Posted by: bgtwindad | March 8, 2011

Locomotion, Part 1: Wheels on Rail

A recent online discussion spurred me to study in some depth just how a locomotive does its job… moving extremely heavy trains at speed.  I thought it would be useful to share an explanation of the science involved, and so here we begin a new series.

For this first installation, we will essentially ignore the difference between steam, electric, Diesel-electric, and even model vs. prototype engines and focus on what is happening between the wheel and the rail.

There are three basic forces at play:  inertia, friction, and the torque applied to the wheels by the motor.  Whoa! you say.  Big words in paragraph three!  Hold on, we’ll get there.

Inertia, you may recall from high school physics, is the tendency of a body at rest to stay at rest, or of a body in motion to stay in motion – in the same direction and at the same speed.  The locomotive must overcome the inertia of the train any time it wants to start, stop, or change the speed of the train.  For simplicity, we are lumping all of the drag forces on the train (wind resistance, bearing friction, etc. etc.) together under “inertia”, even though strictly speaking they are different things.  They all add up to “stuff trying to stop the train (or at least keep it from accelerating)” anyway.  We’ll dice out all those details in a later post.

Friction is the “gripping” force generated between two surfaces in contact with each other.  It is always directly opposed to a force trying to make the surfaces slide.  In our case, the friction is between the wheel and rail, and it is what allows the train to move.  The friction between the wheel and rail is called static friction because even though the wheel is rolling, the “contact patch” between the wheel and rail is not moving.  Once the force reaches the “traction” point – the limiting stating friction – the two surfaces will slip against each other.

Torque is the force applied to the wheel by the locomotive’s engine that tries to make the wheel turn and thus pull the train along.

The locomotive must apply enough torque to overcome the inertia of the train in order to move it, but if it applies too much torque, it will exceed the static friction limit, and the wheels will slip.  If the train’s inertia is higher than the static friction limit, the train is going nowhere, no matter how much torque is applied.  This can happen, for example, on wet or icy rails, or rails that are covered with leaves.  The rails are too slick, and the wheels cannot grip.

In short, one of three things is going to happen:

  • Not enough torque to overcome inertia:  train stalls
  • Enough torque to overcome inertia, but not so much we overcome the wheel/rail friction:  train moves!!
  • Too much torque: wheels slip.

In order to fix the first point – stall – we have little choice but to add more torque – either increase the throttle, or add more locomotives.  To fix the third, we must either reduce the throttle until the wheels stop slipping or do something – like dropping sand on the rails – to increase the friction so the wheels can grip.  Adding more engines can help, only to the extent that they increase the number of wheels (and locomotive weight) on the rail, and therefore increase the total traction (friction) available.

In the YouTube video posted above, you can see the effects of plenty of torque + too much drag + not enough wheel/rail friction.  It takes an hour of work to slowly get this coal train moving on the icy rails with no sand.

A practical example:  Yard goats with slugs.

Something puzzled me for a while… why in a yard, where engines are frequently starting and stopping and moving long cuts of cars around at very low speed, would you have a small, low horspower locmotive connected to a “slug”.  What’s a slug, you ask? A slug is a modified locomotive that has had its “prime mover” engine replaced with a hundred tons or so of concrete.  It usually is also missing a cab, and must be driven by a “real” locomotive.  It is merely an extra set of traction motors and a lot of extra weight.  Why on earth would we tax the poor Diesel under the hood of the main locomotive like this?

The above analysis gives the answer.  The engine and generator in even a small yard switcher can generate considerably more power (torque) than can actually be applied to the rails without causing wheel slip.  This extra power capacity is, essentially, wasted in a low-speed starting-and-stopping scenario.  By adding a slug, we provide eight extra contact points with the rails (assuming a 4-axle slug!), four more traction motors for converting the generator’s power to motion, and a pile of weight to create more friction on those eight extra contact points.

The slug allows us to direct the excess power capacity of the switcher’s engine/generator to the rails without creating too much torque at any given wheel.

Let’s put some (fictional and easy-math) numbers to this.  Let’s say the generator of a 4-axle yard switcher can create 8000 lb-ft total of torque.  Let’s also say that each wheel can apply only 500 lb-ft of torque without slipping on dry rail.  By itself, the switcher can only use 1/2 of its torque capability (500 * 8 = 4000 lb-ft) to the rails without slipping.  If we add a 4-axle slug, we add 8 more wheels (and 4 more traction motors) to the equation, allowing us to devote the full power of the generator (500 * 16 = 8000 lb-ft) to the job of starting the train.

We can see now how adding more weight and more wheels is a big asset when one is frequently starting and stopping trains.   But if the friction force is directly proportional to locomotive weight, why not simply make the engine heavier instead of adding the slug?  Good question.

In addition to the drag and friction and torque, we need to be mindful of the sheer weight on the rails – the loading gauge.  The rails (and the wheels!) can only support a certain maximum amount of weight at each wheel contact point without damaging them.  So there is an upper limit to the friction force at each wheel that is set by the strength of the rails (and the wheels too!).  To add more weight, we must spread that weight over more wheels.  Adding more wheels has the positive side effect of increasing the total contact patch area, which also increases the friction.

Note also that all of this applies to model trains as much as real ones, though it’s highly unlikely we will ever exceed the loading gauge of even N scale steel rails…



  1. Well said without too much parlarva.

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