Posted by Christopher (65.35.121.212) on March 05, 2002 at 22:16:37:
I have something that I'd like to run past anyone who is fluent
in physics related math...
I am toying with a wheel that has "trigger points" every 45 degrees.
When a "trigger point" (TP) is reached weights shift and the
Center of Gravity (CG) moves to the right. This shift unbalances
the wheel and causes it to turn, hopefully, far enough to reach
the next TP or beyond.
I have calculated the CG at 7 points of rotation between 0 and 45
degrees (more than that is not necessary since the CG returns to
the 0 x,y location if we make it to the next TP. In other words,
the CG path repeats every 45 degrees of rotation.
Assuming (0,0) is the center of the wheel, the total of all the
weights is approx. 60 lbs, the wheel radius is 50 inches,
and the wheel is rotating clockwise, would the following CG path
indicate OU?
Degree of Rot. CGX CGY Theta
0 2.82 -2.82 45.00
7.5 2.43 -3.16 37.50
15 1.99 -3.45 30.00
22.5 1.53 -3.68 22.50
30 0.73 -3.46 11.93
37.5 0.03 -3.10 0.52
45 -0.56 -2.63 -12.12
It looks to me like there are 5 points to the right of center
where speed/rotation would be increased, one point in the center
which would probably have little effect, and one point to the left
to slow it down. The start and end Y locations are not even that
different from one another so it's not like the CG has to climb
some gigantic hill at the end.
Seems straightforward to me but I MUST be missing something...