Reduce tangent error on Haig barndoor mount

Over the weekend, I made myself a simple hand-powered Haig barndoor mount with the standard 1 RPM dimensions (11.43" distance of bolt from hinges, 20 per inch thread). Not wanting to deal with hardware complication, I planned to do tangent correction in software (i.e., I made a simple Android app that shows where to turn the circle). But I noticed that when I put in all the parameters, the amount of tangent correction from my app was strangely small.

It turned out that a chance modification I made to the Haig design reduced tangent error quite a bit.

To save a few cents, instead of using an acorn nut on threaded rod, I used a carriage bolt's rounded head to bear on the upper surface of the mount. (Of course I filed and sanded the head for smoothness, by chucking the bolt into a drill press.) The cost of this modification was nil, and the amount of work was a few minutes of filing and sanding.

It turns out that the wide rounded head of the carriage bolt corrects tangent error quite a bit. Assuming that the threaded insert for the bolt is slightly countersunk (I didn't actually do this, but optimum performance would then be achieved) so that at minimum extension we get zero angle in the mount, tangent error after 10 minutes of operation is about one second of arc, versus seven seconds of arc for the standard mount.

Here is a graph of the tangent error. The x-axis is time in minutes and the y-axis is tangent error in seconds of arc. Red line is standard Haig tangent mount and blue is the mount with the rounded head. In the calculations, I assumed the head is spherical in profile, and my estimate of the sphere radius is 0.378. (The larger the sphere radius, the better the correction, I think.)

And here's the mount.