Gradient = change in elevation/distance traveled. When you're finding the gradient from two points, how do you find the change in elevation? How do you find the distance traveled?
Your definition is not quite right.
Gradient: change in elevation/HORIZONTAL distance traveled.
You get the horizontal distance traveled from the map scale.
what about change in elevation?
To find the change in elevation when calculating the gradient between two points, you need to know the difference in the vertical position of the two points. This can be obtained by subtracting the elevation (or height) of one point from the other.
Let's denote the elevation of the first point as h₁ and the elevation of the second point as h₂. The change in elevation (∆e) can be calculated using the formula:
∆e = h₂ - h₁
So, simply subtract the elevation of the first point from the elevation of the second point to find the change in elevation.
To find the distance traveled between the two points, you can use their horizontal positions (usually given as coordinates). Usually, the distance is calculated using the Euclidean distance formula. Let's denote the position of the first point as (x₁, y₁) and the position of the second point as (x₂, y₂).
The distance (∆d) between the two points can be calculated using the formula:
∆d = √((x₂ - x₁)² + (y₂ - y₁)²)
Here, (x₂ - x₁) represents the difference in the x-coordinates, and (y₂ - y₁) represents the difference in the y-coordinates. Taking the square root of the sum of their squares gives us the distance traveled between the two points.
So, to recap:
1. To find the change in elevation (∆e), subtract the elevation of the first point from the elevation of the second point: ∆e = h₂ - h₁.
2. To find the distance traveled (∆d), use the Euclidean distance formula: ∆d = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁, y₁) and (x₂, y₂) represent the coordinates of the two points respectively.