pls, how to calculate the length of a spiral arch ?

[deadlykitten]

hello please, let's consider this spiral :
... angle 0, radius 50
... angle 180, radius 75
... angle 360, radius 100
* thus a spiral starting from diameter 100, going to diameter 200, with a single loop

please, is there a mathematical formula to calculate the length of this spiral, between angles 70* and 123* ?

kindly

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[Jim Dawson]

https://www.giangrandi.ch/soft/spiral/spiral.shtml

Or

https://sciencing.com/calculate-spiral-6544041.html

The math makes my head hurt

[deadlykitten]

thank you jim

[CitizenOfDreams]

I tried to calculate it with integrals but gave up. Should be easy enough for a student who still has fresh calculus in his head.

[BRAIN-HURTS]

There are plenty of free cad programs on the net, why not use one of them and draw what you want,then you can interrogate the drawing to get your answer.

Good luck.