Map reading and topographical sketching

Preface

In this book the author has attempted to record for the benefit of others something of the results of thirteen years of experience in the practice and teaching of topographical surveying and sketching.

There is no short cut to excellence in topographical work.

Good maps result from the patient and careful labor of men

thoroughly instructed in the means and methods of topographical

representation.

West Point, New York, October, 1918

Contents

Page PREFACE v

AUTHORIZED ABBREVIATIONS xi

CHAPTER II.— Map Reading. ^^Scales of Maps — Reading Scales 4

Scales of Maps — Reading Scales — Methods of Stating Scales on Maps — Comparison of Methods of Stating Scales — Construction of Graphical Reading Scales — Examples — Rules for the Construction of Reading Scales — Problems.

CHAPTER III.— Map Reading (Continued)

j/Scaling Distances on Maps 14

Methods of Scaling Distances — Straight Lines — Meandering Lines — Accuracy of Distances Scaled from Maps — Measurement of Distances along Roads — Problems — Other Exercises — -Measurement of Artillery and Infantry Ranges — Map Positions of Points on the Ground — Triangulation Points — Points along Roads — Interior Points.

CHAPTER IV.— Map Reading (Continued). (Working Scales 22

Measurement of Distances in Surveying and Sketching — Determination of Length of Stride — Determination of the Rate of a Horse — Construction of Working Scales — Problems — Problems Involving Erroneous Scales — Example — Problems.

CHAPTER V.— Map Reading (Continued). I/CONVENTIONAL SlGNS 29

Conventional Signs on Topographical Maps — Special Military Symbols — Color Conventions — Relation of Conventional Signs to Map Scales — Familiarity with Conventional Signs — Exercises.

viii CONTENTS

Page CHAPTER VI.— Map Reading (Continued).

" Representation in Relief 45

Methods of Representing Ground Forms — Hachures — Contours — Contours on the Ground — Contour Lines on the Map — Datum Level — Vertical Interval between Contours — Methods of Stating Slopes — Relation between Slope and Distance between Contours — Relation between V.I. and Map Distance between Contours — Construction of Slope Scales — Examples — Problems in Construction of Slope Scales.

CHAPTER VII— Map Reading (Continued). ^Contours (Continued) 57

Forms of Contours — Valley Contours — Spur and Ridge Contours — Summit Contours — Col or Saddle Contours — Representation of Slopes by Contours — Uniform Slopes — Concave Slopes — Convex Slopes — Exercises — Models and Sand Box — Contour Problems — Construction of Profiles — Problems — Visibility — Visibility Problems.

CHAPTER VIII.— Map Reading (Continued). Map Reference 71

Designation of Points on Maps — Map Sheets — Map Reference — Reference Lines — Designation of Map Sheets — Sheet System of Reference — Location of Points in Grid Squares.

CHAPTER IX.— Map Reading (Continued). Directions and Positions on Maps

u Orientation 77

Direction — Determination of Direction — The Magnetic Needle — Approximate North by Polaris — Approximate North by the Sun — Orientation — Orienting a Map by Compass — Orienting a Map by Identified Points — Location of Points on the Map — General Accuracy of Maps — Representation in Plan and in Elevation — Identification of Points on the Ground— Finding Your Own Location on the Map — Relation of Map Scale to Detail — Horizontal Detail — Vertical Detail — Use of Compass with Map — Compass Bearings — Marching by Compass.

CONTENTS ix

Page CHAPTER X.— Topographical Mapping.

- Instruments and Methods 91

Mapping Methods — Standard Sketching Equipment — Sketching Board and Tripod — Alidade — Clinometer — Accessories — Improvised Sketching Equipment — Using the Standard Sketching Equipment — Sketching Paper — Assembling the Sketching Board — Carrying the Sketching Board — Setting up the Sketching Board — Orienting the Sketching Board — Alidade — First Use — Second Use — Clinometer — Slope Board.

CHAPTER XI. — Topographical Mapping (Continued). .^Traversing — Selection of Control Points — Contour Problems 105

Traversing with the Sketching Board — Location by Resection — Contour Problems.

