# How can precession produce a torque in the direction of precession when it has no angular momentum?

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.

Precession

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.

• In my opinion: when it comes to gyrosopes it is necessary to provide a picture/diagram that gives enough view to convey a 3D understanding of the setup envisioned in the question. The words 'the supoorting framework' do not give enough clue. The motion of a gyroscope is inherently in all three spatial dimensions concurrently, there's a lot going on. For the underlying mechanism: my 2012 discussion of gyroscopic precession (This discussion is illustrated with diagrams created with 3D software (ray-tracing)) Jul 25, 2022 at 15:54
• You start your question with: "How would the precession differ if [...] " That is: you are asking about a setup that is modified as compared to what is in the video, but your indication of what you have in mind does not give enough clue. In the video: yeah, that flimsy rod was effective in stopping the precessing motion of that gyro wheel. The subsequent falling bumped the flimsy rod harder than the precessing motion did. Precessing motion is constant angular velocity, and here actually not that fast. With falling there is constant acceleration, resulting in harder hit to the flimsy rod. Jul 25, 2022 at 16:20
• @Cleonis - the falling was claimed to produce the same rate of rotation about the support as it did when precessing, about 1 revolution per second. I recall someone confirming it was close with a slow motion capture of that video. The point the professor was making is there is angular velocity when precessing, but no angular momentum in the direction of precession, which is why the peg was minimally disturbed when it stopped the precessing gyro. Jul 25, 2022 at 19:53
• @Cleonis - I updated my question, asking how much force a frictionless pressure sensor rod would sense if it prevented precession. Jul 26, 2022 at 2:03

Just to be clear: when it comes to the motion of gyroscopes Eric Laithwaite is not an authority. When it comes to gyroscopes Eric Laithwaite managed to sidetrack himself. Any inferences or conclusions stated by Eric Laithwaite arise from him misunderstanding the mechanics of gyroscopic precession.

On the subject of gyroscopic precession my view is as follows:

There is for one thing the physics fact that gyroscopic precession is counter-intuitive.

But then comes the following: the standard way of accounting for gyroscopic precession is by application of the concept of angular momentum vector, using the angular momentum vector in combination with operations such as vector cross product. The concepts of angular momentum vector and vector cross product are themselves abstract concepts, and the act of combining the two is not accessible to intuitive understanding.

Now, we will agree on the following: the whole point of doing physics is to try and gain an understanding of things that are not immediately comprehensible.

Example: when water freezes the ice takes up more volume. All other substances display a monotonic relation of volume as a function of temperature: colder: less volume; hotter: more volume. So what's going on with water? Physics provides understanding: there is the shape of the water molecule, and how water molecules interact with neighbouring water molecules, all of that explains this unusual property of water. You can understand the structural integrity of ice in the way you can understand the structural integrity of, say, an icosahedron. I will refer to that type of understanding as transparent understanding.

Circling back to the concepts of angular momentum and vector cross product: while mathematically correct, they don't provide transparent understanding.

The exposition of gyroscopic precession that I posted in 2012 does not use the concept of angular momentum vector.

I assert that in the specific case of trying to gain a transparent understanding of gyroscopic precession the abstract concept of angular momentum vector is not helpful, but instead a hindrance.

I assert that when you gain transparent understanding of gyroscopic precession you will see the demonstrations by Eric Laithwaite in a new light. Everytime the gyro wheel goes in climbing motion there is an assist.

(This is the most vivid in the demonstration where Laithwaite lifts a very large, very rapidly spinning gyro wheel over his head. Laithwaite provides the assist with a swing in the horizontal plane.)

Electric Unicycles

In response to the videos with electric unicycles:
The relevant case, of course, is when the high power electric unicycle is going at high speed.
(I have a normal unicycle myself. I'm not proficient, but on smooth surface I can get around.)

I gather the forward/rear balancing is the same technology as implemented in Segways.

In the case of cornering at high speed:
I expect the following steering authority is the main contributor.
As the rider approaches a turn: in preparation the rider allows a sideways lean to develop.
There is the center of mass, COM, of the rider plus EUC, and there is the contact patch of the wheel.
During cornering the contact patch has to cover a bit more distance than the COM, since the contact patch is further away from the center of cornering.
In order to provide the contact patch with that bit of extra velocity the rider must use his footplate input to coax the EUC to go a bit faster.
The COM and the contact patch are cornering together; the COM is taking the corner on the inside, the contact patch on the outside.

To get out of the cornering motion the rider must move the contact patch back under the COM. The rider must simultaneously coax the EUC to reduce the velocity a bit, so that it is once again going at exactly the same velocity as that of the COM.

I expect that any gyroscopic effect will be swamped by other larger effects.

I expect that the learning process falls in the realm of subconscious learning. The rider tries, the first attempts are wobbly and erratic. Over time the human subconscious balancing system will figure it out, and over the course of many tries, and nights of good sleep, the cornering becomes smoother and more confident.

I assume the rider is using footplate input all the time to keep forward/rearward balance, all subconsciously. It seems likely to me that the rider will not be consciously aware of the special footplate input that accompanies cornering.

About the video demonstrating high speed cornering, using three different tires. when in a tilted orientation: depending on the profile the tire will have a tendency of its own to move along a curve. By the looks of it: the rider must bring that tendency in alignment with the intended radius of cornering. So, in order to corner with the same radius of cornering with each tire: the rider has to set up the appropriate amount of tilt. As can be seen in the video, this appropriate amount of tilt of the wheel can be different from the amount of overal body lean that is necessary for cornering at the rider's velocity.

• I'm mostly interested in how precession affects electric unicycles (EUC). In this video clip, the EUC in the middle has the most camber effect response, and the rider leans and|or hangs off much more than the EUC is tilted. During a turn, the outwards reaction force from the rider is exerted onto the EUC near the center of the pedals, creating an outwards torque on the EUC. The rider exerts an inwards torque on the EUC to counter the outwards torque. Jul 26, 2022 at 7:48
• Camber effect is mostly independent of speed, so for slow speed tight turns, the rider barely leans but tilts the EUC a lot slow speed tight turns. Depending on the tire, at sufficient speed, the rider leans more than the EUC is tilted moderate speed turns. It takes a while for a beginner to learn how to coordinate lean and tilt depending on speed and turning radius, and for this to become almost reflexive, like riding a bicycle. Jul 26, 2022 at 8:28
• @rcgldr I watched the video with high speed cornering. I added discussion of what I think at high speed is the main factor in cornering. Jul 26, 2022 at 10:15
• I deleted some comments, and I'm adding a section to my question. Jul 27, 2022 at 14:15