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GIFT OF 
 
 
AERIAL NAVIGATION 
 
 PART I. THE COMPASS 
 PART II. THE MAP 
 
 ISSUED BY THE 
 
 DIVISION OF MILITARY AERONAUTICS, U. S. ARMY 
 WASHINGTON, D. C. 
 
 -99- 
 
 WASHINGTON 
 
 GOVERNMENT PRINTING OFFICE 
 1918 
 
t i 
 
AERIAL NAVIGATION. 
 
 Part I. The Compass, 
 
 Introduction , 5 
 
 The compass 7 
 
 True courses 8 
 
 Magnetic courses 10 
 
 Relation between true and magnetic courses 11 
 
 Compass courses 13 
 
 Relation between magnetic and compass courses 14 
 
 Relation between true and compass courses 15 
 
 Course setting with allowance for wind 19 
 
 To find direction and velocity of wind 20 
 
 Radius of action in a given direction 22 
 
 Bearings: 
 
 Definition 23 
 
 Fixing position of a machine 24 
 
 Instruments: _ 
 
 Bearing plate 25 
 
 Aircraft course and distance indicator 27 
 
 Illustrative problem 31 
 
 Checks 34 
 
 Technique 35 
 
 Compass adjustment -. 38 
 
 Deviation card 40 
 
 3 
 
AERIAL NAVIGATION. 
 
 PART II. The Map. 
 
 
 Page. 
 
 Introduction 
 
 43 
 
 Scales 
 
 46 
 
 Time scales , 
 
 . 47 
 
 Metric system , 
 
 50 
 
 Conventional signs 
 
 52 
 
 Contours 
 
 52 
 
 Location of points 
 
 58 
 
 Coordinates 
 
 59 
 
 British maps 
 
 61 
 
 French maps 
 
 63 
 
 4 
 
 
AERIAL NAVIGATION. 
 
 PART I. 
 
 THE COMPASS. 
 
 INTRODUCTION, 
 
 When a pilot travels by airplane from his aerodrome to a point 
 beyond the horizon, he has need of navigation by means of map 
 and compass. The problem of passing from one point to another is 
 evidently one of distance and direction. In both respects the pilot 
 is liable to go wrong. Without proper care he may go many miles 
 out of the way either by going too far or by taking the wrong course. 
 He may even land within the German lines; he may mistake a 
 German aerodrome for his own; he may land at his own aerodrome 
 and think that he is lost. At any rate, without proper care he is 
 apt not to accomplish his mission. 
 
 There are several sources of error which must be guarded against. 
 For one thing, the influence of the wind; for another, the failure of 
 the compass to point to true north; for another, failure on the part 
 of the pilot to fly for a reasonable length of time. It is evident, for 
 example, that a pilot proceeding on a course 30 miles in length at 
 the rate of 90 m. p. h. in still air must not travel for anywhere near 
 an hour. He must not go on and on in the hope of reaching his 
 destination some time or other. 
 
 The influence of the wind is felt by an airplane exactly as the 
 influence of a current of water is felt by a boat. If a man rows a 
 boat across a river, pointing the boat straight across, he is drifted 
 downstream. If the current is swift the downstream drift is con- 
 siderable. So a wind is a stream or current of air which drifts the 
 airplane in the direction it is blowing. 
 
 5 
 
6 AEP-IAL NAVIGATION. 
 
 The 1 , ^y teat of the error which may be caused by the wind is 
 illustrated as follows : 
 
 FIG. 1. 
 
 Suppose a ship has a speed of 60 m. p. h. and the desired course 
 is true south, a distance of 30 miles. Suppose there is a west wind 
 blowing at the rate of 30 m. p. h. If the pilot does not allow for this 
 wind he will find himself, at the end of a half hour, 15 miles to the 
 east of his destination and badly confused as to direction. If he 
 tries to return to his own aerodrome by flying north, he will be 30 
 miles out of his way, supposing he has made no errors with respect 
 to compass and watch. 
 
 On page 31, a problem will be worked out in detail showing how a 
 pilot lays out his course so as to fly from his aerodrome to a given des- 
 tination. If desired, it may be read in this connection or it may be 
 read in its place after the general discussion. Following the dis- 
 cussion of this special problem will be found a paragraph showing 
 how the pilot may check his course roughly for distance and direc- 
 tion and another showing how he may develop technique necessary 
 for navigation. These paragraphs may be read when desired, either 
 before or after the general discussion. 
 
AERIAL 
 
 THE COMPASS: 
 
 The magnetic compass consists of three principal parts a bowl, a 
 needle, and a card. 
 
 The bowl is composed of nonmagnetic metal. In its center is a 
 post or pivot, and on the top of this, which is jeweled to reduce 
 friction to a minimum, is suspended a needle, or system of needles. 
 These are attached to the lower side of a circular card. This card is 
 free to rotate under the influence of the needles and take up a definite 
 position with reference to the earth's magnetism. In aircraft com- 
 passes the bowl is filled with a nonfreezing liquid, generally alcohol 
 or kerosene, which takes some of the weight of the needle and card 
 
 off the pivot and also serves to damp the oscillations and vibrations 
 of the needle. 
 
 On its outer edge the card is marked off into 360 degrees. Start- 
 ing with north as the zero point, the figuring runs clockwise through 
 east, south, and west, to north again. 
 
 The value of the compass is that the needle gives us a fixed direc- 
 tion (compass north) from which to measure the direction our ship 
 is taking. The needle does not follow the changes in direction of 
 the ship. On the contrary, the ship turns around the needle. The 
 direction of the machine is shown by the lubber's line, which is a 
 
NAVIGATION. 
 
 tc\the compass bowl or a line painted on 
 the inside bt the "oowi. 1 ' ^he'lubfter's line and the center of the com- 
 pass give the direction of the fore and aft axis of the machine. Since 
 the needle points north, the angle from the needle to the lubber's 
 line represents the course of the machine. This angle is measured 
 in degrees on the card in a clockwise direction from north. Thus, 
 if the lubber's line is opposite 90, the compass course is east; if the 
 lubber's line is opposite 45, the course is northeast, etc. 
 
 It is convenient to remember the number of degrees corresponding 
 to each of the " cardinal" and "quadrantal" points of the compass. 
 
 N. 
 i \ 
 
 40 
 
 FIG. 6. 
 
 The cardinal points N. E. S. W. correspond to 0, 90, 180, and 270 
 degrees. The quadrantal points NE. SE. SW. NW. correspond to 
 45, 135, 225, and 315 degrees. With these points in mind, it is easy 
 to S3e, for example, that 285 indicates a direction slightly north of 
 west, and that 185 indicates a direction just west of south. 
 
 TRUE COURSES. 
 
 The problem of aerial navigation is to fly from one point to another. 
 This may be divided into two problems one of distance and one of 
 direction. The problem of distance will be discussed later under 
 " Map reading." 
 
 The direction of one point from another is fixed. In order to 
 describe it- in an exact way we must measure the angle which this 
 direction makes with another direction that is known in advance. 
 In navigation problems this known direction is taken as north. 
 
AERIAL NAVIGATION. 9 
 
 The value of the angle which the given direction makes with north 
 measuring clockwise from north is called the course from the point 
 of departure to the destination. 
 
 For example, if A and B are two points on the map, the course 
 from A to B is the number of degrees in the angle NAB, where the 
 direction AN is the direction of the meridians on the map. In the 
 figure, the course from A to B is 40. Courses relative to the map are 
 known as "true" courses. 
 
 N 
 
 )220 
 
 FIG. 4. 
 
 Similarly, the statement "the course from A to B is 220" means 
 that the angle NAB measures 220 in a clockwise direction and 
 AN is the direction of true north from A. 
 
 It is advisable to practice at once, laying off courses from one 
 point to another, choosing a certain direction as North and measur- 
 ing the number of degrees clockwise from this direction in order to 
 get an idea of the values of different angles. 
 
 FIG. 5. 
 
 Example 1: If north is represented by the arrow, what is the course 
 from A to B? Measure with protractor. 1 
 
 *A good protractor for this work is made by a transparent piece of celluloid 4 or 5 
 inches square on which is marked a circle graduated in degrees. At the center of 
 the circle a silk thread is attached which when stretched taut will give the course 
 from the center to any desired point relative to the line joining the center of the 
 circle and the point marked zero or 360. Practice with this protractor is valuable 
 in giving a student a knowledge of the values oi angles. 
 77023 18 2 
 
10 
 
 AERIAL NAVIGATION. 
 
 Example 2: Choosing a certain direction as north, draw figures to 
 represent the following: The course from A to B is 15 , 315, 175, 
 210, 0, 90, 270. 
 
 Example 3: From any map -in your possession make up a number 
 of examples to illustrate the course from one point to another and 
 work them out. For example, given a map of the region about 
 Paris, determine the true course from Nanteuil to Betz, from Nan- 
 teuil to Senlis, from Meaux to Coulommiers. 
 
 MAGNETIC COURSES. 
 
 The magnetic course from A to B, like the true course, is the angle 
 NAB measured clockwise from north, only in this case AN is the 
 direction of magnetic north. 
 
 N 
 
 FIG. 6. 
 VARIATION. 
 
 The compass needle does not point to the geographic North Pole, 
 but (when unaffected by local magnetism) to a point known as the- 
 magnetic North Pole, situated near the northern extremity of the 
 American Continent. The difference between the two directions 
 of magnetic and true north is known as variation or declination. 
 It is described as easterly or westerly, according as the compass 
 needle points to the east or west of true north. It is measured in 
 degrees 15 west, 8 east, etc. 
 
 Variation on the east coast of the United States near Washington is 
 about 8 west, and that in southern California is about 15 east. In 
 northern France it is approximately 13 west. The variation as 
 given on the Ypres sheet of the map of Belgium is 13 34', 1916. 
 
AERIAL NAVIGATION. 
 
 11 
 
 The date of the variation is usually given, for the reason that the 
 variation changes from year to year, though generally not by more 
 than a few minutes. 
 
 RELATION BETWEEN TRUE AND MAGNETIC COURSES. 
 
 In northern France, at present, the magnetic courses differ from the 
 "true 1 ' courses by something like 13. If a pilot did not allow for 
 this fact, he would be about 14 miles out of the way in a 60-mile 
 flight, supposing that all his other calculations were correct. 
 
 The variation of the compass presents two problems: (1) Given 
 the true course and a certain variation to find the magnetic course; 
 
 Variation 15W 
 
 Variation 8E 
 
 FIG. 7. 
 
 FIG. 
 
 (2) given the magnetic course and the variation to find the true 
 course. In either case the angle is read from north (magnetic or true) 
 in a clockwise direction. From figure 7 it is evident that if the 
 variation is 15 west, a clockwise reading from AM will be 15 greater 
 than a clockwise reading from AN. Therefore if the variation is west 
 and the true course is given, say 45, to find the corresponding mag- 
 netic course, add 15, getting 60 as a result. On the other hand, if 
 the magnetic course is given, say 90, to find the true course subtract 
 15, getting 75 as a result. 
 
 If the variation is east, the reverse holds, namely, add the varia- 
 tion in. passing from magnetic to true; subtract the variation passing 
 from true_to_magnetic. 
 
12 
 
 AERIAL NAVIGATION. 
 
 The difficulty in variation problems lies in the fact that they are 
 so simple. It is necessary only to add or subtract a certain amount, 
 but very frequently one adds this amount when he should subtract 
 it, and vice versa. To reduce these errors to a minimum it is advisable 
 to work out a large number of problems, taking care at the outset to 
 make as few mistakes as possible in order that a correct habit may be 
 formed and carrying on the practice over a long period of time. 
 
 It is advisable at the outset to draw a figure in every case. From 
 the figures it will be apparent that if the variation is west, the 
 magnetic reading is greater than the true; and if the variation is east, 
 the magnetic reading will be less than the true. This relation may 
 be remembered by the words 
 
 Variation WEST COMPASS BEST. 
 Variation EAST COMPASS LEAST. 
 
 In remembering these phrases the word "variation*' may be 
 omitted if desired. The student should adopt that method of solving 
 the problems which works best for him in practice. If possible he 
 should visualize the angle NAM. 
 
 The following examples are given by way of illustration: 
 
 Example 1: The true course is 54 var. 13 W., then the magnetic 
 course is 67. 
 
 Example 2: Magnetic course is 300, var. 8 E. ; true course is 308 . 
 
 Example 3: True course 10, var. 15 E.; magnetic course 355. 
 
 Example 4: Magnetic course 15, var. 10 W.; true course 5. 
 
: 
 
 AERIAL NAVIGATION. 
 