CHAPTER XII.— Topographical Mapping (Continued). •'Sketching from a Located Point 115

Selection of Ground for Practice — Scale and Vertical Interval — Control Traverse — Analyzing Ground Forms— Specific Example — Measurements from the Point — Checking Results — The Level of the Eye — Sketching by Estimation — Flat Hill-tops — Valleys — Hillsides.

CHAPTER XIII.— Topographical Mapping (Continued). ^Estimation of Distances, Mounted Sketching

Etc. Lettering 122

Estimation of Distances — Speed in Sketching — Mounted Sketching — Trench Sketches — Lettering on Sketches — Alphabets — Hints for Practice.

CHAPTER XIV.^Fanoramic Sketching 131

Purpose — Perspective — Crest Lines — Distance Effect — Conventions — Sketching Pad — Practice in Panoramic Sketching — Making the Sketch.

AUTHORIZED ABBREVIATIONS

A.

Arroyo.

L.S.S.

Life Saving Station abut.

Abutment,

L.H.

Light House.

Ar.

Arch.

Long.

Longitude.

b.

Brick.

Mt.

Mountain.

B.S.

Blacksmith Shop.

Mts.

Mountains.

bot.

Bottom.

N.

North.

Br.

Branch.

n.f.

Not Fordable.

br.

Bridge.

P-

Pier.

C.

Cape.

pk.

Plank.

cem.

Cemetery.

P.O.

Post Office.

con.

Concrete.

Pt,

Point.

cov.

Covered.

q.p.

Queen-post,

Cr.

Creek.

R.

River.

cul.

Culvert.

R.H.

Roundhouse.

D.S.

Drug Store.

R.R.

Railroad.

E.

East.

S.

South.

Est.

Estuary.

s.

Steel.

f.

Fordable.

S.H.

School House.

Ft,

Fort.

S.M.

Saw Mill.

G.S.

General Store.

Sta.

Station.

gir.

Girder.

St.

Stone.

G.M.

Grist Mill.

str.

Stream.

i.

Iron.

T.G.

Toll Gate.

I. Island

Tres.

Trestle.

Jc.

Junction.

tr.

Truss.

k.p.

King Post.

W.T.

Water Tank.

L.

Lake.

WW.

Water Works. ;.

Lat.

Latitude.

W.

West.

Ldg.

Landing.

w.

Wood.

AND

TOPOGRAPHICAL SKETCHING

Chapter I Introductory

Map reading and topographical sketching are essential tools of the military profession. Topography has an important influence over every military operation. Marches and tactical movements of troops, are planned on maps, and the orders for military operations must in general be based upon some specific map. Such orders can be understood and intelligently carried out only by reference to an identical map. Thus throughout the entire chain of command in the military service a thorough understanding of maps is required.

Since topography is a governing consideration in military operations, it follows that topographical information which is unimportant in the civil uses of maps may be of the utmost importance for military purposes.

A military map is a map showing the topographical information which is important from a military point of view. Much of this detail is temporary in character, such as information concerning annual crops, details as to the character and condition of roads and bridges, etc., and therefore not shown on ordinary topographical maps. Further, the minute detail, such as the smaller irregularities of the ground, fences, cuts and fills, etc., important from a military standpoint, can be shown only on maps of comparatively large scale.

Minute. and temporary topographical detail means high first cost of survey and frequent revision, hence satisfactory military maps of any except possibly a very few important areas will not be available at the outbreak of the war. Practically all nations have completed or are working on general topographical maps of their territory. These are mainly for civil uses, and of too small a scale to be satisfactory for military purposes. The general topographical map of the United States is being prepared by the U. S. Geological Survey, and is on a scale of about one inch to one mile. It is fairly representative of the general character of maps available at the outbreak of the war, or in operations where the forces are shifting position rapidly.

But modern experience shows that war has a tendency to settle down into a series of protracted struggles more or less stationary in character. When such a situation arises, time becomes available for the expansion of the scale and detail of the maps of the areas involved. Furthermore, the character of the operations resulting from such a situation demands the use of maps in great detail and of a high degree of accuracy. Military forces may therefore be called upon to expand the scale of existing maps or even to create new maps for their own use during active operations.

