l Existing Road J 2 S-n 41 -S Fig. 18 Laying otit a new Road. Section. SECTIONS OF ROAPS. fTU Existing Road. 37-25 41 25 19. Laying out a new Road. Section, 36 EXPLORATION OF ROADS. The information relative to the rivers crossed, such as is given above, should always be obtained, in order that the bridges constructed over them may be adequate for the passage of the water brought down in time of floods. A cross section should be taken of each of the existing roads, near their junctions with the intended road ; to show to what extent, if any, the levels of the existing roads might be altered to suit the levels of the proposed new road. Laying out a Road. On the sections Figs. 18 and 19 the line of the road is to be laid down ; in other words, the levels at which it shall be formed are to be determined. As the road should always be dry, it should be placed at least a foot above the level of the flood ; and if it be placed at 37-25 feet above the datum, which is the height of the existing road at i, this object will be effected. Drawing a line at this level upon the section, it appears that an embankment will have to be formed across the valley from the road at i, to the point where the line meets the ground at K; and that the remainder of the road from K to H will be in a cutting. Now, the obvious principle in arranging the levels of a road, would be so to adjust the cuttings and embankments that the ground taken from one should form the other. In the present instance, this is impossible, because the level of the road is determined by other circumstances, and necessitates the formation of a very long embankment with but very little cutting. It therefore becomes necessary that ground for the formation of the embankments should be obtained from some other source. But, in order to produce as much cutting as possible, the line should be kept at the same level as before until it becomes necessary to raise it so as to attain the level of the existing road at H. If an inclination of 1 in 50 be given to this last part of the road, the distance at which the rise will commence will be 200 feet from H, the LEA-ELS OF ROADS. 37 difference of level being 4 feet. There is therefore to be added to the other disadvantages already mentioned, as belonging to the straight line of road, that of the formation of a large embankment, with the necessity for making an excavation in some other place, to supply the earth for that purpose. Examine the section of the deviation-line, and see what improvement can be thereby effected. The level of the lowest portion of the road must, as before, be placed 37-25 feet above the datum ; and if a line be drawn at that level on the section, Fig. 19, it will be found that the quantity of embankment is very much reduced, compared with what would be required for the straight course, and that there is now no difficulty in adjusting the cutting between H and L, so as exactly to afford the amount of filling required. A few trials will show that, if the line be kept at the same level until within sixteen chains of the point H, and then carried up at a regular inclination, this object will be effected, and that the quantities of cutting and embank- ment will be very nearly equal. The deviation-line is, therefore, the line which the engineer would select as the better of the two. Having made his selection, he would proceed to mark the course of the road on the ground, by driving stakes into the ground, on its centre line, at inter- vals of one chain-length, or 66 feet. In the next place, he would take very careful levels of the ground at every one of these points, and at any intermediate point, where an undulation or change of level occurred ; and wherever the level of the ground varied to any extent in a direction at right angles with the course of the road, he would take levels from which he would make transverse or cross sections of the ground. From these levels a working section should be made, to a horizontal scale of not less than five chains to the inch, and a vertical scale of 20 feet to the inch. A portion of 38 EXPLORATION OF ROADS. the section plotted to these scales is shown in Fig. 20 ; the level of the surface of the ground above the datum, at every chain-length, at the points where stakes have been driven into the ground, should be figured-in on the section, as shown in the column A, and the depth of cutting or height of embankment, at the same points, should be given in another column, B. The entries in this last column are obtained by taking the difference between the level of the surface of the ground and the level of the road. It will be observed that, upon the section, there are two parallel lines drawn as representing the line of road ; the upper line is intended to represent the upper surface of the road when finished, while the lower thick line represents what is termed the formation-surface, or the level to which the surface of the ground is to be formed, to receive the foun- dation of the road. In the section, the formation-surface is shown IS inches below the finished surface of the road ; the difference of level is therefore the thickness of the road itself. All the dimensions on the section are understood to refer to the formation-level ; and the height of the latter above the datum should be figured-in wherever a change in its rate of inclination takes place, and should be marked by a stronger vertical line, as shown at a / Jurist 'on with \ Existing Head. s - CHAPTER n. CONSTRUCTION OF ROADS: EARTHWORK AND DRAINAGE. Earthwork. This term is applied to whatever relates to the construction of the excavations and the embankments, to prepare them for receiving the road-covering. When the cuttings are of considerable depth, trial pits should be sunk at intervals of about ten chains, to the depth of the intended cutting, for the purpose of ascertain- ing the nature of the ground, and determining the slopes at which the sides of the cutting would safely stand, as well as the slope at which the same earth would stand when formed into the embankments. The cuttings and embankments should be numbered on the section, and the slopes intended to be given to each should be stated upon the "section. The contents of a cutting or an embankment, that is, the number of cubic yards which will have to be moved for its formation, with the intended slope, should then be calculated and stated upon the section. The man- ner of calculating these quantities will be explained in a subsequent chapter. Wherever rivers or streams are crossed, bridges or cul- EARTHWORK. 