 COMPASS COURSES. 
 
 DEVIATION. 
 
 13 
 
 The compass in an airplane is affected by the iron and steel in the 
 plane so that in general it does not point to magnetic north, but 
 " deviates" from it slightly according to the course the airplane 
 is heading. This means that the compass course, the angle the 
 pilot must fly by, is different from both the true and magnetic 
 courses. 
 
 Delation 3* 
 
 FIG. 10. 
 
 M M 
 
 represented 6y 
 /lr, q /e M/t.C. 
 
 FIG. 11. 
 
 This deviation is similar to variation. As variation is divergence 
 from true north, so deviation is divergence from magnetic north. 
 
 It is described in the same way as variation, 3 E., 5 W., etc. 
 The deviation of an airplane compass varies, both in magnitude and 
 direction, for different positions of the airplane. It must be cor- 
 
14 AERIAL NAVIGATION. 
 
 rected by means of magnets placed near the compass in such a 
 manner as to counteract the local influence on the needle. All 
 compasses have receptacles for these correcting magnets. This 
 process is known as "swinging the compass" and will be described 
 later in more detail under "Compass adjustment." 
 
 RELATION BETWEEN MAGNETIC AND COMPASS COURSES. 
 
 Let us suppose for the present that the deviation corresponding 
 to a given course is known. Two problems are presented: (1) Given 
 the magnetic course and the corresponding deviation to find the 
 compass course; (2) given the compass course and the corresponding 
 deviation to find the magnetic course. 
 
 A number of problems should be worked out, making as few mis- 
 takes as possible at the outset and practicing over a long period of 
 time. As with variation problems, a figure should be drawn at first 
 in each case. The words 
 
 Deviation WEST COMPASS BEST, 
 Deviation EAST COMPASS LEAST, 
 
 express the relation between magnetic and compass readings. That 
 is, when the deviation is west, the compass reading is greater than 
 the magnetic. When the deviation is east, the compass reading is 
 less than the magnetic. In remembering these phrases the word 
 "deviation" may be omitted if 'desired. A student should find the 
 method which works best for him in practice and adopt it to the 
 exclusion of any other method. 
 
 The following examples are given by way of illustration: 
 
 Example 1. Given magnetic 210, deviation 3 W.; compass is 
 213. (Compass best.) 
 
 Example 2. Given magnetic 359, deviation 2 W.; compass is I 6 . 
 (Compass best 361.) 
 
 Example 3. Given magnetic 355, deviation 2 E.; compass is 
 353. (Compass least.) 
 
 Example 4. Given compass 5, deviation 2 E.; magnetic is 7. 
 (Compass least.) 
 
 Example 5. Given compass 35, deviation 3 W., magnetic is 32. 
 (Compass best.) 
 
AERIAL NAVIGATION. 15 
 
 RELATION BETWEEN TRUE AND COMPASS COURSES. 
 
 ORDER OP PROCEDURE. 
 
 We have found the relation (1) between true and magnetic, (2) 
 between magnetic and compass. A combination of these two 
 enables us to find the relation (3) between true and compass. This 
 relation between true and compass is determined by the relation 
 which each bears to magnetic. Thus, magnetic is an auxiliary con- 
 necting true and compass. Whether we pass from compass to true 
 or from true to compass, we must pass through magnetic. The order 
 is either true, magnetic, compass; or compass, magnetic, true. There 
 is no other order. 
 
 This means that when we pass from true to compass we apply 
 variation first and deviation second ; when we pass from compass to 
 
 FIG. 12. 
 
 true we apply deviation first and variation second. A failure to 
 observe this order of procedure might result in large errors. 
 
 The following examples are given by way of illustration with the 
 deviation given for each course. The explanation is made quite 
 full for the sake of review. A number of similar examples should 
 be worked out. 
 
 Given true course 35, variation 15 N., deviation 3 E., find 
 compass. 
 
 The angle NOX, 35, is the true course of the ship. It is evident 
 that if we wish to obtain the magnetic course of the ship, which is 
 MOX, we must add the 15 variation, the angle NOM. This gives 
 us 50 magnetic course. Again, if we wish to obtain the compass 
 course of the ship (that is, the angle its direction makes with the 
 
16 
 
 AERIAL NAVIGATION. 
 
 compass needle, the angle it must fly by), we must subtract from 
 MOX the angle MOC, our 3 deviation, which gives us 47, compass 
 course. 
 
 It will also be clear that if the line OM lay to the right (east) of 
 the line ON, that is, if our variation were 15 east instead of 15 
 west, we should have to subtract MON from NOX, in order to find 
 MOX. In that case the' result would be 20, magnetic course. 
 Similarly, if OC lay to the west of OM instead of to the east of it, 
 we should have to add the angle COM to MOX in order to obtain 
 COX, the compass bearing, which in that case would be 23. 
 
 
 -Q) 2fs ' 
 
 FIG. 13. 
 
 Suppose, with reference to above figure, the compass course, 47, 
 COX, is given us, and we wish to find the true course, NOX. In 
 that case, we shall have to add our 3 easterly deviation to find the 
 magnetic course, 50, and then subtract our 15 westerly variation 
 from that to get true course, which will be 35. 
 
 Example. Given true course 255, variation 8 E., deviation 2 
 W. To find compass course. 
 
 Until the thing is thoroughly understood, it is always well to draw 
 a diagram. 
 
 NOX, our true course, is 255. To find MOX we must subtract 
 8, which gives us 247, magnetic course. To find COX we must 
 add 2, which gives us 249 , compass course. 
 

 AERIAL NAVIGATION. 
 
 17 
 
 Example: Given compass course 357, deviation 2 W., variation 
 5 E. To find true course. 
 Start out by drawing the angle we know, COX, 357. 
 
 
 FIG. 14. 
 
 The deviation being 2 west, the C line must be 2 to the left, or 
 west of the M line. Then draw the M line 2 to the east of the C line. 
 
 M C M 
 
 357 
 
 FIG 15. 
 
 To find magnetic course, MOX, subtract the 2 westerly deviation. 
 This gives 355, magnetic course. 
 
 But the variation being 5 east, the N line must be drawn in 5 
 to the left, or west, of the M line. This makes it identical with the 
 7702318 3 
 
18 AERIAL NAVIGATION. 
 
 X line, the direction in which our ship is heading. In other words, 
 we add 5 easterly variation and get 360, true bearing. The ship 
 is headirg exactly true north, though according to the compass it 
 is heading 3 to the west of north. 
 
 It should always be borne in mind that a course is a clockivise 
 angle from north. In all cases, what it is desired to find is the 
 ang^.e which the X line, the direction of the ship, makes with one 
 of the three lines around north, the N, M, or C lines. 
 
 Variation and deviation are sometimes referred to as plus or 
 minus quantities, e. g., 13, +4. Deviation cards are frequently 
 made out in this way. It is always well to beware of such signs, 
 for their meaning is relative to something variable. Whether we 
 should add or subtract westerly deviation, for example, depends 
 entirely on which way we are going, from true to compass or compass 
 to true. 
 
 Deviation, it must be remembered, is always considered with 
 reference to magnetic, never with reference to true. We have no 
 concern with the ang'e NOG. . 
 
 Remember, therefore, when working from true to compass, to 
 apply variation first, then deviation. Conversely, when working 
 from compass to true, apply deviation first, then variation. 
 
 This would not be necessary if deviation were a constant quantity 
 for every point of the compass. It actually varies considerably, 
 often between quite closely adjacent points, so that a deviation 
 correction applied to a direction representing a true course might 
 differ radically from the deviation which should be applied for 
 that course with the appropriate variation added or subtracted. 
 
 For example, compass course 240, variation 15 W., deviation 
 for 240, 2 E. To find true course. 
 
 Suppose we correct for variation first and subtract our 15 westerly 
 variation, getting 225. Then, desiring to apply correction for 
 deviation and looking at our deviation card, we might discover, 
 especially if the compass had not been particularly well adjusted, 
 that the proper deviation for 225 was 4 W., instead of 2 E. It 
 is clear that the result would be different from that obtained by 
 following the proper order. In the former case it would be 221, 
 in the latter 227. 
 
 In the following examples the table, page 41, is used. 
 
 Example 1: Given true course equals 230, variation 13 W. 
 "Find compass. Magnetic is 243, corresponding deviation is 4 E. 
 Compass is 239. 
 
AERIAL NAVIGATION. 
 
 19 
 
 Example 2 : Given true 47, variation 10 E. Find compass. 
 Magnetic is 37, corresponding deviation 4 W. Compass is 41. 
 
 Working from compass to true we proceed as follows: 
 
 Example 3: Given compass 255, variation 13 W. Find true. 
 Corresponding deviation is 2 E., magnetic 257. True 244. 
 
 Example 4: Given compass 44, variation 8 E. Find true. 
 Corresponding deviation 4 W., magnetic 40. True is 48. 
 
 COURSE SETTING WITH ALLOWANCE FOR WIND. 
 
 In actual practice, it is generally not sufficient to set a course 
 from the map as described above. It is necessary to make due 
 allowance for the wind, which, if blowing with any considerable 
 
 velocity, will deflect the airplane from its course and take it in a 
 direction far from the desired one. The problem is difficult as the 
 wind varies in velocity and direction with time and altitude. 
 However, once the direction and velocity of the wind are known, 
 it is not difficult to map out one's course so as to allow for its influence. 
 Suppose, for example, we wish to fly a course which we find to 
 be 25 true, in a machine whose air speed is 60 m. p. h. The wind 
 at the height at which we wish to fly is blowing at 20 m. p. h. from 
 300 true. 
 
 On the map itself, or on a separate sheet of paper, draw a line 
 
 connecting the points of departure and destination, AB, at an angle 
 
 ' of 55 from true north. Then from A, the point of departure, plot 
 
 out a line directly down wind, proportionate in length to the number 
 
 of miles the wind blows per hour, AC. 
 
20 AERIAL NAVIGATION. 
 
 From C, swing a line equal in length to the air speed of the machine, 
 in miles per hour, till it cuts the line AB. Mark this point D. 
 
 The line CD gives the course to be steered and air speed, AD gives 
 the course to be made good ('"track") and ground speed, while AC 
 gives the speed and direction of the wind. The line AD is evidently 
 the "resultant" of the "components" AC and CD. 
 
 From A draw a line parallel to CD, any convenient length, AB'. 
 The direction of this line will give the course to be steered. In this 
 case, it is 38 true. Then correct for variation and deviation, in the 
 usual way. 
 
 The machine will fly over the course AB, but it will be headed 
 ("crabbing") in the direction AB X . The divergence of this from 
 the course to be made good ("track") will just counteract the side- 
 ways drift caused by the wind. 
 
 For the return journey a new course must be set and a new figure 
 drawn. It will not do to fly back over the reverse of the outward 
 course. The course must also be altered in the air if it is discovered 
 that the wind has changed much in direction or velocity. This can 
 be done in the air by the process described above, but it is generally 
 easier to use the course and distance indicator. (See page 30.) 
 
 The line AD represents the ground speed of the machine in miles 
 per hour. It is often desirable to find this, in order to get some idea 
 of how far you can fly on your supply of petrol . It is easily found on 
 the drawing by measuring it off on the same scale as that used in 
 drawing the lines AC and CD. In this case it is about 67 miles per 
 hour. The scale used on the above drawing is one-sixteenth inch to 
 a mile, or sixteen miles to an inch; this will be found to be a conve- 
 nient scale when working in miles . When working under the metric 
 system, the scale of 1 millimeter to a mile is convenient. 
 
 It will be noted that in the above drawing the ground speed is 
 greater than the air speed. This is because the wind is blowing more 
 from behind the machine than from in front of it, and is conse- 
 quently pushing it forward rather than back. If the wind tends to 
 blow the machine back, the ground speed line will of course be 
 shorter than the air speed line. 
 
 TO FIND DIRECTION AND VELOCITY OF WIND. 
 
 In the foregoing problem it is assumed that the force and direction 
 
 of the wind are known. In practice these data are often furnished 
 
 to the airdrome by an adjacent meteorological station, but this is not 
 
 ' always the case. It is sometimes necessary for a pilot to go up, fly 
 
AERIAL NAVIGATION. 
 
 21 
 
 over a short known course, and from the data thereby obtained work 
 out on pap?r the desired information. This is done by a process 
 similar, or rather converse to, the one just described. 
 