Thus there is required in the military profession not only the ability to read maps, but also the ability to make them. The ability to read maps must be exercised by all grades down to include the non-commissioned officer. The bulk of the work of making maps will fall upon those specially trained and organized for this purpose. But every non-commissioned officer and junior officer should be able to make a sketch which will show accurately the detail of his own surroundings.

INTRODUCTORY 3

Study and practice will give the ability to interpret in a purely mechanical way the topographical symbols on a map. But only by learning to make maps can be acquired that intimate understanding necessary to enable one to interpret and evaluate the topographical information embodied in a map. One who has had experience in topographical work in the field will know from the map where the topographer has been and where he has not been; will know where the map is accurate and where only approximate; will know how much generalization and inaccuracy exist even in the best topographical maps; will know how much the generalization and inaccuracy are affected by the scale of the field work; and will be able to recognize by the topographical " expression " of a map the work of a competent topographer and equally unerringly the work of an incompetent one.

The ability to read maps does not require an extensive course in topographical surveying, but it does require the study of topographical features on the ground itself, and practice in the representation of these features with the degree of accuracy and detail possible on various scales. Such practical work can be carried out satisfactorily with comparatively crude equipment, because the faculty to be cultivated is that of representing the topographical features about a given point. The more or less mechanical manipulation of instruments by which a point is located is of much less importance.

CHAPTER II Scales of Map^ — Reading Scales

There are two essentially distinct elements in the art of reading a map:

1. The ability to interpret in a mechanical way the information to

be found on a map.

2. The ability to weigh the topographical evidence given by a map.

Mechanical interpretation of the information recorded on a map requires familiarity with the scales of maps; familiarity with all of the conventional topographic symbols used in recording data on maps; and familiarity with the conventional methods employed in representing the form of the surface. This knowledge of map reading can be acquired by indoor theoretical work, preferably supplemented by study of models in connection with maps as an aid to visualization and clear comprehension of the ground forms represented.

To be able to weigh the topographical evidence given by a map, practical experience in the work of representing ground on a map is necessary. Only by work on the ground will it be thoroughly understood how utterly impossible it is to locate by measurement every feature shown on a map, and how much of the data even on the best of topographical maps rests upon the estimate of the topographer. Even in the largest scale maps the representation is still very small compared to the area represented. The difficulties, generalizations, and approximations of topographical representation can be thoroughly appreciated only by one who has familiarized himself with the methods used in making maps, and has actually attempted in practice to represent ground on paper. In this practice, a sharp distinction will be encountered in the accuracy of representation in plan as compared to that of the representation of ground forms.

Before attempting the representation of ground on paper, however, familiarity with the conventional methods of representation is necessary. This portion of the subject, which covers also the mechanical element of map reading, will accordingly be discussed first.

Scales of Maps

One of the most frequent uses of a map is to determine the distance between points on the ground represented. In order to furnish this information, distances between points on the map must bear a constant relation to the distances between the same points on the ground. This relation of map distance to ground distance is known as the scale of the map. The term has exactly the same significance as in all other drawings.*

It is well to emphasize the idea that the scale of a map is a simple matter of ratio of distances. The apparent complexity of the subject arises from the fact that, even in the case of large scale maps, the map distance is a matter of inches, whereas the ground distance is a matter of yards or even miles. Consideration of the subject of scales of maps therefore requires a conception of the ratio between very short and very long distances.

* The earth is spheroidal in form, and the absolutely accurate representation of its surface on a plane is impossible. Many forms of map projection have been devised to reduce this distortion to a minimum and it is negligible in the projections in ordinary use. The discussion of the subject of map projections and all other difficulties in map making resulting from the curvature of the earth belongs to treatises on geodetic surveying.

The first difficulty that presents itself is due to the fact that our conception of short distances is in inches, of moderate distances in yards or as a fraction of a mile, and of longer distances in miles. Thus a certain short distance may be readily recognized as 3 inches, but only in map reading and map making are we forced to learn to recognize 3 inches as 21 \ 20 of a mile. Nor does 1,584,000 inches convey a definite impression of distance until the mind has become accustomed to thinking of a mile as 63,360 inches, and we learn that the given distance is 25 miles.

