Hi All

Could someone direct me to the new tractive effort formula that takes into account on the weight on the drivers? The only formula I know of is the following.

T= tractive effort
d=diameter of the cylinder in inches.
L=stoke of the piston in inches
.8 or .85 for the maximum percentage of boiler pressure in the cylinder
P=for boiler pressure
D=Driver Diameter

Which results in the following formula
T=dxdxLx.85p/D

There is a term that I am called factor of adhesion which is calculated by taking the weight on the drivers and dividing it by the tractive effort but I do not think this is what they want to discuss.

But in the modern railfan discussions including this page the constant claim in discussions claim the formula has weight on the drivers. Could someone direct me to this formula. I would be most grateful.

Sincerely
Robby Peartree

I would direct you to Ralph P. Johnson’s The steam Locomotive. My copy is second edition, 1945. In Chapter X, Tractive Force, page 138 the text says “For Steam locomotives…the ratio of adhesion of 4 is generally used or 25%...” The chapter carries on for may pages and discusses many aspects of adhesion including condition of the rail, material of the wheels, speeds, and the Kiesel formula. If you don’t have a copy of this book, I strongly recommend you find a copy. Good stuff.

Robbie, while you could probably develop a single formula that accounts for this, it's better to split it. The formula produces wheelrim torque, which results in the equivalent of drawbar pull, which is opposed to the train resistance to determine acceleration, balancing speed, etc. If the wheels were toothed so there could be no longitudinal slip then all this available thrust converted into torque would be available for traction.

Instead, at right angles to the torque expression, is the adhesive weight, which increases the effective 'friction' between wheel and rail without affecting the torque developed by cylinder thrust. This is what your FA expresses: the net torque appearing at the drawbar for STE divided by the weight or more properly force on drivers. In the United States by convention this is usually a decimal number between the mid-3s and about 5 with conventional wisdom having it about 4 for "normal" slipperiness in practical operation.

We don't put this in the formula because it doesn't mean anything 'as is'; it's just a relative guide to how much torque can be 'engaged' before the wheels slip under particular conditions. There are many other factors affecting where a slip takes place, or whether it will propagate or self-resolve if not 'addressed' when it does. It is possible to tinker with FA in some circumstances, usually with air or steam jacks shifting the weight distribution to put 'more weight on drivers' (this of course isn't limited to steam; the current C4 diesel-electrics move suspension geometry to increase weight on powered axles). This has nothing to do with the actual power output from the reciprocating engine, though; only the amount that can be communicated to the track under largely unpredictable conditions.

When calculating train factor, which is really an economy-based measurement that is intended to prevent stalls or doubling more than to 'get the maximum number of cars the consist will pull', it isn't unusual to see the FA worked into the final assessment of train makeup. But it does not go into indicated tractive effort directly.

Overrmod,

I like the two formulas. But the new railfans seem to know of a calculation that puts a relationship between tractive effort and weight on the drivers. The other possibility is they do not understand either the tractive effort calculation or factor of adhesion calculation. I suspect the latter is true. It gets back understanding the technology. It was pointed out to me that the loss due to fluid flow (the .80 or .85 typically seen of the boiler pressure) of the steam thru the dry pipe and superheaters if applicable, is for the locomotive moving at a walking or better pace. You can (and I have had) full boiler pressure at the pistons to start a train.
CCDW

I have the book you recommend and it has a lot of good material in it. But it is sad to me when a tech book full of information can not sell for $20 but a switch lock sells for $200. There are a number of book out there that can tell you a lot about not only tractive effort but air brakes feed water systems and other locomotive parts. If it is not paint it is not important.

Robby Peartree