Simon Iwnicki (Editor)_ Maksym Spiryagin (Editor)_ Colin Cole (Editor)_ Tim McSweeney (Editor) - Handbook of Railway Vehicle Dynamics, Second Edition-CRC Press (2019)

A History of Railway Vehicle Dynamics
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FIGURE 2.3 Forces acting on a vehicle in a curve according to Mackenzie. (From Mackenzie, J., Proc. Inst.
Civil Eng., 74, 1–57, 1883; With kind permission from CRC Press: Handbook of Railway Vehicle Dynamics,
CRC Press, Boca Raton, FL, 2006, Iwnicki, S. [ed.].)
He then applies similar reasoning to the other wheels, assuming various positions for the wheelsets
in relation to the rails. Thus, Mackenzie’s calculations showed that the outer wheel flange exerts
against the rail a force sufficient to overcome the friction of the wheel treads. Previously, centrifugal
forces were regarded as the cause of many derailments. He also made the comment that ‘the vehicle
seems to travel in the direction which causes the smallest amount of sliding’, which foresaw a later
analytical technique developed by Heumann.
Subsequent work by Boedecker, Von Helmoltz and Uebelacker (described by Gilchrist [9]) was
dominated by the need to avoid excessive loads on both vehicle and track, caused by steam locomotives,
with long rigid wheelbases traversing sharp curves. Hence, in these theories, the conicity of
the wheelsets is often ignored, and the wheels are assumed to be in the sliding regime. The corresponding
forces are then balanced by a resultant flange force, or flange forces. This approach
culminated in the work of Heumann in 1915 [10] and Porter in 1934 to 1935 [11].
Superelevation of tracks in curves was introduced on the Liverpool and Manchester Railway, and
tables giving the relationship between superelevation of the outer rail and maximum speed were
available in the 1830s.
2.4 DYNAMIC RESPONSE, HUNTING AND THE BOGIE
It was thought by some early engineers that the track would be so smooth that no vertical suspension
would be necessary, but many rail breakages showed that it was necessary to reduce the stresses
on the track. William Chapman recognised that, if the weight was spread over several axles, it was
necessary to provide flexibility in a plan view to allow the locomotive to follow the curvature of the
track. In an 1812 patent with his brother Edward Walton Chapman [12], they suggested a scheme in
which the leading wheelset was mounted rigidly in the locomotive body and the trailing wheelsets
mounted in a frame pivoted to the locomotive body, in other words, a bogie. It was envisaged that a
proportion of the weight of the body would be carried by the bogie through conical rollers, so as to
allow rotational freedom of the bogie relative to the body. However, the arrangement was not ideal
in that the wheelsets could not adopt a radial position on curves necessary for pure rolling of the
wheels. As Marshall [13] comments, what was proposed was either a trailing bogie or a doublebogie
locomotive but not a leading bogie with the driving wheels fixed in a frame, which was to
become, eventually, the most successful configuration for the steam locomotive. The concept was
not widely adopted further at that time, probably because rail materials improved.