## Thrust and Horsepower in Model Rockets

The question has come up as to how one can convert thrust from a model or high power rocket into horsepower. The real question is can thrust and horsepower be interchangeable measures? Not really but let’s take a look.

The definition of thrust is a force or pressure (pressure is force applied over an area) exerted on an object and it is usually measured in units of pounds (lb) or Newtons (N). Everyone involved in model rockets knows the first number in a model rocket motor designation is the average thrust in Newtons. Power is defined as the time rate at which work is done. When a force acts on a body to produce motion in the body, the force is said to have done Work. Work is measured as the product of the force applied and the distance an object moves. Power is usually measured in units of horsepower (hp) or kilowatts (kW). Thrust is therefore part of the equation to get to horsepower. The most common equation for power is:

P=W/t or P=F x d/t, (W=F x d)

W=work

t=time

P=power

F=force

d=distance

x means to multiply

/ means to divide

Let us say you are driving your car and it runs out of gasoline. You get out to push your car. You push and push your car as hard as you can but you can’t make it move. Even though you feel like you have done a lot of work you haven’t done any because the car has not moved. Remember the definition of work; force applied to body over a distance. No motion, no work. Now say your buddy gets out of the car and helps push the car. With both of you exerting a force on the car it starts to move. You are now doing work. If you measured the distance to the nearest gas station and you knew the force you applied to the car, you could figure out how much work you and your buddy had done when you get to the gas station. If you knew how fast you pushed the car you could figure out how much power was used to move the car to the gas station.

You may recognize the terms of distance over a given time as velocity. If it took one hour to push the car one mile to the gas station you would have pushed the car at one mile per hour (mph). The above equation can then be rewritten as:

P=F x V

V=velocity or V=d/t

So how does this relate to model rockets? The thrust of a rocket motor is the force in the above equation and velocity is the velocity of your rocket. To make all the units work out correctly we need two more definitions:

Horsepower (hp) = 550 foot-pounds/sec.

and

Pounds = Newtons/4.45 or F(lb)=F(N)/4.45

We can substitute into the P= F x V equation and get:

P=F(lb) x V(ft/sec) x hp/550ft-lb/sec

Multiplying by hp/550ft-lb/sec is the same as multiplying by one, which doesn’t change the value of P. Remember horsepower divided by 550ft-lb/sec is one, as that is its definition.

Note that we now have lb in both the numerator and denominator of the above equation and they therefore cancel each other out. There is also ft/sec in both the numerator and denominator that cancel out leaving hp as the only units left. Power in horsepower is what we were looking for all along.

If we can substitute pounds of force for Newtons of force, we then get the following:

P=F(N)/4.45 x V (hp)/550

Power is now in horsepower, F(N) is the thrust of your rocket in Newtons and V is the velocity of your rocket in feet per second.

Let me give you an example: At the September SEARS 572 club launch I flew my PML ½ Scale Patriot Missile on an Animal Motor Works K650 Red Rhino. The rocket’s maximum velocity at motor burnout was 407 miles per hour, which converts to 597 feet per second. Therefore the average velocity was from the time the rocket start to first move (zero ft/sec) and the max velocity: (597 minus 0)/2=298.5 ft/sec. The K650 designation tells us the average thrust was 650 Newtons. Therefore:

P=650(avg)/4.45 x 298.5(avg)(hp)/550

P=79.27 hp average

By knowing, through measurement or estimating by simulation, the velocity of any rocket while knowing it’s thrust one can calculate the horsepower generated on any given rocket flight.

John Hansel

SEARS 572

NAR 83131

TRA 10910