Okay lets try this: if the tie rod has 14 threads per inch (assumed, based on similar diameter fine thread bolts), then each revolution should move the rod 1/14 of an inch, however there are two ends turning so the result would be doubled, 2/14 or 1/7 (0.143) of an inch per revolution. Does that sound reasonable? (I'm a civil engineer, not a mechanical engineer).
Mechanical engineers build weapons, civil engineers build targets.
I'm not aware of any short steering arms, but only the shorter pitman arm, which doesn't affect the tow in.While I agree with your reasoning, I don't think you went far enough. The steerig arms are much shorter than the diameter of the wheels. We need to consider the diameter rather than the radius because as you screw the tie rod, the front of the wheels might (say) come closer together and the back of them get further apart, thus doubling the effect. The short steering arms exagerate things even more.
To answer the OP's question, I don't know but with a thread gauge and a tape measure, you should be able to get close.
Bill, I was referring to the relative legth of the steering arms in relation to the size of the wheels. The ball joints are much closer to the king pin than the tyres.I'm not aware of any short steering arms, but only the shorter pitman arm, which doesn't affect the tow in.
This is an interesting question, and someone should set the tires to 0 toe in, then turn the tie rod one turn and measure the toe in. If no one does, then I may do it some day.
I just did a similar thing on my 1950 Studebaker, and posted the results on the Studebaker website to help others with the same problem. My steering wheel was at 1 o'clock while driving straight ahead, and my toe in was perfect, so I had to turn each tie rod the same amount to set the steering wheel straight up at 12 o'clock.