What are the dimensions of the opening required to pass a cylindrical object through an inclined plane? (aka The Stovepipe-Problem)
This solution for the stovepipe-problem is best solved by using a trammel. The opening in the rake is elliptical in shape. The value for 1/2 the minor axis is already known it is the same as the radius of the cylinder.
To determine the value for 1/2 the major axis. . .
- Draw two intersecting lines, the angle, between which, is that of the rake.
- One line represents the slope of the rake, and the other represents the “horizontal.”
- From the intersection of the two lines draw an arc whose radius is that of the cylinder and which crosses the “horizontal.”
- From the point where the arc crosses the “horizontal” erect a perpendicular that crosses the line representing the slope of the rake.
The distance between the center of the arc and this point is the value of 1/2 the major axis.
A trammel constructed using these two values will describe the ellipse which must be cut in the rake to pass a cylinder of the stated radius.
Mitering two cylinders together
The same method may be use to create a gauge to mark out the cuts required to miter together (at any angle) two cylinders of the same radius. This is very useful where the diameter of the cylinders is too great to allow it to be cut on available bench tools.
- First, determine the angle at which the two cylinders want to be joined. 1/2 of this angle is the miter line.
- Use this compass and straightedge construction to find 1/2 the angle.
- Use that angle as the slope of the rake in the above.
- The blank, with the ellipse removed can be used to mark out the necessary cuts.
- Care must be taken that the thickness of the gauge does not compromise the marked cut.