The engine and tender resistance is composed of the friction of pistons, cross heads, slide valves, cranks, eccentrics, pumps, the back pressure of the blast, and various erratic movements, rolling, twisting, and pitching together with both wheel and axle friction, which is common to the engine and tender.
The atmospheric resistance is not due to the direct action of the air upon the front and sides of the train entirely, but chiefly to the exhausting action in the rear. The train has, as it were, to pull along a large column of air like the water in the wake of a ship; form or amount of frontage has little or no effect. The resistance depends upon the bulk of the train and its velocity. A train with the same frontage offers more resistance as its bulk increases.
Oscillatory resistance is caused by irregularities in the surface of the rails, and increases with the velocity, and also with increase of height of the centre of gravity of the car or engine.
Frictional resistance may be divided into wheel and axle friction. That of the axle is composed of two parts, the direct vertical friction on the journal, and the side friction on the collar, consequent upon lateral motion. The vertical friction is independent of the surface pressed or of velocity, but is directly proportional to the pressure, and the same remark applies to that of the collars. As the diameter of wheel increases, the oscillation is increased, the centre of gravity being raised. The direct cause of the vertical friction is the weight of the car or engine, and of the lateral irregularities in the surface of the rails, which cause the car to sway from side to side. Wheel friction which acts between the periphery of the wheel and the surface of the rail increases with the load, and decreases as the wheel diameter augments.
For the total resistance to the motion of a railroad train, D. K. Clark gives the following formula:—
V2
171 + 8 = R,
Where R is the resistance in lbs. per ton,
and V the velocity in miles per hour.
From this expression we form the following table:—
| Velocity in miles per hour. | Resistance in lbs. per ton. |
| 10 | 8.585 |
| 12 | 8.842 |
| 15 | 9.315 |
| 20 | 10.339 |
| 25 | 11.655 |
| 30 | 13.263 |
| 40 | 17.356 |
| 50 | 22.620 |
| 60 | 29.052 |
| 100 | 66.480 |