Thanks Nick! Exactly what I was looking for. And thanks to everyone else
who contributed!

"nick" wrote in message
news
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