# Onewheel Physics

Here is a description of an idea I had, to ride with a more defensive stance, the idea being maybe if it nosedives we can have a better chance of leaping off onto our feet instead of eating sh!t.  I got an A in all my physics classes but def not a physics major.  Please correct me where I'm less than correct.
1. The board's control loop gets its feedback from the rider by measuring the angle of the board with respect to the direction of gravity.
2. This angle is affected by the net torque exerted on the board chassis, one component of which is due to the motor twisting the wheel forward against the board chassis.  As the wheel spins in nose-down (forward rolling) direction, there is an opposite, nose-up direction torque on the board chassis (the board wants to pop a wheelie).  This is analogous to a helicopter without a tail rotor, which would spin out of control in the opposite direction as its top rotor.
3. So in normal use, just to avoid popping a wheelie, the user must constantly counteract this nose-up direction torque with an equal torque in the nose-down direction.  The user's constant forward lean fills the role of the helicopter's tail rotor.
4. If the user applies any more or less than this baseline amount of torque, then it will cause the net torque to become non-zero, and the board angle will change in the corresponding direction.  This is how the rider can control the board by stimulating it to accelerate.
5. Because there is nothing to push against, the only facility the user has for asserting torque is changing the distribution of their own weight due to gravity.
6. Torque is produced by applying force at a distance (in the same way pushing on a wrench twists a bolt).  Indeed, Torque = Force * distance
7. So the front foot will produce a torque, in the nose-down direction, equal to the fraction of the rider's weight over that foot times the distance from the foot to the axle. The back foot will produce an opposing torque, in the nose-up direction, equal to that foot's fraction of the rider's weight times that foot's distance from the axle.
8. Usually, people put each foot equally distant from the axle.  Let's analyze this situation: When stopped, with velocity and acceleration = 0, user must maintain equal weight on both feet, standing straight up. At low constant velocity, user has more weight on the front foot than the rear, so leaning forward some, to counter the torque from the motor and maintain board angle. At high constant velocity, even more weight must be over the front foot than the rear. Result is, user leaning forward always, and the faster they go the more forward they must lean.
9. We're hoping if we could ride with a more defensive posture, we'd be more likely to land on our feet when a nosedive happens.  Basically, we want a way to ride which doesn't have us always leaning forward as described in #8.  Put mathematically, we want a lower ratio of front foot weight to rear foot weight.
10. Let's make some variables.  Assign Ff = Weight on front foot, Df = Distance to axle of front foot, and Fr and Dr correspond to for rear foot.  And we said our desire is to have a lower Ff/Fr .
11. The net torque we assert on the axle, in the nose-down direction, is Ff * Df - (Fr * Dr)  .  Can we get lower Ff/Fr without changing this overall net torque value?  Sure!  By increasing Df/Dr
12. You can maximize Df/Dr like this:  Put your front foot as far *away* from the axle as you can, while still reliably triggering the sensors.  And, put your rear foot as *close* to the axle as you can, so it's practically about to rub on the wheel.  Basically, both feet as far forward as you safely can. This is the extreme and best illustrates the effect.
Try it.  First try just maintaining a stopped balanced position.  Notice to keep from moving you have to lean way back.  Now try standing perfectly upright, with equal weight on each foot - this will cause you will accelerate forward pretty fast.
Basically, the overall effect is you will ride in a more leaned-back, defensive position, perhaps more prepared to leap off onto your feet if it nosedives.  It kinda makes my back foot hurt after a while, because so much more weight is on it.
What do you think?