I am working on a watch face with a tourbillon hour hand and a large retrograde minute hand. I am using the expression (490 + (#DWFMS#/ 360 * 260)) and it works fine for 0 - 30 minutes, but then goes wrong.
You can do it with two hands hiding the one that has gone off track . You can use a non liner formula involving sin and rad or you can look at a +/- formula and use abs in it . I will have a look after Dinner . That particular hand is not best for stretching as it will change shape.
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This is a very crude solution following on from your Liner Concept . I found the scale you have a bit misleading . Going from 0 to 55 . Well if you wanted to run it in 5 minute steps that would be fine .
I will have a look at a non liner but someone might get there before me .
BTW I used the Minute hand for this test .
The curve looks elliptic, so using the the formula for an elliptical path, the formula for the height would be (used seconds for easy simulation, you can change to minutes):
(468/(sqrt(1-0.36*sin(rad(#DWFSS#/2)))))
I am assuming 220 degrees path as opposed to @russellcresser - makes it a little easier with the formulas.
So the rotation is: (220-(((#DWFSS#)/(360/80))))
The Hand details (using the standard one in your diagram):
X: 160
Y: 17
Width: (146/(sqrt(1-0.36*sin(rad(#DWFSS#/2)))))
This width makes the hand look proportionate all the time, although it only varies between 146 and 182.
Looking forward to checking that out Tom . When I am simulating angles I use #DWFHS# . Then I can use the time machine slider . I some times use it for positions stuff as well and Write the numbers down for later .