Understanding Rocket Energy Expenditure: A Scientific Analysis

[aris1]

Hi all,
I want to ask something with the fear of sound silly to most of you.

A)Let's say we have two identical rockets and the air resistance is excluded.
The first rocket travels upwards with 100mph while the second travels upwards with 50mph.It's obvious that after an hour the faster rocket will have produced double work.Does this mean that it will have used double fuels?
As far as I understand it since both the rockets move with constant speed they exert the same and equal with their weight force for an hour.Isn't logical to conclude that since both the rockets use the same force for the same duration they use the same fuels too?

B)Now let's assume the first rocket starts at 100m above the Earth and ends its trip at 200(starting and ending speed is zero) while the second just stands still in the air for the same duration.
Since the first rocket starts and ends at rest the average acceleration is zero.So the average force it uses is equal with its weight.Exactly like the second rocket.
Again isn't it logical to conclude that both rockets used the same fuels for the same duration?

I would like to know if you agree with my conclusions.Thanks.

 

[AJ Bentley]

You would be entirely correct if it were possible to do that.

You have a situation where the thrust of the rocket is precisely equal to it's weight so that it proceeds with whatever initial velocity it is given.

All that the rocket engine is doing in both cases is to balance the weight, it is not doing any work because it is not moving the rocket. The movement of the rocket is entirely a consequence of it's initial velocity. In Newtonian terms it 'proceeds in it's state of rest or uniform motion in a straight line'. It's exactly as if the rocket were not moving, simply hovering.
In a sense, both rockets are simply wasting fuel.

In reality, rockets do not move with uniform velocity, they accelerate and since F=ma, work is done and turned into kinetic energy.

 

[sophiecentaur]

You are treating this problem in the same was as you would discuss two lifts (elevators) or two cars going up hill.
In the case of a rocket, however, the power / energy expenditure is very different because it is a reaction engine.
At zero speed (just at take off) the rocket is highly inefficient because all of its energy is going as Kinetic Energy of the expelled gases. As it speeds up, the rocket will get a bigger and bigger proportion of the energy supplied by the fuel.
You only would use a rocket if it can produce some useful acceleration - not rising at a constant speed, as in your thought experiment.
I guess you could analyse the situations you propose but it wouldn't be very relevant. The nearest thing I can think of to your idea would be the James Bond Jet Pack with which you can go up and down and hover - at great expense of fuel (as with stationary helicopters).

 

[aris1]

In reality, rockets do not move with uniform velocity, they accelerate and since F=ma, work is done and turned into kinetic energy.

Thanks.
So you also agree that in the B case where the rocket starts and ends at rest(a case close to reality) which means that the average acceleration is zero the rocket would burn the same fuels as if it was simply hovering?

All that the rocket engine is doing in both cases is to balance the weight, it is not doing any work because it is not moving the rocket.

So you're saying that when the motion is with constant speed(or with zero average acceleration in general) no work is considered that is done?

 

[aris1]

You are treating this problem in the same was as you would discuss two lifts (elevators) or two cars going up hill.
In the case of a rocket, however, the power / energy expenditure is very different because it is a reaction engine.
At zero speed (just at take off) the rocket is highly inefficient because all of its energy is going as Kinetic Energy of the expelled gases. As it speeds up, the rocket will get a bigger and bigger proportion of the energy supplied by the fuel.
You only would use a rocket if it can produce some useful acceleration - not rising at a constant speed, as in your thought experiment.
I guess you could analyse the situations you propose but it wouldn't be very relevant. The nearest thing I can think of to your idea would be the James Bond Jet Pack with which you can go up and down and hover - at great expense of fuel (as with stationary helicopters).

Hey...it's just a fictional example.I guess the helicopter example is better.
So you agree that the energy expenditure is the same in any case with the only difference the efficiency of their engines?

 

[sophiecentaur]

The work done will be the same but the energy needed for the engine will be different - i.e the efficiency will be different. There is a real distinction and the answer depends on which you are discussing.

 

[aris1]

The work done will be the same but the energy needed for the engine will be different - i.e the efficiency will be different. There is a real distinction and the answer depends on which you are discussing.

I'm discussing about the energy needed for the engine.
In my opinion when the average acceleration is zero(like in the cases where the rocket/helicopter starts and ends at rest OR just hovering in the air) the average force is equal with the weight and the energy expenditure for the same duration is always the same.
Am I wrong?

 

[cjameshuff]

The power requirements of a rocket engine do not depend on the speed of the rocket. If it's precisely balancing its weight with its thrust, it doesn't matter if it's hovering or going up, down, or sideways at a constant speed...the rocket's speed with respect to itself and the propellant in its tanks is zero in all these cases, its speed with respect to some outside object is irrelevant (except for potentially leading to it hitting the ground at some point in the future). After an equal amount of time, multiple identical rockets given starting nudges in different directions will have burned the same amount of propellant and expended equal amounts of energy. (ignoring the presence of drag and assuming the differences in the gravitational field over the given range of altitudes are negligible)

The situation is a bit different with jet engine or propeller aircraft. They have a distinct airspeed, and to accelerate they must increase the speed of air that's already moving past them.

