I this video, an 8 lb gyro on a rod supported at one end is spun up to several thousand rpm, and an assist is use to get the axis nearly horizontal. A small stick is used to nearly instantly stop the precession with very little force, since precession has no angular momentum (only the supporting framework would have any angular momentum):
If a gyro supported at one end is just released, initially it will fall downwards, but then transition into precession. If there was some sort of frictionless pressure sensor rod that the other end of the gyro was resting against, that prevented precession so that the gyro just fell down, how much force would that pressure sensor measure (the torque would be that pressure time distance to center of gyro)?
Instead of a rod to prevent precession, what if the supporting frame had significantly more mass (and more angular inertia) then the gyro? My impression is that the gyro would fall much further before transitioning into precession.
I've read that an aircraft with a single propeller at the nose will experience some yaw in response to pitch and vice versa. For example on a tail dragger accelerating from a top, if the aircraft is pitched down to lift the tail, the aircraft will yaw a bit. During the pitch down movement, the downwards moving blades experience more relative air speed and generate more thrust than the upwards moving blades, creating a yaw in the same direction as precession, so it's not clear how much of the yaw response is due to thrust differential versus precession.
Helicopters avoid this issue and the related stress by using a swash plate and hinged rotors, or flexible rotors, or pivoting hubs, or ... , so that the rotor can precess independently of the drive shaft and the rest of the helicopter. This also allows helicopters with wheels to taxi with the rotor tilted forwards, and then lift off with the rotor horizontal.
Electric unicycles (EUC) and the significance of precession effects
EUCs use forwards | backwards balancing algorithm similar to Segways. An EUC uses a 3 axis magnetometer, 3 axis gyro, 3 axis accelerometer, and can sense things like motor torque. The magnetometer uses earth's magnetic field to determine which way is up for tilt sensing, and which way is down so it can eliminate gravity from the accelerometer readings. Tilting the shell forwards | backwards results in acceleration | deceleration, and there is a balancing algorithm to keep the rider from falling.
From a rider's perspective, the rider leans forwards | backwards to accelerate | decelerate. To lean forwards, similar to standing on solid ground, a rider initially presses with the heels to lean forwards. On an EUC, this commands the EUC to decelerate from under the rider, causing the rider to lean forwards. Once the lean is started, and also similar to standing on solid ground, the rider presses with the toes to control the lean angle. When on an EUC, the toe pressure and the self-balancing algorithm accelerate to hold or adjust the forwards lean angle. Similarly, leaning backwards starts off with pressure on the toes, and so on. There's no need for a rider to be aware of all these details, so the rider only has to focus on leaning forwards | backwards to accelerate | decelerate.
Balancing left and right requires the EUC to be steered into the direction of fall to keep the tire's contact patch under the center of mass. At sufficient speed, around 8 mph, an EUC will become stable and self balancing (within reason) due to camber effects, allowing a rider to ride in a straight line without having to focus on balance.
At low speeds, an EUC can be twisted side to side, called yaw steering, to steer for balance and direction. Extending the arms and arm flailing, flail left to steer right and vice versa is somewhat instinctive for most beginners. Example of a 3 year old arm flailing:
At stable speed, an EUC can be leaned left or right, called tilt steering, to cause it to turn. The tire tread is round, and when tilted, the inner part of the contact patch has a smaller radius, than the outer part, similar to a truncated cone, causing the EUC to turn at a fixed radius depending on tilt and lateral load (contact patch flexing inwards will increase radius), mostly independent of speed.
Tire characteristics determine tilt to camber response. A wider tire has more camber response than a thinner tire. A street tire has more camber response than an off-road knobby tire.
Since the turning response to tilt is mostly independent of speed, for a tight turn at lower speed, the rider barely leans while tilting the EUC a lot:
Depending on tire, speed, turning radius, ... , at some point a rider leans inwards more than the EUC is tilted. Link to a 3 view clip, where the middle view is of an EUC with a 4 inch wide tire, which has a lot of camber response, so requires only a small amount of tilt, much less than the rider is leaning:
In this video, a girl is riding an EUC with an 18 inch diameter, 3 inch wide tire, and due to weight, tire, speed, turning radius, ... , the girl leans more than the S18 is tilted at around 15 to 20 mph:
The main issue for learning how to turn well on an EUC is coordinating how much to lean (body) and tilt (EUC), depending on speed and turning radius. For a typical turn, a rider leans inwards (details - the pedal pressure to lean inwards causes an EUC to tilt and steer outwards from under the rider, leaning the rider inwards, counter-steering, but a rider can just focus on leaning inwards), and then the rider tilts the EUC inwards to control lean angle via counter-steering: tilt more to lean less or straighten up, tilt less to lean more.
A combination of tilt and yaw steering can be used, for carving like weaving, or for making tighter slow speed turns: the rider turns upper body inwards while tilting inwards to build up momentum while going straight, then turns legs and EUC inwards using the built up momentum to increase the yaw rate.
During a turn, a rider's outwards reactive force is exerted near the center of the pedals on an EUC, about 6 inches above the contact patch, creating an outwards roll torque on the EUC. The rider's inwards tilt input creates an inwards roll torque on the EUC to counter this, and in a coordinated turn, there is no net torque about the roll axis on an EUC. The EUC is held at a fixed tilt angle required for a coordinated turn, based on speed, turning radius, tire aspects, ... .
Camber effect generates a yaw torque on EUC and rider, but in a constant turn, the only torque involved is what needed to yaw the rotating wheel. This yaw torque times the angular momentum of the wheel would cause a outwards roll precession response, but the rider prevents any precession response, which may result in additional outwards roll torque, but I don't know how to quantify what that additional torque would be. Since the rider will oppose any outwards roll torque on the EUC with an inwards roll torque to hold the EUC at a fixed tilt angle for a coordinated turn, if there is a precession effect, the rider wouldn't be able to distinguish it from camber effect.