41 verts must be introduced ; detail drawings of these should be prepared, and reference should be made to them on the working section. A working plan should be constructed, on the same horizontal scale as the section, upon which the positions of the centre stakes should be shown ; and on this plan the road should be drawn to its correct width at the upper surface, with other lines showing the feet of the slopes. The stakes should be numbered consecutively on the plan, to facilitate reference to any part of the line, and the width of land required at every stake should be calculated in the manner about to be described, and entered in a table, from which the width of land required for the purpose of the road may be ascertained at every chain. Suppose that, in the present instance, the finished width of the road itself is to be 40 ft., and that an additional 6 ft. will be required on each side for the ditch and bank, the half width of the road without any slopes, or where the road is on the same level as the ground, would be 26 ft. ; and it may be observed in the following table, wherever there is no cut- ting or embankments (as at stakes Nos. 1 and 30), this is the width given in the fourth column. To find the heights at the other stakes, the product of the height of embank- ment or depth of cutting (as the case may be) by the ratio of the slope is to be added to the half width, 26 ft. Thus, in the first cutting, the ratio of the slopes being, as stated on the section, 1 to 1, there is simply to add the depths of the cutting at each stake to 26 ft., and the numbers given in the fourth column are obtained. After the 21st stake, the cutting terminates, and the ratio of the slopes then becomes 1$ to 1, and an addition of one and a half times the height of the embankment is to be made to the normal half width, 26 ft., to give the remaining values in the fourth column of the table. 42 EARTHWORK AND DRAINAGE. TABLE No. 2. SIDE WIDTHS. 1 6 11 1 i li 1 "8 1 istance of fence from tre line. 1 33 1 eight of bankment. fc ft W & rt ft Feet. Feet. Feet. Feet. Feet. Feet. 1 o-oo 26-0 17 2-33 28-3 2 0-58 26-6 18 2-52 28-5 3 0-93 26-9 19 2-20 28-2 4 1-20 27-2 20 1-60 27-6 5 1-56 27-6 21 0-75 26-8 6 1-91 27-9 22 0-55 26-8* 7 2-04 28-0 23 2-20 29-3 8 1-87 27-9 24 3-52 31-3 9 1-90 27'9 25 4-00 32-0 10 2-07 28-1 26 3-79 31-7 11 2-17 28-2 27 _ 2-60 29-9 12 2-35 28-4 28 1-25 27'9 13 2-30 28-3 29 0-30 26-5 14 2-25 28-3 30 0-00 26-0 15 2-50 28-5 31 0-33 26-5 16 2-05 28-1 After ascertaining the half widths as shown in the table No. 2, the next operation is to set out the widths on the ground, driving in another stake at every chain-length, at the correct distance on each side of the centre stake. A grip about 4 or 5 in. wide should then be cut from stake to stake, so as to mark both the centre and sides of the road upon the ground by a continuous line. The side lines thus set out, it must be remembered, are not the foot of the slopes, but they include 6 ft. on each side for a bank and a ditch. Another stake should therefore be driven at every chain-length, 6 ft. within the outer stakes on each side, and another grip cut to mark the foot of the slopes. A strong post should next be fixed into the ground, * The slopes here change from 1 to 1, to 1| to 1. EARTHWORK. 43 upon the centre line, wherever a change in the inclination of the road takes place (as at the 17th stake in the present instance), upon which a cross piece should be placed at the intended height of the formation-surface of the road, and intermediate heights should be put up at such distances as will enable the workmen to keep the embankments to their proper level. For cuttings, pits must be sunk correspond- ingly, at certain intervals, to the depth of the formation- surface, to serve as guides to the excavators in forming the cutting. In the foregoing example, the slopes have been taken at ratios of 1 to 1, and H to 1 ; but it should be remem- bered that the inclination of the side slopes demands peculiar attention. The proper inclination depends on the nature of the soil, and the action of the atmosphere and of internal moisture upon it. "In common soils, as or- dinary garden- earth formed of a mixture of clay and sand, compact clay, and compact stony soils, although the side slopes would withstand very well the effects of the weather with a steeper inclination, it is best to give them two base to one perpendicular ; as the surface of the roadway will, by this arrangement, be well exposed to the action of the sun and air, which will cause a rapid evaporation of the moisture on the surface. Pure sand and gravel may require a greater slope, according to circumstances. In all cases where the depth of the excavation is great, the base of the slope should be in- creased. It is not usual to use any artificial means to protect the surface of the side slopes from the action of the weather ; but it is a precaution which, in the end, will save much labour and expense in keeping the roadway in good order. The simplest means which can be used for this purpose, consist in covering the slopes with good sods, or else with a layer of vegetable mould about 4 inches thick, carefully laid and sown with grass seed. These 44 EARTHWORK AND DRAINAGE. means are amply sufficient to protect the side slopes from injury when they are not exposed to any other causes of deterioration than the wash of the rain, and the action of frost on the ordinary moisture retained by the soiL "The side slopes form usually an unbroken surface from the foot to the top. But in deep excavations, and particu- larly in soils liable to slips, they are sometimes formed with horizontal offsets, termed tenches, which are made a few feet wide, and have a ditch on the inner side to receive the surface-water from the portion of the side slope above them. These benches catch and retain the earth that may fall from the portion of the side slope above. "When the side slopes are not protected, it will be well, in localities where stone is plenty, to raise a small wall of dry stone at the foot of the slopes, to prevent the wash of the slopes from being carried into the roadway. "A covering of brush-wood, or a thatch of straw, may also be used with good effect ; but, from their perish- able nature, they will require frequent renewal and repairs. ' ' In excavations through solid rock, which does not disintegrate on exposure to the atmosphere, the sides might be made perpendicular ; but as this would exclude, in a great degree, the action of the sun and air, which is essential to keeping the road-surface dry and in good order, it is necessary to make the side slopes with an inclination, varying from one base to one perpendicular, to one base to two perpendicular, or even greater, according to the locality : the inclination of the slope on the south side in northern latitudes being the greater, to expose better the road-surface to the sun's rays. "The slaty rocks generally decompose rapidly on the sur- face, when exposed to moisture and the action of frost. The side slopes in rocks of this character