Train Resistance on Level Track (Davis Formulas)
The rolling and air resistance of freight cars at steady speed on level, straight track.
Example
You enter
- Gross weight of one car (tons) 132
- Axles per car 4
- Speed (mph) 30
- Air coefficient K (0.07 conventional, 0.0935 container, 0.16 trailer) 0.07
- Cars in the train 100
You get
- Resistance (lb/ton) 1.9833
- Train resistance (lb) 26180
- Power at the rail 2,094 hp
- Same as a grade of 0.099%
Checked against published worked examples from: Conference on Railway Excellence (RTSA).
Details, formula, and sources
Scopein pounds per ton and pounds for the train. It uses the 1970 modified Davis formula, with the AAR RP-548 and original 1926 Davis results beside it because published constants disagree. A hundred 132-ton four-axle cars at 30 mph resist at 1.98 lb per ton, 26,180 lb for the train, which takes 2,094 hp at the rail. Cars only: locomotives, grade and curves are extra. The railroad's own train-performance data governs.
Formula or tablePounds per ton, w = tons per axle, n = axles per car, V = mph. Modified Davis (1970): R = 0.6 + 20/w + 0.01 V + K V^2/(w n), K = 0.07 conventional, 0.0935 containers, 0.16 trailers on flat cars. AAR RP-548: R = 1.3 + 72.5/(w n) + 0.015 V + 0.055 V^2/(w n), printed for a four-axle car and applied as 18.125 lb per axle. Davis (1926), freight cars: R = 1.3 + 29/w + 0.045 V + 0.0005 A V^2/(w n), shown at A = 110 sq ft. Train pull = R x car tons x cars; power at the rail = pull x V/375; equivalent grade in % = R/20.
Source and editionW. J. Davis Jr., The Tractive Resistance of Electric Locomotives and Cars, General Electric Review, 1926; the 1970 modified Davis equation as carried in the AREMA Manual for Railway Engineering, Chapter 16; AAR Recommended Practice RP-548. All cited by name.
Free accessThe 1926 and RP-548 forms were read from F. Szanto, Rolling Resistance Revisited, Conference on Railway Excellence, Melbourne, 2016, eqs. 1 and 2, free at rosap.ntl.bts.gov/view/dot/79083. Its Table 1 lists RP-548 for an 80 tonne four-axle wagon as 11.9, 21.7 and 26.9 N per tonne at 20, 80 and 100 km/h; this tile gives 11.8, 21.6 and 26.8 (the paper rounds its metric constants). The 1970 form and its K values are the widely published ones and were not read from the AREMA Manual itself.
What governsEstimate. AHJ and licensed professional govern.
API field namescar_weight_tons, axles_per_car, speed_mph, air_coefficient, cars, resistance_lb_per_ton, train_resistance_lb, power_hp, equivalent_grade_pct
- Identical cars one weight and axle count for the whole train; run mixed blocks separately and add the poundsscope of this tile
- RP-548 axle term 72.5/(w n) for four axles, taken as 18.125 lb per axle for other countsSzanto (2016) eq. 2
- 1926 frontal area 110 sq ft, the area RP-548 carriesSzanto (2016)
- Level tangent track, steady speed no grade, curve, acceleration or windscope of this tile