I have a math question

[lucky1]

I have a round tower with a outside radius of 5'-9", with a 4/12 pitched roof coming to a peak. To match the existing overhang details at the straight walls i need to cut the tails at an 11" overhang and then wrap a 16" piece of ply wood around the radius from the top of the tails to the wall. Any body know how to figure out the radius i need to cut the 16" ply wood at so that it will wrap around?

[Joe Carola]

I have a round tower with a outside radius of 5'-9", with a 4/12 pitched roof coming to a peak. To match the existing overhang details at the straight walls i need to cut the tails at an 11" overhang and then wrap a 16" piece of ply wood around the radius from the top of the tails to the wall. Any body know how to figure out the radius i need to cut the 16" ply wood at so that it will wrap around?

I'm not following where that 16" piece of plywood is going. Can you be more specific?

[lucky1]

the plywood will be a sub-facia to be covered with a stucco system,but it will be flush with the top of the of the truss tails at an 11" overhang, and then lean in at an angle to be attatched to the radius wall

[Richard A Hetzel]

The radius of the bottom of a cone of 83.15 inches will do it, if the rafter tails are cut perpendicular to the roof slope. However, I'm not sure if you have to cut the plywood to that radius, or to some other radius.

[Joe Carola]

the plywood will be a sub-facia to be covered with a stucco system,but it will be flush with the top of the of the truss tails at an 11" overhang, and then lean in at an angle to be attatched to the radius wall

Is it like this?

[Richard A Hetzel]

Joe, what program do you use to do those sketches? They are mighty nice.

[Joe Bartok]

I have a round tower with a outside radius of 5'-9", with a 4/12 pitched roof coming to a peak. To match the existing overhang details at the straight walls i need to cut the tails at an 11" overhang and then wrap a 16" piece of ply wood around the radius from the top of the tails to the wall. Any body know how to figure out the radius i need to cut the 16" ply wood at so that it will wrap around?
I'm not getting what the detail is ... square hung or perpendicular to the rafters, as has been suggested? If this is the case the radius you need is the length of the surface of the cone perpendicular to the cone of the roof. In other words, the same radius you would use to develop or draw this cone on a flat surface.

Height of Cone Square to Roof = Base Radius × 12/4

Radius of Surface of Cone Square to Roof = √(Base Radius˛ + Height of Cone Square to Roof˛)

If the cone defining the fascia is not square to the roof rafters you'll need to recalculate to find the appropriate height. More information or a rough sketch would help in understanding exactly what your situation is.

I think you will actually need two radii because of the 16" depth of the plywood. See if you can make heads or tails of this thread: http://www.construction-resource.com/forum/showthread.php?t=2504 (http://www.construction-resource.com/forum/showthread.php?t=2504)

I posted what I believe is the correct solution to the tapered post problem in the developed_cone.pdf attached to Post #34 (http://www.construction-resource.com/forum/showpost.php?p=15075&postcount=34). The numbers for your roof will be different than the values in the pdf file, but the underlying principle is the same.

[Joe Carola]

Joe, what program do you use to do those sketches? They are mighty nice.

Richard,

It's Sketchup.You can download it free. You'll love it once you start.

http://sketchup.google.com/download/

[Richard A Hetzel]

I have it, and I can't get it to do what YOU get it to do....I guess I'm just an old pencil-and-paper guy. :D

[lucky1]

the diagram Joe has given is exactly what i have,however the 16" plywood is not perpendicular to the rafter tails,they must be cut at a 22-1/2 degree angle to accomodate the fixed 16" dimension

[Richard A Hetzel]

I don't have time now to calculate it for you, but the large radius of 83.15 inches doesn't change. That would be the radius at the upper tip of the rafter tails, no matter what angle they are cut at. What I'm having trouble visualizing is whether that's the radius at which you need to cut your plywood. I shall have to make a cone and unwrap a piece of paper from it to see that. I'll try it later; I have to measure a house today.

[Joe Bartok]

Lucky1: Here's a diagram of the development of a right circular cone. (That's a stock drawing from my files so the numbers are different than yours. The geometry and steps to obtain a solution remain the same).

Unless you intend to make a model you won't need to calculate the sector angles. Your height, h, is the radius of the base times the tangent of the plywood slope angle measured with respect to level. To find the radius, R, for your plywood use the Pythagorean Theorem to find the diagonal on the nappe of the cone.

http://www.construction-resource.com/forum/attachment.php?attachmentid=1461&d=1220101327