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Encyclopedia > Gyro Monorail

The gyro monorail, gyroscopic monorail, gyro-stabilized monorail, or gyrocar all denote a single track land vehicle, road or rail, which uses the gyroscopic action of a spinning wheel, which is forced to precess, to overcome the inherent inverted pendulum instability of balancing on top of a single rail. A gyrocar is a two-wheeled automobile. ...

The gyroscope actually only supplies the transient moments required to stabilize the vehicle about an equilibrium position. Steady state disturbances, such as laterally offset loads, crosswinds or cornering forces are resisted by leaning into the disturbance, establishing a new equilibrium position, with the gyros near their undeflected state. This article or section does not cite its references or sources. ...


Principles of Operation

Basic Idea

The gyroscopic monorail is associated with the names Louis Brennan, Schilovsky and Scherl, who each developed prototype vehicles using the technology of the early 20th Century. Louis Brennan (1852 – 1932) was an inventor. ...

The vehicle runs on a single conventional rail, so that in the absence of the balancing system, it would topple over.

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A spinning wheel is mounted in a gimbal frame whose axis of rotation (the precession axis) is perpendicular to the spin axis. The assembly is mounted on the vehicle chassis such that, at equilibrium, the spin axis, precession axis and vehicle roll axis are mutually perpendicular.

Forcing the gimbal to rotate causes the wheel to precess resulting in gyroscopic torques about the roll axis, so that the mechanism has the potential to right the vehicle when tilted from the vertical.

If we arranged the actuation such that the rate of rotation of the gimbal is a linear combination of roll rate and roll angle, a stable system should result.

Ideally, we should prefer the actuation to be passive (an arrangement of springs, dampers and levers), but the fundamental nature of the problem indicates that this would be impossible. The equilibrium position is with the vehicle upright, any disturbance from this position reduces the height of the centre of gravity, lowering the potential energy of the system. Whatever restores the system to equilibrium must be capable of injecting this difference in potential energy, and hence cannot consist of passive elements alone. The system must contain an active servo of some kind.

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Now, the rigid feedback system outlined above would be unsatisfactory for a number of reasons. Forcing constant precession rates implies a rigid coupling of the servo to the gimbal, so that servo failure would most likely cause the gimbal to lock, with immediate catastrophic consequences.

Although such safety critical components are commonplace in aerospace design, we should prefer to design the system to have some tolerance of servo failure. The actuation should be designed such that failures cause the servo to ‘float’ and apply minimal forces to the gimbal, so that there may be sufficient time to bring the vehicle to a halt before the situation becomes too serious.

Passive Behavior

The vehicle/gimbal/gyro system described above is essentially a spinning top with toppling moment applied in one plane but not the other. The motion is described as two oscillations – a high frequency nutation mode, and a low frequency precession mode. With no feedback at all to the gimbal, the gyro is just dead weight, so the vehicle would simply topple over.

Gyros work because each particle of a wheel which is simultaneously spinning and precessing follows a trajectory with respect to inertial space which is symmetrical about the spin, and precession axes, but asymmetrical about the third axis, hence applying Newton’s Second Law to each particle, and summing for the whole wheel, there is a net moment around the third axis. That’s it; there is nothing mystical or strange about it.

One minor point: although everything is rotating, it is assumed that the actual spin of the individual particles has no effect on the motion – Newton’s Laws of Motion only describe translational motion. Conventional analysis of the motion of rigid bodies deals only with the effects of the translational motions of the particles, summed over the body.

In order to impart static stability, it is necessary to engineer a toppling moment applied to the gimbal. In order to emulate the spinning top, the action of the gimbal static feedback must tend to force the gimbal further away from the equilibrium position – the gimbal mounting must be unstable. This could be arranged using a toggle mechanism, such as is typically used in a bathroom light switch. The action of this unstable mounting is referred to as ‘acceleration of the precession’.

Image:StaticStability.png Image File history File links StaticStability. ...

The effect of a stable gimbal mounting, which our engineering intuition might prefer, would be catastrophic. The resulting gyroscopic moment would act in the same sense as the toppling moment, rather than opposing it, so the toppling would take place more rapidly than if no feedback at all were applied.

With this feedback, the system behaves a lot like a sleeping top. After a while however, it will start to exhibit an oscillation in roll, which increases in amplitude with time. The friction in the system (gimbal pivots, etc.) dissipates energy – and consequently there must be a tendency to reduce the time-averaged height of the centre of gravity. It isn’t an immediate divergence, as some energy is stored in the precession mechanism, but in the long term, the vehicle will eventually topple.

