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### Mapwork calculations

How to calculate real distance on a map

When you are using a compass, the needle pointing north is actually not pointing to north. The needle is in fact pointing to the Magnetic North pole which is situated roughly north-east of Canada. It shifts every year by approximately 55km.
There is always a difference between the True North, which is at the North Pole, and the magnetic north. However, this difference (angle) changes every year. This change is known as the magnetic declination.

When using a topographic map true north is always at the top of the map. To measure the bearing from one point to the next, the protractor must be aligned so that 0° point to the top of the map (true north). Draw a straight line from your starting point to the end point. Place the protractor on the map, with 0° pointing to the top of the map. Use the line connecting the two points to read the degrees from the protractor. Remember to measure in a clockwise direction from the top.

Let us assume the true bearing is 75°. If a person starts to drive in in a bearing of 75° he will still miss his final destination. Why? You still have to add the difference between True North and Magnetic North, also known as the magnetic declination. Every year the magnetic north shifts, either in a westerly or easterly direction. For an observer in South Africa the Magnetic North will always be west from True North (North Pole). At the bottom of a topographic map (e.g. 1:50 000) you will see a north-south arrow. Next to the north-south arrow the mean magnetic declination and the mean annual change will be indicated. For example: “Mean magnetic declination 16°3’ West of True North (July 2012). Mean annual change 2’ Westwards (2010-2019).”
So, how do you calculate the magnetic bearing?

Step 1: Determine the true bearing
E.g. 75°

Step 2: Determine the difference in years between the current year and the year the      Magnetic declination was measured (on topographic map)
E.g.  2017 – 2012 = 5 years

Step 2: Calculate the total magnetic change
E.g. 5 years x 2’ West = 10’ West      (On the topographic map the change is 2’            West every year)

Step 3: Calculate the current magnetic declination
E.g. 16°3’ West
+ 0°10’ West       When the mean annual change is west you +, and if the change is East, you –.
16°13’ West         Therefore, the magnetic declination for 2017 is 16°13’ west from True North.

Step 4: Calculate the magnetic bearing
E.g. True Bearing + Current Magnetic Declination
= 75° + 16°13’

= 91°13’

How to calculate real distance on a map

This is a very easy calculation! With a ruler and calculator you can do this in three easy steps.

Use the following formula:

You will divide by a 1000 if you need the real distance in meters OR divide by a 1000 000 if you need the real distance in kilometres!

E.g. on a 1:50 000 Topographic map the map distance between Point A and Point B is 47mm.What is the real distance in kilometres?

Distance = Map distance in mm x map scale

1000 000

= 47mm x 50 000

1000 000

= 2,35km

You can also take the map distance in centimetres and multiply it by 0.5

E.g. 4.7cm x 0.5 = 2.35km

How to calculate gradient on a topographic map

How do you calculate the gradient between two points on a 1:50 000 topographic map?

Use the following formula

Step 1: Determine the difference in altitude between the two points

E.g. point A = 1120m and Point B = 1380m

Difference in height = 1380m – 1120m = 260m

Step 2: Calculate the horizontal distance by using the following formula

Distance = Map distance in mm x map scale

1000 OR 1 000 000

Divide by a thousand if you want the distance in meters OR a 1 000 000 if you need the answer in kilometres

In this instance we will need the distance in meters!

E.g. the map distance between Point A and Point B is 23mm

Distance = 23mm x 50 000

1000

= 1150000

1000

= 1150m

Gradient can be expressed in a fraction (e.g. 1:25) format or as a percentage (%)

Horizontal distance

= 260m

1150m

= 260m ÷ 260

1150m ÷ 260

= 1 .

4,42

1:4.42

Therefore, for every 4.42 meters you are moving horizontally the height will change by 1 meter. This is quite steep!!

How to calculate Time

E.g. A cyclest is cycling from point A to point B at an average speed of 14km/h. How long will it take the cyclest to cover the distance? The mapdistance between point A and point B is 78mm and the mapscale is 1:50 000.

Step 1: Calculate the distance between point A and point B in kilometers, because the speed is in kilometers per hour.

Step 2: Now you will apply the information to the Distance formula. Distance = 3,9km and Speed = 14km/h

You will notice that every decimal has been converted into a smaller unit. E.g. 3,58 hours, is 3hours (,58 x 60 = 34,8 minutes and .8 minutes x 60 = 48 seconds)