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Hugh's explanation is essentially correct. To elaborate, rolling resistance is a aggregation of forces that oppose the movement of a train, vary with speed, and must be overcome by the tractive force of the locomotive. It does NOT include grade resistance, which dwarfs rolling resistance for any appreciable gradient. A. Elements of rolling resistance that vary with axle loading include: 1. friction between the wheel tread and the head of the rail, which has many variables (such as presence of rust or moisture or grease, alloy of metal, shape, etc.) and is difficult to determine mathematically. 2. track modulus resistance -- the deflection of the track structure under the weight of the axle, which requires the wheel to constantly be running uphill 3. bearing resistance -- friction in the bearing or journal; which is dependent upon temperature 4. flange resistance -- even on tangent track, the axle does not run straight but zig-zags, and flanges rubbing against the rail add resistance. B. Resistance that varies with the square of the velocity . 1. "Quiet air" resistance, the turbulence beneath and between cars, skin resistance, and the partial vacuum at the rear of a train, in addition to the direct frontal resistance; (what Hugh termed aerodynamic resistance) C. Other resistances include wind resistance (not to be confused with quiet-air resistance), acceleration resistance, and starting resistance (inertia). The Davis formula is fairly reliable at low speeds, but not at high speeds. It doesn't seem to work very well with very heavy cars, either. Moreover, its values are empirically derived, so it's not truly a mathematical formula like one of Newton's laws of motion. If you want something definitive, get Railroad Engineering by William W. Hay. Lots of math, but it's clear-cut. ------------------------------------------------------ Back to the original question. You asked how a ton of empty could have more resistance than a ton of load. The construction of that sentence is word-play; elegant to the expert but otherwise somewhat unclear. So, consider a train with 240 tons, split evenly between 120 "empty" tons consisting of four identical 30-ton empty hoppers, and 120 "loaded" tons consisting of one also identical 30-ton hopper carrying 90 tons of lading. The four empty cars will impart more rolling resistance than the one loaded car because: 1. they make up four-fifths of the quiet-air resistance; 2. the other components of rolling resistance do not vary directly with axle loading.
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