 AB represents the bearing between the two known points, such 
 as two prominent buildings, for example; if the course is flown at 
 night, two srarchlights are used. The bearing AB is 55 true. 
 Starting over A and keeping the point B always in sight, the pilot 
 flics toward it in as straight a line as possible. If there is a wind 
 blowing, he will find himself "crabbing;" that is, in order to fly 
 over the prescribed track, he will have to alfcr the direction or course 
 of his machine. In this case we will call the course AC, 38 true. 
 Naturally the pilot can not take true readings from his compass, but 
 will have to correct his compass reading for deviation and variation 
 
 FIG. 17. 
 
 in order to get a true reading. We will suppose that this has been 
 done, and that the true course thus found is 38. 
 
 It is also n?cessary to have the air speed and ground speed of the 
 machine. The air speed is read from the air speed meter; suppose 
 in this case it is 80 m. p. h. For obtaining the ground speed a stop 
 watch is necessary. By it the pilot discovers the number of seconds 
 it takes him to fly a known distance on his track. Suppcse he 
 traverses 1 mile in 55 S3conds. To turn this into miles per hour, it is 
 only necessary to divide 3,600 (the number of seconds in an hour) 
 by 55. This gives 65 and a fraction. 
 
 Now the pilot lays off a unit of length proportional to his air speed 
 on his course, and a corresponding unit representing his ground speed 
 on his track. A line joining the two will give the direction and velo- 
 city of the wind, in miles per hour. 
 
 This is the line DE, which on being measured is found to be pro- 
 portional to 25 miles in length, with a true bearing of 350. 
 
22 AERIAL NAVIGATION. 
 
 (The measurements in the diagram are on a scale J inch equals 10 
 miles. Any scale will do, regardless of the length we draw AB, so 
 long as the same scale is used for all measurements concerned.) 
 
 Remember that the direction of a wind is always given as true; 
 also that its "direction" means the direction it blows from. 
 
 Similarly, if the course steered, the air speed and the force and 
 direction of the wind are known, the track and ground speed can 
 be obtained. 
 
 For example: Course 112 true; wind, 20 m. p. h. from 60 true; 
 air speed 90 m. p. h., find track and ground speed. 
 
 FIG. 18. 
 
 On AB, drawn at an angle of 112 from the meridian, lay off a dis- 
 tance representing 90 m. p. h. air speed, AC. From C lay off, down 
 wind, at an angle of 60 from the meridian, a distance equal to 20 
 miles, on the same scale. Join A and D; measure the distance 
 between them and the angle AD makes with the meridian, and you 
 have the ground speed of the machine and the true bearing of the 
 track. In this case they are 80 m. p. h. and 125 
 
 RADIUS OF ACTION IN A GIVEN DIRECTION. 
 
 The supply of fuel in an airplane is necessarily limited. A cer- 
 tain amount of gasoline will supply the plane with fuel for a certain 
 time. In making a long trip in a certain direction, it is desirable 
 to consider in advance whether the objective falls within the plane's 
 "radius of action." The radius of action in a given direction is 
 the distance that a plane can fly in that direction and still return, 
 using a certain amount of fuel that is, flying for a certain time. 
 The radius of action may be found as follows : 
 
 Given the air speed of the machine, the direction and speed of 
 the wind, and the number of hours' fiight possible with the supply 
 of gasoline known: 
 
 
 
AERIAL NAVIGATION. 
 
 23 
 
 (1) Compute the ground speed out and the ground speed in as 
 heretofore. 
 
 (2) With these values known, the radius of action will he the 
 number of hours times the product of the ground speeds, divided 
 by the sum of the ground speeds. 
 
 For example, if the ground speed out is 50 m. p. h. and the ground 
 speed in is 64 m. p. h. and the number of hours' flight possible with 
 a given supply of fuel is 5 hours, the radius of action is 
 
 =140 miles. 
 
 The proof for finding the radius of action is not given. 
 
 For one hour's flight the radius of action is the product of the 
 ground speeds divided by the sum of the ground speeds. 
 
 An allowance of 25 per cent should be made for changes in the 
 wind, etc. 
 
 BEARINGS. 
 
 N 
 
 FIG. 19. 
 DEFINITION. 
 
 The bearing of a point B from a point A means the angle NAB 
 measured clockwise from north. Thus the true bearing of B from 
 A is the same as the true course from A to B, the magnetic bearing 
 of B from A is the same as the magnetic course from A to B. The 
 compass bearing of B from A, however, requires special consideration. 
 
 When the airplane is in flight steering a given course, the com- 
 pass bearing of points along the course is the same as the compass 
 course steered. It is often useful, however, for the sake of fixing 
 one's position to take bearings of points off the course that one is 
 flying, say, the bearing of B from A when the course is AC. When 
 reckoned from the course AC the compass bearing of B from A is 
 
24 AERIAL NAVIGATION. 
 
 not the same as the compass course from A to B. The reason is 
 that deviation depends on the direction that the airplane is head- 
 ing and not on the direction that the pilot is looking. The 
 deviation corresponding to the bearing above is the deviation for 
 course AC and not for course AB. 
 
 FIG. 20. 
 FIXING THE POSITION OF A MACHINE. 
 
 The pilot may fix the position of his machine at a given time by 
 its position relative to two known points. This is easily established 
 by takmg the bearings of the two points from the machine. 
 
 Since both bearings can not be taken at once and the machine is 
 rapidly changing its position, it is advisable to choose the first object 
 well on the bow and as far away as possible in order that its bearing: 
 may change as little as possible before the bearing of the second 
 object is taken. The time of the observation is the time when the 
 second bearing is taken. If the objects are chosen in this manner 
 the "fix" of the machine is accurate enough for most purposes. 
 The course of the machine must remain unchanged during this 
 process. 
 
 To illustrate, suppose for convenience that the machine is flying 
 north. At 2 o'clock take the bearing of a distant object A well 
 on the bow, bearing 15 say, and at 2.01 take the bearing of a nearer 
 object B, bearing 100 say. Then the position of the airplane at 
 2.01 is found by the intersection of two lines bearing 195 from A 
 and 280 from B. These last bearings may be found, if desired, 
 
AERIAL NAVIGATION. 
 
 25 
 
 by drawing from A and B lines parallel to ON to represent north 
 at these points. 
 
 In general, given the bearing of B from A, the bearing of A from 
 B is found by adding 180. In case the resulting angle is more 
 than 360, subtract 360 from it. For example, the bearing of B 
 from A is 350. Then the bearing of A from B is 530, which is 
 the same as 170. This gives the same result as if one had sub- 
 tracted 180 from the first bearing and so one might follow the rule 
 to add 180 to the first bearing, unless the result is greater than 
 360, and if this is the case, subtract 180 from the first bearing. 
 
 
 
 FIG. 21. 
 
 INSTRUMENTS. 
 
 BEARING PLATE. 
 
 The bearing of an object from the machine is taken conven- 
 iently by means of the bearing plate, a description of which follows. 
 
 This instrument consists of a fixed plate open in the center with 
 two arrows arranged so that it can be set in the fore and aft line of 
 the machine. 
 
 On this is set a movable flat ring marked off for each 5 from 
 to 360 in a clockwise direction with numbers placed at the marks 
 10, 20, etc. (fig. 22). Fixed to the outer plate is a movable 
 framework with wires stretched across and capable of being rotated 
 around the plate. At either end of this framework are placed up- 
 right pointers to facilitate sighting. 
 
 The chief use of the instrument is to take the compass bearing 
 of an abject. 
 
 7702318 4 
 
26 AERIAL NAVIGATION. 
 
 To do this, read the compass course of the machine and set the 
 movable ring so that the number opposite the forward arrow is 
 exactly the same as the compass course. We see from the figure 
 
 FIG. 22. 
 
 FIG. 23. 
 
 FIG. 24. 
 
 that the bearing plate will then have its zero mark in exactly the 
 same direction as the compass north, and, as long as the course 
 remains the same it can be used as the compass for observing the 
 
AERIAL NAVIGATION. 27 
 
 direction of any object. The compass itself can seldom be used 
 for this purpose as the field of view around it is often restricted. 
 The movable framework can be placed so that the sights or pointers 
 and center drift wires (the wires being called drift wires, as will be 
 seen later) are aligned on the object. 
 
 FIG. 25. 
 
 The reading of the point B will give the bearing of the object 
 as read from compass north. Of course, the horizontal bearing is 
 given, but as the position of the machine is relative to the ground 
 all bearings are those of the point vertically above the object. 
 Now, having found the bearing of any object from the compass, it 
 will require to be corrected for deviation from the course and 
 variation. This will give the true bearing of the object. 
 
 For example: Compass course 200, var. 13 W., dev. 7 E., 
 compass bearing of an object is 120. Find its true bearing. 
 
 CB 120 
 
 Dev. 7 E 
 MB 127 
 
 Yar. 13 W 
 TB 114 
 
 taken from the compass course. 
 
 This gives the true bearing of the object from the machine to be 
 114, and therefore the bearing or direction of the machine from 
 the object is 180 plus 114 equals 294. 
 
 AIRCRAFT COURSE AND DISTANCE INDICATOR. 
 
 The aircraft course and distance indicator (C. D. I.) makes 
 possible the solution of certain problems during flight without the 
 use of pencil, parallel rulers, dividers, etc. 
 
28 AERIAL NAVIGATION. 
 
 DESCRIPTION. 
 
 This instrument consists of (1) an outer ring marked every 5 
 from to 360; (2) a central rotating disk whose radius is marked 
 to represent 120 miles, the disk itself being squared, each side of a 
 square representing 10 miles; (3) two arms A and B pivoted at 
 the* center of the disk, marked to the same scale as the disk with 
 two movable pointers, one on each arm; (4) a central clamp hold- 
 ing the instrument rigid when set. 
 
 PRINCIPLE OF INSTRUMENT. 
 
 The instrument is made to apply the following principle: A 
 force l represented in amount and direction by AM (equals CD) 
 plus a force represented (in amount and direction) by MB is equal 
 to the force represented (in amount and direction) by AB. In 
 this case AB is called the " resultant" of the two " component" 
 forces AM and MB. 
 
 For example, if the line AM is 1 inch in length, and represents a 
 wind of 40 m. p. h. blowing from A, and the line MB is 2 inches in 
 length and represents an air speed of 80 m. p. h. in the direction 
 MB, the resultant speed is about 60 m. p. h. in the direction AB. 
 
 In the following problems we shall have to do with these quantities: 
 
 (1) Speed and direction of the wind. 
 
 (2) Ground speed and track (course to be made good). 
 
 (3) Air speed and course (true). 
 
 It may be noted that the ground speed is always along the track, 
 and the air speed is always along the course (here taken as "true"). 
 
 The direction of the wind is given relative to true north, and rep- 
 resents the direction from which the wind blows; for example, a 
 north wind is blowing from the north. 
 
 RULES FOR USING INSTRUMENT. 
 
 The following rules for using the instrument are given, as it is 
 hoped that by paying strict attention to them confusion may be 
 avoided: 
 
 i Or a velocity. 
 
AERIAL NAVIGATION. 
 
 29 
 
 (1) Arm A should when possible represent your own course and 
 air speed. 
 
 (2) Always keep the general lines of the situation in your head. 
 
 (3) Check each example by the idea more or less; for example, the 
 ground speed will evidently be greater than the air speed if the 
 wind favors the pilot on his course. 
 
 FIG. 27. 
 
 30. 
 
 Problem I: To find the speed and direction of the wind, given the track 
 and ground speed, course (true) and air speed. 
 
 Examples: Machine steers 300 at 50 miles. Track observed to 
 be 260 at 70 miles. Find the speed and direction of wind. 
 
 (a) Set arm and pointer A to course steered (true) and air speed 
 300 and 50. 
 
30 AERIAL NAVIGATION. 
 
 (6) Set arm and pointer B to course made good and ground speed 
 260 and 70. 
 
 (c) Set disk so that arrow is parallel to line AB. 
 
 jfrrow points to direction in which wind is blowing, 215, there- 
 fore wind blows from 35. Length of AB is speed of wind, 44 m. p. h. 
 
 Problem IT: To find what li allowance to make for a wind." 
 
 Given speed and direction of the wind, airspeed, and track desired, 
 to find course (true) and ground speed. 
 
 Example: Wind NE., 40 miles. Machine air speed, 70 mile, 6 ". 
 Pilot Dishes to make good a path W. What course must he steer? 
 
 (<i) Set arrow on disk to course to be made good (track), 270. 
 
 (b) Set arm and pointer B to direction from which wind is blowing 
 and to speed of wind, 45 and 40. 
 
 (c) Set pointer A to air speed of machine, 70. 
 
 (d) Revolve arm A till pointer A is on same line (parallel to arrow) 
 as pointer B. 
 
 Arm points to the course, 295. 
 
