Dear Folks I have a radius of 2440mm on a level surface, now I need to find the new radius for 2440mm on a 32deg slope, please lay out the full formula so I can punch different radius #s and deg from time to time as required Thanks very much (woodworm)

I think you need to explain this problem more thoroughly.

Explanation; this concerns curved stairs, I have a known radius of 2440mm on a level plain now the slope of the stringer going down the stairs from one floor down to the lower floor is at 32deg of slope what would the new radius be? I know that it will be bigger radius (say 2800mm etc) so would like to know the full formula to arrive at the new radius without having to make templates then calculating the new radius off the template by math, as sometimes it is not feasible to travel to the job site and do this to make a moulding from edge of stringer to the drywall.many thanks (woodworm)

I think you need to explain this problem more thoroughly.

Perito ,thank you for your reply, this concerns curved strair moldings; we have a radius of 2440mm on the level plain the stair stringer (that holds the treads) goes down to the lower level at 32deg so what is my new radius? I would expect it could be somewhere in the range of say 2800mm but would like you to lay out the key strokes/formula etc Thanking You (woodworm)

I looked up "helix radius of curvature" on Google and found this iste:

helix and radius of curvature (http://www.physicsforums.com/showthread.php?t=94758)

Which suggests the correct formula is:


R = \frac r {cos ^2 (pitch)}


where r is the "flat radius" and the pitch angle is measured at r.

There is also a site here:
http://ca.geocities.com/web_sketches/calculators/baluster_radius/baluster_radius.html

which gives the same answer in a different form:


R = \frac {4 \pi ^ 2 r^2 + h^2} {4 \pi ^2 r}


where h is the height per full 360 degree turn of the stair case. Note that

h = 2 \pi r * tan(pitch)


For a flat radius of 2.44m and 32 degree pitch both solutions give you R= 3.39m. This assumes that the 32 degree pitch is measured where you want the helical radius (i.e at the outside radius of the tread if that's where the molding is going).

See answer here:
https://www.askmehelpdesk.com/mathematics/radius-slope-321718.html

In the future please don't double post the same question.

Dear Mr ebaines, thank you for your most helpful reply; on the equation
R= r over cos2 pitch, remember that 2440mm was the flat radius and 32deg was the slope so I put 2440 divided by coscos32=3632 where did I go wrong? Could you please put me straight again thanking you (woodworm)

In the future please don't start a new thread if you are following up on a previous question. It makes it very difficult for people to follow the conversation. The previous thread is here:
https://www.askmehelpdesk.com/mathematics/radius-slope-321718.html

You're trying to calculate:


\frac {2440} {cos^2(32)}


Cos(32) = 0.848

So:


\frac {2440} {.848 ^2} = 3393

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