SignalFerret wrote:
I'm trying to figure out how to calculate the smallest circle that will fit
over a trapezoid. No, it not home work -- I need to know what size to make
the hole for the thingy I'm building. I tried asking some coworkers, a PhD
ME, a MSME, and a physicist. I'm just a electronic tech, so assumed they'd
be smarter than me.

The particulars in this case are, the cross section is an trapezoid, 0.310"
bottom width, 0.200" top width, 0.210" height, symmetrical about the Y
axis -- What size hole will that fit in to?

Robert


Let B the bottom width, T the top width, and H the height. In general,
there are two solutions (assume B = T). If H and T are small compared
to B, the smallest circle is one with diameter D=B. To be more specific:

If H = sqrt(B^2-T^2)/2, then D=B.

If H sqrt(B^2-T^2)/2, then

D=sqrt[16*H^4 + 8*H^2*(B^2+T^2) + (B^2-T^2)^2]/(4*H)

In your case ('big H'), this gives D~.34148.

If you put the trapezoid with its base centered on the x-axis (middle of
the base at (0,0)), the center of your circle will be

y=(4*H^2 + T^2-B^2)/(8*H)


Nick