may be cut into steps, and then be covered by a layer of vegetable mould EXCAVATION IN ROCK. 45 sown in grass seed, or else the earth may be sodded in the usual way. "The stratified soils and rocks, in which the strata have a dip, or inclination to the horizon, are liable to slips, or to give way, by one stratum becoming detached and sliding on another ; which is caused either from the action of frost, or from the pressure of water, which insinuates itself between the strata. The worst soils of this character are those formed of alternate strata of clay and sand ; particu- larly if the clay is of a nature to become semi-fluid when mixed with water. The best preventives that can be re- sorted to in these cases are, to adopt a system of thorough drainage, to prevent the surface-water of the ground from running down the side slopes, and to cut off all springs which run towards the roadway from the side slopes. The surface-water may be cut off by means of a single ditch made on the up-hill side of the road, to catch the water before it reaches the slope of the excavation, and convey it off to the most convenient natural water-courses ; for, in almost every case, it will be found that the side slope on the down-hill side is, comparatively speaking, but slightly affected by the surface-water. "Where slips occur from the action of springs, it fre- quently become a very difficult task to secure the side slopes. If the sources can be easily reached by excavating into the side slopes, drains formed of layers of fascines, or brush-wood, may be placed to give an outlet to the water, and prevent its action upon the side slopes. The fascines may be covered on top with good sods laid with the grass side beneath, and the excavation made to place the drain be filled in with good earth well rammed. Drains formed of broken stone, covered in like manner on top with a layer of sod to prevent the drain from becoming choked with earth, may be used under the same circumstances as fascine drains. Where the sources are not isolated, and 46 EARTHWORK AND DRAINAGE. the whole mass of the soil forming the side slopes appears saturated, the drainage may be effected by excavating trenches a few feet wide at intervals to the depth of some feet into the side slopes, and filling them with broken stone, or else a general drain of broken stone may be made throughout the whole extent of the side slope by excava- ting into it. When this is deemed necessary, it will be well to arrange the drain like an inclined retaining-wall, with buttresses at intervals projecting into the earth further than the general mass of the drain. The front face of the drain should, in this case, also be covered with a layer of sods with the grass side beneath, and upon this a layer of good earth should be compactly laid to form the face of the side slopes. The drain need only be carried high enough above the foot of the side slope to tap all the sources ; and it should be sunk sufficiently below the road- way surface to give it a secure footing. "The drainage has been effected, in some cases, by sink- ing wells or shafts at some distance behind the side slopes, from the top surface to the level of the bottom of the ex- cavation, and leading the water which collects in them, by pipes, into drains at the foot of the side slopes. In others, a narrow trench has been excavated, parallel to the axis of the road, from the top surface to a sufficient depth to tap all the sources which flow towards the side slope, and a drain formed either by filling the trench wholly with broken stone, or else by arranging an open conduit at the bottom to receive the water collected, over which a layer of brush- wood is laid, the remainder of the trench being filled with broken stone."* In some instances, the side slopes of very bad soils have been secured by a facing of brick arranged in a manner very similar to the method resorted to for securing the perpendicular sides of narrow deep trenches by a timber-facing. The plan pursued is, to place, at intervals * "A Treatise on Civil Engineering," by D. H. Mahan, 2nd edition, page 411. EMBANKMENTS. 47 along the excavation, strong buttresses of brick on each side, opposite to each other, and to connect them at bottom by a reversed arch. Between these buttresses are placed, at suitable heights, one or more brick beams, formed at bottom with a flat segment arch, and at top with a like arch inverted. The buttresses, secured in this way, serve as piers for vertical cylindrical arches, which form the facing and support the pressure of the earth between the buttresses. " In forming the embankments the side slopes should be made with a greater inclination than that which the earth naturally assumes ; for the purpose of giving them greater durability, and to prevent the width of the top surface, along which the roadway is made, from diminishing by every change in the side slopes, as it would were they made with the natural slope. To protect the side slopes more effectually, they should be sodded, or sown in grass seed; and the surface-water of the top should not be allowed to run down them, as it would soon wash them into gullies, and destroy the embankment. In localities where stone is plentiful, a sustaining wall of dry stone may be advantageously substituted for the side slopes. "To prevent, as far as possible, the settling which takes place in embankments, they should be formed with great care ; the earth being laid in successive layers of about four feet in thickness, and each layer well settled with rammers. As this method is very expensive, it is seldom resorted to except in works which require great care, and are of trifling extent. For extensive works, the method usually followed, on account of economy, is to embank out from one end, carrying forward the work on a level with the top surface. In this case, as there must be a want of compactness in the mass, it would be best to form the outsides of the embankment first, and to gradually fill in 48 EARTHWORK AND DRAINAGE. towards the centre, in order that the earth may arrange itself in layers with a dip from the sides inwards ; this will in a great measure counteract any tendency to slips outward. The foot of the slopes should be secured by buttressing them either by a low stone wall, or by forming a slight excavation for the same purpose."