# Motor rating in horsepower?

#### Cabernut

##### Well-Known Member
We've all heard of references to how many millions of horsepower the Saturn V or Shuttle engines produce(as a way to relate to the public). Out of sheer curiosity, how would our rocket motors be rated in horsepower?

What exactly would the formula be?

I found a series of conversion calculators online that produced the following:
Given 1 G motor producing 160N of force in one second equals 35.969430896 pound-force in one second?
That 35.969 pound-force per second equals 0.0654 HP?

Looks like it could be right. A 100% G motor producing 1/15th of a horsepower for a second?

#### Bat-mite

##### Rocketeer in MD
I don't know.... Could you imagine a 15 G-motor cluster pulling something a horse could pull, even for a second?

I have no clue.

#### Cabernut

##### Well-Known Member
I don't know.... Could you imagine a 15 G-motor cluster pulling something a horse could pull, even for a second?

I have no clue.
That is, of course, unless the horse is the famous Mr. Ed.

A CTI G125-RL has a peak thrust of 171.8N so a cluster of 15 would produce 578lb of lift at peak thrust, so possibly...

#### GregGleason

##### Well-Known Member
Newtons (or lb-force) is a measurement of force, whereas horsepower is a measurement of power.

"The concepts of force and power seem to convey similar meanings and are often confused for each other. But in physics, they are not interchangeable. Force is the fundamental result of an interaction between two objects, while power is an expression of energy consumed over time (work), of which force is an element."

www.diffen.com/difference/Force_vs_Power

So, it's kind of an apples to oranges comparison.

Greg

#### davel

##### Well-Known Member
Where are you guys getting distance? Power = force x distance / time. You can have any arbitrary force exerted over any arbitrary amount of time. But if there is no movement, no work is done so no power is expended. Hold that rocket on the pad and no horsepower is being produced.

#### Cabernut

##### Well-Known Member
It could be measured directly in a lab. Take a K700 for example, secure it perpendicularly to a counterbalanced 1-meter rod which is attached to a pivot point. Now you can measure in newton meters over burn time in seconds. Ignite it and record the torque generated over the burn time of 3.59 sec.

Or possibly calculate using total impulse. If a K700 has a total impulse of 2283.68 Ns, that is equivalent to 2283.68 newtons in 1 second. Correct so far? That 2283.68N on the end of a 1-meter bar will then be 2283.68 N m for 1 sec = 2283.68 N m / s = 3.06 HP.

#### XolveJohn

##### Well-Known Member
Who needs movement? 1 HP is 746 watts. I have a 1500 W electric heater that sits there all day creating 2 HP of heat.

The classic physics concept of "work" is where you need movement, like lifting a mass a certain height.

What you do is use the rocket exhaust to spin a turbine running a generator into a load bank, and measure the watts.

##### Well-Known Member
TRF Supporter
Where are you guys getting distance? Power = force x distance / time. You can have any arbitrary force exerted over any arbitrary amount of time. But if there is no movement, no work is done so no power is expended. Hold that rocket on the pad and no horsepower is being produced.

The classical equation for power = force x velocity illustrates the difficulty of finding the power of a rocket motor. According to this formula if the rocket is not moving it does generate any power. Otherwise, the faster it moves the more power it generates. One can probably find other ways to calculate power. One way would be to look at the burn-rate and find how much total energy is produced per second. Then take a efficiency for the rocket and multiply the efficiency times the total output (Rockets are very inefficient with most of the energy going into untapped thermal energy of the exhaust. A typical coal-fired plant is only 33 percent efficient.) Another way which is really related to this first method is find how much mechanical energy is contained in the exhaust. As I recall 550 ft-lbf/sec is one horsepower.

#### Nytrunner

##### Pop lugs, not drugs
Found a nicely concise quora here:
https://www.quora.com/What-was-the-horsepower-and-torque-of-the-Saturn-V-rocket
The "Horsepower" of the Saturn V was the shaft power of its gas generator and turbopumps.
There are no such components in a solid motor.

Thinking back to system dynamics, Power can be described in terms of Effort*Rate. This works for a majority of dynamic systems:
Effort * Rate
Translational => Force * velocity (actuators, etc..)
Rotational => Torque * Angular velocity (Pumps, car engines, etc..)
Electrical => Voltage * Current (computers, heaters, etc....)
Hydraulic => Pressure * Volumetric flow (drawing a blank on an example here, but the math works!)

(another reason metric is cool, because interactions between the systems are Waaay easier to work through)

Back to rockets, I agree with the quora answer, Power really depends the mass of the vehicle being lifted. Looking at McCord's calculation above, It looks like you'll have to multiply that Total impulse by the acceleration produced before you would have units of power. N*s x m/s^2 = N*m/s.

The concept is uncomfortable to think about if you equate force with power/energy. 550k pounds of thrust going nowhere in a static test? 0 Watts or Horsepower. 0 Energy imparted to the system (ignoring heat, acoustic energy, and material compliance that is).

Buuut, if you really want to know the Horsepower curve of your rocket, take the thrust curve and multiply it by the boost velocity curve and you'll get a power curve.
For example, lets say that during my cert flight, Big SAM was going 90 m/s while its H120 was still putting out 120 N of thrust. That makes 14.4 hp (10.8 kW)
Or if I subtract the weight of the rocket from the thrust (lets say 21.85 N) that'll be 11.8 hp (8.8 kW).

#### Nytrunner

##### Pop lugs, not drugs
Who needs movement? 1 HP is 746 watts. I have a 1500 W electric heater that sits there all day creating 2 HP of heat.

