one 12 millionth part of ½CR2, the rotation energy of the earth.
5. If the preponderance is absent, by making the C·G coincide with O, and if Aμ is insensible compared with G′,
N = −G′μ sin θ,
(1)
the formula which suffices to explain most gyroscopic action.
Thus a carriage running round a curve experiences, in consequence Gyroscopic action of railway wheels. of the rotation of the wheels, an increase of pressure Z on the outer track, and a diminution Z on the inner, giving a couple, if a is the gauge,
Za = G′μ,
(2)
tending to help the centrifugal force to upset the train; and if c is the radius of the curve, b of the wheels, C their moment of inertia, and v the velocity of the train,
μ = v/c, G′ = Cv/b,