# Horsepower to velocity

#### KaiGrid

Hello, I'm building a model train control system, and would like to use real world values and physics to control the trains. I have these specifications about each model of train, and would like to know how I could relate given HP to velocity or Δacceleration.
Given Values are located here: http://www.thedieselshop.us/Data%20EMD%20GP40.HTML

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#### phinds

Gold Member
Hello, I'm building a model train control system, and would like to use real world values and physics to control the trains. I have these specifications about each model of train, and would like to know how I could relate given HP to velocity or Δacceleration.
Given Values are located here: http://www.thedieselshop.us/Data%20EMD%20GP40.HTML
HP does not relate directly to velocity. You could put a 1 HP motor on a real train and it would go at approximately zero mph, or you could put one on a roller skate and it would go maybe 50 mph.

#### KaiGrid

Information

What information would I need to calculate the velocity of this train?

#### tduell

In the link to the "Given values" is says the speed is 65 mph, is that not what you want?

Cheers,
Terry

#### KaiGrid

I'm trying to make a momentum control. In a locomotive, there are 9 engine settings (0-8). Each setting is a different percentage of applied power. Under different loads (mass), the train will accelerate faster or slower. I want a way to calculate how much power is being applied to the train (real life), so that I can apply it to the scale model.

#### tduell

OK. If you ignore rail gradient (a simplification to get started on this) the first thing to account for is rolling resistance. See here <http://en.wikipedia.org/wiki/Rolling_resistance> [Broken] for a coefficient. That will give a (more or less) constant force the engine must provide to maintain any speed. To accelerate you can use F=m.a, i.e for your mass and tractive force/effort you can calculate an acceleration. You will have to guess your tractive effort as a function of engine setting, maybe a simple ratio i.e 8=100%, 4=50% ??
The other thing that affects all this is aero drag which is a drag force usually proportional to speed squared, and will really only play a part at higher speeds, but is you want to include it you will need to find a suitable drag coefficient for your train.
The gradient force is the component of the weight (W.cos.theta) where theta is the angle to the horizontal.
It all gets a bit complicated when you have some of the train on the level, some on the up grade, some on down grade etc!

Cheers,
Terry

Last edited by a moderator:

#### KaiGrid

Thank you so much for the starting point! I will continue to work on it!

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