The Fool on the Hill: Tricycle Stability

A tricycle is a vehicle with three wheels, typically with two wheels, spaced laterally apart, on a single axis, with the third placed laterally centrally with respect to the other two but significantly either forward of aft of their axis. Its contact with the ground is the contact patches of those three wheels. The forces on a tricycle can be considered to act through the centre of mass. These forces will typically be

1. Gravity;
2. Linear acceleration whether through acceleration or through braking;
3. Lateral acceleration as a result of steering.

So long as the resultant vector of these forces, through the centre of mass, intersects the ground within the triangle described by the contact patches of the wheels, the tricycle will remain upright. If it moves outside that triangle, the tricycle will topple, often very suddenly.

This has a number of consequences.

If the centre of mass is directly over the axis of the two paired wheels, then the vehicle will have the same lateral stability (for a given centre of mass height) as that of a four-wheeled vehicle with the same track, but its fore-and-aft stability will be virtually nil. If the centre of mass is directly over the single wheel, then the stability in either direction will be close to nil. The lateral stability, as a proportion to that of a four wheeled vehicle with the same track and same centre of mass height, increases linearly as the centre of mass moves from the end with the single wheel to the end with the two wheels. The fore and aft stability is at its greatest when the centre of mass is midway between these points, where the lateral stability is exactly half that of the four wheeled equivalent.

Obviously, traction is at its greatest when the centre of mass is over the driven wheel(s), and declines linearly as the centre of mass moves towards the other end of the vehicle.

Friends of my parents used to race conventional upright delta tricycles, which are fiendishly difficult vehicles to manage at speed because the centre of mass is relatively high, the track relatively narrow, and, at racing speeds, toppling the tricycle is likely to be catastrophic. To steer, the rider had to lean out from the vehicle as far as possible into the turn — an acrobatic feat. I've ridden those vehicles — many years ago. They look as though they would be docile and easy to manage. They are the very opposite.

Got all that?

Well, on a Mosquito style trike, the centre of mass moves laterally as you steer — and instead of moving into the turn, it moves out of the turn, further destabilising the trike. For a vehicle with the aerodynamic potential to develop quite high speeds, at least on descents, this is significantly problematic.

But there's worse.

It will be fairly easy to calculate the maximum safe lateral acceleration of the trike on a flat horizontal surface. But roads are neither flat nor horizontal. They have camber, and on the outside of a bend that camber is typically adverse, reducing stability. Furthermore, descents are, by their nature, downhill. The gravity vector, and thus the resultant vector, swings forward with respect to the vehicle. And worse again, if, when approaching the limits of stability, you brake in order to reduce speed, the resultant vector swings yet further forward.

If, as in the Mosquito design, the single wheel is at the front, then as the resultant vector swings forward it swings into the zone in which the triangle is getting progressively narrower. So if you're entering a bend on a descent and you feel you're going too fast to make that bend safely, braking is exactly the worst thing you can do.

The location of the centre of mass — inevitably somewhere close to the rider's belly, since the rider will be about 70% of the total weight of the vehicle — is constrained by the fact that the rotational axis of the pedals, and therefore the rider's feet, have to be in front of the front wheel. So the only way to move the centre of mass nearer to the wider end of the triangle is to move the rear axle forward, shortening the wheelbase and probably resulting in a choppier ride, and consequently worse handling.

This is a theoretical problem. The Mosquito prototype has certainly been tested on fast, twisty descents, and it is not reported that it has ever crashed badly. It's also true that the centre of mass of a Mosquito-style trike is pretty low.

Given my idea of a one piece monocoque body which is roughly egg-shaped with two roll-over hoops, in a roll-over the vehicle would almost certainly roll right over, suggesting that a four point harness would be much more relevant than a crash helmet; but, with a four point harness, the rider would stay in the body and would be fairly protected.

But it's nevertheless worrying, and it's making me reconsider whether this is the right design.

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