 speed are likely to cause uneven distribu- 
 tion of the soil. 
 
 Notably some earth-moving contrac- 
 tors require more cut to complete a job 
 than do others. This is due, without 
 doubt, to different tendencies upon the 
 part of the operators of the graders to 
 crown between grade stakes. 
 
 For the average job involving clay 
 loam soils with low moisture content, and 
 from 300 to 500 cubic yards per acre 
 excavation, from 20 to 45 per cent more 
 cut than fill is usually needed, while in 
 
 extreme cases of heavy or light textured 
 soils and deep or shallow excavation the 
 percentage can be as little as 5 per cent 
 and as much as 100 per cent. 
 
 Computations of cut and fill adjust- 
 ments can be found in the appendix on 
 pages 40 and 41. 
 
 Posting Cuts and Fills in the Field 
 
 Responsibility. If the earth-moving 
 contractor is expected to bear the full 
 responsibility of performing his work 
 economically, he should be supplied a 
 copy of the completed base map and the 
 cuts and fills should be posted for him 
 in the field at all of the grid corners in a 
 manner that is easy to understand. He 
 needs the base map to study and to refer 
 to from time to time in order to plan the 
 earth moving efficiently and to check on 
 the excavation being required. The posted 
 cuts and fills are essential for showing 
 the operators of the earth-moving ma- 
 chines where and how much to grade. 
 
 In case direction of the earth moving 
 is the responsibility of the landowner or 
 his engineer, it is not necessary and' may 
 not be desirable to reveal the whole level- 
 ing plan to the earth-moving contractors 
 and his workmen. Instead, the work may 
 be laid out in the field piecemeal by 
 posting cuts and fills as they are needed 
 to keep the graders supplied with work. 
 This procedure requires the constant at- 
 tention of the individual who directs the 
 earth moving, but it gives close control 
 over earth-moving operations and saves 
 reposting of cuts and fills in case it be- 
 comes apparent that too little or too 
 much cut has been allowed in estimating 
 the requirement. 
 
 Methods for posting. A number of 
 methods for posting cuts and fills in the 
 field are used. The important require- 
 ments are: 
 
 1. Establishment by means of a mark 
 placed on each grid corner stake, or by 
 other reference at each grid corner, of 
 an elevation which corresponds to or has 
 a known height with relation to the point 
 
 [18 
 
where the rod was placed for obtaining 
 the original elevation. This reference 
 serves as a level from which the depth 
 of cut or fill called for at the point can 
 be measured quickly and accurately. 
 
 2. The depth of cut or fill must be 
 posted at each grid corner in a manner 
 that will be clearly visible to operators 
 of grading equipment for several hun- 
 dred feet. 
 
 3. The markings should be sufficiently 
 durable to serve until grading is com- 
 pleted. 
 
 Reference. One of the practices fol- 
 lowed requires that a mark to serve as 
 a reference be placed at the height on 
 each grid stake which is one foot higher 
 than the point where the rod was placed 
 to obtain the original ground^surface 
 elevation. It is usually possible to place 
 this mark while obtaining the original 
 ground elevation by noting the point on 
 the stake that corresponds to the one- 
 foot mark on the level rod. In case the 
 rod is too far from the stake to make 
 this possible within the desired degree 
 of accuracy, a second rod reading is pro- 
 cured at the stake and the stake is marked 
 one foot above ground level at the stake 
 minus the difference in the two rod read- 
 ings in case the ground is highest at the 
 stake and plus the difference if it is 
 lower. In case the ground level at the 
 stake is highest by more than one foot, 
 it becomes necessary, in order to keep 
 the reference mark above ground where 
 it may be seen, to raise it one or more 
 feet. In such cases its height is recorded 
 on the stake. 
 
 Another practice requires that a mark 
 to serve as a reference be placed on each 
 grid-corner stake at one foot above 
 grade. In this case it is necessary to de- 
 termine grade beforehand. Thus the sur- 
 vey is made, the grade calculations are 
 completed and the survey instrument is 
 brought into the field again for the pur- 
 pose of placing the one-foot-above-grade 
 marks on the grid-corner stakes. These 
 operations usually include several short- 
 
 cuts which are designed to reduce the 
 possibility of error and to save time. Rod 
 readings instead of elevations are used 
 throughout the job so that heights of 
 ground surface and grade are expressed 
 as rod readings. Also when the survey 
 instrument is returned to the field it is 
 set up at the same spot and height as 
 before. With the instrument in this posi- 
 tion the rod readings originally taken at 
 the grid corners can be duplicated. It 
 follows that one foot above grade can be 
 located for each of the grid corners by 
 placing the rod against the stake, raising 
 it until the horizontal cross hair in the 
 instrument coincides with the rod read- 
 ing that is one foot less than that which 
 represents grade at that point, and mark- 
 ing the stake opposite zero on the rod. 
 If one foot above grade is lower than 
 ground surface, the rod is raised one or 
 more feet further before making the 
 mark and a notation is made to that 
 effect. 
 
 Depth of cut is indicated on stakes 
 by marking with red color or red ma- 
 terial the distance measured downward 
 from the top of the stake which corre- 
 sponds to the depth of cut at that point. 
 In case the reference mark is one foot 
 above ground level, grade is below it a 
 distance of one foot plus the red colored 
 portion of the stake. If the reference 
 mark is one foot above grade, its position 
 is all that is needed to locate grade. In 
 both cases the length of stake colored red 
 shows the grader operator the depth that 
 the original ground surface must be 
 lowered at that particular point. Also he 
 may dismount from his machine at any 
 time and with a foot rule which he 
 carries for the purpose measure from the 
 reference line to determine the exact 
 grade. In case the depth of cut is greater 
 than can be indicated in this manner on 
 the four-foot lath stakes, a red arrow is 
 marked on the stake pointing downward 
 from the top of the stake and the depth 
 of cut is printed in red beneath it. 
 
 Depths of fill are indicated by color- 
 
 [19] 
 
ing solidly blue a band several inches 
 wide around the stake immediately be- 
 neath the level designated as grade. If 
 the reference mark is one foot above 
 ground level and the depth of fill is less 
 than one foot, grade is located at one 
 foot minus depth of fill below the refer- 
 ence mark. If depth of fill is more than 
 one foot, grade is depth of fill minus one 
 foot above the reference. If reference is 
 one foot above grade, its position is all 
 that is needed to locate grade. In case 
 the depth of fill is greater than can be 
 indicated in this manner on the four-foot 
 lath stakes, the stakes are lengthened by 
 nailing two or more of them together. 
 
 Other markings. When the original 
 ground surface is at grade, neither cut 
 nor fill is called for, so the distinctive red 
 
 or blue band does not appear on the grid- 
 corner stakes at these locations. How- 
 ever, some other distinctive marking such 
 as a red or blue circle with an arrow 
 drawn through it may be used to show 
 that the marking of these stakes was not 
 overlooked. 
 
 To avoid the possibility of misinter- 
 pretation and to save unnecessary dupli- 
 cation of engineering work, the materials 
 used for marking the stakes should be 
 distinctive and durable. A strip of water- 
 proof adhesive tape one-quarter inch 
 wide wrapped around a stake serves 
 ideally as reference. The red and blue 
 colors are best made with lumber crayon 
 or with paint applied with a spray gun. 
 
 Earthwork calculations and table can be 
 found in the appendix. 
 
 What You Should Know About Equipment 
 
 Best performance of the equipment 
 currently used for grading land is pos- 
 sible only when it includes an adequate 
 number of machines in good repair and 
 of the type and size best adapted for 
 handling, under the conditions encoun- 
 tered, each operation to be performed. 
 Such ideal equipment make-up should be 
 the aim, but reasonably may not or can- 
 not be realized in all cases. 
 
 When land grading is a side issue, 
 to be performed during spare time with- 
 out hiring extra labor, a high capital 
 investment in earth-moving equipment is 
 neither advisable nor is such investment 
 necessary to get the work done at a rea- 
 sonable cost. If you, as a landowner, 
 undertake this work for yourself or 
 others, you may be in this position. With 
 a small outfit you frequently can show 
 good results. 
 
 Contractors who follow farm-land 
 grading as a full-time business are in a 
 different position. To compete success- 
 fully for jobs they should have the equip- 
 ment that is capable of the highest per- 
 formance. When such equipment is kept 
 
 busy its ownership should be profitable. 
 In reality earth-moving contractors are 
 variously equipped depending on their 
 resources and the class of earth work 
 previously engaged in. It may be impos- 
 sible to find one who possesses the full 
 array of machines of the newest and most 
 efficient type and size to handle a par- 
 ticular land-grading job. To be accept- 
 ably well equipped they should, at least, 
 have the ordinary grader's outfit consist- 
 ing perhaps of somewhat smaller and 
 slower machines than might be best, but 
 all in good working order, and any extra 
 pieces of equipment for which there is 
 special need. Frequently contractors can 
 rent the extra pieces of equipment, or 
 sublet the work requiring them. 
 
 Who should be concerned most with 
 equipment suitability in case of con- 
 tracted work? The answer to this ques- 
 tion depends upon how the operation is 
 
 The following five pages contain photo- 
 graphs of earth-moving equipment and ^k 
 statements of what each machine can be ^m 
 expected to accomplish. 
 
 [20] 
 
CRAWLER TRACTOR 
 
 The crawler tractor is one of the important machines used for grading farm land. The main 
 distinguishing feature, the crawler track, gives superior traction on the varying soil and ground 
 conditions encountered in land grading. It also limits top travel speed to about five miles per 
 hour. Thus it is more capable than other tractors of loading an attached scraper; it is essential 
 as a pusher tractor (bottom) when extra power is required for loading; and it is the best tractor 
 for pulling a ripper. On the other hand when it is pulling a scraper, it is limited— because of its 
 low speed— to relatively shoit hauls. 
 
,%;'W~4rV* 
 
 RUBBER-TIRED WHEEL TRACTORS 
 
 Rubber-tired two- and four-wheel tractors are used for earth moving when the emphasis is on 
 speed rather than drawbar pull. The two-wheel machine (top) is designed for maneuverability 
 in addition to speed, which makes it especially adapted to highway and levee work. The four- 
 wheel tractor (bottom) is built first for speed and second for steady performance. Either machine 
 can be used to great advantage on land-grading jobs requiring extra-long-distance hauling. 
 
 R 
 
CARRIER-TYPE 
 SCRAPER 
 
 The carrier-type scraper is currently used on 
 most land-grading jobs. It consists essentially 
 of a bowl or bucket mounted on rubber-tired 
 wheels with a blade and apron across its front 
 end for cutting, scooping and retaining a load 
 of earth. To load, the bowl is lowered and the 
 apron is partly lifted. In hauling position the 
 apron is closed and the bowl is lifted clear of 
 the ground. To dump or spread, the apron is 
 lifted and the load is pushed forward through 
 the opened end of the bowl by an ejector 
 member which normally rests against the rear 
 of the bowl. With this one tractor-drawn im- 
 plement and one operator earth is excavated, 
 loaded, hauled and spread. The carrier-type 
 scraper used by most contractors for grading 
 land generaly has a maximum capacity rang- 
 ing from approximately 15 to 23 cubic yards. 
 If these sizes are powered and applied prop- 
 erly, each larger unit will give better efficiency, more yardage and less cost per cubic yard. To 
 be used at top efficiency, the depth of cut must be sufficient for rapid loading; the scrapers must 
 be pulled by the right type of tractor, and if extra power can be used to advantage, they should 
 be operated in groups with a pusher tractor. 
 
 ROTARY SCRAPER 
 
 The rotary scraper works on a different principle from that of the carrier-type scraper. It 
 consists essentially of a bladed wheel conveyor which revolves about a cylindrical bowl to 
 remove constantly the excavated earth from the scraper blade and deposit it into the top of the 
 bowl. The bowl revolves to unload. It has a lower production rate and is less durable for rugged 
 service than the carrier-type scraper. On the other hand, it requires much less power to operate 
 than the carrier-type scraper, and it will load to capacity as readily when the depth of cut is 
 extremely light as when it is optimum. These features make rotary scrapers especially suitable 
 for light work with farm-size tractors. 
 
 JV? 
 
 "^ 
 
BOTTOMLESS SCRAPERS 
 
 Bottomless scrapers represent two types of equipment which are designed to remove small 
 grade irregularities. As the name implies the bowl or bucket has little or no bottom and earth 
 moving is accomplished with them by scraping up a load, dragging it a short distance and dump- 
 ing it. To perform these operations well with this type of machine the ground surface must be 
 broken first or the soil must be of a loose texture. A machine of this type is essential for the 
 finishing work on land that is being graded to an even slope of from 0.2% to 0.3% or less. It also 
 helps prepare a seed bed through the pulverizing effect of a rolling action of the scraper load 
 as it is dragged. 
 
 The bottomless scraper with the long frame is one of several makes which is designed to work 
 automatically. It is currently manufactured in lengths up to 80 feet and widths up to 15 feet. 
 The blade is attached to the frame midway of its length at a height which is adjustable. It is 
 mounted on swivel wheels to make it less unwieldy to turn. When in use the blade is permanently 
 set at a level which will maintain about one-third of a load in the bowl. With this adjustment 
 properly made the machine will, as it is drawn across a field, automatically remove high spots 
 and fill depressions of a diameter equal to nearly one-half its length. Obviously the longest 
 machine available will perform the best. It is customary to take care of the final finishing work 
 with a machine of this type by scraping in three directions— in each of the two diagonal directions 
 and in the direction of irrigation. The operation is termed land planing 
 
 The two-wheel bottomless scraper, better known as a drag scraper, is sometimes used ahead 
 of land planing to remove surface irregularities too large to be planed out and too minor to be 
 taken care of economically with a carrier-type scraper. This machine is manufactured in a num- 
 ber of widths to serve various purposes including the extra widths of 12 to 18 feet for rapid 
 handling of light land grading. It is operated to cut and to drag and drop its load by the tractor 
 driver through hydraulic controls. The accuracy with which this must be done calls first of all 
 for an operator who is expert in handling one of these wide drag scrapers. 
 
CHISELS AND RIPPERS 
 
 Chisels and rippers are tractor-drawn implements that are sometimes usea' to break hard soil 
 or subsoil prior to earthmoving. If the surface soil is hard and requires loosening in order that a 
 satisfactory earth moving production rate can be maintained, chiseling will suffice. The implement 
 to use in this case is similar to the one with eight or ten teeth 12 inches or so long mounted on 
 a relatively light carrier. If hard subsoil or hard claypan is to be dealt with, ripping may be 
 called for with the much stronger and heavier implement weighing up to 3 or 4 tons and usually 
 equipped with no more than 2 or 3 teeth from 24 to 36 inches long. It should be determined 
 beforehand that these operations will not increase the uncertainty of how much allowance should 
 be made for the settlement of fills. Any increase in the cloddiness of the soil will have that effect. 
 Chiseling or ripping may be desirable, after land has been graded, to effect needed improve- 
 ment in water intake rate and depth of root penetration. 
 
 ... 
 
to be paid for. Obviously, when work is 
 let by the cubic yard of excavation or 
 by the job, it is to the interest of the con- 
 tractor to be mechanized for the purpose 
 as efficiently as possible. If you, on the 
 other hand, hire the work done by the 
 tractor hour, you bear the unnecessary 
 expense due to unsuitable equipment. In 
 selecting a contractor who is satisfac- 
 torily equipped for the particular job, 
 you will act wisely if you know some- 
 thing about the advantages and limita- 
 tions of at least the principal machines 
 used for grading farm land. 
 
 Crawler vs. Rubber-Tired 
 Wheel Tractor-Scraper Units 
 
 Tractor-scraper units are usually op- 
 erated on a cycle. A carrier-type scraper 
 is loaded, hauled loaded, unloaded, 
 turned, hauled empty, and turned to be 
 ready for loading again as shown in the 
 diagram on this page. If the depth of ex- 
 cavation is sufficient for efficient load- 
 ing, this operation is performed in ap- 
 proximately one minute and by 100 feet 
 of scraping. This time will be the same 
 for any properly matched, pusher tractor 
 aided, tractor carrier-type scraper unit. 
 Likewise the time required for turning 
 and unloading is practically the same for 
 all units since these operations are per- 
 formed at relatively slow speeds. There 
 remains in the cycle the time required 
 for hauling. Obviously this varies greatly 
 with the haul distance and the speed of 
 the haul tractor. All tractor-scraper units 
 
 have a lower production rate and a 
 higher cost per cubic yard of earth 
 moved as the haul distance increases. 
 Hence it is desirable to keep the haul 
 distance as short as possible. The maxi- 
 mum one-way haul distance allowed fre- 
 quently ranges up to one-fourth mile and 
 in some cases extends to one-half mile. 
 Obviously there is a haul distance for 
 each set of ground surface conditions 
 beyond which it is economical to switch 
 from the slow traveling crawler tractor 
 unit to the high speed rubber-tired wheel 
 equipment. How this distance is deter- 
 mined is shown in greater detail in the 
 appendix. 
 
 Equipment for Shallow Grading 
 
 Sometimes farm land grading calls for 
 depth of cut ranging mostly from 0.1 to 
 0.4 foot. When such slight cuts are the 
 rule, earth moving is slow work and may 
 cost from one-fourth to one-half more 
 per cubic yard than when a greater vol- 
 ume of earth is moved. Contractors ap- 
 praise a job in this respect by the aver- 
 age yardage of excavation per acre. Two 
 hundred cubic yards per acre or less is 
 considered costly per cubic yard; from 
 400 to 500 average; and from 800 to 
 1,000 low-unit cost work. 
 
 When carrier-scraper equipment is 
 being used for shallow grading the pro- 
 duction rate decreases and the unit cost 
 of earth moving goes up for two rea- 
 sons. First, too little earth is available to 
 load the scrapers efficiently, i.e., loading 
 
 Return Empty 
 
 Haul Loaded 
 
 Cycle of operation by earth-moving machines while grading land. 
 
 [26] 
 
cannot be completed in one minute and 
 during 100 feet of scraping. Second, par- 
 ticularly where the soil is sandy, or light 
 weight and fluffy as are some alkali soils, 
 the cut earth tends to push ahead and 
 spill to the side of the scraper instead of 
 rising on the blade and entering the bowl, 
 thus making it impossible or uneconomi- 
 cal to obtain a capacity load. 
 