* "In some cases surface drains, termed catch-water drains, are made on the side slopes of cuttings. They are run up obliquely along the surface, and empty directly into the cross drains which convey the water into the natural water- courses. "When the roadway is in side-forming, cross drains of the ordinary form of culverts are made, to convey the water from the side channels and the covered drains into the natural water-courses. They should be of sufficient dimensions to convey off a large volume of water, and to admit a man to pass through them, so that they may be readily cleared out, or even repaired, without breaking up the roadway over them. "The only drains required for embankments are the ordi- nary side channels of the roadway, with occasional culverts to convey the water from them into the natural water- courses. Great care should be taken to prevent the sur- face-water from running down the side slopes, as they would soon be washed into gullies by it. "When the axis of the roadway is laid out on the side slope of a hill, and the road-surface is formed partly by excavating and partly by embanking out, the usual and most simple method is to extend out the embankment gradually along the whole line of excavation. This method is insecure, and no pains therefore should be spared to give the embankment a good footing on the natural surface upon which it rests, particularly at the foot of the slope. For this purpose the natural surface should be cut into steps, or offsets, and the foot of the slope be secured by * "A Treatise on Civil Engineering," by P. H. Mahan, 2nd edition, page 414. ROADS IN SIDE-FORMING. 49 buttressing it against a low stone wall, or a small terrace of carefully rammed earth. "In side-formings along a natural surface of great incli- nation, the method of construction just explained will not be sufficiently secure ; sustaining-walls must be substituted for the side slopes, both of the excavations and embank- ments. These walls may be made simply of dry stone, when the stone can be procured in blocks of sufficient size to render this kind of construction of sufficient stability to resist the pressure of the earth. But when the blocks of stone do not offer this security, they must be laid in mortar, and hydraulic mortar is the only kind which will form a safe construction. The wall which supplies the slope of the excavation should be carried up as high as the natural surface of the ground ; the one that .sustains the embank- ment should be built up to the surface of the roadway ; and a parapet-wall should be raised upon it, to secure vehicles from accidents in deviating from the line of the roadway. 'A road may be constructed partly in excavation and partly in embankment along a rocky ledge, by blasting the rock, when the inclination of the natural surface is not greater than one perpendicular to two base ; but with a greater inclination than this, the whole should be in excavation. "There are examples of road constructions, in localities like the last, supported on a frame-work, consisting of horizontal pieces, which are firmly fixed at one end by being let into holes drilled in the rock, and are sustained at the other by an inclined strut underneath, which rests against the rock in a shoulder formed to receive it. "When the excavations do not furnish sufficient earth for the embankments, it is obtained from excavations termed side-cuttings, made at some place in the vicinity of the embankment, from which the earth can be obtained with the most economy. 50 EARTHWORK AND DRAINAGE. "If the excavations furnish more earth than is required for the embankment, it is deposited in what is termed a spoil-lank, on the side of the excavation. The spoil-bank should be made at some distance back from the side slope of the excavation, and on the down-hill side of the top- surface ; and suitable drains should be arranged to carry off any water that might collect near it and affect the side slope of the excavation. The forms to be given to side-cuttings and spoil-banks will depend, in a great degree, upon the locality; they should, as far as practicable, be such that the cost of removal of the earth shall bd the least possible."* * "A Treatise on Civil Engineering," by D. H. Mahan, 2nd edition, page 415. CHAPTEE HI. RESISTANCE TO TRACTION ON COMMON ROADS. THE following are the general results of the experiments made by M. Morin upon the resistance to the traction of vehicles on common roads : 1st. The resistance to traction is directly proportional to the load, and inversely proportional to the diameter of the wheel. 2nd. Upon a paved or a hard macadamized road the resistance is independent of the width of the tire, when this quantity exceeds from 3 to 4 inches. 3rd. At a walking pace, the resistance to traction is the same, under the same circumstances, for carriages with springs and for carriages without springs. 4th. Upon hard macadamized roads and upon paved roads, the resistance to traction increases with the velocity : the increments of traction being directly proportional to the increments of velocity above the velocity 3-28 feet per second, or about 2J miles per hour. The equal increments of traction thus due to equal increments of velocity, are less as the road is smoother, and as the carriage is less rigid or better hung. 5th. Upon soft roads, of earth, or sand or turf, or roads fresh and thickly gravelled, the resistance to traction is independent of the velocity. 6th. Upon a well-made and compact pavement of hewn stones, the resistance to traction at a walking pace is not more than three-fourths of the resistance upon the best D 2 52 RESISTANCE TO TRACTION ON COMMON ROADS. macadamized roads, under similar circumstances. At a trotting pace, the resistances are equal. 7th. The destruction of the road is, in all cases, greater as the diameters of the wheels are less, and it is greater in carriages without than with springs. The next experiments which may be quoted, are those of Sir John Macneil,* made with an instrument invented by him for the purpose of measuring the tractive force required on different descriptions of road, to draw a wagon weigh- ing 21 cwt., at a very low velocity. The general results which he obtained are given in the following table : TABLE No. 3. RESULTS OF TRACTION FORCE TO DRAW 21 CWT. ON A LEVEL. (Sir John Macneil.) Description of road. Total trac- tive force. Trac'ive force per ton. Ibs. Ibs. 33 31-4 2. On a road made with six inches of broken \ stone of great hardness, laid either on a I foundation of large stones, set in the form of i a pavement, or upon a bottoming of concrete ; 3. On an old flint road, or a road made with a ) 46 44 thick coating of broken stone laid on earth ) 4. On a road made with a thick coating of i 65 62 147 140 Sir John Macneil has also given the following arbitrary formulee,! for calculating the resistance to traction on level roads of various kinds. They have been deduced from a considerable number of experiments made on the different kinds of road specified below, with carriages moving at various velocities. Putting B for the force required to move the carriage, w the weight of the carriage, w that of the load, all expressed in pounds, v the velocity in feet per second, and c a constant number, which depends upon the * Sir H. Parnell on Eoads, p. 73. t Ibid., p. 464, SIR JOHN MACNEIL'S EXPERIMENTS. 