The second difficulty lies in the fact that in topographical surveying distances are measured, not in inches or miles, but in feet or rods; and in topographical sketching distances are measured in still other units, in strides ( = double paces) of the sketcher, or by timing a horse at a gait of known rate.

This confusion of units makes it necessary to use two different classes of scales for maps:

1 . Reading scales for the purpose of ascertaining the ground distances corresponding to distances measured on the map; and

2. Working scales for the purpose of plotting on the map distances which have been measured on the ground.

Reading Scales.

A reading scale is a graphical scale which, when applied to a map, reveals to us the distances between points in units that we understand. For one accustomed to our units of measure, the reading scale may give short distances in feet or yards, but must give longer distances in miles and fractions of miles. Reasonable familiarity with the metric system enables one to use a kilometer scale, but such use is generally accompanied by a menial calculation of the distance in miles by multiplying by f or .6.

The ordinary form of reading scale is shown in Fig. 1, in which the major graduations read miles and the extension quarters and eighths, these being the familiar subdivisions of a mile. A reading scale of kilometers would show kilometers as the main divisions, with the extension subdivided decimally to agree with the metric system. Reading scales of yards are useful mainly in connection with infantry and artillery fire, and therefore applicable generally only to large scale maps. The main divisions represent 100 or 1,000 yards, and the extension is subdivided into decimal parts of the main divisions.

a *

A

5 Mi. d

Fig. 1. — Typical Reading Scale.

To permit a more accurate measurement of distances, recourse m&y be had to the construction of a diagonal scale. Such a scale is used principally for the decimal subdivision of the smallest division of the regular scale. The principle of the construction of a diagonal scale is shown in Fig. 2. Parallel to the line of the

100 50

Fig. 2. — Diagonal Scale.

main scale are ruled ten lines with any convenient equal spacing. The ten subdivisions of the main scale are repeated on the last line, and the extension completed by joining the subdivision points as shown. A scale so prepared has a least reading ^ of the smallest subdivision of the main scale.

A diagonal scale is of little practical value in measuring distances from maps, because its use assumes a higher degree of accuracy than most maps possess. For all ordinary military purposes the least reading of a direct scale is sufficient.

Methods of Stating Scales on Maps.

All maps should either have printed upon them their own reading scales, or else show the data necessary for the preparation of a reading scale.

The data with respect to the scale of the map may be given in one or more* of three ways:

1. As a ratio between the map distance and the corresponding ground distance, expressed as a fraction called the representative fraction (abbreviated R.F.), written j^ , ~^- Q , ^7^, etc. The numerator of the R.F. is the distance on the map, and the denominator is the corresponding distance on the ground, both expressed in the same units. The first fraction means that 1 unit distance (inch, centimeter, etc.) on the map represents 10,000 of the same unit distances (inches, centimeters, etc.) on the ground. To those accustomed to the metric system, it means that 1 centimeter on the map represents 10,000 centimeters or 100 meters on the ground, and enables the regular centimeter scale to be used for scaling distances from the map. In our own units, a scale of 10 1 000 means that 1 inch on the map represents 10,000 inches =833i feet, 277 £ yards, or .1578 mile,— all of which are odd distances bearing no relation to our usual conception of distances.

2. As a simple statement of the relation between map distances and ground distances, both expressed in some familiar unit: as 1 inch = 1 mile, 6 inches = 1 mile, 1 inch = 100 yards, etc.- If the statement is given in some unit with which we have not a working familiarity, it must be translated into our units before it is of practical use.

3. As a graphical scale drawn on the map and so subdivided that the usual units in which ground distances are measured are represented in map distance by the subdivisions of the scale. Thus on a scale of 1 inch = 1 mile, the subdivisions of the graphical scale would be 1 inch in length, but the subdivisions would be designated 1, 2, 3, etc., miles.

Comparison of Methods of Stating Scales.

The persistence of three different methods of expressing the scale of a map is explained by the fact that each has certain advantages not possessed by the others. The R. F. is a statement of ratio which is independent of the unit used, and enables any one to construct a reading scale for the map in units with which he is familiar.

