Map  Scale

Scale is required on maps to measures and to know the distance between any two points or objects. A scale is the ratio of length between two point on a map to its corresponding distance on the ground.

To say that if a map is on the scale 1:25.000 means that a length of 1cm on the map represents 25000 centimeters or 250 m on ground. In other words, 250m distance on ground shown by a length of 1cm on the map.

Expression of Scale

Scales can be expressed in the following manner:

1) The statement scale

2) The RF / Numerical scale 

3) The plain / linear / Graphical scale 

1) The statement scale

 In this case, the numbers of units on map that represent the corresponding number of units on ground are staled

for. e.g.   1cm=200m; 4 cm = 1 km, one inch to a mile; etc

Now-a-day this system is not in more used

2)  The RF / Numerical scale 

 In this case, the proportion existing between the length on the map and the actual length on the ground is indicated by a fraction whose numerator is always one. such fraction is called Rf (Representative fraction).

 for.eg. 1:25000, it represents 1 cm on map, 25000 cm (250m) on ground, widely used and also known as Natural scale. 

 R.F. = M.D/GD

3) The plain / linear / Graphical scale 

This consists of a line drawn at the bottom of the map, conveniently divided of subdivided so that the distances on the map can be easily read from it with the help of a pour of dividers!

 for. e.g.

                                        10 cm

     1 km                     0 km           1               2             3         4km 

 

Types of graphical scale:

Scale is classified into following categories;

1.    Plain scale

2.    Diagonal scale

3.    Vernier scale

4.    Scale of chords

Plain scale:

·       A plain scale is used to indicate the distance in a unit and its nest subdivision.

·       A plain scale consists of a line divided into suitable number of equal units. The first unit is subdivided into smaller parts.

·       The zero should be placed at the end of the 1st main unit.

·       From the zero mark, the units should be numbered to the right and the sub-divisions to the left.

·       The units and the subdivisions should be labeled clearly.

·       The R.F. should be mentioned below the scale.

 

Construct a plain scale of RF = 1:4, to show centimeters and long enough to measure up to 5 decimeters.

•       R.F. = 1/4

•       Length of the scale = R.F. × max. length = 1/4 × 5 dm = 12.5 cm.

•       Draw a line 12.5 cm long and divide it in to 5 equal divisions, each representing 1 dm.

•       Mark 0 at the end of the first division and 1, 2, 3 and 4 at the end of each subsequent division to its right.

•       Divide the first division into 10 equal sub-divisions, each representing 1 cm.

•       Mark cm to the left of 0 as shown.

•       Draw the scale as a rectangle of small width (about 3 mm) instead of only a line.

•       Draw the division lines showing decimeters throughout the width of the scale.

•       Draw thick and dark horizontal lines in the middle of all alternate divisions and subdivisions.

•       Below the scale, print DECIMETERS on the right-hand side, CENTIMERTERS on the left-hand side, and R.F. in the middle.

Diagonal scale:

Diagonal scale is used in engineering to read lengths with higher accuracy as it represents a unit into three different multiple in metres, decimeters, and centimeters . Diagonal scale is an important part in engineering drawings. Diagonal scale follows the principle of similar triangles where a short length is divided into number of parts in which sides are proportional. Divide into required number of equal parts.

Construct a Diagonal scale of RF = 3:200 showing meters, decimeters and centimeters. The scale should measure up to 6 meters. Show a distance of 4.56 meters

•       Length of the scale = (3/200) x 6 m = 9 cm

•       Draw a line AB = 9 cm . Divide it in to 6 equal parts.

•       Divide the first part A0 into 10 equal divisions.

•       At A draw a perpendicular and step-off along it 10 equal divisions,    ending at D. Diagonal Scale

•       Complete the rectangle ABCD.

•       Draw perpendiculars at meter-divisions i.e. 1, 2, 3, and 4.

•       Draw horizontal lines through the division points on AD. Join D with the end of the first division along A0 (i.e. 9).

•       Through the remaining points i.e. 8, 7, 6, … draw lines // to D9.

•       PQ = 4.56 meters

 

Vernier Scale:

It is a device for measuring the fractional part of one of the smallest divisions of a graduated scale. It usually consists of small auxiliary scale which slides along the main scale.

 The principle of Vernier is based on the fact that the eye can perceive without strain and with considerable precision when two graduations coincide to form one continuous straight line.