 Most contractors and manufacturers 
 of earth-moving machines affirm that 
 even with these handicaps carrier-scraper 
 equipment can be depended upon for 
 the best performance to be had. With 
 few exceptions the same rules apply, 
 they say, as when the depths of cut are 
 sufficient for efficient loading. The extra 
 cutting width of the largest carrier- 
 scraper units and their relatively low 
 unit production cost for an operator 
 usually more than offset their higher cost 
 of ownership. Furthermore, the great 
 weight of these machines makes is pos- 
 sible to hold closer to grade than might 
 otherwise be done while removing a thin 
 layer of earth from a hard ground sur- 
 face. Some old model, large carrier-type 
 scrapers are extra wide and for this rea- 
 
 son are highly rated for this class of 
 work. The all rubber-tired wheel equip- 
 ment continues to be superior to the 
 crawler-tractor scraper unit for haul dis- 
 tances in excess of about 500 feet. How- 
 ever, the four-wheel instead of the two- 
 wheel tractor is best to use in this case 
 because its steadier performance allows 
 closer adherence to grade while shallow 
 cuts are being made. Pusher tractors are 
 generally «not required for shallow 
 grading. 
 
 Since plus or minus 0.1 foot is the 
 generally accepted tolerance for rough 
 grading, it may be seen that a consider- 
 able part of what is termed here "shal- 
 low grading" is considered impractical 
 work for carrier-type scrapers. To finish 
 properly a job of rough grading and per- 
 haps also to do work initially consisting 
 entirely of shallow grading calls for the 
 bottomless scraper equipment and pos- 
 sibly the rotary type scraper. Many land- 
 owners arrange to equip themselves with 
 bottomless scrapers or rotary type 
 scrapers and to do shallow grading, or 
 the finishing work during their spare 
 time. 
 
 Suggestions for Contracts and Specifications 
 
 Most land grading work is let accord- 
 ing to verbal agreement as to price and 
 how well the land will irrigate after it is 
 graded. Many misunderstandings arise 
 due to such informality and some injus- 
 tice is done for which there is no re- 
 course. The lack of detailed written con- 
 tracts is due at least in part to the ab- 
 sence of standards to follow. In the 
 interest of promoting the preparation 
 and acceptance of such standards the 
 following suggestions are offered. 
 
 Written contracts may be entered into 
 cither with or without prior invitation 
 and acceptance of bids. In the opening 
 paragraph of the contract give the date 
 of the agreement and names of the parties 
 
 and state that the agreement is made 
 between those persons on that date. After 
 naming the person who undertakes to 
 perform the engineering or land grading 
 services, include "hereinafter called the 
 contractor," and after naming the land- 
 owner or other person for whom the 
 work is to be performed, include "here- 
 inafter called the landowner," and 
 throughout the remainder of the con- 
 tract refer to the parties by those terms. 
 The body of the contract will consist of 
 paragraphs or clauses covering all spe- 
 cific items of the agreement. End the 
 contract with the signatures of the par- 
 ties, each one followed by "contractor" 
 or "landowner" as the case may be. 
 
 [27] 
 
Engineering Contract 
 
 In the usual case the engineering con- 
 tract will not involve calling for bids. If 
 bids are not called for, the landowner 
 is justified in requiring the intending 
 contractor to furnish evidence of his ca- 
 pability including references and a state- 
 ment of his experience. If bids are in- 
 vited, each bidder should be required to 
 furnish such evidence of capability when 
 submitting his bid proposal. 
 
 When staking, surveying, mapping, 
 calculating cut and fill quantities, post- 
 ing of grades, and grade checking for 
 proof of satisfactory completion of con- 
 struction work are services to be ren- 
 dered, the provisions in a written engi- 
 neering contract should include: 
 
 1. Description of site conditions in- 
 cluding location, acreage, vegetal cover, 
 and ground surface. 
 
 2. Any particular kind of construction 
 that the landowner wishes to specify 
 such as: subdivision of property into 
 fields; direction, uniformity, and degree 
 of land slope; locations, heights and 
 widths of ribbon fills for irrigation 
 ditches and roads; locations and carry- 
 ing capacities of drainage ways; etc. 
 
 3. Any particular requirement, pro- 
 cedure or method the landowner wishes 
 to impose with regard to the staking, 
 surveying, mapping, allowance for set- 
 tlement of fills, grade calculations, com- 
 putation of quantities, etc. (See pages 32 
 to 46). 
 
 4. Facilities, materials and assistance 
 which will be available to the contractor. 
 
 5. Date when the job must be ready 
 for construction. 
 
 6. Delivery of map. The requirement 
 that the map or maps of the project be 
 delivered to the landowner showing the 
 original elevations and contours, loca- 
 tions of all proposed ribbon fills and 
 drainage ways, and the depths of cut or 
 fill to be made at each grid corner, 
 
 7. Yardage estimates. Provision re- 
 quiring the contractor to determine and 
 
 make available, if judged necessary by 
 the landowner, the following quantities 
 (cubic yards) of each excavation: 
 
 a. Total for entire area to be 
 graded. 
 
 b. Total for all isolated areas in 
 which the cuts are mostly shal- 
 low and amount to 200 or less 
 cubic yards per acre. 
 
 c. Total for all isolated areas in 
 which the cuts are mostly 
 medium and amount to be- 
 tween 200 and 500 cubic yards 
 per acre. 
 
 d. Total for all isolated areas in 
 which the cuts are mostly 
 heavy and amount to more than 
 500 cubic yards per acre. 
 
 e. Total in areas of cut which lie 
 within 500 feet of areas of fill 
 to which the earth will be 
 moved. 
 
 f. Total in areas of cut which lie 
 more than 500 feet from and 
 within 1,200 feet of areas of 
 fill to which the earth will be 
 moved. 
 
 g. Total in areas of cut which lie 
 more than 1,200 feet from 
 areas of fill to which the earth 
 will be moved. 
 
 8. Cut vs. fill estimates. Agreement to 
 supply to the landowner the total volume 
 of cut in terms of per cent of the total 
 volume of fill which is estimated to be re- 
 quired and which is used for computing 
 the quantities of earth excavation and/or 
 cost of grading. 
 
 9. Follow-up engineering. Assurance 
 that the contractor will promptly make 
 necessary adjustments of the posted cuts 
 and fills, replace grade stakes that are 
 knocked down, and check the grades for 
 proof of completion of construction. 
 
 10. Liability insurance. Proof that the 
 contractor carries sufficient liability and/ 
 or compensation insurance to cover his 
 full liability under the "Workmen's Com- 
 pensation Insurance and Safety Act." 
 
 [28] 
 
11. Payment schedule. Usually the cost 
 will consist of the hourly wages for engi- 
 neer and each assistant, plus transporta- 
 tion and possibly other expenses and will 
 be billed for by the month or by the job. 
 Occasionally a stipulated price per acre 
 is the basis for settlement. 
 
 Contract for Rough Grading 
 
 The operation whereby a land surface 
 is brought sufficiently close to a pre- 
 scribed grade to permit satisfactory com- 
 pletion by floating or planing is termed 
 rough grading. It is desirable in many 
 situations to invite bids for rough grad- 
 ing work, reserving the right to reject 
 any and all bids. Each bidder should be 
 required to submit evidence that his pre- 
 viously performed land grading work 
 has been satisfactory. The successful 
 bidder to whom the award is made, en- 
 ters into a contract with the landowner 
 which comprises a written agreement 
 and the written conditions and specifi- 
 cations and the drawings that have been 
 made available to intending bidders. The 
 written agreement is based upon the offer 
 and acceptance of the bid and specifically 
 makes the conditions, specifications, and 
 drawings a part of the contract. 
 
 The following suggestions assume a 
 call for bids, award to a bidder whose 
 proposal meets the landowner's require- 
 ments, and execution of the written 
 agreement noted in ths immediately pre- 
 ceding paragraph. The suggestions, how- 
 ever, may be adapted to the execution of 
 a written contract without bids by con- 
 sidering all matters of pre-bid procedures 
 in the suggestions as simply part of the 
 informal negotiations that lead up to 
 the signing of the contract. 
 
 Bids for rough grading usually can be 
 obtained by the tractor hour, by the 
 cubic yard of earth excavated, or by the 
 job. 
 
 If payment is made by the tractor 
 hour, the following items should be in- 
 cluded in the contract: 
 
 1. Description of work including loca- 
 
 tion, vegetal cover, topography, soil 
 type, acreage, and total cubic yards of 
 earth excavation. The instruction to the 
 bidders should explain that interested 
 bidders will be expected to visit the prop- 
 erty and will be responsible for accurate 
 appraisal of site conditions. 
 
 2. Time schedule, including required 
 starting and completing dates, with pro- 
 visions for (a) extensions of time 
 granted by the landowner because of de- 
 lays not caused by the fault of the con- 
 tractor, (b) for liquidated and ascer- 
 tained damages for failure to complete 
 the work within the time specified or 
 within extensions of time so granted, and 
 (c) for a performance bond. It is sug- 
 gested that the liquidated and ascertained 
 damages for each day that the work re- 
 mains incomplete be fixed at not to ex- 
 ceed $25 per day in most single-farm 
 grading contracts. With large jobs, for 
 example where the contract amount ex- 
 ceeds $25,000, $50 per day would be 
 appropriate. 
 
 3. Cessation of grading operations for 
 wet soil. Most soils would be damaged if 
 graded during wet weather or while re- 
 maining wet. The landowner should have 
 the right at such times to direct when 
 work must stop and when it may start, 
 subject to the adjustment of the speci- 
 fied time for completing the work thus 
 made necessary. 
 
 4. Preliminary chiseling. Cloddy fill 
 material should be avoided as much as 
 possible by specifying whether chiseling 
 may or may not precede scraping. 
 
 5. Placement of fill material. It is de- 
 sirable to require that cloddy soils be 
 spread in thin (approximately 4 inches) 
 layers to avoid as much as possible un- 
 predictable settlement. 
 
 6. Equipment suitability. A sufficient 
 description of each piece of equipment 
 which it is proposed to use on the job 
 should be called for to show whether or 
 not the equipment layout meets the re- 
 quirements of the work to be performed. 
 
 [29] 
 
Furthermore the landowner should re- 
 serve the right during the progress of 
 the work to stop any operation or the 
 use of any machine which in his judg- 
 ment is inefficient. 
 
 7. Time clocks. The contractor should 
 be required to equip all tractors used on 
 the job with accurate time clocks and to 
 keep an accurate record of the time ac- 
 tually worked by each machine and to 
 furnish the landowner copies of such 
 records. 
 
 8. Time to be paid for. It should be 
 explained in the contract that payment 
 will be made for only the time spent 
 while the equipment is at work. Time 
 used in transporting the machines to and 
 from the job and for their repair and 
 servicing should not be considered as 
 working time to be charged to the land- 
 owner. 
 
 9. Damage due to grading operations. 
 The contract should state that the con- 
 tractor will be required to pay the cost 
 of repairs and replacements necessitated 
 by damage from grading operations, in- 
 cluding that for resetting necessary grade 
 stakes which are knocked down. 
 
 10. Final clean-up. Contractor should 
 be held responsible for cleaning the field 
 and all grounds occupied by him in con- 
 nection with the work of all rubbish, 
 excess material and equipment. 
 
 11. Insurance. Contractor should be 
 required to submit proof that he carries 
 sufficient liability and/or compensation 
 insurance to cover his full liability under 
 the "Workmen's Compensation Insur- 
 ance and Safety Act." 
 
 12. Payment schedule. This should in- 
 clude the right of the landowner to with- 
 hold final payment of 10 per cent to the 
 contractor for 35 days after the record- 
 ing of "notice of completion of work," 
 provided that the landowner records the 
 notice with the county recorder within 
 10 days following the date of completion 
 of the work. This provision is necessary 
 to protect the landowner in the event 
 
 that labor or material liens are filed 
 against his land. It is provided by statute 
 in California that if the landowner re- 
 cords the notice of completion of work 
 within the 10 days, liens may be filed 
 only within the 30 days next following 
 the date of recording. Thirty-five days, 
 however, is considered necessary to pro- 
 vide a proper factor of safety. For work 
 done outside of California, the appli- 
 cable State statute should be consulted. 
 If payment is made by the cubic 
 yard of earth excavation it is sug- 
 gested that items 1 to 5 remain the same 
 as for the preceding contract and that the 
 following be added. 
 
 6. Basis of measurement for payment. 
 For payment purposes a cubic yard of 
 earth excavation is a cubic yard of earth 
 in place, or before it is moved. Earth in 
 areas of cut which is either excavated 
 below or left above grade should not be 
 included. 
 
 7. Computation of earth quantities. 
 Since earth quantities can be computed 
 several ways with different results, it is 
 important to specify the method which 
 is used. The dependable fair accuracy 
 that can be obtained either with the aver- 
 age end areas or the 4-point methods 
 commends its use when payment is made 
 by the cubic yard of earth excavation. 
 
 8. Class of earth excavation. Total 
 yardage of earth excavation should be 
 stated if possible for the bidder's benefit 
 in the three categories called for by 
 items 8-b, 8-c and 8-d of the engineering 
 contract. It should be explained that 
 these quantities are approximate and ten- 
 tative and that the landowner assumes no 
 responsibility for their accuracy. 
 
 9. Lengths of haul. The difficulty of 
 identifying specific lengths of haul in 
 land grading work discourages recogni- 
 tion of haul distance as a measurement 
 for specifying different payments for 
 moving a cubic yard of earth. Instead, 
 the effect of haul distance is usually left 
 for the bidder to appraise. To this end 
 
 [30] 
 
he must be granted the right to study the 
 project map and to use it in event his bid 
 is accepted. Furthermore he should be 
 given the approximate yardages of earth 
 excavation for the three haul distances 
 listed in items 8-e, 8-f and 8-g of the 
 engineering contract. It should be ex- 
 plained that the landowner assumes no 
 responsibility for the accuracy of these 
 figures. 
 
 10. Ceiling on total cost. Owing to 
 sometimes wide discrepancy in the 
 amount of earth excavation used by dif- 
 erent contractors to complete their work, 
 it is desirable and equitable in order to 
 insure careful earth moving and a rea- 
 sonable total cost of grading to place a 
 limit for payment purposes on the 
 amount the volume of cut may exceed the 
 volume of fill (see pages 17 and 18). 
 
 11. Grade tolerance. In case the slope 
 of the graded surface is around 0.2 per 
 cent, as most often is the case, the toler- 
 ance should generally not exceed one- 
 tenth of a foot above or below the pre- 
 scribed grade as determined by nine 
 readings in each grid square, i.e., one at 
 each corner, one on each side midway 
 between corners, and one at the center. 
 Greater deviations are permissible if 
 they are confined to areas of not to ex- 
 ceed 400 square feet. Relatively greater 
 
 departures from a prescribed grade may 
 be allowed for steeper slopes. 
 
 12. Damages due to grading opera- 
 tions. Same as Item 9 for contract B. 
 
 13. Final cleanup. Same as item 10 for 
 contract B. 
 
 14. Insurance. Same as item 11 for 
 contract B. 
 
 15. Payment schedule. Same as item 
 12 for contract B. 
 
 If payment is made by the job, 
 
 items in the contract should be the same 
 as for the preceeding contract except 
 that items 6, 7 and 10 do not apply. 
 
 Contract for Fine-Finish Grading 
 
 If rough grading is completed as 
 should be, to the proclaimed tolerance 
 and the fine finish work remains to be 
 let, a very simple contract or none at all 
 will suffice. The required work consists 
 of planing the ground surface in a suf- 
 ficient number of directions with a ma- 
 chine which is designed to remove auto- 
 matically the grade irregularities in 
 small areas allowed during rough grad- 
 ing. Thus the length of planing machine 
 and the directions to be planed should be 
 specified or understood. The work is 
 usually contracted for either by the hour, 
 or by the acre for each planing. 
 
 [31] 
 
APPENDIX 
 
 I. Methods of Land-Grading Calculations 
 
 Least-Squares and Average Profiles Method. The least-squares method is 
 a statistical procedure for obtaining the best fit to a group of points. It was first 
 adapted to the problem of fitting a plane to the different elevations delineating an 
 uneven land surface of a rectangular tract of land (C. V. Givan, Land grading cal- 
 culations, Agr. Engin. 21(1) : 11-12, 1940). Later its application was extended to 
 include land areas of any shape (G. E. Chugg, Calculations for land gradation, Agr. 
 Engin. 28(10) : 461-463, 1947). The least-squares and average profiles method is 
 another adaptation of the same principle to the problem which appears to be suffi- 
 ciently easy to follow and practical to use to warrant wide acceptance. The solution 
 consists of changing the problem from one of fitting a plane by the least-squares 
 method to a large number of grid corner elevations, which has been the procedure 
 proposed by Givan, to the simpler computation of determining by the method of 
 least squares the slopes of the lines which most nearly fit the average profiles in the 
 two coordinate directions. It will be shown later how the slope of these two lines are 
 used to form a plane which, when properly placed, fits the contour pattern best. The 
 following example explains the method and shows how the calculations are made. 
 
 Let it be assumed that the chart below is the base map of a rectangular area 
 which is to be leveled as a unit. The stakes are set and the elevations are given at 
 100-foot intervals starting 50 feet in from the property lines, thus forming a grid 
 with the elevation known at each grid corner. For grade calculation purposes the 
 
 /- 
 
 Point of Qi-i tjirt 
 
 Column To to la 4S.8 
 Column Average 916 
 
 s~X. /Axij - Station Du+once* 
 2 - — 3 --•? S 
 
 453 
 
 9.06 
 
 
 C~f r '*la' Bo 
 
 unc/or-y 
 
 
 
 
 
 93 
 
 84 7 9 
 
 8 J 
 
 
 
 83 
 
 80 
 
 10.6 
 
 9 5 8 2 
 
 7 9 
 
 
 
 as 
 
 8.1 
 
 
 
 Hm 
 
 - Ce 
 
 nt 
 
 red 
 
 
 
 
 / 
 
 on 
 
 8 45 3 
 
 
 100 
 
 39 9.1 
 
 AT 
 
 
 
 8.1 
 
 18 
 
 84 
 
 94 9./ 
 
 75 
 
 
 
 8 5 
 
 81 
 
 75 
 
 "I 
 
 fi/ 8 3 
 
 72 
 
 
 
 8.2 
 
 18 
 
 476 
 8 52 
 
 384 
 1.68 
 
 399 
 196 
 
 Line 
 
 Totals 
 
 Lme 
 
 8 517 
 
 zS3 .6 - 30 . 8 4SS 
 
 Base map showing the land elevation at grid corners, the location and elevation of the cen- 
 troid, the average profile figures, and the point of origin of the plane to which the field is to 
 be graded. 
 
 [32] 
 
grid corners are located by a system of coordinates. In this case the point of origin 
 "a" is located 50 feet north and 50 feet west of the northwest corner of the field. The 
 locations of the grid corners are designated in stations (number of 100-foot inter- 
 vals) southward along the Y axis and eastward along the X axis from "a." The 
 position of the point with elevation 9.9 would thus be 2 stations east and 3 stations 
 south of "a." 
 