 The distance between pointers A and B will be ground speed, 91. 
 (See fig. 28.) 
 
 Problem ITT: To determine the ground speed when the direction of the 
 wind is known . 
 
 This problem is useful when the direction of the wind is observed 
 to change during a flight or when the direction of the machine is 
 changed. 
 
 Given the direction of the wind, true course, air speed, and track, 
 to find the ground speed. 
 
 (fi) Set arm and pointer A to true course and air speed, say north 
 and 80 m. p. h. 
 
 (b) Set arm B in direction of track, way :WO. 
 
 (c) Move disk until arrow shows the direction of the wind, say 60. 
 
 (d) Set pointer B where parallel to arrow from A cuts arm B. 
 This will give the ground speed along the trac*'. 69 m. p. h. 
 
 The conditions given in this problem allow us also to read from 
 the indicator the speed of the wind. In this case it is <0 m. p. h. 
 
 In case it were desired to fly directly up for down) wind, the wind 
 speed might be computed as above and then subtracted 'or added 
 to give the ground speed. 
 
AERIAL NAVIGATION. 
 
 31 
 
 ILLUSTRATIVE PROBLEM. 
 
 (This problem is given to apply some of the foregoing principles 
 in succession to a particular case. The explanation is made quite 
 full in order that, if desired, the problem may be read in connection 
 with the Introduction, page 6.) 
 
 By means of map and compass the pilot proceeds as follows to lay 
 out his course. First he draws a straight line on his map from aero- 
 drome to destination. Then he measures this distance on the map. 
 This distance is a matter of inches. It is necessary to fly a matter of 
 miles. He finds the correct number of miles as follows: On his map 
 is printed a ''representative fraction." R. F. equals 1/200,000, say. 
 This means that a distance on the ground is 200,000 times as great as 
 on the map. Let us suppose that the distance on the map is 14 inches. 
 This means that the distance on the ground is 200,000 times 14 inches. 
 
 36' 
 
 FIG. 29. 
 
 Since there are 5,280 feet or 63,360 inches in a mile, the distance on 
 the ground corresponding to the observed distance of 14 inches on 
 the map is 44 miles. This disposes of the problem as far as distance 
 is concerned. 
 
 The direction that the pilot is to steer is determined as follows: 
 First he measures his course on the map by means of a protractor, 
 measuring the angle from the meridian indicated on the map to the 
 straight line along which he is to fly. It is not always advisable to 
 fly a straight course, but we will suppose it to be so in this case. 
 He finds this angle to be 36 say, and therefore his "true" course 
 is 36. 
 
 This, however, is not the course which he will steer when rising 
 his compass, because the compass does not point true north. In 
 France a compass unaffected by local magnetism points from 10 to 
 15 to the west of true north, toward the magnetic pole of the earth. 
 
32 
 
 AERIAL NAVIGATION. 
 
 The amount by which the compass differs from true north is known 
 as its variation and is said to be easterly or westerly according as the 
 compass points east or west of true north. Let us suppose that the 
 variation of the compass at the pilot's aerodrome is 15 west. 
 
 One might suppose, then, that his course would be his "true' ?J 
 course plus 15 (36 plus 15 equals 51), and this would be the case 
 if there were no local magnetism in the airplane, but the compass 
 is affected by the iron and steel in the plane, which deflect the needle 
 
 FIG. 31. 
 
 a little this way or that, according to the way the ship is headed. 
 It must be borne in mind that the compass needle tends to point to 
 "magnetic-" north regardless of the direction of the ship, and as the 
 machine changes direction different bodies affect the compass 
 needle; for example, when the ship is flying east, magnetism in 
 
AERIAL NAVIGATION. 
 
 33 
 
 the engine may pull the compass needle toward the east, and when 
 flying west, to the west. It has been found necessary in practice 
 to correct the compass reading for this ft deviation ^ at the points 
 north, east, south, west, and the points halfway between them. 
 The deviation for other points may be computed from these. (See 
 page 41.) 
 
 Let us suppose that the deviation corresponding to the pilot's 
 " magnetic-" course of 51 is 3 west. This means that the " com- 
 pass*' course is 3 plus 51, or 54, and this is the course which the 
 pilot will have to steer or, rather, it is the course which he would 
 steer if there were no wind. 
 
 FIG. 32. 
 
 Let us suppose now that there is a wind from true north blowing 
 20 miles an hour. This means that no matter in what direction the 
 airplane steers it is going to be carried in a southerly direction at 
 the rate of 20 miles per hour. It is evident, therefore, that if the 
 pilot wishes to reach a certain destination he must steer to the north 
 of it by a certain amount. 
 
 Let us compute this amount graphically by protractor and ruler. 
 A wind blowing from the north will delect the machine in a south- 
 erly direction by an amount proportional to 20. From the aero- 
 drome O let us draw a line OA in the direction of true south, say 
 2 inches in length. This will represent the amount that the wind 
 delects the ship. Our problem is to steer a course from A which 
 will keep us on the desired track. With A as a center and a radius 
 
34 AERIAL NAVIGATION. 
 
 
 
 of 9 inches proportional to the speed of the ship, let us cut the track 
 at the point P. Then AP is the direction to be steered by a plane 
 going 90 miles an hour to stay on the track in spite of a north wind 
 blowing 20 m. p. h. If we measure the angle OAP with a protractor, 
 we find it to be 29. This angle represents the true course, allowing 
 for wind. 
 
 From the true course we may find the compass course to be steered 
 by applying the proper variation and deviation getting as a result 
 29 plus 15 plus 3 (supposing the deviation corresponding to 
 magnetic 44 to be the same as for magnetic 51, although this would 
 not always be the case) equals 47, the compass course to be steered. 
 
 To find the time that it will take to make the trip we may proceed 
 as follows: 
 
 We measure the line OP along the track (corresponding to a length 
 of 9 inches along the course to be steered) and find it to be 1\ inches. 
 This means that the ground speed or speed along the track is 75 
 m. p. h. Therefore, to fly the required distance of 44 miles will 
 take 35 minutes. We have now worked out the compass course 
 that the pilot will steer and also the time it will take him to reach 
 his destination. 
 
 CHECKS. 
 
 No matter how carefully a pilot lays out his course and uses his 
 instruments, it is desirable to have certain rough checks on his 
 flight with regard to direction and distance. The mistakes that 
 inexperienced pilots make in 4he air are almost incredible such 
 mistakes as, for example; getting 30 miles out of the way on a 10- 
 mile flight. 
 
 With respect to direction a pilot may check his flight by means of 
 the sun and the map. On most flying days the direction of the sun 
 may be observed, and if the course is known the sun ought to be 
 in about such a position relative to the direction of the plane. While 
 the compass and the calculated course are the chief things of impor- 
 tance, an occasional observation of the sun will prevent a pilot from 
 making hrje errors in direction. Such errors will also be prevented 
 by careful observation of the country over which he is traveling 
 and comparison with his map. 
 
 Observation of the country and the map will also prevent large 
 errors with respect to distance. These errors may also be prevented 
 by a knowledge of the time required to make the trip. Such a 
 check on his flight would prevent the pilot from being 30 miles out 
 
AERIAL NAVIGATION. . 35 
 
 of the way on a 10 mile trip, for if lie flew for the proper length of 
 time (in still air) so large an error would be physically impossible 
 no matter what direction was taken. 
 
 TECHNIQUE. 
 
 In order to take navigation out of the realm of theory and make it a 
 practical matter it is necessary for the pilot to develop his technique 
 in certain respects to a high degree of proficiency. It is necessary to 
 develop (1) a sense of direction; (2) a sense of distance; (3) a sense of 
 quantity (proportion). In each of these respects the pilot should 
 train himself by numerous exercises over a long period of time 
 until accuracy becomes a matter of instinct. The exercises required 
 are so simple and so nearly alike that it is not feasible to print a 
 large number of them. It is left to the pilot to make up a large 
 number, perhaps hundreds of exercises similar to each of these, and 
 to train himself to work them out with speed and certainty. 
 
 FIG. 33. 
 DIRECTION. 
 
 The first exercise consists in drawing angles between and 360, 
 guessing at their size and checking by protractor until the guesses 
 are fairly accurate. For example, how many degrees is a certain 
 angle. 
 . Check by protractor. This angle is about 320. 
 
 Second exercise: The line OP from O to P bears 300 by compass 
 (fig. 34). Draw a line (a) bearing north (fig. 35), (b) bearing 150 
 (fig. 36). 
 
 Third exercise: The following" exercise is for the purpose of pre- 
 venting the pilot from making large errors in direction. The direc- 
 tion of the sun may be observed approximately on most flying days. 
 At. 12 o'clock noon this direction is about south regardless of the 
 
36 
 
 AERIAL NAVIGATION. 
 
 season of the year. At 6 p. m. it is about west; at 6 a. m. about 
 east, etc. Thus knowledge of the direction of the sun at any hour 
 of the day will give the pilot an idea of where to expect north and 
 
 FIG. 34. 
 
 FIG. 35. 
 
 FIG. 36. 
 
 all the other directions, although, of course, it will not enable him 
 to correct small errors in his compass nor get along without his 
 compass. Such knowledge may also keep him from being confused 
 
 FIG. 37. 
 
 at moments when the compass is unreliable, say, after a steep bank 
 or after emerging from a cloud. From the sun is in the direction 
 OP at 2 p. m. Find the direction of north from 0. (Fig. 38.) 
 
 DISTANCE. 
 
 First exercise: How long does it take to go 12 miles at 80 m. p. h.? 
 This exercise should be worked out mentally so as to be approxi- 
 mately correct, as follows: At 60 m. p. h. it would take 12 minutes. 
 
AERIAL NAVIGATION. 37 
 
 At 80 m. p. h. it* would take less than 12 minutes, perhaps 9. The 
 guess should be checked as follows: Since the time is inversely pro- 
 portional to the speed, it would take sixty-eightieths of 12 minutes, 
 equals 9 minutes. Usually the guess will be somewhat out of the 
 way, but the pilot should practice the exercise until his guess is 
 approximately correct. 
 
 Second exercise: Two vertical searchlights are 5 miles apart. It 
 takes 4 minutes 10 seconds to traverse the digtance between them. 
 Required the ground speed. The plane is evidently going more 
 than 60 m. p. h., say 70, for a guess. To check the guess proceed as 
 follows: 4 minutes 10 seconds is 250 seconds. Five miles in 250 
 seconds is 1 mile in 50 seconds. There are 3,600 seconds in an hour. 
 One mile in 50 seconds means 72 miles in an hour, thereby checking 
 the guess. 
 
 Third exercise: How far can one go in 10 minutes at 90 m. p. h.? 
 The guess is 15 miles and may be made correctly at once since 10 
 minutes is one-sixth of an hour, and one-sixth of 90 is 15. 
 
 Fourth exercise: It takes 55 seconds to go a mile. Required the 
 speed. The speed is more than 60 m. p. h., say 70, for a guess. 
 Check as follows: There are 3,600 seconds in an hour; therefore, if 
 1 mile is traveled in 55 seconds, 65 miles will be traveled- in an hour. 
 
 PROPORTION. 
 
 Certain exercises in proportion are implied in the foregoing. 
 Certain others are required when laying out a course to allow for 
 wind, as follows: 
 
 First exercise: An air speed of 70 is represented by a line 2 inches 
 in length. What line represents a wind of 20? Answer: Two- 
 sevenths of 2 inches. 
 
 Second exercise: A wind of 15 is represented by a line 1 inch in 
 length. What line represents an air speed of 90? Answer: Six 
 inches. 
 
 Third exercise: Ground speed 65 is represented by a line 3 inches 
 in length. What line represents an air speed of 75? Answer: 
 Seventy-five sixty-fifths of 3 inches. 
 
 NOTE. In solving these examples in proportion it is first desirable 
 to decide the general question "more or less." Thus, in the pre- 
 ceding exercise it is first desirable to realize that the line representing 
 75 will be more than 3 inches in length before working out exactly 
 
38 AERIAL NAVIGATION. 
 
 how much more. In the first exercise the line would be less, and 
 about one-third of 2 inches. 
 
 Fourth exercise: Free-hand drawing of lines in different directions 
 proportional to different numbers. Check by means of ruler and 
 protractor. For example, draw two lines making the angles 30 
 and 230, respectively, with a given line and proportional, respec- 
 tively, to the numbers 5 and 2. 
 
 The pilot should also have facility with a time scale, described 
 under "Map reading. 1 ' 
 
 COMPASS ADJUSTMENT. 
 