See my post above: Effort x Rate => Voltage x Current

Aerostadt is also right. Because of the inefficiencies of rocket engines, its much more convenient to skip the "Power" of the engine and go directly to thrust produced, and impulse (total or specific)

#### Cabernut

##### Well-Known Member
I agree its a bit of apples vs oranges but somehow someone at NASA has figured out how to convert an apple into an orange:

From Shuttle trivia at nasa.gov: (where are they getting these HP numbers???)

The twin
Solid Rocket Boosters
generate a combined thrust of
5.3 million pounds. That equals about 40 million horsepower
or the energy of 14,700 six-axle diesel locomotives or 400,000
subcompact cars.

#### Rex R

##### LV2
there is movement involved when static testing a motor, the motor is working to accelerate the exhaust gases coming out of the nozzle is it not?
Rex

#### Steve Shannon

##### Well-Known Member
TRF Supporter
there is movement involved when static testing a motor, the motor is working to accelerate the exhaust gases coming out of the nozzle is it not?
Rex

Correct.

Steve Shannon

#### Nytrunner

##### Pop lugs, not drugs
I agree its a bit of apples vs oranges but somehow someone at NASA has figured out how to convert an apple into an orange:

From Shuttle trivia at nasa.gov: (where are they getting these HP numbers???)

The twin
Solid Rocket Boosters
generate a combined thrust of
5.3 million pounds. That equals about 40 million horsepower
or the energy of 14,700 six-axle diesel locomotives or 400,000
subcompact cars.

Not really sure. Although I saw a similar article there that called out units of force, equated it to units of horsepower, then compared it to torque of cars, so I have no idea what kind of relations or conversions went on back there.

there is movement involved when static testing a motor, the motor is working to accelerate the exhaust gases coming out of the nozzle is it not?
Rex

You're correct, but that massflow is the very thing creating the force (P*a+m_dot*v_ex).
Are you talking about switching the control-volume from the motor to....the exhaust plume?
Something about that seems fishy to me.

##### Well-Known Member
TRF Supporter
there is movement involved when static testing a motor, the motor is working to accelerate the exhaust gases coming out of the nozzle is it not?
Rex

Exactly! See post #9. So, take E = .5 m x V^2. Divide m by time to get mdot. Take Isp and divide by 32.2 to get exhaust velocity. Thus, Power = mdot x (exhaust velocity squared.) In this formula you will need to convert the lbm to lbf with gc and remember that 550 ft-lbf/sec is one horsepower. Wallaaa, you have a formula for rocket motor horse power.

#### Igotnothing

##### Well-Known Member
Keep in mind that a horsepower was originally a load a horse could reasonably be expected to pull for a session of work. So it varied widely from pulling a small carriage at high speed, to pulling a stump in one effort.
Later, when standardized units were introduced in an equation, all comparisons to actual horses went bye-bye because the units ruled the equation.

If you use pulleys to multiply the speed of a 3-pound bucket up out of a deep well, and you get the horse to really giddy-up, just how fast can you get that bucket moving? Mach 0.5?

So, yes. Your G motor has impressive horsepower. And a Q? Top-fuel dragster.

#### mccordmw

##### Well-Known Member
TRF Supporter
I'd love to see a Q fire some day. The numbers are impressive!

Q motor class max N-s = 163,840 (or in lbf-s = 36,800)

So it peaks at 219.7 hp.

#### Nytrunner

##### Pop lugs, not drugs
Exactly! See post #9. So, take E = .5 m x V^2. Divide m by time to get mdot. Take Isp and divide by 32.2 to get exhaust velocity. Thus, Power = mdot x (exhaust velocity squared.) In this formula you will need to convert the lbm to lbf with gc and remember that 550 ft-lbf/sec is one horsepower. Wallaaa, you have a formula for rocket motor horse power.

I see what you're going for, but I think more definition is required.

What mass are you taking? Solid propellant weight divided by burn time (simplification)?
What are using for Specific impulse? Mass of motor, or mass of vehicle? I'm assuming you're using mass of motor.

#### tomsteve

##### Well-Known Member
We've all heard of references to how many millions of horsepower the Saturn V or Shuttle engines produce(as a way to relate to the public). Out of sheer curiosity, how would our rocket motors be rated in horsepower?

What exactly would the formula be?

as long as the formula has the end result= bacon, im good. Horsepower is a measurement of energy, a pound of thrust is a measurement of force. can there be an exact equation to convert into HP? i looked into it some time ago and it doesn't seem there is an exact equation everyone can agree on. if there was an exact equation, it would have been given and no disagreements on the topic. its only been discussed and debated for a few years though.

just my opinion, but trying to convert an engines power unit that comes from a liquid fuel into a motors power unit that comes from solid fuel or electricity isn't possible.

now, onto torque- how much torque do rocket motors produce? #### jderimig

##### Well-Known Member
The HP is equal to the thrust of the motor x velocity of the vehicle. P = Tv. The faster you are going the more HP your motor is making. Its simple, look it up. Do not confuse horsepower with power. Horsepower does work, power is just the rate of energy conversion.

#### Cabernut

##### Well-Known Member
Jet engines produce thrust but are also rated in HP. Which led me to the following site which I think demonstrated the difficulty yet possibility in calculating horsepower from an engine that produces thrust by accelerating gas - or in our case, generating and then accelerating gas. Interesting read.

https://blog.juha.net/07-2013/how-much-horsepower-does-jet-engine-have/