Unicycle Physics / Dynamics

A while ago I noted how mentally strenuous I found learning to unicycle.  This article is a primer for understanding the physics of riding a unicycle and hopefully eases some of the mental learning curve.  However, bear in mind this is simplified.  If you are learning I'd advise you continue to make your own observations.

Figure 1

Speed Changes
Getting started, you may have worked out that accelerating requires tipping the unicycle forward (Fig. 1).  And conversely, braking requires the unicycle to tip backward.  Remaining stationary or travelling at constant speed requires the unicycle to stay upright.

Figure 2

Regaining Balance
Consider Figure 2 where we view a rider from above that is situated in the center of a clock face.  The rider faces 12 o'clock.  Given the left-right and front-back symmetry of the device we need only consider the quadrant from 12-3 o'clock.

If a rider were to lose balance in the direction of 12 o'clock, all he need do is drive the wheel forward an adequate distance to regain his balance.  If a rider were to lose balance in the direction of 1 o'clock, he would need to twist at the waist and drive the wheel in the direction of 1 o'clock.  It is worth noting that the rider's upper body would be facing the 11 o'clock direction after a steering changing to the 1 o'clock direction.

When it comes to loss of balance in the 2 or 3 o'clock directions, things get a little more complex due to the rider's limited twisting range.  Regaining balance in these situations requires at least 2 co-ordinated movements.

Figure 4

Figure 3

In the case of falling toward 2 o'clock (Fig. 3), a rider would make a large movement in the 1 o'clock direction followed by a smaller movement toward 5 o'clock.  Regaining balance in the 3 o'clock direction (Fig. 4) is quite difficult and requires a sideways zig-zag in 1 and 5 o'clock directions.

Pedal/Crank Position
The orientation of the cranks has a serious effect on the manouvreability of the unicycle.  Specifically, the power and drive available when the cranks are horizontal (Fig. 5) is significantly greater than when they are vertical (Fig. 6).

Figure 6

Figure 5

Any torque applied to the wheel in the later position causes a reactionary twisting effect on the rider, which can be used to steer whilst riding.  The same reactionary force whilst applying torque in the former (horizontal) position is countered by the riders weight and merely causes a momentary lifting of the rider out of his seat.

Hopefully that's more than enough to get you started.  Enjoy.