 Compass adjustment is the process of eliminating, as far as possible, 
 errors of the compass caused by the magnetic material in the ship. 
 This adjustment is effected by swinging the compass on a temporary 
 or permanent swinging base, which is essentially a central point 
 with the magnetic. cardinal and quadrantal points laid off around it. 
 The process of swinging consists in bringing the plane with the 
 compass in it to the base and successively heading it on .each point. 
 
 A temporary swinging base, such as is constructed at an aerodrome 
 near the fighting line, is located out in the field, at least 50 yards 
 away from any magnetic material. The center is marked with a peg. 
 By means of a prismatic compass (or any oth r type with sighting 
 attachments) set up over this central p g, the pcsi'ions of the eight 
 points are detrmin d and marke d with p gs or stakes. (It takes two 
 men to do this, one to sight and on to p g.) When r stablishc d, each 
 stake should be joiird to the central p g by a taut cord. 
 
 The p rman^nt swinging base, such as is us d at factcri s, schools, 
 and p rman^nt aerodrome s, is made by digging a circular basin 20 
 yards in diamet r and about 1 foot deep, and filling it with cono\ te. 
 When leveled and s t, the platform thus formed is marked off with 
 the cardinal and quadrantal points as above, the lin:s being marked 
 with black paint inst ad of cords and p gs. 
 
 Before the machine and coir pass are taken to the swinging base for 
 the adjustment, the coir pass must be car fully inep ct d for its 
 mechanical condition. Three points are particularly to be observed : 
 
 1. Large bubbl s should be elhonat d. 
 
 2. The card should hang evenly on its pivot. 
 
 3. Th^re should be no friction in the bearing. 
 
 The t:st for the last is to deflect the needle with a magnet and 
 release it. If it does not come back promptly to the reading that it 
 
AERIAL NAVIGATION. 39 
 
 had brfore the deflection, there is friction, and the compass must be 
 replaced. 
 
 The position of the compass in the machine has been worked out 
 and standardized for each type of machine in order to secure the 
 great st ease of reading by the pilot, the gr; at st conveni nee of 
 adjustment, and the least unbalanced influence from the magnetic 
 material in the ship. It follows that the coir pass must be in the 
 authorized position for the given type of machine, and in no other. 
 
 The compass being prep- rly placed and in good working order the 
 machine is set up on the cent r of the flying base, tail raise d to flying 
 position by means of a trestle. A plumb line is dropped from the 
 boss of the prop Her and another from the tail skid or the center 
 line of the tail. Now, by sighting along these and the N. line, one 
 can point the machine's nose due north (magnetic) and ots rve the 
 compass reading. If this is not zero, magnets can be set ath wart- 
 ship in holes provided in the compass case, in such a manner that 
 the deflection will be neutralized. This is called compensation. 
 
 Next the machine is turn: d so as to head exactly east, b ing sighted 
 along the plumb lines and the stake or ground line as before, and the 
 compass reading is again taken. In this position the error will be 
 much greater than in the N.-S. position, for the needle is lying 
 transv rse to the lines of force from the chi f source of magnetic 
 attraction, the engine, which is always in the fore-and-aft line in any 
 single-motor type of ship. Hence more compensating magnets are 
 requir d for correcting on the E.-W. axis than on the N.-S. axis. 
 Th se magnets are plac- d fore and aft in the compass case in order 
 to act at right angles to the needle, which is pointing in the general 
 direction of north; that is, athwartship, the ship having been turned 
 one-quart r turn to the right or east. 
 
 The deviation being corrected on N. and E., the machine is sighted 
 on S. and W. in turn. If the deviation in these positions is no greater 
 than 3, it is best not to compensate for it, since to do 'so would only 
 throw out the already correct reading on N. and E. If, however, the 
 error is greater than 3, it is best to compensate half the error Since 
 the deviation on E. has already been corrected by fore-and-aft 
 needles, alteration of those needles to correct the deviation on W. 
 will create an error on E. approximately equal to the correction on 
 W. Hence, by halving the error on W, we distribute it equally 
 between E, and W., giving each a small amount. 
 
AERIAL NAVIGATION. 
 
 This compensation on the cardinal points as explained serves to 
 neutralize the effect of the permanent magnetism in the ship, i. e., 
 that resident in those hard iron and steel parts which acquired 
 magnetism in the process of manufacture and assembly. In addi- 
 tion to these errors there will still be errors on the quadrantal points, 
 due to induced magnetism in the soft iron of the ship. In the ordinary 
 aero compass these can not be compensated for. What is done is to 
 swing the ship to all these points and note the error on each, along 
 with any uncompensated error on the cardinal points on the devia- 
 tion card. 
 
 The deviation card is then prepared and placed conveniently near 
 the compass, so that both may be read by the pilot at the same time. 
 
 DEVIATION CARD. 
 
 The deviation card represents the minimum to which the devia- 
 tion of a particular compass in a particular machine can be reduced 
 by properly placed magnets. A common form of deviation card 
 follows: 
 
 Magnetic course. 
 
 
 Deviation. 
 
 N. 
 
 
 
 
 
 NE. 
 
 45 
 
 4W. 
 
 E. 
 
 90 
 
 1 W. 
 
 SE. 
 
 135 
 
 5E. 
 
 S. 
 
 180 
 
 2E. 
 
 sw. 
 
 225 
 
 7E. 
 
 w. 
 
 270* 
 
 2W. 
 
 NW. 
 
 315 
 
 3E. 
 
 Compass checked by - 
 
 
 
 
 
 When the compass reading has been corrected as above for the 
 points 0, 45, etc., an approximate correction for points 10, 20, 
 30, etc., is made by interpolation, assuming that the amount of 
 deviation changes regularly from point to point. To illustrate this 
 process, the following table is made out from the deviation card 
 given above, giving the readings from to 90, and from 230 to 
 270. The completion of this table is left as an exercise. 
 
AERIAL NAVIGATION. 
 
 TABLE. 
 
 41 
 
 Magnetic 
 course. 
 
 Devia- 
 tion. 
 
 10 
 
 1 W. 
 
 20 ' 
 
 2 W. 
 
 30 
 
 3W. 
 
 40 
 
 4W. 
 
 50 
 
 4 W. 
 
 60 
 
 3 W. 
 
 70 
 
 2 W. 
 
 80 
 
 2 W. 
 
 90 
 
 1W. 
 
 230 
 
 6E. 
 
 240 
 
 4E. 
 
 250 
 
 2E. 
 
 260 
 
 
 
 270 
 
 2W. 
 
 This form is being supplanted in the United States Air Service by 
 another which is purely visual and saves labor of calculation. It 
 consists of two concentric circles, marked off in degrees like the com- 
 pass card. The inner circle represents magnetic readings, the outer 
 circle compass readings, and lines are drawn in by the compass officer 
 connecting the two, to indicate the appropriate amount of deviation. 
 
 It is desirable, however, to have great facility in working out 
 problems from a deviation card. It is not necessary to interpolate 
 for angles which are not multiples of 10. The deviation corre- 
 sponding to these angles may be taken as the deviation correspond- 
 ing to the nearest multiple of 10. For example, using the table, 
 the deviation for 42 is taken as the deviation for 40 (4 W.) and 
 the deviation for 87 is taken as the deviation for 90 (1 W.), etc. 
 The card and table just given will be used in the following examples: 
 
 Example 1: The compass reading corresponding to magnetic 32 
 is 35. 
 
 Example 2: Corresponding to magnetic 235 we have compass 229. 
 
 It may also be assumed without large error that the deviation corre- 
 sponding to compass 50 is the same as for magnetic 50, etc. With 
 this assumption the table may be used as follows to pass from compass 
 to magnetic readings. 
 
42 AERIAL NAVIGATION. 
 
 Example 3: Corresponding to compass 232. is magnetic 233. 
 
 Example 4: Corresponding to compass 2(56 is magnetic 264. 
 
 Given variation 13 W. and the deviation card and table above: 
 
 Example 5: Find the compass readings corresponding to the true 
 reading 0, 340, 5, 350, 175. 
 
 Example 6: Find the true readings corresponding to the following 
 compass readings: 0, 10, 190, 350, 13. 
 
 Example 7: Given course 250, compass bearing 45, find true 
 bearing. 
 
 Example 8: Given course 54, compass bearing 72 , find true 
 bearing. 
 
 Example 9: Given course 232, compass bearing 21 , find true 
 bearing. 
 
AERIAL NAVIGATION. 
 
 PART II. 
 
 THE MAP. 
 
 INTRODUCTION. 
 
 In our study of aerial navigation so far, we have been concerned 
 primarily with the compass. This instrument helps us to find our 
 objective, once we know the track, but it can not determine the 
 track. 
 
 The map, on the other hand, not only helps us to stay on the track 
 as we go along, but shows us what track to take in order to arrive at a 
 desired point. The plan for a flight must be made from the map. 
 On the map the flight is taken in theory. The pilot with his plane, 
 engine, and compass turns this theory into practice, but he must have 
 exact knowledge of the course to be made good. If it were known 
 only in a general way that Bruges lies somewhere north of Ypres, 
 Bruges would have no fear of bombing raids. 
 
 Without maps, long-distance flying would be a hit-or-miss per- 
 formance of the worst sort. Every voyage would be a voyage of dis- 
 covery and there would be no such thing as proceeding in short 
 order to a point determined in advance unless, of course, one were 
 familiar with the route . Without maps the military value of aviation 
 would be little or nothing. 
 
 The chief characteristics of the map are as follows: 
 
 I. Points on the map represent points on the ground and vice 
 versa. 
 
 At once two problems are presented to the aviator: 
 
 (1) Given a point on the ground to locate it on the map. 
 
 (2) Given a point on the map to locate it on the ground. 
 
 If a point on the ground which we wish to study in its relation to 
 other points (to a battery of 155 's, say) is not on the map already, the 
 aviator must put it on the map. He has three means of doing this: 
 
 43 
 
44 AERIAL NAVIGATION. 
 
 (1) By marking his map. 1 
 
 (2) By making a rough sketch showing this new point in relation 
 to points already known. (Not common.) 
 
 (3) By taking a photograph. 
 
 The last is the best and most common means of putting points on 
 the map, but it can not be treated here as the subject is too large. 
 Since this is the case, we shall consider only the problem of finding 
 a point on the ground that is given on the map. This division of our 
 subject will be called LOCATION OF POINTS. 
 
 II. A map is drawn u to scale." Distances and dimensions on the 
 ground are reduced in a certain proportion as with building plans and 
 working drawings. It follows that map distances must be translated 
 into ground distances and vice versa according to the given propor- 
 tion. This gives the aviator two problems: 
 
 (1) Given a distance on the ground to find the corresponding 
 distance on the map. 
 
 (2) Given a distance on the map to find the corresponding distance 
 on the ground. 
 
 The first of these is more important when we are making a map; 
 the second when we are using a map already made. Therefore, the 
 second problem will be emphasized when we treat of SCALES. 
 
 III. It must be remembered that objects on the ground are shown 
 on the map as if viewed from directly above. Distance between two 
 points on the map means horizontal distance and not distance along 
 the slopes of the ground. So a plan of a gable roof represents the 
 horizontal distance between the eaves and not distance along the 
 roof from eaves to ridgepole and down the other side. 
 
 But how are elevations and depressions to be represented on a 
 map? Evidently they can not be given by distances because all 
 distances that can appear on the map are accounted for already as 
 horizontal distances. Therefore, irregularities of elevation (hills, 
 plateaus-; watercourses) are represented by symbols called CON- 
 TOURS, which show the elevation of certain points and lines above 
 mean sea level, and enable us from these to estimate the elevation 
 of other points. From contours we are able to tell whether a slope 
 is going up or down, whether it is gentle or steep, whether a certain 
 neighborhood is a plain or a rolling country or whatnot with respect 
 to elevation. 
 
 1 This is the same problem as fixing the position of the machine, Part I, page 24. 
 
AERIAL NAVIGATION. 45 
 
 IV. But there are many other objects on the ground besides ele- 
 vations and depressions which have to be represented, if at all, by 
 symbols. Map position shows where a thing is, but not what it is. 
 For military purposes it is convenient to have certain other CON- 
 VEN'f IONAL SIGNS, as well as contours. -. Thus we may represent 
 the forest of Villers-Cotterets by a green patch on the map; we may 
 surround Dickebiisch Lake by a blue line; we may represent 
 barbed-wire entanglements by XXXX; machine-gun emplacements 
 by M. G., and so on. 
 
