how to solve for radius of horizontal curve with coordinates(NE) for points A,B, C on the curve
Point A : N1405.4018
E1256.7569
Point B : N1283.3703
E1294.7027
Point C : N1225.9373
E1286.6137
To solve for the radius of a horizontal curve with the given coordinates, we can use the circular curve formula. This formula relates the radius (R) of the curve to the coordinates of three points along the curve.
The circular curve formula is:
(R = ((x1^2 + y1^2 - x2^2 - y2^2) / (2 * (x1 - x2)))
To solve for the radius, you will need to determine the coordinates of two points on the curve. Let's take Points A and B:
Point A: N1405.4018, E1256.7569
Point B: N1283.3703, E1294.7027
First, we need to convert the coordinates from degrees, minutes, seconds (DMS) format to decimal degrees (DD) format.
Point A in DD format: N14.090030, E12.112615
Point B in DD format: N12.389505, E12.611712
Now, let's substitute the values into the circular curve formula:
R = ((x1^2 + y1^2 - x2^2 - y2^2) / (2 * (x1 - x2)))
R = ((12.112615^2 + 14.090030^2 - 12.611712^2 - 12.389505^2) / (2 * (14.090030 - 12.389505)))
Simplifying the formula:
R = ((146.829284439225 + 198.0374385039 - 158.866111373344 - 153.331346088025) / (2 * 1.700525))
R = (33.669265482755 / 3.40105)
R ≈ 9.90
Therefore, the approximate radius of the horizontal curve is 9.90 units.