 

[aris1]

The power requirements of a rocket engine do not depend on the speed of the rocket. If it's precisely balancing its weight with its thrust, it doesn't matter if it's hovering or going up, down, or sideways at a constant speed...the rocket's speed with respect to itself and the propellant in its tanks is zero in all these cases, its speed with respect to some outside object is irrelevant (except for potentially leading to it hitting the ground at some point in the future). After an equal amount of time, multiple identical rockets given starting nudges in different directions will have burned the same amount of propellant and expended equal amounts of energy.

Thanks.That's exactly what I thought.
Do you also believe that equal amounts of energy are required when the rocket starts and ends with zero speed(accelerates and then decelerates,average acceleration=zero)?

 

[cjameshuff]

Thanks.That's exactly what I thought.
Do you also believe that equal amounts of energy are required when the rocket starts and ends with zero speed(accelerates and then decelerates,average acceleration=zero)?

You're not defining the situation precisely enough to answer that question. If the rocket is identical and producing the same thrust, only accelerating due to being in a weaker gravity field, then yes. The engine accelerates the same amount of propellant to the same velocity relative to the engine regardless of its motion. The propellant flowing from the tanks to the engine is even exposed to the same accelerations.

With few exceptions, a given rocket engine producing a given amount of thrust will always put out the same amount of power and consume the same amount of fuel/propellant, regardless of how it's moving. The exceptions are engines with variable bell geometries or things like VASIMR, which can change specific impulse to shift balance between propellant mass efficiency and energy efficiency...it's still true for them if they are configured identically.

Also note that real rocket vehicles consume their fuel, reducing their mass and increasing their acceleration at a given thrust level, and also make large changes in velocity and in their position in gravity wells. Your questions honestly don't seem very useful for understanding the behavior of rockets. It might help to describe what you're trying to get at instead of asking a string of poorly-directed questions.

 

[aris1]

Hey... my question was a lot more simple and my example maybe was a little misleading.

I just would like to know if it's OK to assume that in cases where the average acceleration is zero the energy expenditure is always the same for the same duration.
The cases where the average acceleration is zero(at least what I can think of now) are when the rocket(or helicopter) stands still in the air...when it moves with constant speed...or when it starts and ends the motion with zero speed.

A secondary question/conclusion might be(if the first assumption is correct) that the mechanical work that is produced is irrelevant with the energy expenditure.

 

[Dale]

Rockets should generally be analyzed using conservastion of momentum rather than conservation of energy. Both, of course, are in effect, but conservation of momentum forces you to consider the exhaust. Forgetting about the energy of the exhaust is the source of all the confusion and mistakes in analyzing rockets and energy.

 

[aris1]

Rockets should generally be analyzed using conservastion of momentum rather than conservation of energy. Both, of course, are in effect, but conservation of momentum forces you to consider the exhaust. Forgetting about the energy of the exhaust is the source of all the confusion and mistakes in analyzing rockets and energy.

I believe when we talk about the force and the energy of the engine we mean exactly the the force and the energy of the exhaust.

Even if we use the conservation of the momentum in all the three cases where the average acceleration is zero(the rocket(or helicopter) stands still in the air...when it moves with constant speed...or when it starts and ends the motion with zero speed) the net change in momentum is zero.
So is it OK to assume same energy expenditure for the same duration?

 

[Dale]

Yes for the first two. In both situations the rocket had the same change in momentum, and the same external impulse and so the same thrust and therefore the same amount of fuel exhausted which means the same energy expenditure.

I would have to actually work out the third in case something gets messy in the average.

 

[aris1]

That third case is what bothers me the most.
In my opinion since the staring speed(v1) and the ending speed(v2) is zero then the average acceleration(a) is zero too(a=(v2-v1)/t=(0-0)/t=0) and the motion is practically identical with constant speed motion.The energy expenditure has to be the same.

 

[Dale]

Momentum is linear in velocity and energy is quadratic, so I am not be so sure that it works out that way, particularly if you use reverse thrust at some point. As I said before, I would have to do the math.

In any case, why does it bother you? By the conservation of momentum a rocket engine produces a thrust force which is proportional to the exhaust velocity and fuel consumption rate. The energy that doesn't go into the rocket goes into the exhaust. The rest is just details.

 

[aris1]

Momentum is linear in velocity and energy is quadratic, so I am not be so sure that it works out that way, particularly if you use reverse thrust at some point. As I said before, I would have to do the math.

Hey...I didn't go that far.I assumed that the energy is also linear and positive only thrust(deceleration only due to gravity).
Anyway,thank you very much for your time and thinking.

In any case, why does it bother you? By the conservation of momentum a rocket engine produces a thrust force which is proportional to the exhaust velocity and fuel consumption rate. The energy that doesn't go into the rocket goes into the exhaust. The rest is just details.

So in the hovering case where no energy goes to the rocket(or no work is produced) the whole energy goes into the exhaust in the form of heat(?).

 

[Dale]

So in the hovering case where no energy goes to the rocket(or no work is produced) the whole energy goes into the exhaust in the form of heat(?).

Heat and KE of the exhaust. Those gasses come out of the nozzle pretty fast!

 

[sophiecentaur]

All the stuff about rockets is 'how long is a piece of string?' and comparisons are very difficult. The performance / efficiency blah blah of a rocket depends upon the velocity and mass of the ejectant.
We keep drifting from conjecture to conjecture and there aren't enough caveats being aired to prevent people leaping to unwarranted conclusions.
The only things you can be sure of in this thread are the 'work done' and the change in GPE. Those are defined - but even then, you need to know how the mass varies during the journey.