 Orientation. When using a map in connection with the ground 
 which it represents, it is best to " orient" the map. This means to 
 place it "square with the world"; that is, so that any line on the 
 map which represents a certain direction on the ground is actually 
 pointing in that direction. The line most commonly used to orient 
 a map is the north and south line, either true or magnetic, although 
 any line may be utilized. One very common error made in orien- 
 tation is that of comparing true north on the map with magnetic 
 north on the ground, or vice versa. Care must be taken to compare 
 true north with true north only, and magnetic north with magnetic 
 north only, unless the proper correction has been made to work from 
 one to the other. Maps which have no north line marked upon them 
 may be assumed to be drawn with the direction of true north parallel 
 the side of the map and pointing toward the top. 
 
 The pilot usually orients his map by means of the bearing plate. 
 The bearing plate is set so that its zero mark coincides with the direc- 
 tion of compass north. Deviation of the compass is determined 
 from the deviation card according to the compass course of the ship. 
 The problem may then be stated: Given compass north; find the 
 compass bearing of true north 1 (or magnetic north). This has been 
 treated in Part I under the heading "Bearing plate." When the 
 compass bearing of true north is found, it is necessary only to set 
 the drift wires of the bearing plate in this direction and to make the 
 meridians on the map take the direction of the wires. 
 
 The four general divisions of our subject that have been indicated 
 above will be treated in the order scales, conventional signs, con- 
 tours, location of points, as follows: 
 
 1 For example, if the compass needle allowing for variation and deviation points 
 10 to the west of true north, then true north bears 10 to the east of compass north; 
 that is, the compass bearing of true north is 10. 
 
46 AERIAL NAVIGATION. 
 
 SCALES. 
 
 Every map should have in some form or other a scale or statement 
 of the proportion between distance on the map and distance on the 
 ground. A scale should be the first thing that the pilot lotfks for 
 as he starts to read a map. It may be indicated in three ways: 
 
 (1) By equation: 1 inch equals 3 miles; 1 mile equals 3 inches. 
 
 (2) By graphical representation: Laying off on a straight line dis- 
 tances that correspond to a certain number of miles or kilometers. 
 
 I 1 1 1 - I 
 
 Miles.. 01234 
 
 FIG. 1. 
 
 (3) By representative fraction (R. F.), for example, 1/200,000. 
 This means that a distance of 1 inch on the map represents a distance 
 of 200,000 inches on the ground. So 1/20,000 means that 1 inch on 
 the map stands for 20,000 inches on the ground. Evidently the 
 dimensions of an object on the second map are ten times as great 
 as on the first. 
 
 Relation between scales. The special advantage of the R. F. is that 
 it -is equally significant whether we are dealing with British maps 
 which speak of miles and inches or French maps, which speak of 
 kilometers and centimeters. It is often convenient, however, for the 
 aviator to think in terms of so many miles to an inch or so many inches 
 to a mile. If he is using a French map, these forms of the scale will 
 not appear and he will have to construct them. He may proceed 
 as follows: There are 63,360 inches in a mile. Therefore the fraction 
 1/63,360 stands for 1 inch to a mile or 1 mile to an inch. To solve 
 the problem in inches to a mile for a given representative fraction, 
 we must answer the question, "Will there be more or less than 1 inch 
 (to a mile), and how much? " Since 1 inch on the map corresponds 
 to 200,000 inches on the ground, the map will evidently have less 
 than 1 inch to a mile, and exactly 63,360 divided by 200,000 equals 
 0.32 inch to a mile. 
 
 By the same reasoning it appears that on this map there will be 
 more than 1 mile to an inch, and exactly 200,000 divided by 63,360 
 equals 3.16 miles to an inch. 
 
 Therefore, to determine the number of inches to a mile or miles to 
 an inch corresponding to a given representative fraction, we either 
 divide into 63,360 or divide by it according to the idea "more or 
 
AERIAL NAVIGATION. 47 
 
 less." As a check on the correctness of our work we may notice 
 that 3 miles to an inch is about 190,000 inches to an inch, proving at 
 a glance that we are not far out of the way. 
 
 If it is desired to lay off accurately the scale 0.32 inch to a mile 
 and our foot rule is graded to sixteenths, we may get a reasonable 
 degree of accuracy by using the scale of numbers 
 
 }=0.25 A=0.0625 
 
 J=0.125 ^-0.0313 
 
 from which it appears that 0.32 is about J plus -^ or -^ of an inch, 
 (Evidently 0.32 is more than 0.25 and less than 0.50. It is less than 
 0.25+0.125=0.375. It is about 0.25+0.0625=0.3125.) The error is 
 75/10,000 of an inch, which in this connection is small. This will 
 give as accurate a scale as a pilot will probably need, for short 
 distances. 
 
 For long distances the corresponding scale would be 3.2 inches 
 equals 10 miles. With a foot rule this might be laid off as 3 rg- inches 
 equals 10 miles, the error on the ground amounting to only 200 yards 
 or so in 10 miles, and in air work this error is considered small. For 
 still closer approximation, using thirty-seconds of an inch (taking 
 points midway between sixteenths) the error could be further re- 
 duced to about 1 mile in 1,000. 
 
 There is also a simple geometrical method for solving this problem, 
 but it will not be given here, since without good instruments it is 
 not as accurate as the arithmetical method and the arithmetic scale 
 if forgotten can be readily found through successive divisions by 2. 
 
 TIME SCALES. 
 
 (In the following it must be borne in mind that speed and m. p. h. 
 refer to ground speed and not air speed.) 
 
 We have seen that map scales show relations between distances on 
 the ground and distances on the map. It is also desirable for the 
 pilot to have a scale of map distances in terms of the time it takes 
 to fly them at different ground speeds. The value of tl^s scale is 
 that it enables the pilot to measure on his map the time it takes to 
 fly from point to point without computing the number of miles 
 traveled. If the time is known and the pilot has a supply of fuel 
 for a certain number of hours, the number of miles in the trip makes 
 no difference. 
 
 The time scale is constructed by choosing a convenient time unit, 
 for example, 10 minutes, and laying off the distances which may be 
 
48 AERIAL NAVIGATION. 
 
 traveled in this time at different ground speeds. Suppose the R. F. 
 of the map is 1/200,000. This amounts to -0.32 inch to the mile, or 
 3.2 inches for 10 miles, or 3.2 inches for 10 minutes at 60 m. p. h. 
 ground speed. At 70 m. p. h. ground speed we are going as fast as 
 before, and so for 10 minutes the map distance will be JX3.2=3f 
 inches (about) . At 80 m. p. h. ground speed we are going | as fast as 
 at 60 m. p. h, and the corresponding map distance for 10 minutes 
 will be 4J inches. At 90 m. p. h. ground speed the map distance 
 is 4.8 inches, and so on. The completed scale is on page 49. 
 
 It must be remembered that the length on the scale from zero to a 
 certain ground speed is the map distance traveled in 10 minutes at that 
 speed; for example, referring to the map of Paris, a plane going at 
 the rate of 70 m. p. h. ground speed could fly in 10 minutes from 
 Notre Dame, in Paris, to St. Germain, about 3| inches, regardless of 
 the number of miles traveled over the ground. 
 
 So in 20 minutes at the same ground speed 7J inches map distance 
 might be covered; for example, from Chateau-Thierry to Soissons. 
 
 To find the time required to fly from Paris to Soissons at 90 m. p. h. 
 ground speed, find the number of times that the distance from to 
 90 on the scale will be contained in the given map distance. This 
 number of times turns out to be 4. Therefore at 90 m. p. h. ground 
 speed, it will take about 4X10 minutes for the flight. 
 
 To fly from Paris to Meaux, a map distance of 8 inches at 90 m. p. h. 
 ground speed will take, applying the tune scale, about 2JX10 
 minutes, equals 23 minutes. 
 
 These examples may be worked out to whatever degree of accuracy 
 is required by the circumstances; for example, in the foregoing, 23 
 minutes would be a sufficient degree of accuracy. 
 
 On the time scale it will be found that 60 is twice as far from as 30 
 and that 120 is twice as far from as 60, etc. ; that is, the rate repre- 
 sented is proportional to the distance from on the scale. For this 
 reason interpolation may be easily applied; for example, 55 would 
 lie half way between 50 and 60, and so on. 
 
 If desiftd, any other convenient unit of time might be used 
 instead of 10 minutes; for example, 12 minutes. If the scale is 
 graduated for 10 minutes on one edge and for 12 minutes on the 
 other, it will be easy to compute the ground speed for any short 
 distance since any one of the numbers, 2, 3, 4, 5, 6 is contained 
 either in 10 or 12. For example, a pilot finds that he has covered a 
 certain map distance in 6 minutes. Using the 12-minute scale he 
 
o 
 
 PJ 
 
 o. 
 o> 
 
 8- 
 
 in 
 
 60 
 M/A/LfTIS 
 
 2.00, 
 
 60 
 
 50 
 
 <D 
 
 CM 
 
 N. 
 
 8 
 
 <b 
 QJ 
 
 J- 
 
 o: 
 
 % 
 
 V 
 
 Q) 
 Q> 
 
 .^ 
 
 ^ a* 
 
 &* 
 
 49 
 
50 AERIAL NAVIGATION. 
 
 finds that the corresponding distance on the scale shows the speed 
 of 65 m. p. h. It follows that his ground speed is 130 m. p. h. In 
 examples of this sort the idea "more or less" must be kept in mind; 
 for example, if the time is less to go a certain distance, the speed is 
 more, and so on. 
 Other examples similar to the above should be worked out. 
 
 METRIC SYSTEM. 
 
 An aviator should be familiar with the metric system, since this 
 system is used on French and Italian maps. Paragraph 2 of General 
 Orders No. 1, January 2, 1918, reads as follows : 
 
 "The metric system has been adopted* for use in France for all 
 firing data for artillery and machine guns, in the preparation of 
 operation orders, and in map construction. * * * Instruction 
 in the metric system will be given to all concerned * * *." 
 
 For quick and fairly accurate results the following relations suffice 
 to connect the metric system with the English : 
 
 1 centimeter =f inch. 
 5 centimeters =2 inches. 
 10 centimeters=4 inches. 
 1 meter =1 "long" yard. 
 100 yards =90 meters. 
 200 meters=220 yards. 
 1 kilometer=| 
 
 10 kilometers =6 miles. 
 10 miles=16 kilometers. 
 
 More exact relations are as follows: 
 
 1 inch=2.54 centimeters. 
 1 centimeter =0.4 inch. 
 1 yard =0.9 meter. 
 1 meter =1.1 yards. 
 1 mile=1.6 kilometers. 
 1 kilometer=0.62 mile. 
 
 A good way to familiarize one's self with the metric system is to 
 construct geometrical figures, such as circles, squares, etc., of known 
 dimensions in inches and then change the dimensions to centimeters. 
 Another way is to measure with a meter stick ordinary objects in a 
 room, such as desks, chairs, tables, etc. It is often useful also to 
 pace off a distance previously measure^ in meters. 
 
AERIAL NAVIGATION. 51 
 
 The following examples are given for practice on scales with 
 English and metric systems: 
 
 Examples. 
 
 (1) If a map is made on a scale of 6 inches to the mile, give the 
 R. F. of the map. 
 
 (2) Construct a graphical scale of miles for a map whose R. F. is 
 1/200,000. 
 
 (3) The distance between two towers on the map is 10 inches. If 
 the R. F. of the map is 1/200,000, what is the actual distance in 
 kilometers on the ground? 
 
 (4) Two points on the ground are 10.5 kilometers apart. What is 
 the distance between them in inches on a map whose R. F. is 
 1/100,000? 
 
 (5) Two points are 6 inches apart on a map whose R. F. is 1/40,000. 
 Give the distance on the ground in miles. 
 
 (6) (a) The scale of a map is 3 inches to the mile. Give its R. F. 
 (6) To what French map does it correspond? 
 
 (7) The distance between two trees is measured and found to be 
 500 yards; on the map they show to be 2 inches apart. What is the 
 R. F. of the map? 
 
 (8) If two points are 6.7 inches apart on a map whose R. F. is 
 1/100,000, find the distance in miles (kilometers). 
 
 (9) The scale of the map is 1/20,000. 2.7 inches on that map equal 
 how many miles on the ground? 
 
 (10) Express the scale 1/10,000 graphically in terms of yards. 
 
 (11) A map is 48 inches square. If the R. F. is 1/200,000, what is 
 the area of the country represented in square miles? 
 
 (12) Traveling at the rate of 150 m. p. h. ground speed, what would 
 be the map distance in inches for a 20-minute flight given a 10-minute 
 time scale and a 1/200,000 map? 
 
 (13) Traveling at the rate of 120 m. p. h. ground speed, what would 
 be the map distance in inches for a 20-minute flight and a 1/200,000 
 map? 
 
