The curve radius can be calculated using the distance across the curve and the distance from the midpoint of that line to the curve itself.
Calculating Curve Radius: Using the Chord Method
This method, often referred to in contexts like road design or woodworking, involves measuring a chord (a straight line connecting two points on the curve) and the mid-ordinate (the distance from the midpoint of the chord to the curve).
Here's the formula:
R = (D²/8M) + (M/2)
Where:
- R = Radius of the curve
- D = Distance of the chord (the straight line distance across the curve)
- M = Mid-ordinate (the distance from the midpoint of the chord to the curve)
Step-by-Step Calculation:
- Measure the Distance (D): Measure the straight-line distance (chord) across the inside of the curve. This is 'D' in the formula.
- Measure the Mid-ordinate (M): Measure the distance from the midpoint of that line (the chord) to the edge of the curve. This is 'M' in the formula.
- Apply the Formula: Substitute the values of 'D' and 'M' into the formula above and solve for 'R'.
Example:
Let's say you measure a distance (D) of 4 feet across the curve, and the mid-ordinate (M) measures 0.5 feet.
- D = 4 feet
- M = 0.5 feet
- R = (4²/8 * 0.5) + (0.5/2)
- R = (16/4) + 0.25
- R = 4 + 0.25
- R = 4.25 feet
Therefore, the radius of the curve is 4.25 feet.
Simplified Explanation:
Essentially, you're using a simplified geometric relationship to estimate the radius of a circle (or arc) based on easily measurable distances. This method is particularly useful when you cannot directly measure the radius itself.
