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Im trying to figure out how to find the height of the arc or maybe the distance between arc and line given than both of these lines/curves have exact same start and end points...the only difference is that the arc is curved and thus its longer than the straight line. I am attaching an image to better illustrate the problem.

enter image description here

Also, I used 3d modeling software to create an example and get actual numbers. So if you have L1, which is a straight line equal to 100cm and L2, the arc curve is 102.6 cm, then D = 10cm. What is the formula that I can apply to always find D given I know the lengths of L1 and L2. D is in the center (midpoint) of straight line and arc.

Thanks in advance!

Dheeraj Gujrathi
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vitbladez
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1 Answers1

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Assuming it is a true arc (part of a circle) and not a more general curve, if possible I would draw out the full circle, draw radii from the circle's center to the endpoints of the arc, draw the chord between the endpoints of the arc, calculate the central angle, use trig to calculate $a$ below, then subtract $a$ from the radius to find the sagitta, $s$. You might be able to create a formula that involves these steps. enter image description here

Nate
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  • Im not sure if this is the correct approach... i only know the lengths of 2 lines, and the fact that both have exact same endpoints, its just one line is straight and the other has a slight curve to it forming an arc... i dont know R, if i dont know R then any circle based calculations will not work... And my question is basically "How does the 3D modeling program know all this???" There must be some formula or a set of formulas which can find the distance between midpoints of arc (curve) and straight line given their endpoints are the same and the curve is the only difference. – vitbladez Dec 04 '23 at 17:17