The actual ratios used as the scales of maps are dependent upon the units familiar to those who make and use the maps. Thus the convenient ratios for those familiar with the metric system are all decimal, as 5i00 ^, io.ooo> 20 00c 4o.ooo> so.ooo 10O ' 00l) , etc., because these ratios give directly the relation between the small units of the ordinary metric scale in which map distances are measured and the large units in which ground distances are measured. In fact, a representative fraction such as those written above gives directly all the information necessary to use an ordinary centimeter scale for the purpose of reading distances in kilometers from the map.

For the same reasons that cause the use of decimal ratios in the metric system, we are forced to use in our maps a system of representative fractions running j^, r^J^, 21 ,i ao , 31> S 80 > 63 ,3 60 > etc., because these are the ratios which obtain when inches on the map represent familiar fractions of a mile on the ground, thus enabling us to use an ordinary scale of inches as a reading scale for our maps.

From the above discussion, it is seen that the ratios expressed by the representative fractions of maps are inseparably connected with the units of measure familiar to those for whose use the maps are principally intended, and that those ratios convenient for one system are inconvenient for another.

However, if the representative fraction is recorded on a map, it furnishes the data for the construction of a reading scale in any system of units of measure, and is therefore generally regarded as an essential piece of information to be entered on a map.

The simple statement of the relation of map distance to ground distance merely tells how to use an ordinary scale for measuring distances on a map. The simple statement is simple only as respects the system of units of measure to which the scale of the map is conveniently related. Thus a statement that the scale of a map is 1 inch = 1 mile is good news to one provided with an inch scale and familiar with ground distances in miles, but it does not help much to know that the scale is one centimeter = one kilometer unless we have a centimeter scale and are familiar with ground distances in kilometers.

It is manifest that a graphical scale whose subdivisions represent ground distance units with which we are familiar is, after all, the only reading scale that is convenient for our use. Such a scale is more convenient if detached from the map, but there are two good reasons for printing a graphical scale on a map. One is that it will not be lost or missing when wanted, and the other is that it forms a record of the scale of the map which remains correct if the map is enlarged or reduced by photographic means. If the scale is given either by R.F. or by simple statement, the data are falsified by photographic enlargement or reduction, hence it is very desirable that the map shall bear on its face a graphical scale, even though the scale is also stated or the R.F. given.

To be convenient for our use, a map must bear a graphical scale in our own units, or must be drawn to a scale conveniently related to our units. In the latter case, an ordinary foot rule forms the desired detached scale for use in measuring distances on the map. But if neither of these conditions be fulfilled, then it is necessary to construct a graphical scale suitable for the map to be used.

Construction of Graphical Reading Scales.

If the scale of the map is in some unfamiliar unit, it is necessary that the data with respect to the scale be in some form that makes it possible to determine the R.F. of the map. Thus if we assume a Russian map with a graphical scale of versts printed on it, we could measure directly the length of the divisions representing versts, but could proceed no further unless we happened to know that a verst is 3,500 feet. However, the difficulty of obtaining a great deal of useful information from a map with the names printed in Russian characters suggests that the discussion be confined to the more usual case of maps based on the metric system. These maps practically invariably show the representative fraction of their scale. If not, remembering that one meter =39.37 inches, a careful direct measurement of the graphical kilometer scale will serve to reveal the R.F., especially as the denominator is certain to be some multiple of 1,000, except in the scale R.F. 2 J 00 .

Example 1. Let us assume that the R.F. of the map has been determined to be 80 * 000 , showing a scale smaller than 1 inch = 1 mile. Let it be required to construct a reading scale of miles.

Solution. In this case it will be desirable to construct a reading scale with 1 mile as the main division, and showing 10 miles on the main scale and 1 mile on the extension, or 11 miles total length. Eleven miles = 11 X 63,360 inches = 696,960 inches. With R.F. 80 1 000 , the map length of 11 miles would be 696,960 -f- 80,000 = 8.712 inches, which is the total length of the scale to be constructed. Draw a line and lay off by scale 8.712 inches as nearly as practicable. Divide this by the usual oblique geometrical construction into eleven equal parts, and subdivide the left-hand division into eighths by the same construction. This construction is shown (not to scale) in Fig. 3. The equal divisions on the oblique line are laid off by an inch scale and projected back on the line to be subdivided by lines parallel to the line B C.

