It has been quite a long time since I did any rotation of geometric shapes or mechanical drawing, and I need a refresher to jog my memory.

The goal is to make a template from construction paper which can be used as a guide when cutting sheet metal to make a pipe boot that sits over the ventilation pipe on the roof. The boot consists of a flat rectangular base (with a centered cutout for the pipe) and the cylinder that fits over the pipe. The two are soldered together.

Pipe boot/flashing

For the sake of simplicity, assume the pipe on the roof has a 100mm O.D.

The roof pitch is 28 degrees.

The cutout hole for the pipe must be adjusted for that angle of rotation.

The flat sheet which gets formed into the cylinder must be curved on the bottom, so that it will have an oval-shaped base. Where to position the stationary leg of a drawing compass to form that oval curve?

  • Sounds like a math problem. If nothing else I would model that in Google Sketchup. You know you can just buy that stuff, right? – Harper Dec 26 '16 at 21:48
  • 1
    Many of the prefab ones are made of lead (squirrels chew them up) or have an elastomer on the base which dries out and cracks over time. I want to fabricate it with the metal of my choice. – TRomano Dec 27 '16 at 1:38
  • I think @MichaelKaras got it right. Easiest thing to do is cut the pipe, then transfer the profile to the sheet metal with layout fluid and a scribe or just a felt-tipped pen. If the "flat" sheet needs to be bent, it will only make the hole seem smaller (ex. the pipe will no longer fit), so just use a file to adjust it to size. – Hari Ganti Mar 3 '17 at 18:24
  • This is a 1940s era black iron pipe already penetrating the roof. If I were doing this with a new PVC pipe, I could use a piece of pipe cut at the correct angle to transfer the ellipse. – TRomano Mar 3 '17 at 18:36

You want to draw an ellipse. Drawing an ellipse by hand with a compass has many steps and is better demonstrated visually. I found a good step by step visually guide by a Tim Closs on Slideshare. Here are his steps from that site:

  1. Line up paper with T-square parallel
  2. Tape down Top corners
  3. Tape down Bottom corners
  4. Find the Center of your paper using the cross technique (see last weeks notes)
  5. Layout vertical axis using :• 45/90 Triangle• T-square• Pencil
  6. Layout horizontal axis using :• T-square• Pencil
  7. Mark Minor Axis• Set compass to approximately 2 inches• Mark vertical axis
  8. Mark Major Axis• Set compass to approximately 3 1/2 inches• Mark horizontal axis
  9. Mark center O• Mark major axis A B• Mark minor axis C D
  10. Set compass from O to C• Make a mark on the right side of major axis• Label E
  11. Using your triangle draw a Line from C to B
  12. Set compass to E B• Set compass on C and swing an arc intersecting line C B
  13. Label intersection F
  14. Bisect line F B (see earlier lessons on bisecting a line)
  15. Extend Bisector to make point H
  16. Mark point G where bisector intersected line AOB
  17. Set compass O to H• From O make a mark above C and label it K
  18. Set compass O to G• From O make a mark to the right A and label it J
  19. Using your triangle draw a Line from H through J
  20. Using your triangle draw a Line from K through J
  21. Using your triangle draw a Line from K through G
  22. Set compass to G B• Having the center on G swing an arc to both Tangency lines
  23. Set compass to J A• Having the center on J swing an arc to both Tangency lines
  24. Set compass to H C• Having the center on H swing an arc to both Tangency lines
  25. Set compass to K D• Having the center on K swing an arc to both Tangency lines

In step 7, the minor axis would be the OD of the pipe that you are using (100mm). You’ll need to determine the major axis in step 8 by drawing on another pice of paper a horizontal the length of the pipe OD (100mm). Then draw a line at the angle of your roof (28°) under it. Now extend parallel lines down from both ends of the upper line until they intersect with the angle line. Measure along the angle line the distance between the two intersections and that is the length of the major axis.


You have to make the round vertical piece with the angle cut on it's end first. Get that cut nicely so that it meets your needs even if it takes a couple of iterations to get the correct angle and the shape when it sits on a flat work surface.

The next step is to position the angle cut part on the flat sheet in the center area. Use a felt tip permanent marker to trace around the outside of the tube piece onto the flat base piece. Cut out the oval shaped hole along the inside edge of the marker trace line. After cutting the residual marker can be removed with rubbing alcohol.

If you decide to have bend up tabs to rivet and solder to the vertical piece you will have to arrange for those before you set out to cut out the oval hole.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.