in connection with Figs. 33 to 36. This action continues until side B is heavier than side B′, when the reversed unbalanced condition of the car body causes a reversed precessional movement of the gyrostat wheels. This reversed precession continues steadily and unhastened so long as the heavy side B is balanced by the contact of the idle wheel i′ with the table L′, that is, until the projecting ends of the axles of spin A and A′ are brought forwards (in the figure) into the plane of the paper. Then the continuation of the reversed precession brings the axle A′ upon the table H′, the reversed precessional motion is then hastened, and this hastened precession raises the side B and lowers the side B′ of the car-frame, thus bringing the car-frame into its initial unbalanced condition (side B′ heavier than side B). The above-described action is then repeated, and so on.
The stability of the Brennan car is due to the hastened precession which is caused by rolling action of one or the other of the projecting axles of spin upon the tables H and H′, while the axles of spin are departing from a line at right angles to the length of the car, and to the steady and unhastened precession, while the axles of spin are moving towards a line at right angles to the length of the car. The hastened precession on the one hand quickly alters the condition of balance of the car so as to limit the departure of the axles of spin from a line at right angles to the length of the car, and the steady and unhastened precession, on the other hand, insures the complete return of the axles of spin to a line at right angles to the length of the car.
The hastened precession is accomplished with great friction losses by the rolling axles A and A′ in Fig. 37, and it is reported that Brennan is working upon an automatic motor-driven mechanism to produce the hastened precession without exhausting the energy of the gyrostat wheels.
Two devices like Fig. 37 with their rocker-axles at right angles to each other would hold a one-legged body in equilibrium; indeed, such a double mechanism would make it possible to use a one-wheeled car, but the wheel would have to have a deep double flange to make it roll along a rope or rail. Such a one-wheeled car, a sort of hyper-wheelbarrow car, would be of no value for practical use, and, indeed, most of us believe that Brennan's two-wheeled car is nothing more than a scientific toy.
Calculation of Torque-Reaction Due to Precession
Let n be the revolutions per second of a spinning wheel, P the revolutions per second (or the fraction of a revolution per second) of the axis of spin due to the precession, and K the moment of inertia of the spinning wheel in pound feet squared. Then the torque reaction is equal to poundal-feet or pound-feet.
- See Franklin and MacNutt'a "Elements of Mechanics," p. 150.