 The first step in the calculations consists of adding the elevations along each line 
 and in each column as shown on the map and computing the average elevation of 
 each line and each column. The average elevation changes from north to south and 
 from west to east across. the field are thus shown by the line and column averages 
 respectively. 
 
 The second step consists of locating the centroid, "H m ," and determining its 
 elevation. The centroid is the exact center of the grid. Its elevation in this case is the 
 average of all the grid-corner elevations. If the outside grid corners are spaced 
 other than one-half the interval between grid corners from the boundaries of the 
 field, or so the elevation of each grid corner applies to different size areas than 
 10,000 square feet, the elevations of these points must be weighted for determining 
 H m in accordance with the land areas represented by each of them. This point 
 determines the position in elevation of the plane which best fits the contour pattern. 
 The location of H m is its average station distances from "a" on the X and Y axes, 
 or X m and Y m . X m and Y m for the problem being presented thus would be : 
 
 v 1 + 2 + 3 + 4+5 + 6 01/ JX7 1+2 + 3 + 4 + 5 „ 
 
 X m = = 3y 2 ; and Ym = - =3 
 
 o 5 
 
 The third step consists of determining slopes of the lines which most nearly fit 
 the average profiles in the two coordinate directions. At this point it is desirable 
 for the purpose of illustration to plot the average line elevations and the average 
 column elevations as shown in the two graphs on page 34. To avoid confusion 
 with the diagram on page 32, the coordinates for these two graphs are designated as 
 H for elevations and S for distance in stations from the point of origin "a." Accord- 
 ing to the least squares method, the slope of the line which best fits the points on 
 each of these two profiles is: 
 
 S(SH) - (SS)(SH) 
 Gns ° r Gwe = 
 
 2(S) 2 -(2S) : 
 
 n 
 where G W e = Slope of the line which best fits the points which represent the average 
 land slope in a west to east direction across the field. 
 G NS = Slope of the line which best fits the points which represent the average 
 land slope in a north to south direction across the field. 
 ■2 - The sum of a number of values. 
 2(SH) =The sum of the products of the station distance and elevation of each 
 of the plotted points on each of the graphs on page 34. 
 2S2H = The product of the sums of the station distances and the elevations of 
 each of the plotted points on each graph, 
 n = The number of plotted points on each graph. 
 2(S) 2 = The sum of the squares of the station distances of each of the plotted 
 
 points on each graph. 
 (2S) 2 = The square of the sum of the station distance of each of the plotted 
 points on each graph. 
 
 [33] 
 
9.0 
 
 c8.5 
 q 
 
 a 
 > 
 
 0) 
 
 8.0 
 
 7.5 
 
 
 \^— «^* <r Av. West-East Profile 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Vi 
 
 G W E 
 
 
 
 
 
 
 
 
 ^\. 
 
 2 3 4 5 
 
 Distance in Stations from Point of Origin 
 
 Average land profile from west to east (top) and from north to south (bottom). 
 
 9.0 
 
 8.5 
 
 o 8.0 
 
 7.5 
 
 7.0 
 
 
 
 
 
 
 
 
 
 -Av. North-So 
 
 uth Profile 
 
 
 < 
 
 / 
 
 
 
 \ d ^ N 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2 3 4 
 
 Distance in Stations from Point of Origin 
 
 [34] 
 
The G NS and G WE slopes for the problem being presented are thus computed as 
 follows: 
 
 Computation of G W e or the slope which best fits the original topography 
 in a west to east direction across the field 
 2(SH) = (1x9.16) + (2x9.06) + (3x8.52) + (4x7.68) + (5x8.32) + (6x7.98) 
 = 173.04 
 2S = 1 + 2 + 3 + 4 + 5 + 6 
 
 = 21 
 2H = 9.16 + 9.06 + 8.52 + 7.68 + 8.32 + 7.98 
 = 50.72 
 2(S) 2 =l + 4 + 9 + 16 + 25 + 36 
 = 91 
 n = 6 
 
 21 x 50.72 
 
 173.04 
 
 Then Gwe 
 
 91 
 
 (2ir 
 
 = - 0.256' per 100 feet. (Minus sign indicates slope is eastward from "a") 
 
 Computation for G N s or the slope which best fits the original topography 
 in a north to south direction across the field 
 5(SH) = (1x8.367) + (2x8.80) + (3x8.733) + (4x8.517) + (5x7.850) 
 = 125.484 
 2S=l+2+3+4+5 
 
 = 15 
 2H = 8.367 + 8.80 + 8.733 + 8.517 + 7.850 
 = 42.267 
 2(S) 2 = l+4 + 9+16 + 25 
 = 55 
 n = 5 
 
 15 x 42.267 
 
 125.48 
 
 Then Gi 
 
 55 
 
 (15) 2 
 
 = - 0.131' per 100 feet. (Minus sign indicates slope is southward from "a") 
 The time required for computing G N s and G W e will be reduced materially by tabu- 
 
 *: r__ __ • *u_ «.„ui_ l l _il :ui_ ..„i £ ""*° J v/cu \-*^>j • 
 
 laung iui u 
 
 
 
 
 n 
 
 n 
 
 n 
 
 2S 
 n 
 
 (S) 2 (ES)2 
 
 n 
 
 n 
 
 2S 
 n 
 
 (S) 2 (2S)2 
 
 n 
 
 2 
 
 1.5 
 
 0.5 
 
 15 
 
 8.0 
 
 280.0 
 
 3 
 
 2.0 
 
 2.0 
 
 16 
 
 8.5 
 
 340.0 
 
 4 
 
 2.5 
 
 5.0 
 
 17 
 
 9.0 
 
 408.0 
 
 5 
 
 3.0 
 
 10.0 
 
 18 
 
 9.5 
 
 484.5 
 
 6 
 
 3.5 
 
 17.5 
 
 19 
 
 10.0 
 
 570.0 
 
 7 
 
 4.0 
 
 28.0 
 
 20 
 
 10.5 
 
 665.0 
 
 8 
 
 4.5 
 
 42.0 
 
 21 
 
 11.0 
 
 770.0 
 
 9 
 
 5.0 
 
 60.0 
 
 22 
 
 11.5 
 
 885.5 
 
 10 
 
 5.5 
 
 82.5 
 
 23 
 
 12.0 
 
 1012.0 
 
 11 
 
 6.0 
 
 110.0 
 
 24 
 
 12.5 
 
 1150.0 
 
 12 
 
 6.5 
 
 143.0 
 
 25 
 
 13.0 
 
 1300.0 
 
 13 
 14 
 
 7.0 
 7.5 
 
 182.0 
 
 227.5 
 
 26 
 
 13.5 
 
 1462.5 
 
 [35] 
 
It is also of some practical importance to note that G NS and G WE may be determined 
 without the least squares computations by merely fitting a line as closely as can be 
 determined by inspection to each of the two average profile graphs on page 34. The 
 slopes of these lines expressed as the difference in elevation per station distance are 
 then assumed to be G NS and G WE . Ability to approximate in this manner the results 
 obtained by least squares depends largely on the shape of the profiles. If the lines can 
 be placed on the profiles with fair confidence that they approach closely the best fit 
 and if some practice is had with duplicating in this manner the results obtained by least 
 squares, the error involved in using this short cut may be small. 
 
 The fourth step consists of using slopes Gns and Gwe an d the elevation of the 
 centroid to delineate the plane which best fits all of the grid-corner elevations in the 
 diagram on page 32. To this end the known values for G NS , G W e 5 and H m are sub- 
 stituted in the equation for a plane to determine the elevation at the point of origin, 
 "a." Then the new elevation for each of the grid corners is found by adding alge- 
 braically the elevation at the origin and the product of the slope and distance in 
 stations in both coordinate directions, thus: 
 
 The equation of the plane is: H m = a + (G WE ) (X m ) + (G NS ) (Y m ) in which 
 
 H m = elevation of the centroid 
 
 a = elevation of the point in the plane at the origin 
 
 X m and Y m = the horizontal and vertical coordinates of Hm 
 
 G NS and G W e = slopes of the plane in the Y and X directions respectively. 
 
 In the diagram on page 37, H m = 8.453 
 
 X m = 3.5 
 Y m = 3 
 Thus, a = 8.453 - (- 0.256 x 3.5) - (- 0.131 x 3) 
 
 = 9.742 
 
 The new elevation that would correspond with the old elevation 9.9, three stations 
 south and two west of point of origin a, would then be found as follows: 
 
 H = a+(Gw E )(X) + (G NS )(Y) 
 
 = 9.742 + (- 0.256 x 2) 4- (- 0.131 x 3) 
 = 8.837 
 
 If these calculations are completed to the third significant figure beyond the deci- 
 mal, the resulting plane will require almost exactly the same amount of cut as fill 
 and the total amount of earth moved will be a minimum. 
 
 Most irrigated fields are suitably shaped for using the methods of grade calcu- 
 lation so far explained. That is, they are four-sided with opposite sides approximately 
 parallel. G. E. Chugg in the before-mentioned publication describes a precise method 
 of calculation for also fitting a plane to the topography of an irregularly shaped field. 
 Unfortunately, however, his method has proved too intricate to be adopted generally 
 to land grading and no way has been found to simplify it. So, as a general practice 
 to follow in such cases it is recommended: First, that the best coverage possible, of 
 
 [36] 
 
9.35$ 
 
 m&_ 
 
 2J_ Q± 
 
 r\r>c p 
 
 o/sc. 
 
 14 
 
 SLZl 
 
 3.G 
 
 ZSL 
 
 S99F 8.843 
 
 O77" 
 
 6Z9F 
 
 2.5 
 
 _&2_ 
 
 41 
 
 8.3 
 
 M3F- 8587 
 J 893~F 
 
 873 r. 
 
 3£- 
 
 12. 
 
 12 &2_ 
 
 284F- 8.331 
 
 t *7F 
 2I7F 
 
 3J- 
 
 6LL 
 
 J2J_ 
 
 8.0 
 
 &3ff- 8.075 
 039 C. 
 
 3.5 
 
 JSJL 
 
 4.0 
 
 Q 2S F 
 .005 F 
 
 3,9 
 
 S.Z24 
 
 1QJL 
 
 /.376C. 8.968 
 I.446C. 
 
 Z*o_ 
 
 23. 
 
 S3i^-. 
 60Z C. 
 
 ZA 
 
 8.11? 
 
 _2J_ 
 
 &2-Z 8456 
 
 s ir-? p 
 
 .TV t r 
 
 442 F 
 
 5&>F 8.200 
 
 .446-F 
 
 4SGF 
 
 .3&*~e. 7944 
 
 330 C 
 
 370c 
 
 Zl. 
 
 JJL 
 
 45_ 
 
 8.1 
 
 33- 
 
 18_ 
 
 456 &■ 
 
 2ZGC 
 ±1 
 
 3.093 
 
 &A. 
 
 9 07C 8837 1063 C . 8.581 
 
 .957 C 
 
 377 C. 
 
 36 
 
 9.4 
 
 1.133 C. 
 2.6 
 
 £19 G 8.325 
 
 J69C 
 
 589 C 
 
 .8 25 £ 8069 
 
 m~F- 
 
 9.1 
 
 2.9 
 
 11. 
 
 755F 
 
 Z5_ 
 
 £A. 
 
 03i-e. 
 
 . 08 i C 
 
 . 101 c. 
 
 3.5 
 
 7.813 
 
 8.2 
 
 V fJ ~ 
 
 051C 
 38 
 
 8.96? 
 
 £€*€ 8.706 
 \J&-F- 
 A9ZF 
 
 1A. 
 
 &SL 
 
 j8± 
 
 .6 94 C. 
 
 . ATT fc. 
 
 ■764 C 
 
 21 
 
 8.450 
 
 6S OG 8.194 
 
 /ft/ c . 
 
 .720 C. 
 
 3JL 
 
 2J_ 
 
 7JL 
 
 69+-F 
 C41F 
 .624 F. 
 
 4.8 
 
 7.938 
 
 8.Z 
 
 5 6 ? C. - 1682 
 vt c c. 
 632 C 
 
 3.8 
 
 7.8 
 
 5J8 C 
 
 r s a /- 
 
 5880 
 
 ±1 
 
 8.83\*h334-f. 857S\ 
 t.ttiF. 
 
 qj5 F 
 -425F 
 
 8319 
 
 ,04*^ 8063 
 
 £ 63 F 7.807 
 
 OtJr. 
 
 3 9 3 C. 
 413C 
 
 7.551 
 
 .299 C 
 
 .4oSf. 
 
 ~d~BTc: 
 
 31*3 C. 
 
 J.26IF. 
 
 793 F 
 
 463C. 
 
 Map showing elevations and cuts and fills. It contains three sets of figures representing either 
 cuts or fills at each grid corner. The top row of figures represent the cuts and fills as would be 
 calculated by the least-square method. The second row represents the cut and fills when all 
 elevations are lowered 0.05 foot. The third set of figures represents the cut and fills when all 
 elevations are lowered 0.07 foot. The latter set of figures is presumed to give the required excess 
 volume of cut. 
 
 the land to be graded as one field, be obtained with one or more of the four-sided 
 areas. Second, that the previously described procedure for determining G NS and 
 G W e be employed. Third, that the slopes so determined be extended arbitrarily be- 
 yond the four-sided areas to the boundaries of the property to be leveled. Fourth, 
 that sharp changes in slope, due to subdivision of a field into more than one part and 
 determination of Gns and G W i; separately for each part, be modified by merging 
 the slopes into each other. 
 
 It will be found in some instances that slopes calculated by the least squares aver- 
 age profiles method are either too flat or too steep to suit the crop or preferred method 
 of irrigation. In such cases another plane which passes through the centroid but has 
 the different desired slope may be adopted. It will be understood that any change of 
 this kind will increase the amount of earth to be moved and also the length of haul. 
 
 The least squares average profiles method of calculating land grades is serviceable 
 only when the lay of the land, depth of soil and other factors favor grading to a 
 plane or a series of planes which may be merged with slight grade change one into 
 
 137] 
 
the other. Otherwise it is necessary to adhere closer to the original topography than 
 can be done with a plane. This may be accomplished by using the cross-section and 
 two-way profile methods of determining the grades. 
 
 Cross-Section Method: The following steps are necessary when the cross-section 
 method is used: 
 
 1. Profiles of each grid line paralleling the direction of irrigation are constructed. 
 
 2. Grade lines are tentatively fitted to each of these profiles. This is accomplished 
 by placing a straightedge on each profile to represent a possible grade line and shift- 
 ing it so that the areas above it and below the ground profile properly balance those 
 below it and above the ground profile. The slope of these lines may not be uniform 
 and it may vary from one line to another, but it must be kept within the allowable 
 limits for irrigation as indicated in the table on pages 6 and 7. 
 
 3. The elevations along these tentative grade lines are noted and used to plot pro- 
 files in the other coordinate direction. This second set of profiles must satisfy the 
 cross-grade limitations listed in the table on pages 6 and 7. 
 
 4. If it is found necessary, the first set of grade lines are altered until the cor- 
 responding profiles in the other coordinate direction are satisfactory. Considerable 
 shifting of grade lines may be necessary in order to accomplish this purpose. In the 
 end the grade lines will delineate a land surface which will be satisfactory though 
 probably less than ideal for irrigation. 
 
 5. The differences in elevation of the original ground surface and the approved 
 grade line along these profiles at the points which correspond to the grid corners are 
 observed and recorded on the base map as cuts and fills. 
 
 6. The depths of cut and fill so obtained are adjusted in the same manner as for 
 the least squares and average profiles method to obtain the proper balance between 
 volume of cut and volume of fill. 
 
 A long narrow field in which both the most earth moving and the direction of 
 irrigation are crosswise of the tract is especially easy to handle by this method. 
 Small triangular or extremely irregular fields to which it is difficult or impossible to 
 fit rectangular grids likewise can be dealt with in this way. On the other hand, use 
 of the cross-section method for large areas should be avoided. With such areas this 
 trial and error procedure becomes too involved to be practical. Instead the two-way 
 profile method can be used to better advantage. 
 
 Two-Way Profile Method: The advantage to be gained by using the two-way 
 profile method is that both the irrigation and cross grades are fitted to the original 
 ground surface simultaneously. The following steps explain how this is done. 
 
 1. A relief map or two-way profile of the ground surface must first be prepared. 
 This is accomplished as shown in the diagram on page 39. The base for this map, 
 UjZjZ-U,, consists of a plane with an elevation of 7.0 feet which, it is estimated, will 
 be lower than any point in the area after the grading. The map represents a field 500 
 feet by 600 feet staked off as a grid in 100-foot squares. The ground surface, 
 A^jA-jF-, is plotted relative to this base by subtracting the elevation of the base 
 from the elevation of each grid corner and laying off the difference first horizontally 
 to the right and then vertically from the position of each respective grid corner on 
 the base. For example, to plot the ground surface B { , which is 150 feet east and 250 
 feet south of the northwest corner of the field, subtract 7.0 feet, the elevation of the 
 base, from 9.9 the elevation at B ;! . This 2.9-foot difference is measured off first to 
 the right and then up from V 3 to locate B 3 . The scale used for plotting these ground 
 
 [38] 
 
W--E 3 
 
 Technique employed in drawing a relief map when two-way profih 
 method of calculating grades is used. 
 
 surface points must be large compared to that of the base in order to give necessary 
 prominence to variations in elevation along the two-way profiles, 20 times in this 
 case. The lines joining the points so plotted, as AjA- joining the points A 1 A 2 A 3 A 4 A r , 
 and A 2 F 2 connecting points AoBX 2 D L ,E 2 Fo, form the ground surface profiles in the 
 two directions, or the two-way profiles. 
 
 2. The direction of irrigation is determined by studying the two sets of profiles 
 on the two-way profile map. Grade lines are temporarily fitted to a sufficient number 
 of individual profiles in each of the two directions to discover approximately what 
 slopes can be made available. The direction of irrigation usually will be that of the 
 most favorable slope. 
 
 3. With the direction of irrigation known and the two-way profile available, the 
 next step consists of fitting simultaneously to the profiles the grade lines which suit 
 the requirements of the irrigation slope in the one direction and the cross slope in 
 the other. 
 
 If it is required by site conditions or need to keep land grading costs at a mini- 
 mum, the slopes in both of these directions are made to follow as closely as may be 
 the original ground surface. The grade in the direction of irrigation may be altered 
 slightly at any grid corner so long as the slope is not reversed and is neither steeper 
 nor flatter than is specified in the table on pages 6 and 7. The cross slope also may be 
 changed at successive grid corners, and it is important only to see that it does not 
 exceed the maximum allowable for the irrigation method to be used. 
 
 If site conditions and land grading costs permit, it is more desirable to have the 
 grade uniform at least in the direction of irrigation. This is done by fitting to the 
 successive profiles in the direction of irrigation uniform grade lines which are suf- 
 ficiently near the same slope and elevation to provide a cross grade which in no 
 place is excessive. 
 
