john_childs said:Have you run any sample calculations for constant foot acceleration
compared to constant foot speed? I'm too lazy to run the numbers right
now and it has also been a long time since I've done any dynamics so I'm
all rusty with the equations.
Yes, but before I go on, I'm not claiming this is very useful. The
problem being that as cranks get really short, you lose mechanical
advantage for controlling the unicycle and watse energy trying to
maintain stability.
That said, the equations are pretty simple. The magnitude of
acceleration, a, needed to keep your foot spinning on the pedal is
a = l*v^2/r^2
where l is crank length,
v is the unicycle's speed, and
r is the wheel's radius
Keeping forward speed and pedal speed constant yields the equation
l1 / r1^2 = l2 / r2^2
In words, crank length grows with the square of wheel size.
Concretely, taking a coker with 175mm cranks as the largest likely
combination and scaling down yields the following table of
iso-accelerated unicycles:
36" with 175mm cranks
29" with 113mm
26" with 91mm
24" with 78mm
20" with 54mm
To compare a different combination, you can multiply all the crank
lengths by the constant of your choice.
Ken