Types of Vernier:

1.    Direct Vernier

2.    Retrograde Vernier

 

 

 

Scale of Chords:

·       Scale of chords is used to measure angles when a protractor is not available, by comparing the angles subtended by chords of an arc at the center of the arc.

·       Draw a line AO of any suitable length.

·       At O, erect a perpendicular OB such that OB – OA

·       With O as center, draw an arc AB

·       Divide the arc in to 9 equal parts by the following method.

1.    On arc AB, mark two arcs with centers A and B and radius – AO. By this the arc AB is divided in to three equal parts.

2.    By trial and error method, divide each of these three parts in to three equal subdivisions.

·       The total length of AB is now divided in to 9 equal parts. Number the divisions as 10, 20, 30, 40, etc. Transfer all the divisions on the arc to the line AO by drawing arcs with A as a center and radii equal to the chords A-10, 10-20, 20-30, …. AB.

Construct the linear degree scale by drawing the rectangles below AC. Mark the divisions in the rectangle with zero below A and number the divisions subsequently as 10o , 20o , 30o , 40o , ….., 90o

 

Shrunk scale and shrinkage factor

Shrunk scale and shrinkage factor are both related to how the size of something has been reduced. Here's a breakdown of each:

Shrunk Scale:

·         This refers to the new scale of an object or image after it has been shrunk due to variation in the atmospheric conditions.

·         It is essential to find the shrunk scale of the plan/map.

·         It's typically expressed in the same way as the original scale. For example, a map with an original scale of 1 cm : 10 m (1 centimeter on the map represents 10 meters in real life) might have a shrunk scale of 1 cm : 12 m (after shrinkage, 1 cm represents 12 meters).

Shrinkage Factor:

·         This is a numerical value that represents the proportion by which something has shrunk.

·         It's calculated by dividing the shrunk size by the original size.

·         A shrinkage factor of 1 indicates no shrinkage, while a factor less than 1 indicates a reduction in size.

Here's how they relate:

·         The shrunk scale can be obtained by multiplying the original scale by the shrinkage factor.

For example, imagine a blueprint that originally had a scale of 1 cm: 2 m (1 cm on the blueprint represents 2 meters of the actual building). If the blueprint shrinks due to aging, and a line that was originally 2 cm on the blueprint now measures 1.8 cm, we can find the shrinkage factor and shrunk scale:

·         Shrinkage factor = New size / Original size = 1.8 cm / 2 cm = 0.9

·         Shrunk scale = Original scale * Shrinkage factor = 1 cm : 2 m * 0.9 =   1 cm : 1.8 m

In this case, the blueprint shrunk by a factor of 0.9, and the shrunk scale is now 1 cm: 1.8 m

 

Importance and uses of map scale:

1.    To determine the actual size of an object on the map

2.    To plan route or to determine the size of an area that needs to be surveyed.

3.    To navigate by map.

4.    To measure distance or area on map.

5.    To compare the size and area of objects on different maps.

 

Effect of measurement from wrong measuring scale:

To obtain true measurements of lines and areas on a map using a wrong scale, the following formulae are used:

Enlargement and reduction:

Enlargement and reduction of map scale refer to adjusting the size of a map relative to the actual area it represents. Maps are typically created to represent real-world locations in a smaller, more manageable format. The scale of a map indicates the ratio between the distance on the map and the corresponding distances on the ground.

Enlargement (Magnification):

When you enlarge a map, you increase its scale, making the map appear larger than the area it represents in reality. This is useful when you need to focus on smaller details or cover a larger area in more detail. For example, if you have a small-scale map covering a large region, you might enlarge a portion of it to show specific streets or landmarks in more detail.

Reduction (Minification):

Conversely, when you reduce a map, you decrease its scale, making the map appear smaller than the actual area it represents. This is useful when you need to fit a larger area onto a smaller piece of paper or screen. For instance, if you have a detailed map of a city but want to show the entire city on a single page, you might reduce the scale of the map.

 

Enlargement and reduction of map scale involve adjusting the scale factor, which is the ratio between map distances and ground distances. This is often expressed as a fraction or a ratio (e.g., 1:10,000 means one unit on the map represents 10,000 units on the ground).

In practical terms, when enlarging a map, you multiply all distances on the map by the enlargement factor, while in reduction; you divide all distances by the reduction factor.

 

 

For example:

•       If you have a map with a scale of 1:50,000 and you want to enlarge it to 1:25,000, you would multiply all distances on the map by 2.

•       If you have a map with a scale of 1:10,000 and you want to reduce it to 1:50,000, you would divide all distances on the map by 5.