 4. Just as with the cross-section method, the cuts and fills are first scaled from the 
 profiles and then adjusted to obtain the proper balance between the total volumes 
 of cut and fill. 
 
 [39] 
 
II. Computation of Cut and Fill Adjustments 
 
 If it is estimated that 30 per cent more cut than fill is needed, it follows that the 
 total volume of cut must equal 130 per cent of the total volume of fill, or 
 
 Total Volume of Cut 
 
 Total Volume of Fill 
 
 x 100 = 130% 
 
 If the grid system is laid out as in the diagram on page 37 with the outside grid 
 corners one-half the interval between grid corners from the boundaries of the field, 
 or so the elevation of each grid corner applies to the same size area (10,000 square 
 feet) it is sufficiently true for this purpose, as will be shown later, to assume that the 
 sums of the depths of cut (2 Cut) and fill (2 Fill) at all of the grid corners are pro- 
 portionately the same as the total volumes of cut and fill. If any of the outside corners 
 represents a different size area than that of the inside corners,- the depths of cut or 
 fill at these points must be weighted accordingly to make 2 Cut and 2 Fill equivalent 
 to the approximate total volumes of cut and fill. The preceding formula thus may be 
 simplified to: 
 
 1^x100-130% 
 2 Fill 
 
 Hence, the depths of cut and fill first obtained by subtracting the original elevation 
 of each grid corner from the corresponding calculated or graphically determined 
 elevation, or vice versa, are totaled and the percentage difference computed. It is 
 known by this step how cut and fill, as first determined, balance. If the total depth 
 of cut is found to be too small to agree with the estimated requirement, the calcu- 
 lated or graphically determined elevation at all grid corners is lowered by trial and 
 error an amount which will increase the cuts and decrease the fills so that 2 Cut will 
 exceed 2 Fill by the estimated requirement. This adjustment usually amounts to a 
 lowering of all the calculated or graphically determined elevations by less than 0.1 
 foot. To prevent accumulative error it is advisable while making these calculations 
 to maintain an accuracy to the second place beyond the decimal or to the nearest 0.01 
 foot. 
 
 To illustrate, proceed with problem presented in the diagram on page 32, as re- 
 stated and further developed in the diagram on page 37. From depths of cut and fill 
 as first obtained by subtracting the original elevation at each grid point from the 
 corresponding calculated elevation, 
 
 2 Cut = 7.950 feet 
 2 Fill = 7.940 feet 
 and 
 
 7.950 
 
 7.940 
 
 x 100 = 100.1% 
 
 The total cut in this case is approximately 100 per cent of the total fill instead of the 
 130 per cent estimated to be required, so adjustment is necessary. If all the calcu- 
 lated grid-corner elevations are lowered by 0.05 foot 
 
 2 Cut = 8.737 feet 
 2 Fill = 7.227 feet 
 and 
 
 ggx 100-1*% 
 
 [40] 
 
Try a lowering of 0.07 foot, which makes 
 
 2 Cut = 9.092 feet 
 2 Fill - 6.982 feet 
 and 
 
 9 092 
 
 — x 100 = 130.2% 
 
 The cuts and fills first obtained are altered accordingly on the base map and with 
 one exception are posted in the field without further change. The exception pertains 
 to the depths of fill. It is known from experience with leveled land that settling occurs 
 in the fills after the grading is completed. It is customary at the time of posting in 
 the field to add 10 per cent to the adjusted depths of fill listed on the base map. Very 
 likely there is considerable difference in the allowance that should be made depend- 
 ing upon the structure of the soil as it goes into the fill. Clean, dry sand should settle 
 very little, while dry, cloddy clay or adobe might be expected to consolidate more 
 than the 10 per cent. It is often the experience that some regrading must be done due 
 to too little crowning of the fills. 
 
 Final adjustments are made after the work of grading the land has progressed far 
 enough to show the need for it. The prescribed slope in the direction of irrigation 
 should remain unchanged with two possible exceptions. If the volume of cut in rela- 
 tion to the volume of fill proves insufficient, it may be increased by flattening the 
 slope in the first 50 feet and/or steepening it in the last 50 feet of the irrigation run. 
 These changes may even improve the irrigation slope in some cases by providing 
 better opportunity for the irrigation stream to spread before it starts down slope 
 and by affording better surface drainage at the lower end of the field. Any necessary 
 additional adjustment should be confined to alteration of the cross slope. This is 
 accomplished by lowering or raising as need be the posted elevations at all grid 
 corners on any line parallel to the direction of irrigation. The lines so changed 
 should be selected to avoid excessive cross slope at any point. 
 
 III. Earthwork Calculations 
 
 The yardage of excavation, or total volume of cut, is the principal basis for esti- 
 mating equipment requirements and costs. If the work is to be paid for by the cubic 
 yard of excavation, it is reasonable to expect, unless agreement otherwise has been 
 reached, that this yardage is accurately calculated. Other uses for the information 
 usually require less accuracy with a corresponding saving of time or expense. 
 
 The volume of cut in a grid square which lies entirely within an area of cut is 
 most accurately computed by the prismoidal formula, but the degree of accuracy 
 warranted may be obtained by the less involved method of average end areas, which 
 may be expressed as: 
 
 A(C 1 + C 2 + C 3 + C 4 ) 
 
 cubic yards 
 
 27x4 
 
 in which V = cubic yards of cut in the grid square 
 
 A = area of the grid square in square feet 
 
 C 19 C 2 , C 3 , and C 4 = depths of cut in feet at the four grid corners 
 
 If the grid system is laid out as illustrated in the chart on page 10 with all four 
 corners one-half the distance between grid corners from the boundary of the field 
 and it is assumed that no change or break in slope occurs other than as indicated 
 by the grid corner levels, the sum of the volumes of cut (2 V) of all grid squares 
 
 [41] 
 
which lie entirely within areas of cut may be accurately obtained by extending the 
 above formula to: 
 
 v 2 A [ (CJ (nj + (C 2 ) (n 2 ) + (C 3 ) (n 8 ) + . . . . (C n ) (n n ) 1 ,. 
 
 V - 27^^ cubic yards 
 
 in which 2 A = sum of the area of all of the grid squares in square feet. 
 
 Cj, C 2 , C 3 , C n = the. different numerical values of the depths of cut at grid 
 
 corners. 
 
 n i> n 2> n 3> n n = the total number of times each of these numerical values (Cj, 
 
 C 2 , C 3 , . . . . C n ) would be used were the volumes of the grid squares calculated 
 separately. 
 
 5 n = the sum of all the n's defined above 
 This formula reduces to the simpler form : 
 
 (S cuts at all grid corners in feet) (Area of one grid square in sq. ft.) 
 
 V = 
 
 27 
 
 The volume of cut in each of the remaining grid squares, or those which lie only 
 partially in areas of cut, cannot be accurately determined in the same way, though 
 at least a part of the error is compensating and for a whole field it may be insignifi- 
 cant. Such is the assumption in the procedure followed in making the cut and fill 
 adjustment. Also the total volume of earth excavation is frequently calculated entirely 
 in this manner for jobs which are paid for by the tractor hour in order to check the 
 cost against the fair cost of earth excavation by the cubic yard. Furthermore, if 
 agreed to beforehand, it can be the basis for settlement even when the work is let by 
 the cubic yard of excavation. 
 
 If volume of cut must be calculated with greater accuracy as, perhaps, should 
 be the case when land grading is contracted on the yardage basis, it is necessary to 
 determine more precisely the volume of cut in those grid squares which are only 
 partly in areas of cut. With cut called for only one, two, or three of the four grid 
 corners of the volume of cut can still be calculated by the average end areas method 
 with the fair accuracy required. However, it can be determined as well by the less 
 difficult but not so well known 4-point method which will be described later. 
 
 In case the average end areas method is used, the grid square and earth mass to be 
 excavated is divided for this purpose into areas and volumes which can be computed 
 separately and combined to give the total volume of cut in each grid square. Thus in 
 the left diagram below, in which three corners are in cut and one in fill, the grid 
 square may be divided into rectangles TSUW and XTVY and triangle SUV. These 
 areas would then be computed as follows 
 
 o.i F 
 
 Q.3F 
 
 O.IF 
 
 2. OF 
 
 Left: Division of cut area into triangles and rectangles for computing volumes of earth 
 
 excavations when three corners of a grid square are in cut. 
 
 Center: When two grid corners are in cut. Right: When one grid corner is in cut. 
 
 [42] 
 
(See Searles, W. H., Ives, H. C, and Kissam, P. Field Engineering. John Wiley, N.Y., 
 2d Ed., 1949.): 
 
 AreaofTSUW=(WU) (TW) (The distances WU and TW are obtained by inter- 
 polation as previously explained) 
 
 = (3/8x100) (5/7x100) 
 = 2679 square feet. 
 Area of XTVY 
 
 = (XY) (VY) 
 = 100 (2/7x100) 
 = 2857 square feet. 
 Area of SUV 
 
 = %(SV>(SU) 
 =i %xl00) (5/7xl00) 
 
 = 2232 square feet. 
 
 The volumes of the three earth masses which have as their bases rectangles TSUW 
 and XTVY, and triangle SUV can then be computed and combined to obtain the 
 total volume of cut in the grid square, thus: 
 
 Volume of cut in WXYVU = { 2 679 (-3 + + .456 + .729) + ^ (.729 + 0, .2 + .9) 
 
 + 2232 (0 + f 6 + 0) }^27 
 = 97.7 cubic yards. 
 
 When two of the corners are in cut and two in fill as shown in the central diagram 
 on page 42 two areas and two volumes must be determined to obtain cubic yards 
 of cut, thus: 
 
 Area WSTX = (8/11 x 100) 100 
 = 7273 square feet. 
 Area TSU = (14/15x100-8/11x100) 1Q0 
 
 = 1030 square feet. 
 
 v i wqty 797* (1-4 + 0.309 + + 0.8) 
 
 Volume WSTX = 7273 
 
 4 
 
 = 4560 cubic feet. 
 
 v . TQTT (0.309 + + 0) ln „ A 
 
 Volume lbU = 10a0 
 
 o 
 
 = 106 cubic feet. 
 Volume TXWU =— — — = 173 cubic yards. 
 
 In the only remaining case when one isolated corner is in cut as shown in the 
 right diagram on page 42 it is necessary to compute only one area and one volume, 
 thus: 
 
 AreaSUwJ 4/5xl ° 0)( 9 4/12xl00) 
 
 - 1,333 square feet. 
 
 xr i crm/ i- 333 (0.0 + 0.4 + 0.0) 
 Volume SUW = 
 
 3x27 
 6.6 cubic yards. 
 
 [43] 
 
Base map of field to be graded showing the distribution of cut and the volume of 
 
 cut by grid squares. 
 
 In case the grid system consists of grid blocks that are not square, it is necessary 
 to know the interior angles of the grid blocks and to compute the fractional areas 
 by trigonometry which makes the procedure much more involved and time con- 
 suming. 
 
 The yardage of excavation of the square grid system shown above has been 
 computed both by the above unit volume method and formula V = A2C/27 in which 
 A is the area of one grid square. As the yardages were computed by this unit volume 
 method, each result was written within the corresponding grid square on the map. 
 Thus by inspection it could be seen that the calculated quantities were consistent and 
 complete. 
 
 The total quantity of earth excavation arrived at in this manner is 23,749 cubic 
 yards, while that obtained less accurately by the formula V = A2C/27 is 25,555 cubic 
 yards. Different results — some showing closer agreement and some greater disagree- 
 ment — may be expected for each parcel of land considered. 
 
 [44] 
 
IV. Haul Distance Calculations 
 
 The haul distance beyond which it is economical to switch from the slow traveling 
 crawler tractor unit to the high speed rubber-tired wheel equipment is determined 
 by the relative costs of moving a cubic yard of earth the different haul distances. To 
 obtain this unit cost it is necessary to know the costs of ownership and operation 
 and the production rates for each machine. The following items make up the owner- 
 ship and operation cost. 
 
 Fixed cost based on 10,000 hours operation : 
 
 Depreciation 
 
 Interest, insurance and taxes 
 Variable cost: 
 
 Fuel 
 
 Gasoline for cleaning and starting 
 
 Lubricating oil and grease 
 
 Labor for oiling and greasing 
 
 Repairs — labor and parts 
 
 Tires 
 
 Operator 
 The production rate per hour of operation, or cubic yards of earth moved per hour 
 is arrived at by knowing the capacity in cubic yards of each equipment unit and 
 noting the number of loads moved per hour for each haul distance. The resulting 
 rates apply, of course, only when the scrapers are being loaded to capacity. 
 
 >5-V> 
 
 
 500 1,000 1.500 2,000 2,500 3,000 3,500 
 
 Haul Distance — One Way in Feet 
 
 Production curves for different types and size of size of earth-moving equipment. 
 
 [45] 
 
The 4-point method referred to on page 42 gives only slightly different results. 
 Earth volumes are calculated for each grid square by the following formula (see 
 Engineers Handbook, Region V, Soil Conservation Service) : 
 
 27 
 
 \Sf+ C Ic)( 4 C ) 
 
 V c = Cubic yards of cut in the grid square 
 A = Area of one grid square in square feet 
 
 2c = Sum of the depths of cut at the four corners of the grid square 
 2f = Sum of the depths of fill at the four corners of the grid square 
 
 Similarly 
 
 V 
 
 
 108 
 V ( = Cubic yards of fill in the grid square 
 
 Thus for case 1, page 42 
 
 TT 10,0C 
 
 \ 0.5 + 1.4 J 
 
 108 
 = 95.5 cubic yards. 
 
 Obviously when computed by these formulas the total volume of cut or fill in a 
 single grid square remains the same for each set of cut and fill depths regardless of 
 whether the total depth occurs at 1, 2, 3 or 4 corners. Thus the corresponding earth 
 volume for each combination of cut and fill depths that might occur in a grid square 
 can be tabulated so the calculations need not be repeated. Such a tabulation is shown 
 (p. 48) for a 100 foot square grid. Similar tables can be prepared for 50 and 75 foot 
 grids. By using this table the volume of cut for each grid square can be quickly found 
 at the intersection of the vertical column headed 2c (sum of the depths of cut — ) and 
 the horizontal column headed 2f (sum of the depths of fill) . Thus V c for case 1 page 
 42 is found at the intersection of the vertical column headed 1.4 and the horizontal 
 column headed 0.5 to be 95.5 cubic yards. The total volume of cut for the grid 
 shown on page 42 as determined from this table is 23,704 cubic yards which is 45 
 cubic yards less than that computed by average end areas. 
 
 The unit cost of earth moving for each machine, for each haul distance and for the 
 one set of ground surface conditions may then be computed as follows: 
 
 Fixed cost + variable cost per hour ~ , . , . . , 
 
 ~ . . ; - r ; r \ = Cost per cubic yard oi earth moved. 
 
 Cubic yards oi earth moved per hour 
 
 To be always comparable this cost should be based on bank or cut measure, or 
 
 Depth of cut in feet x area in square feet „ . . , . 
 
 — * — 4 = Cubic yards ol excavation, cut measure. 
 
 — I 
 
 [46] 
 
• 
 Carrier-type scraper capacities are usually described as the contents of the bowl when 
 level full (struck load) , or when heaped (heaped load) . The comparable cut measure 
 (pay load) for different kinds of soil is less than these capacities by approximately 
 20 per cent for loamy soils, 25 per cent for average soils, and 33 per cent for dense 
 clay. 
 
 By examining the unit cost of earth moving by the different sizes and types of 
 equipment, or by plotting them as shown in the diagram on page 45 for a fairly firm, 
 even ground surface it can be readily seen that: 
 
 The cost per cubic yard of moving earth is lower for each larger earth mover 
 
 of the same type. 
 There occurs a haul distance beyond which it rapidly becomes uneconomical to 
 use crawler tractor-drawn carrier scrapers. 
 
 According to recent dealer-manufacturer information, the one-way haul distance 
 at which properly matched and aided crawler tractor and rubber-tired wheel tractor 
 carrier scraper units can operate at approximately the same unit cost is 500 feet. 
 The lack of precision with which tractor-scraper units and a pusher tractor operate, 
 when the one-way haul distance is 500 feet or less, cancels out any advantage in haul 
 speed. Under extremely unfavorable soil conditions, this break-even point might be 
 800 feet or more. 
 
 Recent experiments with weighting and increasing the bearing surface of four- 
 wheel, rubber-tired tractors to give them more effective power while loading prom- 
 ised to increase materially their production rates and to make them superior at all 
 haul distances. Also the recently introduced 4-wheel drive tractor may prove to have 
 similar superiority. 
 
 On the following six pages you will find a table showing .Jfc| 
 earthwork quantities calculated by the four-point method. *^r 
 
 [47] 
 
SUM OF THE DEPTHS OF CUT AT THE FOUR CORNERS OF A 100-FOOT GRID 
 
 0.1 0.2 0.3 0.4 5 6 0.7 8 0.9 1.0 1.1 
 
 VOLUME OF CUT IN CUBIC YARDS 
 
 
 0.0 
 
 9.3 
 
 18.5 
 
 27.8 
 
 37.0 
 
 46 3 
 
 55.6 
 
 64.8 
 
 74.1 
 
 83 3 
 
 92.6 
 
 101.9 
 
 
 0.1 
 
 4.6 
 
 12.4 
 
 20.8 
 
 29.6 
 
 38.6 
 
 47.6 
 
 56.7 
 
 65.8 
 
 75.0 
 
 84.2 
 
 93.4 
 
 
 0.2 
 
 3.1 
 
 9.3 
 
 16.7 
 
 24.7 
 
 33.1 
 
 41.7 
 
 50.4 
 
 59.3 
 
 68.2 
 
 77.2 
 
 86.2 
 
 
 0.3 
 
 2.3 
 
 7.4 
 
 13.9 
 
 21.2 
 
 28.9 
 
 37.0 
 
 45.4 
 
 53.9 
 
 62.5 
 
 71.2 
 
 80.0 
 
 
 4 
 
 1.9 
 
 6.2 
 
 11.9 
 
 18.5 
 
 25.7 
 
 33 3 
 
 41.3 
 
 49.4 
 
 57.7 
 
 66.1 
 
 74.7 
 
 
 0.5 
 
 1.5 
 
 5.3 
 
 10.4 
 
 16.5 
 
 23.2 
 
 30 3 
 
 37 8 
 
 45.6 
 
 53.6 
 
 61.7 
 
 70.0 
 
 
 0.6 
 
 13 
 
 4.6 
 
 9.3 
 
 14.8 
 
 21.1 
 
 27.8 
 
 34 9 
 
 42 3 
 
 50 
 
 57.9 
 
 65 9 
 
 
 0.7 
 
 1.2 
 
 4.1 
 
 8.3 
 
 13.5 
 
 19.3 
 
 25 6 
 
 32.4 
 
 39 5 
 
 46.9 
 
 54.5 
 
 62 2 
 
 
 8 
 
 1.0 
 
 3 7 
 
 7.6' 
 
 12.4 
 
 17.8 
 
 23 8 
 
 30 3 
 
 37.0 
 
 44.1 
 
 51.4 
 
 59 
 
 
 0.9 
 
 0.9 
 
 3 4 
 
 6.9 
 
 11.4 
 
 16.5 
 
 22.2 
 
 28 4 
 
 34.9 
 
 41.7 
 
 48.7 
 
 56.0 
 
 
 1.0 
 
 0.8 
 
 3 1 
 
 6.4 
 
 10 6 
 
 15.4 
 
 20 8 
 
 26.7 
 
 32 9 
 
 39.5 
 
 46.3 
 
 53.4 
 
 
 1.1 
 
 0.8 
 
 2 9 
 
 6.0 
 
 9 9 
 
 14.5 
 
 19.6 
 
 25.2 
 
 31.2 
 
 37.5 
 
 44.1 
 
 50 9 
 
 Q 
 
 1.2 
 
 0.7 
 
 2.7 
 
 5.6 
 
 9.3 
 
 13.6 
 
 18 5 
 
 23 9 
 
 29.6 
 
 35.7 
 
 42.1 
 
 48.7 
 
 O 
 
 1.3 
 
 0.7 
 
 2.5 
 
 5.2 
 
 8.7 
 
 12.9 
 
 17.5 
 
 22.7 
 
 28 2 
 
 34.1 
 
 40 3 
 
 46.7 
 
 M 
 
 1.4 
 
 0.6 
 
 2 3 
 
 4 9 
 
 8.2 
 
 12.2 
 
 16.7 
 
 21 6 
 
 26 9 
 
 32 6 
 
 38.6 
 
 44.8 
 
 o 
 o 
 
 u. 
 