 (14) Two points on the ground are 10 kilometers apart. Find the 
 distance in inches on a 1/200,000 map. 
 
52 AERIAL NAVIGATION. 
 
 CONVENTIONAL SIGNS. 
 
 Conventional signs should fulfill two requirements: (1) They 
 should be as simple as possible; (2) they should suggest the objects 
 represented . 
 
 The number of these signs in use is large; a few of the most im- 
 portant ones appearing on military maps are presented here. Prac- 
 tice with the map should be given until the student is perfectly 
 familiar with them. 
 
 Standard abbreviations of letters or groups of letters are often used 
 in connection with conventional signs. No attempt will be made 
 to present these here, as the student will soon be accustomed to 
 those in use upon the maps with which he is working. 
 
 It should be remembered that the list of conventional signs given 
 below is general, and that any particular map must be studied care- 
 fully with a view to the signs which appear on that map. 
 
 CONTOURS. 
 
 The earth looks quite flat to an aviator at any considerable distance 
 above it. He is unable to tell whether it is sloping up or down or 
 whether he is passing over a hill or a valley or le\ ; el country. For 
 this reason the contour lines on his map are of special value. 
 
 Contours are lines obtained by cutting the earth's surface by 
 horizontal planes at certain distances from each other. These 
 distances are taken at convenience. The contours are marked on 
 the map to show their distances above a certain plane of reference 
 (datum) usually taken as mean sea level. A system of contours 
 may be illustrated by considering an island in the center of a body 
 of water. (See figs. 3 and 4.) The shore line is a contour. Imagine 
 the surface of the water to be raised a distance of 10 feet. The 
 shore line thus formed is a contour whose elevation is 10 feet above 
 the first. Successive contours representing equal increases in ele- 
 vation can be secured in a similar manner. These contours when 
 projected upon a single plane represent a contour map. (See figs. 
 5 and 6.) The vertical distance between the successive elevations 
 is known as the contour or vertical interval (abbreviated to V. I.). 
 The distance measured on the map between two successive contours 
 is called the map distance. 
 
CONVENTIONAL SIGNS 
 BRITISH 
 
 J \J U W V/ I 
 
 
 j i 
 
 Infantry, moving in column of route 
 
 L^L 
 
 Any trench organized for fire 
 
 L^-T- 
 
 Cavalry, moving in column of route 
 
 
 Approximate line, reported by 
 
 zr -= 
 
 Artillery, moving in column of route 
 
 . - 
 
 observers and not yet confirmed 
 
 [J] 
 
 Post 
 
 
 by photographs 
 
 J* 
 
 Patrol 
 
 X XXXX 
 
 Wire entanglements 
 
 CJ lH 1 l|l 
 
 Holding line in action 
 
 ^SiSi) 
 
 Ground cut up by artillery fire 
 
 oooo 
 
 Gun emplacements 
 
 
 
 O 
 
 Battery of guns, inactive 
 
 _,_.._._,_ 
 
 Enemy tracks 
 Buried pipe line or cable 
 
 V_y 
 
 O O O 
 
 Single guns, inactive 
 
 
 Air line 
 
 T 
 
 Battery of howitzers, active 
 
 A 
 
 Supply depot 
 
 *4 
 
 Single howitzers, active 
 
 
 
 Observation post 
 
 At ' 
 
 Doubtful battery, active 
 
 g 
 
 Dugout 
 
 ^^ 
 
 Doubtful guns or howitzers, active 
 
 9 
 
 Earthwork 
 
 ^^ 
 
 Hedge, fence, or ditch 
 
 Q* orM.G. 
 
 Machine gun emplacement 
 
 ^^^D^ 
 
 Ditch, permanent water 
 
 orT.M. 
 
 Trench mortar emplacement 
 
 "V ^ - 
 
 3= =o= ^ 
 
 Woods 
 
 LorLP. 
 
 [ istening post 
 
 O 
 
 
 * 
 
 Mine crater, unfortified 
 
 
 
 
 
 Orchard 
 
 
 
 "== = = "sJ^'rs 11 
 
 Brushwood or undergrowth 
 
 
 Mine crater, fortified 
 
 
 
 
 
 1 1 1 M 1 1 n rt^T 
 
 Faults in chalk country 
 
 O ooo 
 
 Organized shell holes 
 
 
 Embankment 
 
 m-rrmnrrrr 
 
 0r 
 
 Anti-aircraft gun 
 
 4- 
 
 Cutting 
 
 
 Hutments 
 
 O 
 
 Church 
 
 ."" 
 
 Aerodrome 
 
 
 Wind mil! 
 
 fn? 1 
 
 Airship shed 
 
 -0- 
 
 Water mill 
 
 f 
 
 Balloon 
 
 ^^r 
 ^/frTTft Y/////)( 
 
 Houses, standing 
 Houses, ruined 
 
 A 
 
 Barge 
 
 F e"Cd Unienced 
 
 Roads, 1st class 
 Roads, 2d class 
 
 
 
 p 
 
 Fire 
 
 
 Roads 3d class 
 
 
 
 Railhead 
 
 . 
 
 Railways, double 
 
 r"H- 
 
 Mechanical transport, moving 
 
 ' t^ 
 
 Railways, single 
 
 Pg-v 
 
 Mechanical transport, stationary 
 
 , , ( 
 
 Narrow gage railway 
 Trench railway 
 
 .| j * 
 
 Horse transport, moving 
 
 .^erry ^^ 
 
 Ferry 
 
 | i 
 
 Horse transport, stationary 
 
 ^^^ 
 
 Railway over river 
 Marsh 
 
CONVENTIONAL SIGNS 
 FRENCH 
 
 German 
 
 
 I:;;;;; National road 
 
 loopholes *$!* 
 
 
 R ep j rtmenta , . . , . h 
 
 <VV^Kfe! 
 
 
 D'rt d 
 
 >|l| ^E|O 7> 
 
 
 
 jPSW 
 
 Trenches 
 
 Path, cleared line 
 -S3 eS Standard gage single track R.R. 
 
 ssJornsJ- 
 
 
 **-~-*-CT^ Narrow gage R. R. 
 
 
 Trenches, from report 
 
 8 ^I>r' d6e 
 
 ^W^B^? Large stream 
 
 
 
 Trenches, abandoned 
 
 K ^ -)f- Small stream 
 
 Isolated ' ' I \ 
 
 Batteries 
 
 11 1 ' Canal 
 
 painP -*-*--* 1 
 
 
 Towpath 
 
 
 
 Anti-aircraft gun 
 
 P nd 
 
 Camp. 
 
 
 o Spring 
 
 ^^ 
 
 Camps, Wa g"P arks 
 
 Well 
 
 s 
 
 Munition depots 
 
 Err: UKa^ Inundated land 
 
 J~- rv -^^v 
 
 
 ^S"*-^r- \ Wall 
 
 
 Works 
 
 
 C V^vrx~X 
 
 
 o- -0----0--- o Hedge 
 
 xxxxxx 
 
 Wire entanglements 
 
 r T Iron wire fence 
 
 m/mmm 
 
 Abatis 
 
 i i i i i i i I i i i i i i \ I Earth embankment or fill 
 
 IZIadZb 
 
 Shelters 
 
 ^^/2^ 
 
 oob. ap.c 
 
 Screened gun pits 
 Observation, post commanders 
 
 ^^^m Vi " age 
 
 o 
 
 Shell or mine craters 
 
 Steeple 
 + i Wayside cross 
 
 AM &B 
 
 Machine guns, bombthrowers 
 
 6 <) Chapel 
 
 XCR \ 
 
 Revolving cannon 
 
 l*tt| Cemetery 
 
 
 
 Standard gage, R. R. 
 Narrow gage, R. R. 
 
 {J Water mill 
 
 French 
 
 
 O Smokestack 
 
 - .. ,,jni.^ 
 
 Advanced line 
 
 W'/A Vines 
 
 m 
 
 Infantry 
 
 ^jjitil [''''.| Gardens and orchards 
 
 & 
 
 Cavalry squadron 
 
 ^?^;S/?6-:^ Woods 
 
 r 
 
 
 |^ A ^/j Fir or pine thicket 
 
 B 
 
 Cavalry regiment 
 
 & ;:^v '-' Brush 
 
 m 
 
 Field battery, occupied 
 
 o^o o o o | so)ated trees 
 
 ti 
 
 Field battery, prepared 
 
 -i^~> ^r*. Marsh or swamp 
 
 ICXDl 
 
 Aero squadron 
 
 /^^[iej^n Contours and elevations 
 
 ICXDj 
 
 Aero park 
 
 >* 
 
 /^? 
 
 
 >^!3 O Sand dunes 
 
 vJ 
 
 Balloon 
 
 I^<7\ 
 
 
 
 
 ^^ Quarry 
 
 P ^ 
 
 Automobile service 
 
 ,IM..,,,mi..-rr g^gp s | p es 
 
AERIAL NAVIGATION. 
 
 
 
 53 
 
 FIG. 3. 
 
 FIG. 4. 
 
 FIG. 5. 
 
54 AERIAL NAVIGATION. 
 
 In general, a contour is quite irregular in shape although every 
 point of it is at the same distance above mean sea level. To make 
 the matter clearer, let us illustrate by a square pyramid placed on 
 a table. Let the surface of the table be the datum. Let the vertical 
 interval, V. I., be taken as 1 inch. Imagine the pyramid cut by a 
 horizontal plane 1 inch above the table top. The line of intersec- 
 
 FIG. 6. 
 
 tion (contour) is a square, every point of which is 1 inch above the 
 table. This square might be called "the 1-inch contour." If we 
 pass another plane through the pyramid 2 inches above the table, 
 we have a smaller square every point of which is 2 inches above the 
 table. This square is "the 2-inch contour." 
 
 FIG. 7. 
 
 If we replace the pyramid by a circular cone and pass horizontal 
 planes as before, the contours will be circles. If we replace the 
 cone by a triangular pyramid the contours will be triangles, and so 
 on. 
 
 By means of contours on a map it is possible to form a fair idea of 
 the general appearance of ground we have never seen. For example, 
 
AERIAL NAVIGATION. 
 
 55 
 
 we can tell that one object must be higher than another because it 
 is on a higher contour. We can tell that a slope is steep because the 
 contours are close together, or that it is gentle because the contours 
 are far apart, or that there is very little change in elevation on the 
 ground because the contours are not a prominent feature of the map. 
 
 So far we have been considering elevations. Contours serve 
 equally well to show depressions. For a downward slope proceed- 
 ing in a certain direction the elevation of the contours becomes less 
 and less as we go along. For example, if the vertical interval is 10 
 meters, the contours along the slope might be numbered 150, 140, 
 130, etc., while evidently for an upward slope they would be num- 
 bered in the "reverse order. 
 
 If the contours are not numbered at the place on the map which 
 we are studying, it may be possible to determine whether the ground 
 is sloping up or down by the appearance of rivers or streams, which 
 branch toward their sources and not in the direction they are flowing. 
 
 
 FIG. 8. 
 
 It follows that the point A in figure 8 is higher than point B, 
 although the contours are not marked. 
 
 The more irregular the country which we wish to represent, the 
 closer together should be the contours; that is, the smaller should 
 be the contour interval in order that small irregularities may be 
 shown. The scale and size of the map are also factors of importance 
 in determining what contour interval shall be taken. 
 
 The following facts about contours should be well noted: 
 
 (1) Contours are continuous closed lines (for example the circles, 
 squares, and triangles referred to above). If a contour does not close 
 upon itself within the limits of the map, it means that the map is not 
 large enough to show the entire contour. 
 
56 
 
 AERIAL NAVIGATION. 
 
 (2) All points on a contour are at the same elevation, because the 
 contour lies in a horizontal plane . 
 
 (3) Contour lines do not branch. A branch or spur projecting 
 from a contour would indicate a ridge the top of which is an abso- 
 lutely level " knife-edge." This, of course, is never found in 
 nature. 
 
 FIG. 
 
 (4) Contours of different elevations do not cross each other except 
 in the case of an overhanging cliff, and this case is so rare that any 
 case of crossed contours may be considered an error. Contours at 
 different elevations may approach each other closely, and in fact 
 may appear as one line in the case ot a vertical cliff. 
 
 / $/0/>e 
 
 FIG. 10. 
 
 (5) When the contour interval is constant (as it is on most maps) 
 the spacing of the contour lines indicates the degree of the slope; 
 that is, the nearer together the contours, the steeper the slope; 
 the farther apart, the gentler the slope; if the contour lines are 
 equally distant the slope is regular. 
 
