Train Resistance & Locomotive Tractive Effort Calculator
Calculate total train motion resistance via the modified Davis equation, grade and curve penalties, available wheel-rail tractive effort, and ruling grade performance.
Train Consist & Rolling Stock
Track Gradient & Locomotive Traction
Resistance & Traction Force Balance
| Davis Level Tangent Drag (R_davis): | -- kN |
| Grade Resistance (R_grade): | -- kN |
| Curve Drag Resistance (R_curve): | -- kN |
| Locomotive Available Tractive Effort: | -- kN |
| Wheel-Rail Adhesion Limit (Dry μ=0.33): | -- kN |
| Net Acceleration / Braking Force: | -- kN |
| Train Acceleration Rate: | -- m/s² |
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Frequently Asked Questions
What are the three components of the Davis train resistance equation?
Formulated by W.J. Davis in 1926, the equation models total train resistance as R = A + B*V + C*V². The "A" term represents mechanical rolling friction independent of speed (journal bearings and track deflection). The "B" term accounts for flange friction and wheel-rail shock impacts proportional to velocity. The "C" term represents aerodynamic drag (head-end pressure, skin friction along cars, and base drag) proportional to velocity squared.
What is wheel-rail adhesion limit and why does it cap locomotive pulling capacity?
No matter how many horsepower an engine produces, pulling force is mechanically limited by the friction between steel wheels and steel rails: Tractive Effort (max) = mu * W_adhesive, where mu is the coefficient of adhesion (typically 0.30 to 0.38 for dry sanded rail, dropping to 0.15 on wet leaves or frost). Excess torque beyond this limit causes the wheels to spin out uncontrollably.
How does grade resistance compare to aerodynamic drag on steep mountain grades?
On a 1.5% to 2.2% mountain grade, grade resistance is overwhelmingly dominant—often accounting for 70% to 85% of total train resistance. Gravity pulls back every metric ton of train with 9.81 N per 0.1% of grade, requiring thousands of kilowatts of locomotive power just to overcome elevation gain regardless of aerodynamic streamlining.