How to cut a plate onto a tube at an angle?

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SUMMARY

This discussion focuses on calculating the correct radius for a plate that will fit onto a 6-inch tubing at an angle. Two formulas were explored: R=(.5mM)÷√(m² + M²) and R=(H÷2)+(W² ÷ 8H), where m represents the minor diameter and M the major diameter, while H and W denote the height and width of the arc, respectively. The second formula provided a close approximation, but further clarification on the angle of the plate is necessary for precise calculations. A specific example using a 30-degree angle indicates that the major axis can be calculated as 6.928 inches.

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  • Familiarity with the properties of ellipses
  • Basic knowledge of trigonometric functions (SOH-CAH-TOA)
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  • Research the properties of ellipses in relation to angular cuts
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TL;DR
Formula for a plate to sit on end on a tube at an angle
I'm trying to draw a file for a plate that will sit on a piece of 6inch tubing at an angle. I can't quite get the radius right. I've tried
R=(.5mM)÷square root of (m squared + M sqaured) m=minor diameter M=major diameter
And I've tried R=(H÷2)+(W squared ÷ 8H)
H= height of arc W=width of arc
The second one gets close but its still not quite right. Is there another formula for this?
 
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I'm sure there are other ways. I'm not quite sure where you are running into trouble.

Do you know the angle of the plate to the tubing?
What result is it that you are looking for? The properties of the ellipse, drawn on your plate?

Obviously the minor axis will be six inches. You should be able to work out the major axis AB pretty easily using soh-cah-toa:
1730137795084.png


For example, if angle α is 30 degrees, that should make for a major axis of 6.928":
1730137272867.png

1730137320503.png
 
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