 15 
 
 0.6 
 
 2.2 
 
 4.6 
 
 7.8 
 
 11.6 
 
 15.9 
 
 20.6 
 
 25 8 
 
 31.3 
 
 37.0 
 
 43.1 
 
 1.6 
 
 0.5 
 
 2.1 
 
 4.4 
 
 7.4 
 
 11.0 
 
 15.2 
 
 19.7 
 
 24.7 
 
 30.0 
 
 35.6 
 
 41.5 
 
 6 
 
 o 
 
 1.7 
 
 0.5 
 
 2 
 
 4.2 
 
 7.1 
 
 10 5 
 
 14.5 
 
 18 9 
 
 23.7 
 
 28 8 
 
 34 3 
 
 40.0 
 
 1.8 
 
 0.5 
 
 1.9 
 
 4.0 
 
 6.7 
 
 10.1 
 
 13.9 
 
 18.2 
 
 22 8 
 
 27 8 
 
 33.1 
 
 38 6 
 
 < 
 
 1.9 
 
 0.5 
 
 1.8 
 
 3.8 
 
 6.4 
 
 9.7 
 
 13.3 
 
 17.2 
 
 22.0 
 
 26 8 
 
 31 9 
 
 37.3 
 
 u. 
 
 2 
 
 0.4 
 
 1.7 
 
 3.6 
 
 6.2 
 
 9.3 
 
 12.8 
 
 16 8 
 
 21.2 
 
 25 9 
 
 30 9 
 
 36.1 
 
 o 
 
 2.1 
 
 0.4 
 
 1.6 
 
 3 5 
 
 5.9 
 
 8.9 
 
 12 3 
 
 16 2 
 
 20.4 
 
 25.0 
 
 29.9 
 
 35.0 
 
 
 2 2 
 
 0.4 
 
 1.5 
 
 3.3 
 
 5.7 
 
 8.6 
 
 11.9 
 
 15.7 
 
 19.8 
 
 24.2 
 
 28.9 
 
 34.0 
 
 Ul 
 
 z 
 
 2.3 
 
 0.4 
 
 1.5 
 
 3 2 
 
 5.5 
 
 8.3 
 
 11.5 
 
 15.1 
 
 19.1 
 
 23.4 
 
 28.1 
 
 33 
 
 o 
 
 2.4 
 
 0.4 
 
 1.4 
 
 3.1 
 
 5.3 
 
 8.0 
 
 11.1 
 
 14.6 
 
 18.5 
 
 22.7 
 
 27.2 
 
 32.0 
 
 2.5 
 
 0.4 
 
 1.4 
 
 3.0 
 
 5.1 
 
 7.7 
 
 10.8 
 
 14.2 
 
 18.0 
 
 22.1 
 
 26.5 
 
 31.1 
 
 a. 
 
 2.6 
 
 0.3 
 
 1.3 
 
 2.9 
 
 4.9 
 
 7.5 
 
 10.4 
 
 13.8 
 
 17.4 
 
 21.4 
 
 25.7 
 
 30.3 
 
 3 
 
 o 
 
 2.7 
 
 0.3 
 
 1.3 
 
 2.8 
 
 4.8 
 
 7.2 
 
 10.1 
 
 13.3 
 
 16.9 
 
 20.8 
 
 25.0 
 
 29.5 
 
 u. 
 
 2.8 
 
 0.3 
 
 1.2 
 
 2.7 
 
 4.6 
 
 7.0 
 
 9.8 
 
 13.0 
 
 16.5 
 
 20.3 
 
 24.4 
 
 28.7 
 
 Ill 
 
 I 
 
 2.9 
 
 0.3 
 
 1.2 
 
 2.6 
 
 4.5 
 
 6 8 
 
 9.5 
 
 12.6 
 
 16.0 
 
 19.7 
 
 23.7 
 
 28.0 
 
 *- 
 
 3.0 
 
 0.3 
 
 1.2 
 
 2.5 
 
 4.4 
 
 6 6 
 
 9.3 
 
 12.3 
 
 15.6 
 
 19.2 
 
 23.2 
 
 27.3 
 
 *- 
 < 
 
 3.1 
 
 0.3 
 
 1.1 
 
 2.4 
 
 4.2 
 
 6.4 
 
 9.0 
 
 11.9 
 
 15.2 
 
 18.7 
 
 22 6 
 
 26.7 
 
 _J 
 
 3 2 
 
 0.3 
 
 1.1 
 
 2.4 
 
 4.1 
 
 6 3 
 
 8.8 
 
 11.6 
 
 14.8 
 
 18.3 
 
 22 
 
 26.0 
 
 -1 
 
 3.3 
 
 0.3 
 
 1.1 
 
 2 3 
 
 4 
 
 6.1 
 
 8.5 
 
 11.3 
 
 14.5 
 
 17.9 
 
 21.5 
 
 25.5 
 
 
 3.4 
 
 0.3 
 
 1.1 
 
 2.3 
 
 3.9 
 
 5.9 
 
 8.3 
 
 11.1 
 
 14.1 
 
 17.4 
 
 21.0 
 
 24.9 
 
 o 
 
 3 5 
 
 3 
 
 1.0 
 
 2.2 
 
 3.8 
 
 5.8 
 
 8.1 
 
 10.8 
 
 13.8 
 
 17.0 
 
 20.6 
 
 24.4 
 
 «/> 
 
 3 6 
 
 0.3 
 
 1.0 
 
 2.1 
 
 3.7 
 
 5 6 
 
 7.9 
 
 10.6 
 
 13.5 
 
 16.7 
 
 20.1 
 
 23.8 
 
 z 
 
 3.7 
 
 0.3 
 
 0.9 
 
 2.1 
 
 3.6 
 
 5.5 
 
 7.8 
 
 10.3 
 
 13.2 
 
 16.3 
 
 19.7 
 
 23.3 
 
 o. 
 
 Ul 
 
 3.8 
 
 0.2 
 
 0.9 
 
 2.0 
 
 3.5 
 
 5.4 
 
 7 6 
 
 10.1 
 
 12.9 
 
 16.0 
 
 19.3 
 
 22.9 
 
 Q 
 
 3.9 
 
 0.2 
 
 9 
 
 2.0 
 
 3.4 
 
 5.3 
 
 7.4 
 
 9.9 
 
 12.6 
 
 15.6 
 
 18.9 
 
 22.4 
 
 ul 
 
 X 
 
 4 
 
 2 
 
 9 
 
 1.9 
 
 3.4 
 
 5.1 
 
 7.2 
 
 9.7 
 
 12.3 
 
 15.3 
 
 18.5 
 
 22.0 
 
 ►- 
 
 4.1 
 
 2 
 
 9 
 
 1.9 
 
 3.3 
 
 5.0 
 
 7.1 
 
 9.5 
 
 12.1 
 
 15.0 
 
 18.2 
 
 21 5 
 
 u. 
 
 o 
 
 4.2 
 
 0.2 
 
 8 
 
 1.9 
 
 3.2 
 
 4.9 
 
 6.9 
 
 9.3 
 
 11.9 
 
 14.7 
 
 17.8 
 
 21.1 
 
 3 
 
 4 3 
 
 0.2 
 
 0.8 
 
 1.8 
 
 3.2 
 
 4.8 
 
 6.8 
 
 9.1 
 
 11.6 
 
 14.4 
 
 17.5 
 
 20.7 
 
 4.4 
 
 0.2 
 
 0.8 
 
 1.8 
 
 3.1 
 
 4.7 
 
 6.7 
 
 8.9 
 
 11.4 
 
 14.2 
 
 17.1 
 
 20.4 
 
 u> 
 
 4.5 
 
 0.2 
 
 0.8 
 
 1.7 
 
 3.0 
 
 4 6 
 
 6.5 
 
 8.7 
 
 11.2 
 
 13.9 
 
 16 8 
 
 20.0 
 
 
 4.6 
 
 0.2 
 
 0.8 
 
 1.7 
 
 3.0 
 
 4.5 
 
 6.4 
 
 8.6 
 
 11.0 
 
 13.6 
 
 16.5 
 
 19.7 
 
 
 4.7 
 
 0.2 
 
 0.8 
 
 1.7 
 
 2.9 
 
 4.5 
 
 6.3 
 
 8.4 
 
 10.8 
 
 13.4 
 
 16.2 
 
 19.3 
 
 
 4 8 
 
 2 
 
 0.7 
 
 1.6 
 
 2.8 
 
 4.4 
 
 6.2 
 
 8.2 
 
 10.6 
 
 13.2 
 
 16.0 
 
 19.0 
 
 
 4 9 
 
 0.2 
 
 0.7 
 
 1.6 
 
 2.8 
 
 4.3 
 
 6.1 
 
 8.1 
 
 10.4 
 
 12.9 
 
 15.7 
 
 18.7 
 
 
 5.0 
 
 0.2 
 
 0.7 
 
 1.6 
 
 2.7 
 
 4.2 
 
 6 
 
 8.0 
 
 10 2 
 
 12.7 
 
 15.4 
 
 18.4 
 
 
 5 1 
 
 0.2 
 
 0.7 
 
 1.5 
 
 2.7 
 
 4.1 
 
 5.8 
 
 7.8 
 
 10.0 
 
 12.5 
 
 15.2 
 
 18.1 
 
 
 5 2 
 
 2 
 
 0.7 
 
 1.5 
 
 2.6 
 
 4.1 
 
 5.7 
 
 7.7 
 
 9 9 
 
 12.3 
 
 14.9 
 
 17.8 
 
 
 5.3 
 
 2 
 
 7 
 
 1.5 
 
 2.6 
 
 4.0 
 
 5 6 
 
 7.6 
 
 9 7 
 
 12.1 
 
 14.7 
 
 17.5 
 
 
 5.4 
 
 2 
 
 0.7 
 
 1.5 
 
 2.6 
 
 3.9 
 
 5.6 
 
 7.4 
 
 9.6 
 
 11.9 
 
 14.5 
 
 17.2 
 
 
 5.5 
 
 0.2 
 
 6 
 
 1.4 
 
 2.5 
 
 3.9 
 
 5.5 
 
 7.3 
 
 9.4 
 
 11.7 
 
 14.2 
 
 17.0 
 
 
 5 6 
 
 0.2 
 
 6 
 
 1.4 
 
 2.5 
 
 3.8 
 
 5.4 
 
 7.2 
 
 9.3 
 
 11.5 
 
 14.0 
 
 16.7 
 
 
 5.7 
 
 0.2 
 
 6 
 
 1.4 
 
 2.4 
 
 3.7 
 
 5.3 
 
 7.1 
 
 9.1 
 
 11.4 
 
 13.8 
 
 16.5 
 
 
 5.8 
 
 2 
 
 0.6 
 
 1.4 
 
 2.4 
 
 3.7 
 
 5.2 
 
 7.0 
 
 9.0 
 
 11.2 
 
 13.6 
 
 16.2 
 
 
 5.9 
 
 2 
 
 6 
 
 1.3 
 
 2.4 
 
 3.6 
 
 5.1 
 
 6.9 
 
 8.8 
 
 11.0 
 
 13.4 
 
 16.0 
 
 
 6.0 
 
 2 
 
 0.6 
 
 1.3 
 
 2.3 
 
 3 6 
 
 5.1 
 
 6.8 
 
 8.7 
 
 10.9 
 
 13.2 
 
 15.8 
 
 [48] 
 
SUM OF THE DEPTHS OF CUT AT THE FOUR CORNERS OF A 100-FOOT GRID 
 
 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 
 
 VOLUME OF CUT IN CUBIC YARDS 
 
 
 111.1 
 
 120 4 
 
 129.6 
 
 138 9 
 
 148.2 
 
 157.4 
 
 166.7 
 
 175.9 
 
 185.2 
 
 194.4 
 
 203.7 
 
 213 
 
 
 102.6 
 
 111.8 
 
 121.0 
 
 130 2 
 
 139 4 
 
 148.7 
 
 157.9 
 
 167.1 
 
 176.4 
 
 185.6 
 
 194.9 
 
 204.1 
 
 
 95.2 
 
 104 3 
 
 113.4 
 
 122.6 
 
 131.7 
 
 140 8 
 
 150.0 
 
 159.2 
 
 168.4 
 
 177.6 
 
 186.7 
 
 195 9 
 
 
 88.9 
 
 97 8 
 
 106.8 
 
 115.7 
 
 124.8 
 
 133 8 
 
 142 9 
 
 151.9 
 
 161.0 
 
 170.1 
 
 179.3 
 
 188.4 
 
 
 83 3 
 
 92.1 
 
 100.8 
 
 109.6 
 
 118.5 
 
 127.4 
 
 136.4 
 
 145.3 
 
 154.3 
 
 163.4 
 
 172.4 
 
 181.4 
 
 
 78.4 
 
 86 9 
 
 95 5 
 
 104 2 
 
 112 9 
 
 121.6 
 
 130.4 
 
 139.3 
 
 148.2 
 
 157 
 
 166.0 
 
 174.9 
 
 
 74.1 
 
 82.4 
 
 90.8 
 
 99 2 
 
 107.8 
 
 116 4 
 
 125.0 
 
 133.7 
 
 142.4 
 
 151.2 
 
 160.1 
 
 168.9 
 
 
 70 2 
 
 78 3 
 
 86.4 
 
 94.7 
 
 103.1 
 
 111 5 
 
 120 
 
 128.6 
 
 137.2 
 
 145.8 
 
 154.5 
 
 163 3 
 
 
 66.7 
 
 74.5 
 
 82 5 
 
 90.6 
 
 98 8 
 
 107.1 
 
 115.4 
 
 123.8 
 
 132 3 
 
 140 8 
 
 149.4 
 
 158 
 
 
 63.5 
 
 71.1 
 
 78 9 
 
 86.8 
 
 94 8 
 
 102 9 
 
 111.1 
 
 119.4 
 
 127.7 
 
 136.1 
 
 144.6 
 
 153.1 
 
 
 60 6 
 
 68 
 
 75 6 
 
 83 3 
 
 91.2 
 
 99.1 
 
 107.2 
 
 115 3 
 
 123 8 
 
 131.7 
 
 140.1 
 
 148.4 
 
 
 58 
 
 65.2 
 
 72 6 
 
 80.1 
 
 87.8 
 
 95 6 
 
 103.5 
 
 111.4 
 
 119.5 
 
 127.6 
 
 135 8 
 
 144.1 
 
 Q 
 
 55 6 
 
 62 6 
 
 69 8 
 
 77.2 
 
 84.7 
 
 92 3 
 
 100.0 
 
 107.8 
 
 115.8 
 
 123.7 
 
 131.8 
 
 140.0 
 
 O 
 
 53 3 
 
 60.2 
 
 67.2 
 
 74.4 
 
 81.7 
 
 89.2 
 
 96.8 
 
 104 5 
 
 112.2 
 
 120.1 
 
 128.1 
 
 136.1 
 
 1= 
 
 51.3 
 
 58.0 
 
 64.8 
 
 71.8 
 
 79 
 
 86 3 
 
 93.8 
 
 101.3 
 
 108 9 
 
 116.7 
 
 124.5 
 
 132.4 
 
 O 
 
 o 
 
 Ik 
 
 49 4 
 
 55.9 
 
 62.6 
 
 69.4 
 
 76.5 
 
 83 6 
 
 90 9 
 
 98 3 
 
 105.8 
 
 113.4 
 
 121.2 
 
 128 9 
 
 47.6 
 
 54.0 
 
 60.5 
 
 67.2 
 
 74.1 
 
 81.1 
 
 88 2 
 
 95.5 
 
 102.9 
 
 110.4 
 
 118.0 
 
 125.6 
 
 o 
 o 
 
 46 
 
 52 2 
 
 58.6 
 
 65 1 
 
 71.8 
 
 78.7 
 
 85.7 
 
 92.9 
 
 100.1 
 
 107.5 
 
 114.9 
 
 122.5 
 
 44.4 
 
 50 5 
 
 56.7 
 
 63.1 
 
 69.7 
 
 76.5 
 
 83.3 
 
 90.4 
 
 97.5 
 
 104.7 
 
 112.1 
 
 119.5 
 
 < 
 
 43 
 
 48.9 
 
 55 
 
 61.3 
 
 67.7 
 
 74.3 
 
 81.1 
 
 88.0 
 
 95.0 
 
 102.1 
 
 109.3 
 
 116.6 
 
 u. 
 