AERIAL NAVIGATION. 
 
 57 
 
 (6) Contours are usually drawn as brown lines. 
 
 (7) Dotted contours are sometimes inserted at odd elevations to 
 show special features of the country; for instance, a 33-foot contour 
 dotted might be inserted between the 30-foot and the 40-foot contour. 
 
 FIG. 11. 
 
 (8) It is customary to break contours when crossing roads, rail- 
 roads, etc., continuing them on the other side. 
 
 
 FIG. 12. 
 Examples. 
 
 The following examples are given to illustrate the principles of 
 conventional signs and contours: 
 
 (1) Illustrate by means of 10-foot contours: (a) A hill of 75 feet 
 elevation, rising for the first 30 feet gradually and being very steep 
 for the last 45 feet; (b) a hill of the same elevation rising steeply for 
 the first 30 feet, gently the last 45 feet; indicate a stream on the last 
 hill. 
 
 (2) Would you expect to find a small contour interval or a large 
 contour interval on a map of a very rugged country? Give your 
 reasons.- 
 
58 AERIAL NAVIGATION. 
 
 (3) Represent the following by contour sketches: Valley, hill, 
 depression, ridge, steep slope, flat slope, gorge. 
 
 (4) Make a sketch showing two streams joining, a ridge between the 
 streams and rising from them, steep ground on one side, gently 
 sloping ground on the other. 
 
 (5) Using the conventional signs of the map of Belgium, draw a 
 map of a southward sloping plain 5 kilometers square, maximum 
 elevation 20 meters, with an elongated ridge rising 30 meters above 
 its north edge. A stream flows down the south slope to the sea. A 
 single-track railroad follows the south base of ridge and crosses under 
 a first-class road along which are houses, a church, windmill, and 
 several trees. A footpath leads from a house to a depression near by. 
 
 (6) Imagine you are standing at the intersection of the roads shown 
 at point 21395-29410, map of Belgium. Describe briefly the topog- 
 raphy of the surrounding country within a circle of radius 2 kilo- 
 meters with your position as the center, the description to be based 
 upon the contours and conventional signs shown within the territory 
 mentioned. Which, if any parts of this country would not be visible 
 from your position, and why? 
 
 (7) Imagine you are walking down the Hazebeek stream from 
 point 21350^28840 to its junction with an unnamed stream at point 
 21522-29130. Describe what you can see on each side as you walk, 
 judging from the contours and conventional signs on the map. 
 
 (8) Imagine you are riding on the rai'road from Walkrantz station, 
 point 22285-29575, to the depot at point 22323-29160. Describe the 
 country within view on each side as you ride along, judging from 
 the contours and conventional signs on the map. 
 
 (9) Imagine you are flying in a straight line from the town of 
 Dickebusch to the town of Elverdinghe. Describe the country 
 over which you fly, judging from the conventional signs and contours 
 as shown on the map. 
 
 LOCATION OF POINTS. 
 
 It is not only in long flights that accurate navigation is necessary. 
 Short flights often require special precision because of the nature of 
 the objective. A machine-gun emplacement or an ammunition 
 dump carefully camouflaged is invisible from the air unless the 
 .aviator knows in advance exactly where to look for it. This precise 
 knowledge is furnished him on maps drawn to a larger scale than 
 those used for cross-country flights, bombing raids, and the like. 
 
AERIAL NAVIGATION. 
 
 But no matter what map is used the principle of locating a point is 
 the same. It consists of inclosing the point first, within a large 
 square designated by a number or a letter; then (British system) 
 within a smaller square inclosed by the first, and so on. Finally 
 there comes a time when this method of inclosure within squares 
 has been carried as far as it is practical. The British use three 
 inclosing squares; the French only one. 
 
 COORDINATES. 
 
 The last square, however, be it large or small, represents an area 
 and not a point. A point is fixed by its relation to the western and 
 southern boundaries of the square. Perpendicular distances from 
 these boundaries will fix the point exactly. 
 
 N 
 
 
 
 M 
 
 FIG. 13. 
 
 Suppose, for example, that the square given in the figure is 10 
 units on a side and that ON gives the direction of north. The point 
 A is 3 units to the east of the western boundary and 5 units to the 
 north of the southern boundary. These distances are called the 
 ' coordinates of the point A. 
 
 Instead of fixing the position of the point by distances from the 
 boundaries, we may fix it by distances along the boundaries measured 
 from the southwest corner of the square as a point of reference. For 
 example, the point A might be fixed by (1) the distance along the 
 southern boundary from O to a point M directly south of A (in this 
 case 3 units), and (2) the distance from M to A (equal to the distance 
 along the western boundary from to a point directly west of A, 
 in this case 5 units). 
 
60 
 
 AERIAL NAVIGATION. 
 
 When stating these distances it has become conventional to state 
 first the distance along the southern boundary (from the western 
 boundary) and to state second the distance along the western bound- 
 ary (from the southern boundary), just as in geometry we always 
 state the x coordinate first and the y coordinate second when locating 
 a point. 
 
 Exercises. 
 
 N 
 
 FIG. 14. 
 
 (1) Give the "pin-point" location of the points A, B, C, D, E, 
 assuming the same square as given above. 
 
 FIG. 15. 
 
 (2) Without changing the position of the page "pin-point" F, G, 
 H, I, K. 
 
 (3) Drawing a certain square and taking points O and N as above, 
 locate the points whose coordinates are 5-5, 3-3, 0-0, 6-4, 9-2, 1-9. 
 
 It is conventional never to use the coordinate 10 because a per- 
 pendicular distance of 10 from the boundary of one square carries 
 us to the boundary of another square. For example, the northeast 
 
AERIAL NAVIGATION. 
 
 61 
 
 corner of a given square would not be located as 10-10 with reference 
 to that square, but as 0-0 with reference to an adjacent square 
 lying northeast of the first. 
 
 BRITISH MAPS. 
 
 Let us take the ordnance map of Belgium, 1/20,000 as an example 
 of British maps. This map, which is part of a system of maps, 
 represents a section 13,500 yards in width by 11,000 yards in height. 
 For convenience in locating points the maps in the system are 
 divided into a series of squares, the first row being lettered A, B, C, 
 D, E, F; the second row being lettered G, H, I, J, K, L, with G under 
 A, II under B, etc. On this map only the squares A, B, G, H are 
 found. On the adjoining map to the east we should find square 
 C matching up with B and I with H. 
 
 FIG. 16. 
 
 Each lettered square is subdivided into 30 or 36 smaller squares. 
 Always there are six squares from west to east and five or six squares 
 from north to south. 1 The large squares lettered A, B, C, etc., are 
 6,000 yards wide and 5,000 or 6,000 yards high. The smaller squares 
 which make up the large squares are numbered from 1 to 30 or 36 
 (fig. 17). Each small square is 1,000 yards in width and in height. 
 These numbered squares are divided into four minor squares 
 whose sides measure 500 yards. These minor squares are considered 
 as lettered a, b, c, d, but only squares numbered 6 are actually so 
 lettered, to avoid unnecessary confusion on the map. 
 
 1 In converting the French and Belgian maps, laid out according to the metric 
 measurements, to the English system of map squaring in yards, etc., the grid lines 
 do not coincide, and this discrepancy in the English map is compensated for by 
 making some lettered squares contain 30 squares and others 36. 
 
62 
 
 AERIAL NAVIGATION. 
 
 To locate a point within a small square, consider the sides divided 
 into 10 parts (fig. 18) and define the point by taking so many tenths 
 from west to east along the southern side first, and then so many 
 tenths from south to north, the southwest corner always being taken 
 as the origin. If square c belongs to square 14 in big lettered square 
 H (fig. 18), then the designated points would be located as follows 
 
 J atH!4c60. 
 K at H14d05. 
 L at H14c05. 
 NatH14cOO. 
 R at H14c67. 
 
 19- 
 
 -2J5- 
 
 .3-. 
 
 --2-1- 
 
 -7- 
 
 T30- 
 
 b- 
 
 -3f. 5v- 
 
 -3-0 
 
 T 
 
 FIG. 17. 
 
 It will be noted that a point is not designated as 10, since 10 is 
 the of the next square. If a point is on the upper horizontal line of 
 the square, it is zero of the square above, and if the point occurs on 
 the right line of the square it is zero of the square to the right. Thus 
 the point Z would be located as H14a40, Q would be H14bOO, and 
 K would be H14d05. Since each small square represents 500 yards, 
 more accurate locations may sometimes be desired , and in such cases 
 the sides of the small lettered squares may, in imagination, be 
 divided into 100 parts instead of 10 parts. This would necessitate 
 the use of four figures instead of two as before. Thus point G would 
 be located at H14c3565 and X would be located at H14c0847, de- 
 noting 08 parts east and 47 parts north of origin. Use 0, but not 10; 
 use either two or four figures, but do not use fractions, as 8J, 4J, etc. 
 
AERIAL NAVIGATION. 
 
 63 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 R 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 !_ 
 
 
 
 
 f 
 
 * 
 
 
 
 
 
 
 
 * 
 
 
 
 V 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ,N 
 
 
 
 
 
 
 J 
 
 
 
 
 FIG. 18. 
 FRENCH MAPS. 
 
 The method of locating a point on a French military map is by ref- 
 erence to grid lines, which are 1 kilometer apart each way. These 
 lines are approximately N.-S. and E.-W., though not exactly so. 
 They are designated by numbers reading from west to east and from 
 south to north, as in the following figure. 
 
 C. 
 
 FIG. 19. 
 
 Assuming each of these squares divided into 10 spaces from west to 
 east and 10 spaces from south to north, the point A, figure 19, would 
 be designated as 2165-2925, point B as 2173-2931, and point C as 
 2178-2904. 
 
 Under certain circumstances there is no confusion caused by drop- 
 ping the first two figures, making the location of point A read 65-25, 
 point B 73-31, and point C 78-04. It must be remembered, however, 
 if the first two numerals are dropped, that every 10 kilometers north, 
 south, east, and west, there will be points designated by the same 
 numbers. Whenever there is danger of confusion three figures are 
 used, as 165-925. 
 
 In actual work on the front the lines of the grid are given letter 
 designations, which may be changed from week to week. Point A 
 
64 AERIAL NAVIGATION. 
 
 might be called U5-S5 one week and Q5-K5 the following week. 
 In this way the enemy is kept from knowing the zone to which 
 wireless messages may refer. Various keys of letters are in use, and 
 from time to time orders are- issued substituting one for another. 
 In using this letter system repetition of the same letter would occur 
 every 25 kilometers along the whole front (the number of letters in 
 the French alphabet). 
 
 Exercises. 
 
 The following exercises are given to illustrate the practical use of 
 compass and map: 
 
 Example 1: Fly from the church in Elverdinghe to the church in 
 Boesinghe, to the church in Brielen, and back to the starting point. 
 Make a diagram of the course, giving the magnetic bearings and the 
 names of the places with the pin-point location under them. Let 
 an arrow indicate the direction of each flight. 
 
 Example 2: Fly from the church in Ypres to the church in Voor- 
 mezeele, to the church in Dickebusch, to the church in Vlamertinghe, 
 and back to starting point. This will make a four-sided diagram. 
 State the magnetic bearing of each line, give the pin-point location 
 of the corners of the course under their names, and estimate the 
 length of each course in kilometers. 
 
 Example 3: Fly from Goed Moet Mill near Ouderdom to the church 
 in Reninghelst, to the lower church in Poperinghe, to the crossroads 
 in Busseboom, to the church in Vlamertinghe, and back to starting 
 point. Indicate on the diagram the magnetic bearing of each line, 
 the name and pin-point location of each corner of the course, and 
 the length of each course in kilometers. 
 
 Example 4: From your aerodrome at 2175-2885 course 45 (mag. 
 bearing) fly to a point 4.5 kilometers away. Give pin-point of the 
 end of the course. 
 
 Example 5: From your aerodrome at 2175-2885 fly 3.5 kilometers 
 course 60 (mag. bearing), then 4 kilometers course 300, then back 
 to starting point. What is the length and magnetic bearing of the 
 last course? Pin-point the other two corners of the course. 
 
 Example 6: From church in Reninghelst course 10 33 X fly for 
 a distance of 3.5 kilometers and from there fly to churcl} in Vlamer- 
 tinghe. From that point fly back to starting point. Make diagram 
 showing all magnetic bearings, pin-point corners of course to five 
 places, let arrows indicate direction of flight, and give distance in 
 kilometers from corner to corner of course. 
 
 o 
 
I M UOC I 
 
 
 
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 1932 
 
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 id 
 
 1947