53 nature of the surface over which the carriage is drawn, and the value of which for several different kinds of road is as follows : On a timber surface .... On a paved road ..... On a well-made broken stone road, in a dry clean state On a well-made broken stone road, covered with dust On a well-made broken stone road, wet and muddy On a gra-vel or flint road, in a dry clean state On a gravel or flint road, in a wet and muddy state Stage wagon, B=^J" + ^ + (!) Stagecoach, B = ^- w + f Q + (2.) EULE 1. Divide the gross weight of the carriage when loaded, in pounds, by 93 if a wagon, or by 100 if a coach, and to the quotient add one-fortieth of the weight of the load only ; to the sum, add the product of the velocity in feet per second, by the proper constant for the particular kind of road. The sum is the force in pounds required to draw the carriage at the given velocity upon that descrip- tion of road. For example : What force would be requisite to move a stage-coach weighing 2,060 Ibs., and having a load of 1,100 Ibs., at a velocity of 9 ft. per second, along a broken- stone road covered with dust ? By the rule, 2060^1100 + noo + (8 x 9H131 . X , bs the force required. To consider, next, the additional resistance which is occasioned when the road, instead of being level, is inclined against the load, in a greater or less degree. In order to simplify the question, suppose the whole weight to be supported on one pair of wheels, and that the tractive force is applied in a direction parallel to the surface of the road. Let A B, Fig. 21, represent a portion of an inclined 54 RESISTANCE TO TRACTION ON COMMON ROADS. road, c being a carriage just sustained in its position by a force acting in the direction c D. The carriage is kept in position by three forces, namely, by its own weight w, acting in the vertical direction c F, by the force F, applied in the direction c D pa- rallel to the surface of the road, and by the pressure P, which is exerted by the carriage against G~ the surface of the road acting in pig. 21.-Gravity on an inclined the direction c E, perpendicular to the surface. To determine the relative magnitude of these three forces, draw the horizontal line A G, and the vertical line B G ; then, since the two lines c F and B G are parallel, and are both cut by the line A B, they must make the two angles c F B and A B G equal ; also the two angles c E F and A o B are equal, being both right angles ; therefore the remaining angles F c E and BAG are equal, and the two triangles c F E and A B G are similar. And as the three sides of the triangle c F E are proportional to the three forces by which the carriage is sustained, so also are the three sides of the triangle A B G ; that is to say, A B, or the length of the road is proportional to w, or the weight of the carriage ; B G, or the vertical rise is pro- portional to F, or the force required to sustain the carriage on the incline ; and A G, or the horizontal distance for the rise is proportional to P, or the force with which the car- riage presses upon the surface of the road. Therefore, W * A B I I F I G B, and w : A B : : P : A G, And if A G be made of such a length that the vertical rise, B G, of the road, is exactly one foot, then, F = = = w . sin B . . . (3.) AB v/AG- + 1 V ; RULES FOR RESISTANCE. . ', , = w . cos /3 . . . (4.) A a v/A G 2 -j- 1 in which /3 is the angle B A o. These formulae reduced to verbal rules are as follows : RULE 2. To find the force requisite to sustain a carriage upon an inclined road (the effects of friction being neglected], divide the weight of the carriage, including its load, \>y the inclined length of the road, the vertical rise of which is one foot, and the quotient is the force required. RULE 3. To find the pressure of a carriage against the sur- face of an inclined road, multiply the weight of the loaded carriage by the horizontal length of the road, and divide the product by the inclined length of the same ; the quo - tient is the pressure required. Example. What is the force required to sustain a car- riage weighing 3,270 Ibs. upon a road, the inclination of which is one in thirty, and what is the pressure of the carriage upon the surface of the road ? Here the horizontal length of the road, A o, being equal to 30, for a rise of 1 foot, the inclined length, A B = VA G 2 + 1 = 30-017, and by the first rule, 3,270 -f- 30-017 = 108-93 Ibs. for the force required to sustain the carriage on the road. By the second rule, 3,270 x 30 * 30-017 = 3,269-9 Ibs., the pressure of the carriage upon the surface of the road. Since the pressure of a carriage on a sloping road is found by multiplying its weight by the horizontal length of the road and dividing by the inclined length, and as the former is always less than the latter, it follows that the force with which a carriage bears upon an inclined road is less than its actual weight. In the foregoing example, it is about two pounds less; but, unless the inclination is very steep, it is not necessary to distinguish the difference of pressure, as the pressure may be assumed to be equal to the weight of the carriage. 50 RESISTANCE TO TRACTION ON COMMON ROADS. If the resistance which is to be overcome in moving a carriage, at a given rate, upon a horizontal road, be ex- pressed by K, then E + F is the resistance in ascending a hill, and B F descending a hill, with the same velocity ; neglecting the decrease in the weight of the carriage pro- duced by the inclination of the road. Taking, however, this decrease into consideration, the following modification in the formula) (1.) and (2.) will be requisite to adapt them to an inclined road : in the case of a common stage wagon ; and in that of stage coach, the upper sign being taken when the vehicle is drawn down the incline, and the lower when it is drawn up the same. To ascertain the resistance in passing up or down a hill, therefore, the resistance on a level road is first to be calcu- lated, by Kule 1, page 53. To this is to be added the force necessary to sustain the carriage on the incline, in ascending, calculated by Kule 2, page 55 ; or, in descending, the same force is to be subtracted from the resistance on a level. As an example, take, as before, the case of a stage coach weighing 2,060 Ibs., besides a load of 1,100 Ibs., at a velo- city of 9 ft. per second, up a broken stone road of which the surface is covered with dust, and which is inclined at the rate of one in thirty. The force to sustain the coach on this slope is, by Kule 2, 1^- = 105-3 Ibs. Adding this force to the force already found at page 53, requisite to move the same coach on a level road, the sum is (105-3 + 131-1 =) 236-4 Ibs., for the force required to RULES FOR RESISTANCE. 