 41.7 
 
 47.4 
 
 53 4 
 
 59 5 
 
 65.8 
 
 72.3 
 
 79.0 
 
 85.7 
 
 92 6 
 
 99.6 
 
 106.7 
 
 113.9 
 
 o 
 
 40.4 
 
 46.0 
 
 51.9 
 
 57.9 
 
 64.1 
 
 70.4 
 
 76.9 
 
 83.6 
 
 90.3 
 
 97.2 
 
 104.2 
 
 111.3 
 
 
 39 2 
 
 44.7 
 
 50.4 
 
 56 3 
 
 62.4 
 
 68 6 
 
 75.0 
 
 81.5 
 
 88.2 
 
 95 
 
 101.8 
 
 108.9 
 
 in 
 
 Z 
 
 38.1 
 
 43.5 
 
 49.1 
 
 54.8 
 
 60 8 
 
 66.9 
 
 73.2 
 
 79.6 
 
 86.1 
 
 92.8 
 
 99.6 
 
 106.5 
 
 ec 
 
 u 
 
 37.0 
 
 42.3 
 
 47.8 
 
 53.4 
 
 59.3 
 
 65.3 
 
 71.4 
 
 77.7 
 
 84.2 
 
 90 8 
 
 97.4 
 
 104.2 
 
 36 
 
 41.2 
 
 46 5 
 
 52.1 
 
 57.8 
 
 63.7 
 
 69.8 
 
 76.0 
 
 82.3 
 
 88.8 
 
 95.4 
 
 102.0 
 
 ee 
 
 35.1 
 
 40.1 
 
 45.4 
 
 50 8 
 
 56.5 
 
 62 2 
 
 68.2 
 
 74.3 
 
 80.5 
 
 86.9 
 
 93.4 
 
 100.0 
 
 3 
 
 o 
 
 34 2 
 
 39.1 
 
 44 3 
 
 49.6 
 
 55.1 
 
 60.8 
 
 66.7 
 
 72.7 
 
 78.8 
 
 85.1 
 
 91.5 
 
 98.0 
 
 u. 
 
 33 3 
 
 38.2 
 
 43.2 
 
 48.4 
 
 53.9 
 
 59.5 
 
 65.2 
 
 71.1 
 
 77.2 
 
 83.4 
 
 89.6 
 
 96.1 
 
 Ill 
 
 32.5 
 
 37.3 
 
 42.2 
 
 47.3 
 
 52.7 
 
 58.2 
 
 63 8 
 
 69.6 
 
 75.6 
 
 81.7 
 
 87.9 
 
 94.2 
 
 ►- 
 
 31 8 
 
 36.4 
 
 41.2 
 
 46.3 
 
 51.5 
 
 56.9 
 
 62.5 
 
 68 2 
 
 74.1 
 
 80.1 
 
 86.2 
 
 92.4 
 
 s 
 
 31.0 
 
 35.6 
 
 40.3 
 
 45.3 
 
 50.4 
 
 55.7 
 
 61.2 
 
 66.9 
 
 72.6 
 
 78.5 
 
 84.6 
 
 90.7 
 
 -J 
 
 30.3 
 
 34.8 
 
 39.5 
 
 44.3 
 
 49.4 
 
 54.6 
 
 60.0 
 
 65.5 
 
 71.2 
 
 77.0 
 
 83.0 
 
 89.1 
 
 -1 
 
 29 6 
 
 34 
 
 38 6 
 
 43.4 
 
 48.4 
 
 53.5 
 
 58.8 
 
 64.3 
 
 69 9 
 
 75.6 
 
 81.5 
 
 87.5 
 
 u. 
 
 29.0 
 
 33.3 
 
 37.8 
 
 42.5 
 
 47.4 
 
 52.5 
 
 57.7 
 
 63.1 
 
 68.6 
 
 74.2 
 
 80 
 
 85.9 
 
 
 
 28.4 
 
 32 6 
 
 37.0 
 
 41.7 
 
 46.5 
 
 51.5 
 
 56.6 
 
 61.9 
 
 67.3 
 
 72.9 
 
 78.6 
 
 84.5 
 
 in 
 
 X 
 
 27.8 
 
 31 9 
 
 36 3 
 
 40.8 
 
 45.6 
 
 50.5 
 
 55.6 
 
 60.8 
 
 66.1 
 
 71.6 
 
 77.3 
 
 83.0 
 
 27.2 
 
 31.3 
 
 35.6 
 
 40.1 
 
 44.7 
 
 49.6 
 
 54.5 
 
 59.7 
 
 65 
 
 70.4 
 
 76.0 
 
 81.6 
 
 Ill 
 
 26.7 
 
 30.7 
 
 34.9 
 
 39.3 
 
 43 9 
 
 48.7 
 
 53 6 
 
 58 6 
 
 63.9 
 
 69.2 
 
 74.7 
 
 80.3 
 
 O 
 
 26.1 
 
 30.1 
 
 34.2 
 
 38.6 
 
 43.1 
 
 47.8 
 
 52.6 
 
 57 6 
 
 62 8 
 
 68.1 
 
 73.5 
 
 79.0 
 
 ui 
 
 X 
 
 25.6 
 
 29.5 
 
 33 6 
 
 37 9 
 
 42 3 
 
 46.9 
 
 51.7 
 
 56.7 
 
 61.7 
 
 66.9 
 
 72.3 
 
 77.7 
 
 1- 
 
 25.2 
 
 29.0 
 
 33 
 
 37.2 
 
 41.6 
 
 46.1 
 
 50.8 
 
 55.7 
 
 60.7 
 
 65.9 
 
 71.1 
 
 76.5 
 
 u. 
 
 o 
 
 24.7 
 
 28.5 
 
 32 4 
 
 36 5 
 
 40.9 
 
 45.4 
 
 50 
 
 54.8 
 
 59.7 
 
 64.8 
 
 70.0 
 
 75.4 
 
 3 
 
 24.2 
 
 27.9 
 
 31.8 
 
 35 9 
 
 40.2 
 
 44.6 
 
 49.2 
 
 53.9 
 
 58.8 
 
 63.8 
 
 68.9 
 
 74.2 
 
 23.8 
 
 27.5 
 
 31.3 
 
 35 3 
 
 39.5 
 
 43.9 
 
 48.4 
 
 53.1 
 
 57 9 
 
 62.8 
 
 67.9 
 
 73.1 
 
 Vi 
 
 23.4 
 
 27.0 
 
 30.8 
 
 34.7 
 
 38.9 
 
 43.2 
 
 47.6 
 
 52.2 
 
 57.0 
 
 61 9 
 
 66.9 
 
 72.0 
 
 
 23.0 
 
 26.5 
 
 30.2 
 
 34.2 
 
 38 2 
 
 42.5 
 
 46.9 
 
 51.4 
 
 56.1 
 
 60.9 
 
 65.9 
 
 71.0 
 
 
 22.6 
 
 26.1 
 
 29.8 
 
 33 6 
 
 37.6 
 
 41.8 
 
 46.2 
 
 50.6 
 
 55 3 
 
 60 
 
 64.9 
 
 70 
 
 
 22.2 
 
 25.7 
 
 29.3 
 
 33.1 
 
 37.0 
 
 41.2 
 
 45.5 
 
 49.9 
 
 54.5 
 
 59.2 
 
 64.0 
 
 69 
 
 
 21.9 
 
 25.2 
 
 28.8 
 
 32.6 
 
 36.5 
 
 40.5 
 
 44.8 
 
 49.2 
 
 53.7 
 
 58.3 
 
 63.1 
 
 68.0 
 
 
 21.5 
 
 24.8 
 
 28.4 
 
 32.1 
 
 35.9 
 
 39.9 
 
 44.1 
 
 48.4 
 
 52 9 
 
 57.5 
 
 62.2 
 
 67.1 
 
 
 21.2 
 
 24.5 
 
 27.9 
 
 31.6 
 
 35.4 
 
 39.4 
 
 43.5 
 
 47.8 
 
 52.2 
 
 56.7 
 
 61.4 
 
 66.2 
 
 
 20.8 
 
 24.1 
 
 27.5 
 
 31.1 
 
 34 9 
 
 38.8 
 
 42.9 
 
 47.1 
 
 51.4 
 
 55.9 
 
 60.6 
 
 65.3 
 
 
 20.5 
 
 23.7 
 
 27.1 
 
 30.6 
 
 34.4 
 
 38.2 
 
 42.3 
 
 46.4 
 
 50 7 
 
 55.2 
 
 59.8 
 
 64.4 
 
 
 20.2 
 
 23.4 
 
 26.7 
 
 30.2 
 
 33.9 
 
 37.7 
 
 41.7 
 
 45.8 
 
 50.0 
 
 54.4 
 
 59.0 
 
 63 6 
 
 
 19.9 
 
 23.0 
 
 26 3 
 
 29.8 
 
 33.4 
 
 37.2 
 
 41.1 
 
 45.2 
 
 49.4 
 
 53.7 
 
 58.2 
 
 62.8 
 
 
 19.6 
 
 22.7 
 
 25.9 
 
 29.3 
 
 32 9 
 
 36.7 
 
 40.5 
 
 44.6 
 
 48.7 
 
 53.0 
 
 57.5 
 
 62.0 
 
 
 19.3 
 
 22.4 
 
 25.6 
 
 28.9 
 
 32.5 
 
 36.2 
 
 40.0 
 
 44.0 
 
 48.1 
 
 52.4 
 
 56.7 
 
 61.2 
 
 
 19.0 
 
 22.0 
 
 25.2 
 
 28.5 
 
 32.0 
 
 35.7 
 
 39.5 
 
 43.4 
 
 47.5 
 
 51.7 
 
 56.0 
 
 60.5 
 
 
 18.8 
 
 21.7 
 
 24.9 
 
 28.2 
 
 31.6 
 
 35.2 
 
 39.0 
 
 42.9 
 
 46.9 
 
 51.0 
 
 55.3 
 
 59.7 
 
 
 18.5 
 
 21.4 
 
 24.5 
 
 27.8 
 
 31.2 
 
 34.8 
 
 38.5 
 
 42.3 
 
 46.3 
 
 50.4 
 
 54.7 
 
 59.0 
 
 49] 
 
SUM OF THE DEPTHS OF CUT AT THE FOUR CORNERS OF A 100-FOOT GRID 
 
 2.4 2.5 26 2.7 2.8 2.9 3.0 3 1 3.2 3.3 3.4 3.5 
 
 VOLUME OF CUT IN CUBIC YARDS 
 
 0.0 222.2 231.5 240.7 250.0 259.3 268.5 277.7 287.1 296.4 305.6 314.8 324.1 
 
 0.1 213.4 222.6 231.8 241.1 250.3 259.5 268.8 278.1 287.3 296.5 305.9 315.1 
 
 0.2 205.1 214.3 223.6 232.8 241.9 251.2 260.5 269.7 278 8 288.2 297.3 306.6 
 
 0.3 197.5 206.7 215.9 225.0 234.2 243.4 252.5 261.7 271.0 280.1 289.4 298.5 
 
 0.4 190.5 199.6 208.6 217.8 226.9 236.0 245.1 254.3 263.4 272.6 281.7 290.8 
 
 0.5 183.9 192.9 201.9 211.0 220.0 229.0 238.1 247.2 256.3 265.4 274.4 283.6 
 
 0.6 177.8 186.7 195.6 204.6 213.5 222.5 231.5 240.5 249.5 258.5 267.6 276.7 
 
 0.7 172.1 180.9 189.7 198.5 207.5 216.3 225.3 234.2 243.1 252.1 261.0 270.1 
 
 0.8 166.7 175.4 184.1 192.9 201.6 210.5 219.3 228.1 237.1 245.9 254.9 263.7 
 
 0.9 161.6 170.2 178.9 187.5 196.2 205.0 213.7 222.5 231.2 240.1 248.9 257.7 
 
 1.0 156.8 165.4 173.9 182.5 191.1 199.7 208.4 217.0 225.8 234.5 243.2 252.1 
 
 1.1 152.4 160.8 169.2 177.7 186.1 194.7 203.2 211.9 220.5 229.1 237.9 246.6 
 9 1.2 148.2 156.4 164.7 173.1 181.5 189.9 198.5 206.9 215.5 224.1 232.7 241.3 
 © 13 144.2 152.3 160.5 168.8 177.0 185.4 193.8 202.2 210.7 219.2 227.7 236.3 
 _ 1.4 140.4 148.4 156.5 164.6 172.9 181.1 189.4 197.8 206.1 214.5 223.0 231.5 
 2 1.5 136.7 144.7 152.6 160.7 168.8 177.0 185.2 193.5 201.7 210.1 218.5 226.9 
 
 1.6 133.3 141.1 149.0 157.0 165.0 173.1 181.2 189.3 197.5 205.8 214.1 222.5 
 
 O 
 
 g 1.7 130.1 137.8 145.5 153.4 161.4 169.3 177.3 185.4 193.5 201.7 209.9 218.2 
 
 - 1.8 127.0 134.6 142.2 150.0 157.8 165.7 173.6 181.6 189.6 197.8 205.9 214.0 
 
 < 1.9 124.0 131.5 139.1 146.8 154.5 162.2 170.1 178.0 186.0 194.0 202.0 210.1 
 
 "■ 2.0 121.2 128.6 136.1 143.6 151.2 159.0 166.7 174.5 182.3 190.3 198.3 206.3 
 
 ° 2.1 118.5 125.8 133.2 140.6 148.2 155 8 163.4 171.2 178.9 186.8 194.7 202.5 
 
 a 2.2 116.0 123.1 130.4 137.8 145.2 152.7 160.3 167.9 175.6 183.4 191.1 198.9 
 
 Z 2.3 113.5 120.6 127.8 135.0 142 4 149.8 157.2 164.8 172.4 180.0 187.7 195.5 
 
 g 2.4 111.1 118.1 125.2 132.4 139.6 146.9 154.4 161.8 169.3 176.9 184.5 192.2 
 
 u 2.5 108.9 115.8 122.8 129.8 137.0 144.2 151.6 158.9 166.3 173.8 181.4 189.0 
 
 tt 2.6 106.7 113.5 120.4 127.4 134.5 141.6 148.8 156.1 163.4 170.9 178.4 186.0 
 
 O 2.7 104.6 111.3 118.1 125.0 132.0 139.0 146.2 153.4 160.7 169.0 175.5 182.9 
 
 •*■ 2.8 102.6 109.2 115.9 122.8 129.6 136.6 143.6 150.8 158.0 165.3 172.6 180.1 
 
 g 2.9 100.6 107.2 113.8 120.5 127.3 134.2 141.2 148.3 155.4 162.6 169.9 177.3 
 
 *" 3.0 98.8 105.3 111.7 118.4 125.1 132.0 138.9 145.9 152.9 160.1 167.2 174.6 
 
 S 3.1 97.0 103.3 109.8 116.4 123.0 129.8 136.6 143 5 150.5 157.6 164.7 171.9 
 
 _, 3.2 95.2 101.5 107.9 114.4 121.0 127.7 134.4 141.2 148.1 155.1 162.2 169.3 
 
 g 3.3 93.6 99.8 106.1 112.5 119.0 125.6 132.3 139.0 145.9 152.8 159.8 166.8 
 
 b. 3.4 92.0 98.1 104.3 110.7 117.1 123.6 130.2 136.9 143.7 150.5 157.4 164.4 
 
 O 3.5 90.4 96.5 102.6 108.9 115.2 121.7 128.2 135.0 141.5 148.3 155.1 162.0 
 
 |g 3.6 88.9 94.9 101.0 107.1 113.4 119.8 126.3 132.8 139.4 146.1 152.9 159.8 
 
 S 3.7 87.4 93.3 99.4 105.5 111.7 118.0 124.4 130.9 137.4 144.0 150.8 157.5 
 
 | 3.8 86.0 91.9 97.8 103.8 110.0 116.2 122.5 129.0 135 4 142.0 148.7 155.4 
 
 3.9 84.7 90.4 96.3 102.3 108.3 114.5 120.8 127.1 133 5 140.0 146.6 153.3 
 
 E 4.0 83.3 89.0 94.8 100.7 106.8 112.9 119.0 125.3 131.7 138.1 144.6 151.2 
 
 4.1 82.1 87.7 93.4 99.3 105.2 111.2 117.4 123.6 129.9 136.3 142.7 149.2 
 
 8 4.2 80.8 86.4 92.0 97.8 103.7 109.7 115.7 121.9 128.1 134.4 140.8 147.3 
 
 5 4.3 79.6 85.1 90.7 96.4 102.2 108.2 114.2 120.2 126.4 132.7 139.0 145.4 
 
 3 4.4 78.4 83.9 89.4 95.1 100.8 106.7 112.6 118.6 124.8 131.0 137.2 143.6 
 
 4.5 77.3 82.7 88.2 93.7 99.4 105.2 111.1 117.1 123.1 129.3 135.5 141.8 
 
 4.6 76.2 81.5 86.9 92.5 98.1 103 8 109.6 115.6 121.6 127.6 133.8 140.0 
 
 4.7 75.1 80 4 85.7 91.2 96.8 102.5 108.2 114.1 120.0 126.0 132.1 138.3 
 
 4.8 74.1 79.3 84.6 90.0 95.5 101.1 106.8 112.6 118.5 124.5 130.5 136.7 
 
 4.9 73.1 78 2 83.5 88.8 94.3 99.8 105.5 111.2 117.1 123.0 129.0 135.0 
 
 5.0 72.1 77.2 82.4 87.7 93.1 98.6 104.2 109.9 115.6 121.5 127.4 133.4 
 
 5.1 71.1 76.1 81.3 86 5 91.9 97.3 102.9 108.5 114.2 120.0 125.9 131.9 
 
 5.2 70.2 75.2 80.2 85.4 90.7 96.1 101.6 107.2 112.9 118.6 124.5 130.4 
 
 5.3 69.3 74.2 79.2 84.4 89.6 95.0 100.4 105.9 111.5 117.2 123.0 128.9 
 
 5.4 68.4 73.3 78.2 83.3 88.5 93.8 99.2 104.7 110.2 115.9 121.6 127.4 
 
 5.5 67.5 72.3 77.3 82.3 87.5 92.7 98.0 103.5 109.0 114.6 120.3 126.0 
 
 5.6 66.7 71.4 76.3 81.3 86.4 91.6 96.9 102.3 107.7 113.3 118.9 124.6 
 
 5.7 65.8 70.6 75.0 80.4 85.4 90.5 95.8 101.1 106.5 112.0 117.6 123.3 
 
 5.8 65.0 69.7 74.5 79 4 84 4 89.5 94.7 100.0 105.3 110.8 116.3 122.0 
 
 5.9 64.3 68.9 73.6 78 5 83.4 88.5 93.6 98.9 104.2 109.6 115.1 120.7 
 6.0 63.5 68.1 72.8 77.6 82.5 87.5 92.6 97.5 103.1 108.4 113.9 119.4 
 
 [50] 
 