By careful design, the time taken for the roll oscillation to build up may be sufficient to render the vehicle safe by other means. It seems possible to design a balancing system, which in the event of servo failure degrades to a system which is statically stable, but dynamically unstable.

Damping the Precession

Simply by applying mechanical feedback to the gimbal we appear to have achieved our main design objective of getting the vehicle to stand up at all. However, the divergent oscillation which will always be present using a passive system, is clearly unsatisfactory, and some means of countering it is required. It is in the methods of damping out this oscillation that the differences between the Brennan and the Schilovsky balancing systems become apparent.

Some authors classify the systems on the basis of the orientation of the gyros; Brennan preferred horizontal spin axes, whilst Schilovsky preferred vertical. This reflects a rather superficial understanding of the principles of operation of the two designs. August Scherl used vertical axis gyros, but the precession mechanism was based on the same principles as that of Brennan. This similarity became the basis of a copyright dispute, but it is reasonable to surmise that the two pioneers arrived at their designs independently.

We start with the Scherl/Brennan solution. The cause of the divergence in the vehicle roll angle was traced to friction in the gimbals, so the cure would appear to provide positive velocity feedback (effectively negative friction) to the gimbal. After all, positive static feedback appeared to render the system statically stable.

As already mentioned, the motion is characterised by a high frequency (nutation) oscillation and a low frequency (precession) oscillation. The effect of friction is to damp out the nutation but provide negative damping to the precession, hence the divergent oscillation seen in practice. Reversing the sign of the friction would, on the face of it, have a catastrophic effect. The precession would indeed be positively damped, but the nutation would now be negatively damped. Rather than having a gradual, fairly benign, failure mode, the vehicle would topple immediately.

However, the cost of a servo which can respond sufficiently quickly to influence the nutation at all would be prohibitive. By choosing a servo bandwidth roughly equal to the pendulum period of the vehicle (i.e. the period it would have if suspended from the rail, rather than resting on it), the positive rate feedback would only influence the lower frequency precession mode, and would have negligible effect on the nutation. Hence by applying the feedback through a relatively slow (and consequently inexpensive) servo, both modes may be stabilised.

Schilovsky, and quite a few modern authorities, considered the Brennan design intrinsically flawed. His approach followed a different line of reasoning. He reasoned that a system designed to cancel roll angle must include roll angle explicitly as a feedback. Actually, by choosing the servo bandwidth suggested above, the servo behaves as an estimator of roll angle, so one could argue that the Brennan/Scherl design uses implicit roll angle feedback.

All Schilovsky designs used explicit feedback of roll, usually through various pendulum mechanisms. Unlike Scherl and Brennan, who each used linear-proportional actuation (either electric or pneumatic), Schilovsky always arranged for the actuation energy to be extracted from the gyro, and actuation was consequently intermittent. The resulting vehicle motion would inevitably include a steady state limit cycle, ‘wobble’, which may not be acceptable. There is no reason in principle why linear proportional actuation cannot be used with roll angle feedback.

Explicit roll angle feedback reduces the requirement for such a wide separation between the nutation and precession modes. This separation is determined by the size and spin rate of the gyro, hence the Schilovsky design can use smaller gyros than the Brennan design. The system does require a more rapid, and consequently more expensive, servo. Also when subjected to a contact side load (e.g. cross-wind or laterally offset load), the gimbal would exhibit a steady state deflection at equilibrium. With the bang-bang mechanisms which Schilovsky proposed, this would manifest itself as an increase in limit cycle amplitude. This effect could be removed by integral feedback, but Schilovsky never proposed this as a possible solution.

Whilst Schilovsky’s ideas would result in superior overall performance, their practical implementation requires a more sophisticated controller than the intermittent mechanisms proposed by him.

Side Loads

Once endowed with basic stability, how does the vehicle respond to disturbances? Inertial side forces, arising from cornering, cause the vehicle to lean into the corner. A single gyro introduces an asymmetry which will cause the vehicle to lean too far, or not far enough for the net force to remain in the plane of symmetry, so side forces will still be experienced on board.

In order to ensure that the vehicle banks correctly on corners, it is necessary to remove the gyroscopic torque arising from the vehicle rate of turn.

The roll torques generated by the gyro arise from the precession with respect to inertial space, but the control system deflects the gimbal with respect to the chassis. It follows that the pitch and yaw motion of the vehicle will introduce additional unwanted, gyroscopic torques. These give rise to unsatisfactory equilibria, but more seriously, cause a loss of static stability when turning in one direction, and an increase in static stability in the opposite direction. Schilovsky encountered the problem with his road vehicle, which could not make sharp left hand turns.

