Math Experts -- I need a hand (arcs)

[bighammer]

I'm trying to stake out a utility easement for our new home. It follows a road (2track) but has irons set at stategic points. My stumper is a long sweeping curve with a radius of 520. 85' for a distance (along the arc) of 284. 87'. A little to long to just eyeball.



I'm hoping to break it up a bit so maybe every 50' I can accurately place stakes. (and no, I don't have a 520' tape either) Is there a formula to figure arc height knowing the length and radius? I could keep breaking it in half so it's manageble.

 

[klenger]

I don't remember my geometry, but I do know how to use AutoCAD. Here is the geometry for the arc. Ignore any position coordinates as they vary depending on where the arc starts. The length of the arc (as the crow flies is 281. 3326' and the height is 19. 3545'.

 

[bighammer]

WOO HOO, I got the same result figuring on paper. I found the angle to be 31. 337* and bisected it and used the COS of half of it to be (520. 85 -x)/520. 85





Thanks

 

[klenger]

You're smarter than me. I cheated.