SUM OF THE DEPTHS OF CUT AT THE FOUR CORNERS OF A 100-FOOT GRID 
 
 3 6 3 7 3 8 3 9 4.0 4 1 4 2 4 3 4 4 4.5 4 6 4.7 4.8 
 
 VOLUME OF CUT IN CUBIC YARDS 
 
 333.3 342.7 351 9 361 1 370 4 379 6 388 9 398 1 407 4 416 7 425.9 435 2 444.4 
 
 324.4 333 6 342 8 352.1 361.3 370.6 379 8 389 1 398 4 407.6 416 8 426 1 435.4 
 315.8 325.0 334.3 343.4 352.8 362 371 2 380 5 389 7 398 9 408 2 417.4 426 7 
 307 7 316 9 326 1 335 4 344 5 353 7 363 372 2 381 4 390 6 399 8 409.1 418.3 
 300 309 1 318.4 327.5 336 6 345 9 356 1 364 3 373 5 382 7 391 9 401.1 410.3 
 292.6 301 9 310 9 320 329 3 338 4 347 5 356 7 365 8 375 384.2 393.3 402.5 
 285 8 294 8 303 8 313.0 322 1 331 2 340.3 349 4 358 5 367 6 376 8 385 9 395 1 
 279 288 297 2 306 2 315 2 324 3 333 3 342 4 351 5 360 6 369 7 378 8 387.9 
 272 7 281 7 290 7 299 6 308 6 317 6 326 7 335 7 344 7 353 8 362 8 371 9 381.0 
 266 7 275 6 284 5 293 4 302 4 311 3 320 3 329 2 338 2 347 2 356 2 365 2 374.3 
 260 9 269 7 278 6 287 5 296 3 305 2 314 1 323 332 340 9 349 9 358 8 367 8 
 255.3 264 .1 272 9 281 7 290 6 299 3 308 2 317 325 9 334 8 343 7 352 6 361.6 
 250 258 7 267 4 276 2 285 293 7 302 5 311 3 320 1 328 9 337.8 346.7 355.6 
 
 O 244.9 253.5 262.2 270 9 279 5 288.2 297.0 305 7 314.5 324 3 332 1 340.9 349.7 
 
 ,_ 240.0 248 6 257 2 265 7 274 4 283 291.7 300.4 309 1 318 326 5 335.3 344.1 
 
 9 235.4 243.8 252 3 260 9 269 4 277.9 286 5 295 2 303.8 312 5 321.2 329.9 338 6 
 
 230.8 239.2 247.7 256.1 264 5 273 1 281 6 290.2 298.8 307 4 316 324.7 333.3 
 
 Q 
 
 O 
 
 § 226.4 234.8 243 2 251.4 259 8 268 4 276 8 285 3 293 9 302 4 311.0 319.6 328 2 
 
 - 222.3 230.5 238 7 247.0 255 4 263.8 272 2 280 7 289 1 297.6 306.1 314.7 323.2 
 
 < 218.3 226.3 234.5 242 8 251 259.4 267.8 276.1 284.5 293.0 301.4 309.7 318.4 
 
 u. 214.2 222.3 230.5 238 6 246.9 255.2 263.4 271.8 280 1 288 5 296 9 305.3 313.7 
 
 ° 210.5 218.5 226 6 234 7 242 9 251 259 3 267.5 275 8 284 1 292 4 300 8 309.2 
 
 2 206.8 214 8 222 8 230 9 238 9 247.1 255.2 263.4 271 6 279.9 288 1 296 4 304 8 
 
 Z 203.3 211.2 219.2 227 1 235.2 243 2 251 3 259 4 267.6 275.7 284 292 2 300.5 
 
 g 200.0 207 8 215 6 223 6 231.5 239 5 247.5 255.5 263.6 271.7 279 9 288 1 296 3 
 
 U 196.7 204.4 212 3 220 1 228 235 8 243.8 251 8 259.8 267 9 276 284.1 292.2 
 
 tt 193.5 201 2 209 216.7 224 5 232 3 240 2 248 1 256.1 264.1 272 1 280 2 288.3 
 
 190.5 198 1 205 8 213 4 221 1 228 9 236 7 244 6 252.5 260.4 268 4 276.4 284.4 
 "■ 187.5 195 1 202.6 210 2 217 9 225 6 233 3 241 1 249 256.8 264 8 272.7 280.7 
 
 1 184.7 192 1 199 6 207 2 214 7 222 4 230 237 8 245 6 253 4 261 2 269.1 277.1 
 *~ 181.8 189 2 196 7 204 1 211 7 219 2 226.9 234 5 242 2 250 257 8 265 6 273 5 
 5 179 1 186 4 193 8 201 2 208 7 216 2 223 7 231 4 239 246.7 254 4 262 2 270.0 
 _, 176 5 183 7 191 198 4 205 8 213 2 220 7 228 3 235 9 243 5 251 2 258 9 266.7 
 g 173 9 181 1 188 3 195 6 202 9 210 3 217 8 225 3 232 8 240 4 248 255 7 263.4 
 „. 171.4 178 5 185 7 192 9 200 2 207 5 214 9 222 3 229 8 237 3 244 9 252 5 260.2 
 
 169 176 1 183 2 190 3 197 5 204 8 212 1 219 5 226 9 234.4 241 9 249 4 257 
 £ 166 7 173 6 180 7 187 8 194 9 202 1 209 4 216 7 224 1 231 5 238 9 246 4 254 
 i- 164.4 171 3 178 3 185 3 192 4 199 5 206 8 214 221 3 228 7 236 1 243 5 251 
 2i 162.2 169 175 9 182 9 189.9 197 204 2 211 4 218 6 225 9 233.2 240 6 248.1 
 
 160.0 166 8 173 6 180 6 187 5 194.6 201 6 208 8 216 223.2 230 5 237 8 245 2 
 
 1 157.9 164 6 171 4 178 3 185 2 192 2 199 2 206 3 213.4 220 6 227 8 235 1 242 4 
 *2 155 8 162 5 169 2 176 182 9 189 8 196 8 203 8 210 9 218 225 2 232 4 239 7 
 O 153.8 160 5 167 1 173 9 180 7 187 5 194 4 201 4 208 4 215 5 222.6 229 8 237 
 s 151.9 158 4 165 1 171 7 178 5 185 3 192 2 199 1 206 213.1 220.1 227.3 234 4 
 => 150.0 156 5 163 1 169.7 176 4 183 1 189 9 196 8 203.7 210.7 217.7 224.8 231 9 
 
 148.1 154 6 161 1 167 7 174 3 181 187.7 194 5 201 4 208 3 215.3 222.3 229 4 
 146 3 152 7 159 2 165 7 172 3 178 9 185 6 192 4 199 2 206 213.0 219.9 227 
 144 6 150 9 157 3 163 8 170 3 176 9 183 5 190 2 197 203 8 210.7 217 6 224 6 
 142 9 149 1 155 5 161 9 168.4 174 9 181 5 188.1 194 8 201.6 208.4 215.3 222 2 
 
 141.2 147 4 153 7 160 166.5 172 9 179 5 186.1 192 8 199.5 206 2 213.1 219.9 
 139.5 145 7 151 9 158 2 164.6 171 177 5 184 1 190.7 197.4 204.1 210.9 217 7 
 137.9 144 150.2 156 5 162 8 169 2 175 6 182 1 188.7 195 3 202.0 208 7 215 5 
 136.4 142.4 148 6 154 8 161 167 4 173 8 180 2 186 7 193 3 199.9 206.6 213 3 
 
 134.8 140.8 146 9 153 1 159 3 165 6 171 4 178 3 184 8 191.3 197.9 204 5 211 2 
 
 133.3 139 3 145 3 151 4 157 6 163 8 170 1 176 5 182 9 189 4 195 9 202 5 209 2 
 
 131.9 137 8 143 8 149 8 155 9 162 1 168 4 174 7 181 1 187.5 194.0 200 5 207.1 
 
 130.4 136.3 142 2 148 2 154 3 160 5 166.7 172 9 179 3 185.6 192.1 198 6 205.1 
 129.0 134.9 140.7 146 7 152 7 158 8 165 171 2 177 5 183.8 190.2 196 7 203.2 
 127.7 133.4 139 3 145 2 151 2 157 2 163 3 169 5 175 7 182.0 188.4 194 8 201.3 
 126.3 132.0 137 8 143.7 149 6 155 6 161 7 167 8 174 180.3 186 6 193.0 199.4 
 125.0 130.7 136 4 142 3 148 1 154 1 160 1 166 2 172.4 178.6 184.8 191.2 197.5 
 
 [51] 
 
SUM OF THE DEPTHS OF CUT AT THE FOUR CORNERS OF A 100-FOOT GRID 
 
 49 5.0 5.1 5.2 53 54 5 5 56 5 7 5.8 
 
 VOLUME OF CUT IN CUBIC YARDS 
 
 
 
 
 
 
 453.7 
 
 463 
 
 472 
 
 2 
 
 481 
 
 5 
 
 490 7 
 
 500 
 
 509 
 
 3 
 
 518 
 
 5 
 
 527 8 
 
 537 
 
 546 3 
 
 
 
 
 1 
 
 444.6 
 
 453 9 
 
 463 
 
 1 
 
 472 
 
 4 
 
 481.7 
 
 490 
 
 9 
 
 500 
 
 2 
 
 509. 
 
 4 
 
 518 
 
 7 
 
 527 9 
 
 537 2 
 
 
 
 
 2 
 
 435.9 
 
 445.2 
 
 454 
 
 4 
 
 463 
 
 6 
 
 472 9 
 
 482 
 
 1 
 
 491 
 
 4 
 
 500 6 
 
 509 
 
 9 
 
 519.1 
 
 528 4 
 
 
 
 
 3 
 
 427.5 
 
 436.8 
 
 446 
 
 455. 
 
 2 
 
 464 5 
 
 473 
 
 7 
 
 482 
 
 9 
 
 492. 
 
 2 
 
 501. 
 
 4 
 
 510 6 
 
 519 9 
 
 
 
 
 4 
 
 419.5 
 
 428.7 
 
 437 
 
 9 
 
 447 
 
 1 
 
 456 3 
 
 465 
 
 5 
 
 474 
 
 7 
 
 484 
 
 493 
 
 2 
 
 502.4 
 
 511.6 
 
 
 
 
 5 
 
 411.7 
 
 420.9 
 
 430 
 
 1 
 
 439 
 
 2 
 
 448.4 
 
 457 
 
 6 
 
 466 
 
 8 
 
 476 
 
 
 
 485 
 
 2 
 
 494.4 
 
 503 6 
 
 
 
 
 6 
 
 404.2 
 
 413.4 
 
 422 
 
 5 
 
 431 
 
 7 
 
 440 8 
 
 450 
 
 
 
 459 
 
 2 
 
 468 
 
 3 
 
 477 
 
 5 
 
 486 7 
 
 495 9 
 
 
 
 
 7 
 
 397 
 
 406.1 
 
 415 
 
 2 
 
 424 
 
 4 
 
 433 5 
 
 442 
 
 6 
 
 451 
 
 8 
 
 460 9 
 
 470 
 
 1 
 
 479 2 
 
 488 4 
 
 
 
 
 8 
 
 390 
 
 399.1 
 
 408 2 
 
 417 
 
 3 
 
 426.4 
 
 435 
 
 5 
 
 444 
 
 6 
 
 453 
 
 7 
 
 462 
 
 8 
 
 471.9 
 
 481 1 
 
 
 0.9 
 
 383 3 
 
 392 3 
 
 401 
 
 4 
 
 410.4 
 
 419 5 
 
 428 6 
 
 437 
 
 6 
 
 446.7 
 
 455.8 
 
 464.7 
 
 474 
 
 
 1 
 
 
 
 376 8 
 
 385 8 
 
 394 8 
 
 403 
 
 8 
 
 412 8 
 
 421 
 
 9 
 
 430 
 
 9 
 
 440 
 
 449. 
 
 
 
 458.1 
 
 467 1 
 
 
 1 
 
 1 
 
 370.5 
 
 379 5 
 
 388 
 
 4 
 
 397 
 
 4 
 
 406 4 
 
 415 
 
 4 
 
 424 
 
 4 
 
 433 
 
 4 
 
 442. 
 
 4 
 
 451.4 
 
 460 4 
 
 o 
 
 O 
 
 1 
 
 2 
 
 364 5 
 
 373 4 
 
 382 3 
 
 391 
 
 2 
 
 400 1 
 
 409 
 
 1 
 
 418 
 
 
 
 427.0 
 
 436 
 
 445 
 
 454 
 
 1 
 
 3 
 
 358 6 
 
 367.4 
 
 376 3 
 
 385 2 
 
 394.1 
 
 403 
 
 411. 
 
 9 
 
 420 8 
 
 429. 
 
 8 
 
 438.7 
 
 447.7 
 
 i- 
 
 1 
 
 4 
 
 352.9 
 
 361 7 
 
 370 
 
 5 
 
 379 
 
 3 
 
 388 2 
 
 397. 
 
 1 
 
 405 
 
 9 
 
 414. 
 
 8 
 
 423. 
 
 7 
 
 432 6 
 
 441 5 
 
 O 
 
 o 
 
 1 
 
 5 
 
 347 4 
 
 356.1 
 
 364. 
 
 9 
 
 373 
 
 7 
 
 382 5 
 
 391. 
 
 3 
 
 400 
 
 1 
 
 409 
 
 
 
 417 
 
 8 
 
 426.7 
 
 435 6 
 
 1 
 
 6 
 
 342 
 
 350 7 
 
 359 
 
 5 
 
 368 
 
 2 
 
 376 9 
 
 385 
 
 7 
 
 394 
 
 5 
 
 403 
 
 3 
 
 412. 
 
 1 
 
 420.9 
 
 429 8 
 
 o 
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 1 
 
 7 
 
 336 8 
 
 345 5 
 
 354 
 
 2 
 
 362 
 
 9 
 
 371 6 
 
 380 
 
 3 
 
 389 
 
 
 
 392 8 
 
 406 
 
 5 
 
 415.3 
 
 424.1 
 
 
 1 
 
 8 
 
 331 8 
 
 340.4 
 
 349 
 
 
 
 357 7 
 
 366 3 
 
 375. 
 
 
 
 383 
 
 7 
 
 392 
 
 4 
 
 401 
 
 1 
 
 409 8 
 
 418 6 
 
 < 
 
 1 
 
 9 
 
 326 9 
 
 335 5 
 
 344. 
 
 
 
 352 
 
 6 
 
 361 2 
 
 369 
 
 9 
 
 378 
 
 5 
 
 387.2 
 
 395 
 
 8 
 
 404 5 
 
 413.2 
 
 u. 
 
 o 
 
 2 
 
 
 
 322.2 
 
 330 7 
 
 339 
 
 2 
 
 347. 
 
 7 
 
 356 3 
 
 364 
 
 9 
 
 373 
 
 5 
 
 382 
 
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 390 
 
 7 
 
 399 3 
 
 408 
 
 2 
 
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 317.6 
 
 326 
 
 334 
 
 5 
 
 343. 
 
 
 
 351 5 
 
 360 
 
 368 
 
 5 
 
 377. 
 
 1 
 
 385 
 
 7 
 
 394 3 
 
 402 9 
 
 
 2 
 
 2 
 
 313.1 
 
 321 5 
 
 329 
 
 9 
 
 338 
 
 3 
 
 346 8 
 
 355 
 
 3 
 
 363 
 
 8 
 
 372 
 
 3 
 
 380 
 
 8 
 
 389 4 
 
 397 9 
 
 z 
 
 2 
 
 3 
 
 308 8 
 
 317.1 
 
 325 
 
 5 
 
 333 
 
 8 
 
 342 2 
 
 350 
 
 6 
 
 359 
 
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 367 6 
 
 376 
 
 384 5 
 
 393 1 
 
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 2 
 
 4 
 
 304.5 
 
 312 8 
 
 321 
 
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 329 
 
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 337 8 
 
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 363 
 
 
 
 371 
 
 4 
 
 379 9 
 
 388 3 
 
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 300 4 
 
 308 6 
 
 316 9 
 
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 333 5 
 
 341 
 
 8 
 
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 358 
 
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 375 3 
 
 383.7 
 
 D 
 
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 2 6 
 
 296 4 
 
 304 6 
 
 312 
 
 8 
 
 321 
 
 
 
 329 2 
 
 337 
 
 5 
 
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 362 
 
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 370 8 
 
 379 2 
 
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 292 5 
 
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 325 1 
 
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 3 
 
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 288 7 
 
 296 8 
 
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 329 
 
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 2 
 
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 285 
 
 293 
 
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 309 
 
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 281 4 
 
 289 4 
 
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 3 
 
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 271.1 
 
 278 9 
 
 286 
 
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 267 8 
 
 275 6 
 
 283 
 
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 260.1 
 
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 241.1 
 
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 231 6 
 
 238 6 
 
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 4 
 
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 229 2 
 
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 226 9 
 
 233 8 
 
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 269 
 
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 291 1 
 
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 224 6 
 
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 238 
 
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 259 
 
 6 
 
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 5 
 
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 236 
 
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 243 
 
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 1 
 
 264 
 
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 271 
 
 4 
 
 278 
 
 5 
 
 285 8 
 
 293 
 
 
 5 
 
 2 
 
 220 1 
 
 226 9 
 
 233 
 
 8 
 
 240 
 
 7 
 
 247 7 
 
 254 
 
 7 
 
 261 
 
 8 
 
 268 
 
 9 
 
 276 
 
 
 
 283 2 
 
 290 4 
 
 
 5 
 
 3 
 
 218 
 
 224 7 
 
 231 
 
 6 
 
 238 
 
 4 
 
 245 4 
 
 252 
 
 3 
 
 259 
 
 3 
 
 266 
 
 4 
 
 273 
 
 5 
 
 280 6 
 
 287 8 
 
 
 5 
 
 4 
 
 216 8 
 
 222 6 
 
 229 
 
 4 
 
 236 
 
 2 
 
 243 1 
 
 250 
 
 
 
 257 
 
 
 
 264 
 
 
 
 271 
 
 
 
 276 1 
 
 285 2 
 
 
 5 
 
 5 
 
 213 8 
 
 220 5 
 
 227 
 
 2 
 
 234 
 
 
 
 240 8 
 
 247 
 
 7 
 
 254 
 
 6 
 
 261 
 
 6 
 
 268 
 
 6 
 
 275 6 
 
 282 7 
 
 
 5 
 
 6 
 
 211.7 
 
 218 4 
 
 225 
 
 1 
 
 231 
 
 8 
 
 238 6 
 
 245 
 
 5 
 
 252 
 
 3 
 
 259 
 
 3 
 
 266 
 
 2 
 
 273 2 
 
 280 3 
 
 
 5 
 
 7 
 
 209 7 
 
 216 3 
 
 223 
 
 
 
 229 
 
 7 
 
 236 4 
 
 243 
 
 2 
 
 250 
 
 1 
 
 257 
 
 
 
