Locomotive Tonnage Rating on a Ruling Grade

it is just the component of weight along the slope, and it dwarfs everything else on the list. On the level a train resists at three to five pounds per ton; put it on a one percent grade and grade resistance alone adds twenty, so a modest hill multiplies the required pull several times over. THAT IS WHY THE RULING GRADE SETS THE TRAIN. The steepest sustained grade on the route, curve resistance included, determines the tonnage rating for the whole run, and a single short hill sets the makeup for hundreds of level miles behind it. Curvature adds about eight tenths of a pound per ton per degree, which is small beside a grade and large beside nothing, and it belongs in the ruling grade calculation rather than beside it. THE SECOND CONSTRAINT IS ADHESION AND IT IS A SEPARATE CEILING. A locomotive cannot deliver more tractive effort than friction between wheel and rail allows -- roughly twenty five to thirty five percent of the weight on its drivers with modern adhesion control, and much less on wet, leafy, or contaminated rail. The rating follows whichever of the two is LOWER, and which one governs is reported here in words, because it is easy to compute an adhesion limit, find it larger than the consist's own tractive effort, and mistakenly use it. A tonnage rating that assumes tractive effort the locomotives cannot put down is a train that stalls, and the fall-back on a rated hill is helpers or doubling the hill -- both planned from this same arithmetic. A steady-state rating at constant speed. It does not address acceleration, starting resistance -- which is higher than running resistance and is why a train that stalls may be unable to restart on a grade -- train dynamics, slack action, or drawbar and coupler limits, which cap how much tonnage may be pulled behind a given point regardless of power. It does not compute the Davis or any other speed-dependent resistance formula: rolling resistance is entered, and it rises at low speed and again at high speed. It says nothing about braking, dynamic brake capacity, or the descending side of the hill, which is a different and often harder problem. The railroad's own tonnage tables, the locomotive builder's tractive effort curves, and the operating department govern.

total resistance = 20 lb/ton per 1% of grade + the entered rolling resistance + 0.8 lb/ton per degree of curve; tonnage rating = governing tractive effort / total resistance, where the governing effort is the LOWER of the consist's tractive effort and the adhesion ceiling (weight on drivers x adhesion factor).

The train resistance components by name, with the 20 lb/ton per 1% grade constant shared with the haul-road resistance calculation so the two cannot disagree about what a grade costs. Adhesion runs roughly 0.25 to 0.35 dry with modern control and much less on wet or contaminated rail. Steady state at constant speed: no starting resistance, slack action, drawbar limits, or braking. The railroad's own tonnage tables, the locomotive builder's tractive effort curves, and the operating department govern.

Three multiplications and a division; no railroad tonnage table is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: tractive_effort_lb, ruling_grade_pct, rolling_resistance_lb_per_ton, curve_degrees, weight_on_drivers_lb, adhesion_factor, alternate_grade_pct, grade_resistance_lb_per_ton, curve_resistance_lb_per_ton, total_resistance_lb_per_ton, adhesion_limited_te_lb, tonnage_rating_tons, level_tonnage_tons

• Steady state at constant speed no acceleration, starting resistance, slack action or drawbar limitsthe operating department
• Rolling resistance is entered it rises at low speed and again at high speed; no Davis formula is appliedthe railroad's own data
• Nothing about braking the descending side of the hill is a different and often harder problemthe railroad's train handling rules