Brennan and Scherl were fully aware of this problem, and implemented their balancing systems with pairs of counter rotating gyros, precessing in opposite directions. With this arrangement, all motion of the vehicle with respect to inertial space causes equal and opposite torques on the two gyros, and are consequently cancelled out. With the double gyro system, the instability on bends is eliminated and the vehicle will bank to the correct angle, so that no net side force is experienced on board.

Image:Cornering.png Image File history File links Cornering. ...

Schilovsky claimed to have difficulty ensuring stability with double-gyro systems, although the reason why this should be so is not clear. His solution was to vary the control loop parameters with turn rate, to maintain similar response in turns of either direction. The asymmetry would still result in a net side force being experienced on board.

Offset loads similarly cause the vehicle to lean until the centre of gravity lies above the support point. Side winds cause the vehicle to tilt into them, to resist them with a component of weight. These contact forces are likely to cause more discomfort than cornering forces, because they will result in net side forces being experienced on board.

The contact side forces result in a gimbal deflection bias in a Schilovsky loop. This may be used as an input to a slower loop to shift the centre of gravity laterally, so that the vehicle remains upright in the presence of sustained non-inertial forces. This combination of gyro and lateral cg shift is the subject of a 1962 patent. A vehicle using a gyro/lateral payload shift was buit by Ernest F. Swinney, Harry Ferreira and Louis E. Swinney in the USA in 1962.

Why Bother?

When proposed, the gyro monorail could only be constructed by nations which had extensive railway networks, and consequently had no use for it.

Unlike conventional railways, a monorail can turn corners and climb gradients, so that less capital outlay is required in viaducts, tunnels, etc. required to keep the track straight and level. Typical high speed train designs have radius of turn of 7km, with relatively few options for new routes within developed countries, where all the land is owned by somebody.

Whilst the individual vehicles are likely to be expensive, the greatest cost arises from the construction and maintenance of the permanent way, which, for a single rail at ground level must be cheaper.

Safety is more an imagined than a real problem. It is evident that the risks inherent in the gyrotrain are orders of magnitude less severe than those inherent in civil aviation. The latter are tolerated by the travelling public for no reason other than familiarity. The angular momentum in the gyros is so high that loss of power will not present a hazard for a good half hour in a well designed system. Servos, being force, rather than position, demand can be easily designed to prevent locking in the event of failure, and sufficient residual stability is available to bring the vehicle safely to a halt. In any case, duplexing should not be a major problem.

When considering failure modes, two-track vehicles only have familiarity to recommend them. When the side force builds up, there are no cues that the situation is becoming dangerous, until at a critical value, the vehicle starts to topple. Unfortunately, the resisting moment of the two track vehicle then actually decreases as toppling proceeds, and there is no hope of recovery.

Image:Toppling.png Image File history File links Toppling. ...

Contrast that with the gyrotrain. The more the side force builds up, the further the vehicle leans into it, giving obvious early warning of a dangerous situation. The resisting force always increases with toppling, to resist the toppling moment further. This is gracious degradation, whilst the two track response is brittle failure; a feature of bad design, which is tolerated only because it reflects traditional comfortable modes of thought, not because it has any real merit.

When testing the roll stability of two-track vehicles it is standard practice to place them on a tilting ramp, and increasing the tilt until toppling occurs. Under the same circumstances, a gyrotrain would stay upright regardless of the angle of tilt of the ramp.

Then we have the equally specious objection on the grounds of weight. Schilovsky pointed out that his designs were actually lighter than the equivalent duo-rail vehicles. The gyro mass, according to Brennan accounts for 3-5% of the vehicle weight, which is comparable to the bogie weight saved in using a single track design. If anything, the monorail solution would be lighter.

High speed conventionally requires straight track, introducing a right of way problem in developed countries. Wheel profiles which permit sharp cornering tend to encounter the classical hunting oscillation at fairly low speeds. Running on a single rail is an extremely effective means of suppressing hunting.


  • Schilovsky P P - The Gyroscope, It's construction and Practical Application, E Spon Publications 1922
  • Cousins H - The Stability of Gyroscopic Single Track Vehicles, Engineer Nov 21, Nov 28, Dec. 12 1913
  • Graham R - Brennan, His Helicopter and other Inventions, Aeronautical Journal, Feb. 1973

See Also

A gyrocar is a two-wheeled automobile. ...

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