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# Tractive effort

Tractive effort is the pulling force exerted, normally by a locomotive, though the term could also be used for anything else that hauls a load. It is normally understood to be the actual force on the locomotive's drawbar or rear coupler. When a bare figure for tractive effort is quoted without a speed qualification, this is normally for starting tractive effort, i.e. at a dead start with the wheels not turning.

In most cases, especially for [steam locomotive]s, this figure is a calculated, not measured one. The normal formula used (measurements in pounds and inches) is:

where
• t is tractive effort
• c is a constant representing losses in pressure and friction; normally 0.85 is used
• P is the boiler pressure in pounds per square inch
• d is the piston diameter (bore) in inches
• s is the piston stroke in inches
• D is the driving wheel diameter in inches

The constant .85 was the AAR standard for such calculations, and certainly over-estimated the efficiency of some locomotives and underestimated that of others. Modern, roller bearing fitted locomotives were probably underestimated in this calculation.

European designers used a constant of .60 instead of .85, so the two cannot be directly compared without a conversion factor.

Tractive effort is the figure most often quoted when people are comparing the power of different steam locomotives, but the use can be misleading, because tractive effort shows the ability to start a train, not the ability to do work by hauling it. Possibly the highest figure for starting tractive effort ever recorded was for the Virginian Railroad's 2-8-8-8-4 Triplex locomotive, which in simple expansion mode had a starting T.E. of 199,560lbs — but this did not translate into power, for the boiler was undersized and could not produce enough steam to haul at speeds over 5 mph.

Of more successful large steam power, the Union Pacific's famous Big Boys had a starting T.E. of 135,375 lbs, the Norfolk & Western's 2-8-8-2 Y6a had a starting T.E. of 152,206 lbs in simple expansion mode, and the Pennsylvania Railroad's freight Duplex Q2 attained 114,860 lbs — the highest for a rigid framed locomotive. Later two cylinder passenger locomotives were generally at the 70-80 thousand pounds of T.E. mark.

For a diesel-electric or electric locomotive, starting T.E. can be calculated from the stall torque of the traction motors (the turning force it can produce while at a dead stop), the gearing, and the wheel diameter.

A related statistic is a locomotive's factor of adhesion, which is simply the weight on the locomotive's drivers divided by the starting tractive effort.