Why does a rocket engine increase power with speed if the burn rate is constant?

A rocket produces constant thrust with speed, and that means increasing power with speed.

Where does this increase in power come from if the fuel burn rate is constant? How can we explain this in the reference frame of the rocket without violating the laws of physics?

Does a turbo fan and turbo jet also produce constant thrust with speed?

• "Rocket produce constant thrust with speed,that mean increase power with speed." I think you have a real need for evidence to support this claim. Acceleration increases as the rocket burns, because the mass of fuel it's accelerating decreases. Many launch vehicles (especially human-carrying ones) actually reduce their power/thrust in order to keep acceleration within tolerable limits. See the answer here: space.stackexchange.com/questions/7829/… Nov 7 '21 at 17:44
• I would have expected such a question on Space Exploration. Its "Rockets" tag has 1055 questions. Nov 7 '21 at 22:40
• "A rocket produces constant thrust with speed, and that means increasing power with speed." Not correct. Rocket thrust is not related to the speed of the rocket, only to the propellant consumed. Jets and props push against the air around them to gain thrust, rockets do not. Nov 8 '21 at 12:15
• @PeterMortensen: Or on Physics: one, two, three, asking the same question.
– ymb1
Nov 8 '21 at 12:33
• @PaulSmith -- re" Rocket thrust is not related to the speed of the rocket," -- that's exactly what Jurgen said, that's the whole premise of the question. Nov 8 '21 at 12:56

Put simply, the variation in power is due to the distinction between the exhaust jet power and mechanical power added to the vehicle. The power of the exhaust gas stream measured in the rocket-fixed reference frame is only dependent on the rate of energy release by the propellant. The rate of kinetic energy addition to the vehicle depends on the thrust developed by the engine and the velocity of the vehicle measured in some other reference frame.

These two powers will only match momentarily when the vehicle velocity equals the exhaust velocity (when the exhaust is left at rest).

Intuitively you could say something like this:

When the rocket is moving slower than its own exhaust velocity, the power deficit (exhaust power - vehicle power) ends up as residual kinetic energy in the exhaust. When the rocket is moving faster than its own exhaust velocity, the power excess comes from the kinetic energy present in the propellant.

Here is a plot of total system energy for a rocket of mass ratio 5 accelerating from rest. The kinetic energies of the rocket structure, onboard propellant, and exhaust gases as well as the internal (chemical) energy of the propellant are shown, just to demonstrate the total remains constant regardless of how much fuel has been burned. • "When the rocket is moving faster than its own exhaust velocity.." How on earth (or in space) can it do so? Nov 7 '21 at 21:37
• @Jpe61 it's basically like using a catapult to take off from an aircraft carrier that has just stopped is engines and is still drifting forwards. Despite accelerating the plane to much higher speed than the carrier could ever make, the carrier is still going forward in the end. — The trick is to push yourself off a reaction mass that's bigger than yourself. In a rocket, that mass is the fuel. Nov 7 '21 at 23:45
• Yea did some quick reading on this. Oh boy, talk about something being counterintuitive! Nov 8 '21 at 0:52

Power = Work/time = Force × distance/time = mass × acceleration × Velocity

We must remember these definitions were created for draft horses before the age where aerodynamic drag was significant.

"Power" more accurately describes the Energy state of an object.

In a vacuum, away from a gravitational field, a rocket under constant thrust force will have more and more power (as an impactor) as its speed increases.

A turbofan and turbojet, operating in the atmosphere, are limited in the amount of thrust they produce by oxygen available and limited in velocity by drag. In extreme cases (such as hypersonic flight), friction heating from drag also plays a significant role.

Turbofans generally operate subsonicly for greater fuel efficiency.

"Power" vs drag graphs are popular for aviation training programs, but can be confusing unless Power = Thrust x Velocity is applied.

Thrust is an easier way to quantify engine output. Even for propeller driven aircraft, "horsepower" can be described as torque at a given rpm.

• "'Power' more accurately describes the Energy state of an object", power is a rate not a state, the rate at which energy is (can be) transferred.
– mins
Nov 7 '21 at 12:55
• @mins well, you see that's where the confusion lies. Velocity is a state, rate of energy input (fuel burn, thrust) can be constant, but velocity is determined (initially) by time, later by drag. Nov 7 '21 at 13:03
• @mins but your statement is not incorrect as (working through units) power input (fuel burn) can be described as mv$^2$/time. Nov 7 '21 at 13:20
• "In a vacuum, away from a gravitational field, a rocket under constant thrust force will have more and more power (as an impactor) as its speed increases." - from this we deduce that it gets very difficult to make a rocket that can keep applying a high constant acceleration over a very long time period. All the energy in the impactor was originally chemical energy in the fuel. You don't get anything for free, even in space. The difficulty in making a long-burn rocket is that if you add fuel to make a longer burn time, the rocket's initial weight is higher, so it initially accelerates slower. Nov 8 '21 at 3:32
• "All the energy in the impactor was originally chemical energy in the fuel (and oxidizer)" Yes, this is what BowlOfRed pointed out. In aviation, we wind up burning fuel against drag, part of drag makes lift. Fortunately, there is enough O2 for combustion, (solar electrics are making it on Mars). Nov 8 '21 at 12:34

Rocket produce constant thrust with speed,that mean increase power with speed.

If you limit "power" to mean the change in energy over time of the vehicle + unburned fuel, then yes, that's correct.

Where this increase in power come from if fuel burn rate is constant,how explain this in reference frame of rocket without violate physics laws?

It comes from only looking at part of what the engine is doing. The other change the engine makes is a change in energy of the fuel/exhaust.

At the first instant that the engine is running (when the rocket is still stationary), 100% of the combustive power of the engine goes into accelerating the fuel into exhaust. The power going into the vehicle is zero, but the engine is still doing something.

As the rocket accelerates in that frame, we see the ratio of where the power goes changes. More power goes into accelerating the vehicle and less power goes into accelerating the exhaust.

If we assume the engine is running with nearly constant fuel flow, then we would see at any instant

$$\Delta E_{\text{combustion}} = \Delta E_{\text{rocket}} + \Delta E_{\text{fuel}}$$

As it accelerates away, the amount going into the rocket term is increasing while the amount going into the fuel term is decreasing. (And in fact that final term can become negative so that the energy going to the rocket is greater than the energy from combustion).

Does turbo fan and turbo jet also produce constant thrust with speed?

That's a useful approximation over a large range of operating conditions. But unlike a rocket, airplanes have increasing drag forces as they accelerate. This limits the top speed and the acceleration possible. Since most airplanes fly with a cruise (non-accelerating) portion dominating, the idea of how the KE of the airframe changes over time is much less interesting.

• a thoughtful answer but ... from the rocket reference frame isn't exhaust velocity always the same? Isn't that force always accelerating the rocket? That is the "power" quandary. As the rocket speeds up, it by definition P= Fxv, it has more power. Nov 7 '21 at 16:07
• In the rocket reference frame, 100% of combustion goes into a constant speed exhaust. There is no change in power that I see. Nov 7 '21 at 18:45