How To Determine And Interpret The Gradient Of A Slope On Topographic Maps.

Slopes represent the rising or falling of the land surface. Slopes can either be gentle or steep.  The slope is said to be steep when the land surface is rising/falling sharply and said to be gentle when the rising/falling of the land surface is mild.
A gradient is usually used to measure how steep or how gentle the slope is. In other words, it measures the rate at which the slope is rising/falling. However, due to the fact that the surface of the land is rarely uniform, gradient measures the average steepness of the slope of a piece of land.

A gradient is basically the average rate at which the ground slopes.
With the help of contours, the gradient of a given slope or a terrain feature can be conveniently determined from a topographic map. This article will show you how to determine gradient from a topographic map, how to express it and, how to interpret it.

DETERMINING GRADIENT OF A SLOPE ON TOPOGRAPHIC MAPS

On topographic maps, gradient is usually calculated with reference to two points. A line connecting these two points on the map represents the slope whose gradient is to be determined.
In order to calculate the gradient of a slope, the Vertical Increase (rise), as well as the Horizontal Equivalent (run) of the two points, need to be first determined.

Vertical Increase (also called Vertical Rise) means the difference in elevation between any two points on the map, whereas, Horizontal Equivalent is the actual ground distance between any two points on the map.

Gradient is calculated by simply dividing the Vertical Increase by the Horizontal Equivalent of the two points on a map.

Procedures for Determining Gradient on Topographic Maps (A Step-By-Step Guide)

Take the example of the figure below which shows a hypothetical map along with its linear scale.  The contour interval used is 150m. Assume that you are required to find the gradient of the slope between the spot height on top of the hill and point X.

The following are the procedures to be followed in order to determine the gradient of slopes on maps.

 Step 1:            Identify the location of the two points whose gradient is to be calculated/determined on the map. 

Step 2:.            Draw a straight line joining these points.

Step 3:            Determine the horizontal equivalent.

The procedures for determining the horizontal equivalent of two points is exactly the same as that of determining the distance of straightly-elongated features.

You place a straight-edged piece of paper against the two points on the map and mark off the two points along the edge of the piece of paper clearly. You then take this marked piece of paper and place it along the linear scale then read off the distance between the two points, as shown in figure (a) and (b) below

The horizontal equivalent is 4km

Step 4:            Determine the elevations of each of these points, and then calculate the Vertical Increase.

   From the figure above, the elevation of spot height is 3050m and that of point x is 1850m. 
Therefore;
            Vertical Increase (VI) = 3050m − 1850m = 1200m.

Step 5:            Express the vertical increase and horizontal equivalent into similar units.

Do this if the units of vertical increase and horizontal equivalent are different. As seen in step (iii) and (iv), the vertical increase is 1200m whereas the horizontal equivalent is 4km. Since the units are different, one of these measurements has to be expressed in the units of the other measurement.

In this example, we can convert 4 kilometers of horizontal equivalent into meters, to make it 4000 meters.

Step 6:            Calculate the gradient of a slope.

The basic idea of calculating gradient is to divide vertical increase by horizontal equivalent. However, the exact method/formula to be used for finding the gradient of a slope depends on which way this gradient is expected to be expressed in.
Gradient can be expressed either as a percentage, an angle, or a proportion. 

a)      Gradient Expressed In Proportions
In terms of proportion, a gradient is found by simply dividing the Vertical Increase and the Horizontal Equivalent.

For the example above;

It is then expressed in either of the three forms; (fraction, ratio or statement). Thus, for the example above, the gradient of the slope may be expressed either as 1/3.33, 1:3.33 or 1in3.33.

Usually, the form to be used depends on the country and the industry standards. For an instant, the statement form (i.e. 1in3.33) is generally the method used to describe railway grades in Australia and the UK. 

b)      Gradient Expressed In Percentage

The gradient of a slope expressed in percentage is obtained by multiplying the quotient of the Vertical Increase and the Horizontal Equivalent by 100%.

For the example above;

Therefore, the gradient of the slope is 30%.

c)       Gradient Expressed As An Angle of Inclination (or in Degrees)

The gradient of a slope expressed in degrees is calculated by using the arctangent of the quotient of the Vertical Increase and the Horizontal Equivalent.

For the example above;

Therefore, the gradient of the slope is 16.7°.

Usually, the way in which gradient of a slope will be expressed in depends on the standards of a given professional field or the standards of a given country.

INTERPRETING GRADIENT OF A SLOPE

The interpretation of the gradient of a slope usually varies from one industry to another. While a gradient of 12% is considered moderate enough for bike racing, it is extremely steep for the adhesive railways. Also, a gradient of 30% can be considered extremely steep for agricultural activities, but it is not steep enough for the funicular railways.
For describing the relief of an area or a terrain, the gradient is usually interpreted as shown in the table below;

Gradient (in %)	Interpretation
0% - 2%	Little or no slope
3% - 15%	Gentle slope
16% - 35%	Moderate slope
36% – 100%	Steep slope
Greater than 100%	Extremely steep slope

Interpreting the gradient of a slope when  describing the relief

APPLICATION OF GRADIENT OF SLOPES IN REAL LIFE

Engineers, architects, developers, military soldiers, geologists, environmentalists, farmers and other field experts often use the knowledge of gradient of slopes to perform and assess various tasks in their fields of work. The following are some areas of interest in which the knowledge of gradient of slopes is often applied;

Agriculture/Irrigation: Gradient of a slope can help farmers determine the suitability of a certain piece of land for agricultural activities.

Construction of infrastructures: Gradient of a slope can help engineers, architects and developers determine the suitability of establishing buildings, roads, railways and other infrastructures on a certain piece of land.

Establishment of HEP stations: Gradient of a river/stream can help determine the suitability for establishing a hydro-electric power station.

Geology: Knowing the gradient of a slope can help geologists to determine and assess the effect of slope on the geomorphic processes like erosion and deposition. 

Others areas include bike racing


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