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
If a line is horizontal, it is not a curve and the radius is infinity. What are the units of your numbers?
Your question does not make sense to me.
its an arc definition curve with pts A, B, C and have to find the radius of the curve
The center of the circle containing those three points is located where the perpendicular bisectors of AB and BC intersect. Get the equations of the bisectors and solve for their intersection point.
To solve for the radius of a horizontal curve using the coordinates of points A, B, and C on the curve, you can follow the steps below:
Step 1: Convert the coordinates from Northings (N) and Eastings (E) to Cartesian coordinates (X and Y).
Point A:
N1405.4018, E1256.7569
Convert to X and Y coordinates using a conversion factor:
X = E - E0
Y = N - N0
E0 is the Easting reference point, which is a known value.
N0 is the Northing reference point, which is also a known value.
Point B:
N1283.3703, E1294.7027
Convert to X and Y coordinates using the same conversion factor.
X = E - E0
Y = N - N0
Point C:
N1225.9373, E1286.6137
Convert to X and Y coordinates using the same conversion factor.
X = E - E0
Y = N - N0
Step 2: Calculate the coordinates of the center point of the curve (Cx, Cy).
To find the center point, you can use the formula:
Cx = (X1 + X2) / 2
Cy = (Y1 + Y2) / 2
where (X1, Y1) and (X2, Y2) are the coordinates of any two points on the curve.
Choose points A and B or B and C to calculate the center point.
Step 3: Calculate the distance from the center point to any point on the curve.
You can use the formula for distance between two points in a Cartesian coordinate system:
d = sqrt((X - Cx)^2 + (Y - Cy)^2)
Choose any point on the curve – A, B, or C – and calculate the distance from the center point.
Step 4: Calculate the radius of the curve.
The radius of the curve can be found by taking the reciprocal of the curvature, which is the inverse of the distance from the center point to any point on the curve.
R = 1 / d
Once you have completed these steps, you will have successfully solved for the radius of the horizontal curve using the given coordinates.