57 move the coach with a velocity of 9 ft. per second up the inclined road of one in thirty. To draw the coach down the same incline, at the same velocity, the resulting force re- quired is the difference of the two forces already found, or it is (131-1 105-3=) 25-8 Ib, The same example worked by formula (6) will give ( 2 j^j 1 ) '9995 + (2060 + 1100) -0333 +(8x9) = 236-3 Ibs, when the carriage is drawn up the incline ; and ' 9995 ~ (206 + 110 > ' 333 + ( 8 x 9 ) = 25-84 Ibs., when the carriage is drawn down the incline, the result being the same as that given by the rule. The following table has been calculated in order to show, with sufficient exactness for most practical purposes, the force required to draw carriages over inclined roads, and the comparative advantage of such roads and those which are perfectly level. The first column expresses the rate of inclination, and the second the equivalent angle ; the two next columns contain the force requisite to draw a common stage wagon weighing with its load 6 tons, at a velocity of 4*4 ft. per second (or 3 miles per hour) along a macadamized road in its usual state, both when ascending and descending the hill ; the fifth and sixth columns con- tain the length of level road which would be equivalent to a mile in length of the inclined road, that is, the length of level road which would require the same mechanical work to be expended in drawing the wagon over it, as would be necessary to draw the wagon over a mile of the in- clined road. The next four columns contain the same information as the four just described, with reference to a stage coach supposed to weigh with its load 3 tons, and to travel at the rate of 8*8 ft. per second, or 6 miles per hour. D 3 58 RESISTANCE TO TRACTION ON COMMON ROADS. TABLE No. 4. RESISTANCE TO TRACTION ON INCLINED ROADS. g FOB A STAGE WACK/H. FOB A STAGE COACH, 1 6 tons gross. 3 tons gross. 1 M oa . "3 a . 1 a - 5 1 I 3 !" 3 fa A 08 53 g i*| 8 11 fsf fit l| 111 M i P| w lit llf Pj PI ill ||| s ill ill III i*i jJJ ||| rt s H o Well-laid pavement Broken stone surface on a bottom of i rough, pavement or concrete . . j 31-4 44 48 i n Iin7l linSl Broken stone surface laid on an old flint ) road / 62 1 35 1 in 36 Gravel road .... 140 3 35 lin 18 The following table of gradients is of considerable value in laying out and arranging roads. The first column con- tains the gradient, expressed in the ratio of the height to the length ; the second and third columns contain the ver- tical rise in a mile and a chain respectively ; the fourth column, the angle of inclination with the horizon ; and the last column, the sine of the same angle, which is inserted for facilitating the calculation of the resistances occasioned by the gradient. GRADIENTS. 67 TABLE No. 5. GRADIENTS AND ANGLES OF INCLINATION OF ROADS. Vertical rise in a mile. 1 Vertical rise in a 1 chain. Angle (/3) which gradient makes with the horizon. Sine of angle /3. j OS .5 1 I Vertical rise in a | chain. Angle O) which gradient makes with the horizon. Sine of angle /3. linlO 528-0 6.60 5 42 58 09960 Iin60 88-0 1-10 57 18 01667 11 480-0 6-00 5 11 40 '09054 65 81-2 1-02 52 54 01539 ii 12 440-0 '5-50 4 45 59 08309 70 75-4 94 49 7 01429 ii 13 406-1 5-08 4 23 56 07670 75 70-4 88 45 51 01334 14 377-1 4-71 4 5 14 07128 80 66-0 82 42 58 01250 15 352-0 4-40 3 48 51 06652 85 62-1 78 40 27 01177 16 330-0 4-12 3 34 35 06238 90 58-7 73 38 12 01111 ii 17 310-6 3-88 3 21 59 05872 95 55-6 69 36 11 01053 ii 18 293-3 J3-67 3 10 47 05547 100 52-8 66 34 23 01000 ii 19 277-9 '3-47 3 46 05256 110 48-0 60 31 15 00909 ii 20 264-0 3.30 2 51 21 04982 120 44-0 55 28 39 00833 ii 21 251-4 3-14 2 43 35 04757 130 40-6 51 26 27 00769 22| 240-0 3-00 2 36 10 04541 140 377 47 24 33 00714 23 229-6 2-87 2 29 22 04344 150 35-2 44 22 55 00666 ,, 24 220-0 2-75 2 23 10 04163 160 33-0 41 21 29 00625 ii 25 211-2 2-64 2 17 26 03997 170 31-1 39 20 13 00588 26 203-1 2-54 2 12 2 03840 180 29-3 37 19 6 00556 ii 27 195-5 2-42 272 03694 190 27-8 35 18 6 00527 28 188-5 2-36 225 03551 200 26-4 33 17 11 00500 29 182-1 2-28 58 34 03448 210 25-1 31 16 22 00476 ,i 30 176-0 2-20 54 37 03333 220 24-0 30 15 37 00454 31 170-3 2-13 50 55 03226 230 23-0 29 14 57 00435 ,i 32 165-0 2-06 47 27 03125 240 22-0 27 14 19 00417 ,, 33 160-0 2-00 44 12 03031 260 21-1 26 13 45 00400 ,, 34 155-3 1-94 41 8 02941 260 20-3 25 13 13 00385 ,, 35 150-9 1-88 38 14 02857 270 19-6 24 12 44 00370 ,, 36 146-7 1-86 35 28 02777 280 18-9 24 12 17 00357 i> 37 142-7 1-78 32 53 02702 290 18-2 23 11 51 00345 ,, 38 138-9 1-74 30 27 02631 300 17-6 22 11 28 00334 ,i 39 135-4 1-69 1 28 8 02563 325 16-2 20 10 35 00308 ,, 40 132-0 1-65 25 57 02500 350 15-1 19 9 49 00286 ,, 41 128-8 1-61 23 60 02438 375 14-0 18 9 10 00267 i 42 125-7 1-57 21 50 02380 400 132 17 8 36 00250 ,, 43 122-8 1-53 19 56 02325 425 12-4 16 085 00235 ,i 44 120-0 1-50 18 7 02272 450 11-7 15 7 38 00222 45 117-3 1-47 16 24 02222 475 11-5 14 7 14 00210 46) 114-8 1-44 14 43 02173 500 10-6 13 6 53 00200 47J 112-31-40 13 8 02127 525 10-1 12 6 33 00191 48 ( 110-0 1-37 11 37 02083 550 9-6 12 6 15 00182 49! 107-7 1-35 10 9 02040 ii 575 9-2 11 5 59 00174 50| 105-6 1-32 8 6 01981 600 8-8 11 5 44 00167 55 96-0 1-20 2 30 -01818 68 ON THE SECTION OF ROADS. Width and Transverse Section of Roads. It is recom- mended that roads should be wide. It is an error to suppose that the cost of repairing a road depends entirely upon the extent of its surface, and increases with its width. The cost per mile of road depends more upon the extent and the nature of the traffic ; and it may be asserted, generally, that the same quantity of material is necessary for the repair of a road, whether wide or narrow, subjected to the same amount of traffic. On the narrow road, the traffic, being confined very much to one track, the road would be worn more severely than when the traffic is spread over a larger surface. The expense of spreading the material over the wider road would be somewhat greater, but the cost for material might be taken as the same. One of the advantages of a wide road is, that the air and the sun exercise more influence in keeping its surface dry. The first cost of a wide road is certainly greater than that of a narrow road, nearly in the ratio of the widths. For roads situated between towns of importance, and exposed to much traffic, the width should not be less than 30 ft., which would admit of four vehicles abreast ; besides a footpath of 6 ft. In the immediate vicinity of large towns and cities, the width should be greater. The form of the cross section of a road is a subject of much importance, and it is one upon which much difference of opinion exists. Some persons advocate a considerable degree of curvature in the upper surface of the road, with the view of facilitating the drainage of its surface ; whilst others are averse to a road being much curved. It is the practice of others, again, to form the road on a flat surface transversely; whilst others give a dip to the formation- surface each way from the centre, supposing that the drainage of the road is thereby facilitated. The only advantage resulting from the curving of the MACADAM'S VIEWS. 