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TABLE 9.1
Empirical Formulas for Propulsion Resistance–Freight Rollingstock
Description Equation 9.20
Modified Davis equation (U.S.A.) K a [2.943 þ 89.2/m a þ 0.0306V þ 1.741k adV 2 /(m a n )]
K a ¼ 1.0 for pre 1950, 0.85 for post 1950, 0.95
container on flat car, 1.05 trailer on flat car,
1.05 hopper cars, 1.2 empty covered auto racks,
1.3 for loaded covered auto racks,
1.9 empty, uncovered auto racks
k ad ¼ 0.07 for conventional equipment, 0.0935
of containers and 0.16 for trailers on flatcars
French Locomotives 0.65m a n þ 13n þ 0.01m a nV þ 0.03V 2
French Standard UIC vehicles 9.81(1.25 þ V 2 /6300)
French Express Freight 9.81(1.5 þ V 2 /(2000…2400))
French 10 tonne/axle 9.81(1.5 þ V 2 /1600)
French 18 tonne/axle 9.81(1.2 þ V 2 /4000)
German Strahl formula 25 þ k ( V þ D V )/10 k ¼ 0.05 for mixed freight
trains, 0.025 for block trains
Broad gauge (i.e., 1.676 m) 9.81[0.87 þ 0.0103V þ 0.000056V 2 ]
Broad gauge (i.e., , 1.0 m) 9.81[2.6 þ 0.0003V 2 ]
K a is an adjustment factor depending on rollingstock type; k ad is an air drag constant depending on car type; m a is mass
supported per axle in tonnes; n is the number of axles; V is the velocity in kilometres per hour; and D V is the head wind speed,
usually taken as 15 km/h.
Ref. 14 and work by Profillides. 15 All equations are convertedtoSIunits and expressedasNewtons
per tonne mass (see Table 9.1 and Table 9.2).
Even with the number of factors described in Table 9.1 and Table 9.2, the effects of many
factors are not, and usually cannot be, meaningfully considered. If the rollingstock design area
is considered, how are the instances of poor bogie steer causing wheel squeal quantified? The
equations do not include centre bowl friction, warp stiffness or wheel–rail profile information. In
the area of air resistance, wagon body design is more variable than suggestedbythe few adjustment
factors presented here. The dynamicist should therefore be aware that considerable differences
between calculations and field measurements are probable.
TABLE 9.2
Empirical Formulas for Propulsion Resistance–Passenger Rollingstock
Handbook of Railway Vehicle Dynamics
Description Equation 9.21
French passenger on bogies 9.81(1.5 þ V 2 /4500)
French passenger on axles 9.81(1.5 þ V 2 /(2000…2400))
French TGV 2500 þ 33V þ 0.543V 2
German Sauthoff Formula Freight (Intercity Express, ICE) 9.81[1 þ 0.0025V þ 0.0055((V þ D V )/10) 2 ]
Broad gauge (i.e., 1.676 m) 9.81[0.6855 þ 0.02112V þ 0.000082V 2 ]
Narrow gauge (i.e., , 1.0 m) 9.81[1.56 þ 0.0075V þ 0.0003V 2 ]
K a is an adjustment factor depending on rollingstock type; k ad is an air drag constant depending on car type; m a is mass
supported per axle in tonnes; n is the number of axles; V is the velocity in kilometres per hour; and V is the head wind speed,
usually taken as 15 km/h.
© 2006 by Taylor & Francis Group, LLC