Example 2. Assuming a map scale of 20 * 000 , let it be required to construct a reading scale of yards for this map.

Solution. One yard on the map represents 20,000 yards on the ground, hence 1,000 yards will be represented by f-§- of an inch = 1.8 inches, hence we select 1,000 yards as the main division of the scale. A reading scale showing 6,000 yards will therefore be 10.8 inches long. By a construction similar to that shown in Fig. 3, divide a line 10.8 inches long into six equal parts. Subdivide the .extension into ten equal parts. The main scale will show five divisions each representing 1,000 yards, and the extension 1,000 yards with a least reading of 100 yards. If a diagonal scale be constructed as in Fig. 2, the least reading will be 10 yards.

Fig. 3. — Division of Scales.

Rules for the Construction of Reading Scales. In general, to construct a reading scale:

1. Determine the R.F. of the map. If this determination results in a near approximation to a decimal ratio or to one of the fractions representing the inch-to-mile ratios, it should be assumed that the actual ratio is the nearest decimal or inch-to-mile fraction.

2. Select as the main division of the scale a convenient unit, as 1 mile, 5 miles, 100 yards, 1,000 yards, such that the main division will be not less than about | inch in length. For large scale maps, the main scale and the extension may each represent 1 mile.

3. Determine a convenient number of main divisions of the scale such that, with one division added for the extension, the total length of the scale will be between and 1 2 inches.

4. Calculate the total length of the scale.

5. Subdivide into the proper number of divisions, and subdivide the extension into convenient fractions of the main divisions.

6. Mark the divisions of the scale properly.

Problems in the Construction of Reading Scales.

Problem 1. Construct a reading scale of miles and fractions of miles for

Problem 2.

Problem 3.

Problem 4.

Problem 5.

a map scale of

20.000

Construct a reading scale of yards for a map scale of j.

5.0 00'

Construct a reading scale of yards for a map scale of 6 inches = 1 mile.

A kilometer reading scale is shown on a map. The distance representing 10 kilometers measures scant 4 inches. Construct a reading scale of miles and fractions.

A certain distance is measured on the ground and found to be 3 miles. The corresponding map distance is 4f inches. Construct a reading scale of yards.

CHAPTER III. Scaling Distances on Maps

Methods of Scaling Distances.

Straight Lines. Straight-line distances may be measured byapplying a graphical reading scale directly to the map, or by measuring the distance with a pair of dividers or on the edge of a piece of paper, and then applying the length so found to a graphical reading scale.

Meandering Lines. Meandering lines may be measured in several different ways:

(a) Directly by applying the scale successively to short lengths, each of which approximates to a straight line, and summing the total distance measured.

(b) The total length may be accumulated on a pair of dividers by setting the dividers at the initial point and measuring the first portion approximating a straight line; then swinging the rear leg of the dividers into prolongation of the next portion of the line to be measured and setting the rear leg on the paper; then extending the forward leg to the new forward point, and so continuing until the total distance is accumulated. Then apply the dividers to the scale.

(c) By a process similar to (6), successive distances may be accumulated along the edge of a sheet of paper, and the total distance applied to the scale.

(d) For continuously curving lines, a thread or string may be made to conform to the line, and the total length thus determined applied to the scale.

(e) An instrument called a "map measure" is sold by instrument dealers. It is provided with a contact wheel which when rolled over the map, records by a pointer and dial the distance in inches passed over. The map measure may be used on straight lines, but is particularly convenient for measuring sinuous lines.

If the scale of the map is in inches-to-the-mile, the map measure reveals the ground distance directly. For other scale ratios, the map measure must be rolled backwards over the divisions of the graphical scale to determine the ground distance. In this process, the map measure must be rolled over such numbers of even divisions that from the dial it becomes evident that one more division will cause the pointer to pass the zero. Then it is rolled over the extension scale until the pointer reaches zero to determine the fractional part of the reading.

Accuracy of Distances Scaled from Maps.

Measurements of distances on maps are made for two principal purposes :

(a) Along roads for determining the distances between towns, the points which marching columns will reach at given times, and for various purposes in connection with the movements of troops and transport.

(b) Along straight lines for the purpose of determining ranges for artillery and infantry fire.