69 transverse section of the road is, that the water, which would otherwise collect upon its surface, is allowed to drain freely off into the side ditches. It has been urged that, in laying on fresh material upon a road, it is necessary to keep the centre much higher than the sides ; because, in consequence of the greater number of carriages using the middle of the road, that portion wears more quickly than the sides, and that, unless it is made originally much higher, when so worn it necessarily forms a hollow or depression, from which water cannot drain. Now it is entirely overlooked by those who advance this argument, that the cause of carriages using the middle in preference to the sides of a road, is its rounding form, since it is only in that situation that a carriage stands upright. If the road were comparatively flat, every portion would be equally used ; but on very convex roads, the middle is the only portion of the road on which it is safe to travel. On this subject, Mr. Macadam remarks, in his evidence before a committee of the House of Commons,* "I consider a road should be as flat as possible with regard to allowing the water to run off it at all, because a carriage ought to stand upright in travelling as much as possible. I have generally made roads 3 in. higher in the centre than I have at the sides, when they are 18 ft. wide; if the road be smooth and well made, the water will run off very easily in such a slope." And, in answer to the question, " Do you consider a road so made will not be likely to wear hollow in the middle, so as to allow the water to stand, after it has been used for some time?" he replies, " No ; when a road is made flat, people will not follow the middle of it as they do when it is made extremely convex. Gentlemen will have observed that in roads very convex, travellers generally follow the track in the middle, which * Parliamentary Report on the Highways of the Kingdom, 1819, page 22. 70 ON THE SECTION OF ROADS. is the only place where a carriage can run upright, by which means three furrows are made by the horses and the wheels, and water continually stands there ; and I think that more water actually stands upon a very convex road than on one which is reasonably flat." On the same subject, Mr. Walker remarks,* "A road much rounded is dangerous, particularly if the cross section approaches towards the segment of a circle, the slope in that case not being uniform, but increasing rapidly from the nature of the curve, as we depart from the middle or vertical line. The over-rounding of roads is also injurious to them, by either confining the heavy carriages to one track in the crown of the road, or, if they go upon the sides, by the greater wear they produce, from their constant tendency to move down the inclined plane, owing to the angle which the surface of the road and the line of gravity of the load form with each other; and, as this tendency is perpendicular to the line of draught, the labour of the horse and the wear of the carriage wheels are both much increased by it." f The drainage of the surface of the road is then the only useful purpose answered by making it convex. But the surface of a road is much more efficiently drained by a small inclination in the direction of its length, than by a much greater transverse slope. On this subject, Mr. Walker has very justly remarked, J " Clearing the road of water is best secured by selecting a course for the road which is not horizontally level, so that the surface of the road may, in its longitudinal section, form, in some degree, an inclined plane ; and when this cannot be obtained, owing to the extreme flatness of the country, an artificial * Parliamentary Eeport, 1819, page 49. t Kemarks on the evils of " barreled roads," as they were called, have been made in the Historical chapter, page 4. EDITOR. J Parliamentary Report, 1819, page 48. TRANSVERSE GRADIENTS. 71 inclination may generally be made. When a road is so formed, every wheel-track that is made, being in the line of inclination, becomes a channel for carrying off the water much more effectually than can be done by a curvature in the cross section or rise in the middle of the road, without the danger or other disadvantages which necessarily attend the rounding a road much in the middle. I consider a fall of about 1| inches in 10 feet to be a minimum in this case, if it is attainable without a great deal of extra expense." Whilst, then, the advantages attending the extreme con- vexity of roads is so small, the disadvantages are consider- able. On roads so constructed, vehicles must either keep to the crown of the road, and so occasion an excessive and unequal wear of its surface, or use the sides, with the liability of being overturned. The evidence of coach- masters and others, taken before the committee of the House of Commons, and appended to the report already quoted from, fully bears out the view here taken, and shows that many accidents have arisen from the practice of forming roads with an excessive amount of convexity. With reference to the above remarks, it is only intended to express disapproval of the practice of forming roads with cross sections rounding in an extreme degree and not to advocate a perfectly, or nearly, flat road, as many, who have fallen into the opposite error, have done. It is recommended, as the best form which could be given to a road, that its cross section should be formed of two straight lines inclined at the rate of about 1 in 30, and connected at the middle or crown of the road by a segment of a circle, having a radius of about 90 feet. This form of section is shown in Fig. 22, and the rate of inclination there given is quite sufficient to keep the surface of a road drained, provided it is maintained in good order, free from ruts. If the maintenance is neglected, no degree of convexity which can be given to the road will 72 ON THE SECTION OF ROADS. be of any avail, as the water will remain in the hollows or furrows. The form of cross section here suggested is equally adapted to all widths of road, as the straight lines have merely to be extended at the same rate of inclination, until they meet the sides of the road. Professor Mahan is of the same opinion with respect to the proper section of a road namely, that it should be formed of two straight sides, connected at the middle by a flat circular arc. The slope which he recommends is 1 in 48, or 1 inch in 4 feet. With regard to the form which should be given to the bed upon which