 263 
 
 9 
 
 270 9 
 
 277 9 
 
 
 5 8 
 
 207 8 
 
 214 3 
 
 220 
 
 9 
 
 227 
 
 6 
 
 234 3 
 
 241 
 
 1 
 
 247 
 
 9 
 
 254 
 
 7 
 
 261 
 
 6 
 
 268 5 
 
 275 5 
 
 
 5 
 
 9 
 
 205 8 
 
 212 4 
 
 218 
 
 9 
 
 225 
 
 6 
 
 232 2 
 
 238 
 
 9 
 
 245 
 
 7 
 
 252 
 
 5 
 
 259 
 
 3 
 
 266 2 
 
 273 1 
 
 
 6 
 
 204 
 
 210 4 
 
 217 
 
 
 
 223 
 
 5 
 
 230 2 
 
 236 
 
 8 
 
 243 
 
 6 
 
 250 3 
 
 257 
 
 1 
 
 264 
 
 270 9 
 
 52] 
 
SUM OF THE DEPTHS OF CUT AT THE FOUR CORNERS OF A 100-FOOT GRID 
 
 6.0 6.1 6.2 6.3 6 4 6.5 6 6 6.7 6 8 6.9 7.0 7 1 7 2 
 VOLUME OF CUT IN CUBIC YARDS 
 
 555.6 564.8 574.1 583.3 592.6 601.9 611.1 620.4 629.6 638 9 648 1 657.4 666 7 
 546.4 555.7 565.0 574.2 583.5 592.7 602 611.2 620.5 629 8 639.0 648 3 657 5 
 
 537 6 
 
 546 9 
 
 556.1 
 
 565 4 
 
 574.6 
 
 583 9 
 
 593 1 
 
 602.4 
 
 611.6 
 
 620.9 
 
 630 1 
 
 639 4 
 
 648 6 
 
 529 1 
 
 538 3 
 
 547.6 
 
 556.8 
 
 566.1 
 
 575 3 
 
 584.5 
 
 593.8 
 
 603.0 
 
 612 3 
 
 621.5 
 
 630 8 
 
 640 
 
 520 8 
 
 530 1 
 
 539.3 
 
 548.5 
 
 557.7 
 
 567.0 
 
 576.2 
 
 585.4 
 
 594 6 
 
 603.9 
 
 613.1 
 
 622.3 
 
 631 6 
 
 562.8 
 
 522.0 
 
 531.2 
 
 541.4 
 
 549.7 
 
 558 9 
 
 568.1 
 
 577.3 
 
 586.5 
 
 595.7 
 
 604 9 
 
 614.2 
 
 623 4 
 
 505 
 
 514.2 
 
 523.4 
 
 532 6 
 
 541.8 
 
 551.0 
 
 560.2 
 
 569.4 
 
 578 6 
 
 587.8 
 
 597.0 
 
 606.2 
 
 615.4 
 
 497.5 
 
 506.7 
 
 515 8 
 
 525.0 
 
 534.2 
 
 543 3 
 
 552.5 
 
 561.7 
 
 570.9 
 
 580.0 
 
 589 2 
 
 598 1 
 
 607.6 
 
 490 2 
 
 499.3 
 
 508.5 
 
 517.6 
 
 526.7 
 
 535 9 
 
 545 
 
 554.2 
 
 563 4 
 
 572.5 
 
 581.7 
 
 590.8 
 
 600 
 
 483.1 
 
 492.2 
 
 501.3 
 
 510.4 
 
 519.5 
 
 528.7 
 
 537.8 
 
 546.9 
 
 556 
 
 565 2 
 
 574.3 
 
 583.4 
 
 592 6 
 
 476.2 
 
 485 3 
 
 494.3 
 
 503 4 
 
 512.5 
 
 521 6 
 
 530 7 
 
 539 8 
 
 548 9 
 
 558 
 
 567.1 
 
 576 2 
 
 585 4 
 
 469 5 
 
 478.5 
 
 487.6 
 
 496.6 
 
 505.7 
 
 514.7 
 
 523 8 
 
 532.9 
 
 542 
 
 551 
 
 560 1 
 
 569 2 
 
 578 3 
 
 9 463.0 
 
 472 
 
 481 
 
 490 
 
 499.0 
 
 508 1 
 
 517.1 
 
 526.1 
 
 535 2 
 
 544.2 
 
 553.3 
 
 562 4 
 
 571.4 
 
 g 456.6 
 
 465.6 
 
 474.6 
 
 483 6 
 
 492 5 
 
 501 5 
 
 510 5 
 
 519 6 
 
 528.6 
 
 537.6 
 
 546.6 
 
 555.7 
 
 564 7 
 
 _ 450.4 
 
 459.4 
 
 468 3 
 
 477.3 
 
 486 2 
 
 495 2 
 
 504 2 
 
 513.1 
 
 522.1 
 
 531.1 
 
 540 1 
 
 549 1 
 
 558 1 
 
 O 444.4 
 2 438 6 
 
 453 3 
 
 462.2 
 
 471.2 
 
 480.1 
 
 489.0 
 
 497.9 
 
 506.9 
 
 515 8 
 
 524 8 
 
 533 8 
 
 542.7 
 
 551 7 
 
 447.5 
 
 456.3 
 
 465.2 
 
 474.1 
 
 483 
 
 491.9 
 
 500 8 
 
 509.7 
 
 518 6 
 
 527.6 
 
 536 5 
 
 545.5 
 
 g 432 9 
 
 - 427.4 
 
 441.7 
 
 450 5 
 
 459 4 
 
 468 2 
 
 477.1 
 
 485.9 
 
 494 8 
 
 503 7 
 
 512 6 
 
 521.5 
 
 530 4 
 
 539 3 
 
 436 1 
 
 444.9 
 
 453.1 
 
 462.5 
 
 471.3 
 
 480 2 
 
 489 
 
 497.8 
 
 506 7 
 
 515 6 
 
 524.4 
 
 533 3 
 
 < 421.9 
 
 430 7 
 
 439.4 
 
 448.2 
 
 456.9 
 
 465 7 
 
 474 5 
 
 483 3 
 
 492 1 
 
 500 9 
 
 509 8 
 
 518.6 
 
 527 5 
 
 u. 416 7 
 
 425.4 
 
 434.1 
 
 442.8 
 
 451.5 
 
 460 2 
 
 469 
 
 477.8 
 
 486 5 
 
 495 3 
 
 504 1 
 
 512 9 
 
 521 7 
 
 ° 411.5 
 
 420 2 
 
 428 8 
 
 437 5 
 
 446.2 
 
 454 9 
 
 463 6 
 
 472 3 
 
 481.1 
 
 489 8 
 
 498 6 
 
 507 3 
 
 516.1 
 
 S 406 5 
 
 415 1 
 
 423.7 
 
 432 4 
 
 441.0 
 
 449.7 
 
 458 3 
 
 467 
 
 475.7 
 
 484 4 
 
 493 2 
 
 501 9 
 
 510 6 
 
 5 401.6 
 
 410 2 
 
 418.7 
 
 427.3 
 
 435 9 
 
 444.5 
 
 453 2 
 
 461.8 
 
 470 5 
 
 479.2 
 
 487.9 
 
 496 6 
 
 505 3 
 
 g 396 8 
 8 392 2 
 
 405.3 
 
 413 9 
 
 422.4 
 
 431 
 
 439.6 
 
 448 1 
 
 456 8 
 
 465 4 
 
 474 
 
 482.7 
 
 491 3 
 
 500 
 
 400 6 
 
 409.1 
 
 417.6 
 
 426 1 
 
 434 7 
 
 443.2 
 
 451.8 
 
 460 4 
 
 469 
 
 477.6 
 
 486 2 
 
 494 8 
 
 tt 387.6 
 
 396 
 
 404 5 
 
 412.9 
 
 421.4 
 
 429 9 
 
 438.4 
 
 446 9 
 
 455.5 
 
 464 
 
 472 6 
 
 481'. 2 
 
 489 8 
 
 g 383.1 
 
 391 5 
 
 399 9 
 
 408 3 
 
 416 8 
 
 425 2 
 
 433 7 
 
 442.2 
 
 450 7 
 
 459 2 
 
 467.7 
 
 476 3 
 
 484.8 
 
 «■ 378 8 
 
 387.1 
 
 395 5 
 
 403 8 
 
 412.2 
 
 420 6 
 
 429.1 
 
 437.5 
 
 446 
 
 454 5 
 
 463 
 
 471 5 
 
 480 
 
 £ 374 5 
 
 382 8 
 
 391.1 
 
 399 5 
 
 407 8 
 
 416 2 
 
 424.6 
 
 433 
 
 441.4 
 
 449 8 
 
 458.3 
 
 466 8 
 
 495 2 
 
 •" 370 4 
 
 378 6 
 
 386.9 
 
 395 2 
 
 403 5 
 
 411.8 
 
 420.1 
 
 428.5 
 
 436 9 
 
 445 3 
 
 453.7 
 
 462.1 
 
 470.6 
 
 J 366 3 
 
 374.5 
 
 382.7 
 
 391 
 
 399 2 
 
 407.5 
 
 415 8 
 
 424.1 
 
 432 5 
 
 440 8 
 
 449.2 
 
 457 6 
 
 466 
 
 _, 362 3 
 
 370 5 
 
 378 6 
 
 386 8 
 
 395 1 
 
 403 3 
 
 411.6 
 
 419 8 
 
 428 1 
 
 436 5 
 
 444 8 
 
 453 2 
 
 461 5 
 
 =j 358 4 
 
 366 5 
 
 374.7 
 
 382 8 
 
 391 
 
 399 2 
 
 407.4 
 
 415 6 
 
 423 9 
 
 432 2 
 
 440 5 
 
 448 8 
 
 457.1 
 
 Z 354.6 
 
 362 7 
 
 370 8 
 
 378 9 
 
 387 
 
 395 2 
 
 403.3 
 
 411.5 
 
 419 8 
 
 428 
 
 436 3 
 
 444 5 
 
 452 8 
 
 O 350 9 
 
 358 9 
 
 366 9 
 
 375 
 
 383.1 
 
 391 2 
 
 399 3 
 
 407.5 
 
 415 7 
 
 423 9 
 
 432 1 
 
 440 3 
 
 448 6 
 
 </> 347 2 
 
 355 2 
 
 363 2 
 
 371.2 
 
 379 3 
 
 387 3 
 
 395 4 
 
 403 5 
 
 411.7 
 
 419 8 
 
 428 
 
 436 2 
 
 444 4 
 
 IE 343 6 
 
 351 6 
 
 359 5 
 
 367 5 
 
 375 5 
 
 383 5 
 
 391.6 
 
 399.7 
 
 407.8 
 
 415 9 
 
 424.0 
 
 432 2 
 
 440.4 
 
 Si 340.1 
 
 348 
 
 355 9 
 
 363 9 
 
 371 8 
 
 379 8 
 
 387 8 
 
 395.9 
 
 403 9 
 
 412.0 
 
 420 1 
 
 428 2 
 
 436.4 
 
 ° 336 7 
 
 344.5 
 
 352.4 
 
 360 3 
 
 368 2 
 
 376 2 
 
 384.1 
 
 392.1 
 
 400.1 
 
 408 2 
 
 416 2 
 
 424.3 
 
 432.4 
 
 I 333 3 
 
 341.1 
 
 348 9 
 
 356 8 
 
 364 7 
 
 372 6 
 
 380.5 
 
 388 5 
 
 396 4 
 
 404 4 
 
 412.5 
 
 420 5 
 
 428 5 
 
 •" 330 
 
 337 8 
 
 345 6 
 
 353 4 
 
 361 2 
 
 369 1 
 
 376 9 
 
 384.9 
 
 392 8 
 
 400 8 
 
 408.7 
 
 416 7 
 
 424 8 
 
 O 326 8 
 
 334 5 
 
 342 2 
 
 350 
 
 357 8 
 
 365 6 
 
 373 5 
 
 381 3 
 
 389.2 
 
 397 1 
 
 405.1 
 
 413.1 
 
 421.1 
 
 s 323 6 
 3 320 5 
 
 331.3 
 
 339.0 
 
 346 7 
 
 354 4 
 
 362 2 
 
 370 
 
 377.9 
 
 385 7 
 
 393 6 
 
 401 5 
 
 409 4 
 
 417.4 
 
 328.1 
 
 335 8 
 
 343 5 
 
 351 2 
 
 358 9 
 
 366 7 
 
 374 5 
 
 382 3 
 
 390 1 
 
 398 
 
 405 9 
 
 413 8 
 
 " 317.5 
 
 325 
 
 332 6 
 
 340 3 
 
 347 9 
 
 355 6 
 
 363 4 
 
 371.1 
 
 378 9 
 
 386 7 
 
 394 5 
 
 402 4 
 
 410 3 
 
 314 5 
 
 322 
 
 329 6 
 
 337 2 
 
 344 8 
 
 352.4 
 
 360.1 
 
 367.8 
 
 375.6 
 
 383 3 
 
 391.1 
 
 398 9 
 
 406.8 
 
 311 5 
 
 319 
 
 326 5 
 
 334 1 
 
 341 7 
 
 349 3 
 
 356 9 
 
 364 6 
 
 372 3 
 
 380 
 
 387.8 
 
 395 6 
 
 403 4 
 
 308 6 
 
 316.1 
 
 323 6 
 
 331.1 
 
 338 6 
 
 346 2 
 
 353 8 
 
 361 4 
 
 369 1 
 
 376 8 
 
 384 5 
 
 392 2 
 
 400.0 
 
 305 8 
 
 313.2 
 
 320 7 
 
 328 1 
 
 335 6 
 
 343 2 
 
 350 7 
 
 358 3 
 
 365 9 
 
 373 6 
 
 381 3 
 
 389 
 
 396.7 
 
 303 
 
 310.4 
 
 317 8 
 
 325.2 
 
 332.7 
 
 340.2 
 
 347.7 
 
 355 3 
 
 362 8 
 
 370 4 
 
 378 1 
 
 385 8 
 
 393.4 
 
 300 3 
 
 307 6 
 
 315 
 
 322 4 
 
 329 8 
 
 337.2 
 
 344.7 
 
 352 2 
 
 359 8 
 
 367 4 
 
 375 
 
 382.6 
 
 390 2 
 
 297 6 
 
 304 9 
 
 312 2 
 
 319 6 
 
 326 9 
 
 334 4 
 
 341 8 
 
 349.3 
 
 356 8 
 
 364 3 
 
 371 9 
 
 379.5 
 
 387.1 
 
 295 
 
 302 2 
 
 309 5 
 
 316 8 
 
 324 2 
 
 331 5 
 
 338 9 
 
 346 4 
 
 353 8 
 
 361 3 
 
 368 9 
 
 376.4 
 
 384.0 
 
 292 4 
 
 299 6 
 
 306.8 
 
 314.1 
 
 321 4 
 
 328 7 
 
 336 1 
 
 343 5 
 
 350 9 
 
 358 4 
 
 365 9 
 
 373.4 
 
 381.0 
 
 289 9 
 
 297.0 
 
 304 2 
 
 311.4 
 
 318 7 
 
 326 
 
 333 3 
 
 340 7 
 
 348 1 
 
 355 5 
 
 363 
 
 370.4 
 
 378 
 
 287 4 
 
 294.5 
 
 301 6 
 
 308 8 
 
 316 
 
 323 3 
 
 330 6 
 
 337 9 
 
 345 3 
 
 352.7 
 
 360 1 
 
 367.5 
 
 375 
 
 284 9 
 
 292 
 
 299 1 
 
 306 2 
 
 313 4 
 
 320 7 
 
 327 9 
 
 335 2 
 
 342 5 
 
 349 9 
 
 357.2 
 
 364.7 
 
 372 1 
 
 282 5 
 
 289 5 
 
 296 6 
 
 303.7 
 
 310 9 
 
 318 1 
 
 325 3 
 
 332 5 
 
 339 
 
 347.1 
 
 354.5 
 
 361 8 
 
 369 2 
 
 280 1 
 
 287.1 
 
 294 2 
 
 301.2 
 
 308 3 
 
 315 5 
 
 322 7 
 
 329 9 
 
 337 1 
 
 344.4 
 
 351.7 
 
 359 
 
 366 4 
 
 277.8 
 
 284.7 
 
 291.7 
 
 298.8 
 
 305 9 
 
 313 
 
 320.1 
 
 327.3 
 
 334 5 
 
 341.7 
 
 319.0 
 
 356.3 
 
 363.6 
 
 [53 
 
In order that the information in our publications may be more intelligible it is sometimes 
 necessary to use trade names of products or equipment rather than complicated descriptive or 
 chemical identifications. In so doing it is unavoidable in some cases that similar products which 
 are on the market under other trade names may not be cited. No endorsement of named products 
 is intended, nor is criticism implied of similar products which are not mentioned. 
 
 Co-operative Extension work in Agriculture and Home Economies, College of Agriculture, University of California, and United States Department of Agriculture 
 cooperating. Distributed in furtherance of the Acts of Congress of May 8, and June 30, 1914. George B. Alcorn, Director, California Agricultural Extension Service 
 
 20m-8,'57(C5915)JF 
 
 [55] 
 
j&^&fGHOUyERj 
 
 3k**£ 
 
 
 
 1 "stnnt". . . 
 
 This is probably the world's largest plow — it was built about 1910. It plowed 
 an acre in four and one-quarter minutes. A swath 60 feet wide was turned 
 under by 55 bottoms, pulled by three oil-burning tractors. The monster plow 
 was built in sections and assembled for several test runs in the midwest. 
 
 Impractical? ... no! 
 
 This "stunt" yielded new knowledge about hitches . . . knowledge that agri- 
 cultural engineers have used in designing many of today's farm implements. 
 
 For more than 40 years agricultural engineering has offered opportunity to 
 young men of mechanical bent with an interest in agriculture. And as 
 mechanization increases on farms, opportunities in agricultural engineering 
 expand . . . with the GOOD JOBS going to those who are WELL TRAINED. 
 
 Many leaders in the field were trained at the University of California at 
 Davis. The staff at Davis is recognized nationally and internationally for 
 its accomplishments in teaching and in research. The Department of Agri- 
 cultural Engineering is accredited ... a graduate is eligible for examina- 
 tion for a Professional Engineer's license, or he may continue study toward 
 a master's or doctor's degree. The growing College of Letters and Science 
 on the same campus broadens the student's educational and social back- 
 grounds. 
 
 For further information ... 
 
 about courses and careers in agricultural engineering, write Mr. Roy Bainer, 
 Chairman, Department of Agricultural Engineering, University of California, 
 Davis. 
 
 Or . . . See the College Entrance Advisor in the office of your local Farm 
 Advisor.