the road is to be formed, a similar dif- ference of opinion exists as to whether it should be flat or rounding. Except where the surface upon which the road is to be formed is a strong clay, or other soil imper- vious to water, no benefit results as far as drainage is con- cerned, in making the formation-surface or bed of the road convex. It should be borne in mind that, after the road materials are laid upon the formation-surface, and have been for some time subjected to the pressure of heavy vehicles passing over them, they become, to a certain extent, intermixed : the road materials are forced down into the soil, and the soil works up amongst the stones, and the original line of separation becomes entirely lost. If the surface upon which the road materials are laid were to remain a distinct flat surface, perfectly even and regular, into which the road materials could not be forced, then it would be useful to give such an inclination to it as would allow any water which might find its way through the crust or covering of the road, to run off to the sides. Even so, it would have to force a passage between the road materials and the surface on which they rest. Such is, however, far from being the case ; and, therefore, unless under peculiar circumstances, no ON THE SECTION OF ROADS. 73 water which finds its way through the hard compact surface of the road itself is arrested by the comparatively soft sur- face of its bed, and carried off into the side ditches, what- ever the slope which might be given to the bed. While, however, it is believed, that, as far as drainage is con- cerned, it is useless to form the bed or formation surface of the road with a transverse slope, it should, nevertheless, be formed to the same outline as that recommended for the outer surface ; making the two surfaces parallel, and thus bestowing an equal depth of road material over every portion of the road. Nevertheless, some road-makers not only recommend a less depth of road materials to be put on the sides than on the middle of the road, but they further advise that an inferior description of material should be employed at the sides. On this subject the following remarks of Mr. Hughes are very much to the purpose:* "A very common opinion is, that the depth of material in the middle of the road should be greater than at the sides, but, for my part, I have never been able to discover why the sides of the road should be at all inferior to the middle in hardness and solidity. On the contrary, it would be a great improvement in general travelling, if carriages could be made to adhere more strictly to the rule of keeping the proper side of the road ; and the reasonable inducement to this practice is, obvi- ously, to make the sides equally hard and solid with the middle. In many roads, even where considerable traffic exists, the only good part of the road consists of about 8 or 10 feet in the middle, the sides being formed with small gravel quite unfit to carry heavy traffic ; and the consequence is, that the whole crowd of vehicles is forced into the centre track of the road ; thus at least doubling or trebling the wear and tear which would take place if * "The Practice of Making and Repairing Roads," by Thomaa Hughes, 1838, page 12. X i 4 ON THE SECTION OF ROADS. tlie sides were, as they ought to be, equally good with the centre. Another mischievous consequence is, that when it becomes necessary to repair the centre of the road, the carriages are driven off the only good part on to the sides, which consist of weak material, and are often even dan- gerous for the passage of heavily-laden stage coaches. On the other hand, if equal labour and materials be expended on the whole breadth of the road, it is evident that the wear and tear will be far more uniform ; and when any one part requires repair, the traffic may with safety be turned on to another part. Hence, I should always lay on the same depth of material all over the road : and this alone will of course render it necessary to curve the bed of the road." Great attention should be paid to the drainage of roads, with respect to their upper surface as well as to the sur- face of the ground on which they rest. To promote the surface-drainage, the road should be formed with the transverse section shown in Fig. 22, and on each side of the road a ditch should be formed of sufficient capacity to receive all the water which can fall upon the road, and it should be of such a depth and with such a declivity as to conduct the water freely away. When footpaths are to be constructed on the sides of the road, a channel or water- course should be formed between the footpaths and the road, and small drains, formed of tiles or earthern tubes, such as are used for underdraining lands, should be laid under the footpath, at such a level as to take off all the water which may collect in this channel, and convey it into the ditch. In the best- constructed roads, these side channels are paved with flints or pebbles. The drains under the footpath should be introduced about every 60 feet, and should have the same inclination namely, t in 30, as is recommended for the sides of the road, as shown in Fig. 22. A greater inclination would be objec- ON THE SECTION OF ROADS. 75 tionable. It is a very frequent mistake to give too great a fall to small drains, for such a current through them is produced as may wash away or undermine the ground around them, and ultimately cause their destruction. When a drain is once closed by any obstruc- tion, no amount of fall which could be given to it would suffice again to clear the passage ; whilst a drain having a considerable current through it, would be much more likely to be stopped by foreign matter carried into it, than a drain with a less rapid stream. When the surface of a road, constructed of suitable materials, compactly laid, is drained in the manner which has just been described, very little water finds its way to the sub- stratum. For some descriptions of soil, how- ever, it is desirable to adopt additional means for maintaining the foundation of a road in a dry state ; as, for instance, when the surface is a strong clay through which no water can percolate, or when the ground beneath the road is naturally of a soft, wet, or peaty nature Under such circumstances a species of under- drainage should be provided. When the sur- face of the ground is formed to the level intended for the reception of the road materials, trenches should be cut across the road from a foot to eighteen inches in depth, and about a foot wide at the bottom, the sides being sloped as shown in Fig. 23. The distances at which these drains should be formed depends in a great measure on the nature of the soil ; in the case of a strong clay soil, or a soil which is naturally very wet, there should be a cross E2 i