# The Naked Scientists Forum

### Author Topic: Will rockets accelerate until they run out of fuel?  (Read 14210 times)

#### wolfekeeper

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##### Will rockets accelerate until they run out of fuel?
« Reply #25 on: 05/07/2010 03:12:15 »
Well, yeah... but...

Ok, let's take an example.

Exhaust speed 3500 m/s.

Rocket is travelling at 7800 m/s (it's an upper stage, and it's just about reaching orbit).

For the sake of argument let's say it's generating 1000 N of thrust.

So the fuel burn rate is 1000/3500 = 0.29 kg/s.

For the sake of arguments let's say the fuel's energy is 14MJ/kg. (It's about right for a LOX/Kero rocket propellant mix to give an exhaust velocity of 3500m/s).

So the rocket is generating 1000 * 7800 = 7.8MW

But the chemical power generated is 0.29*14e6 = 4MW

So there's a mysterious 3.8MW that's appearing from nowhere?

Where is it coming from?

#### wolfekeeper

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##### Will rockets accelerate until they run out of fuel?
« Reply #26 on: 05/07/2010 03:14:11 »
Well, yeah... but...

Ok, let's take an example.

Exhaust speed 3500 m/s.

Rocket is travelling at 7800 m/s (it's an upper stage, and it's just about reaching orbit).

For the sake of argument let's say it's generating 1000 N of thrust.

So the fuel burn rate is 1000/3500 = 0.29 kg/s.

For the sake of arguments let's say the fuel's energy is 14MJ/kg. (It's about right for a LOX/Kero rocket propellant mix to give an exhaust velocity of 3500m/s).

So the rocket is generating 1000 * 7800 = 7.8MW (power = force * distance per second)

But the chemical power generated is 0.29*14e6 = 4MW

So there's a mysterious 3.8MW that's appearing from nowhere?

Where is it coming from?
« Last Edit: 05/07/2010 03:16:45 by wolfekeeper »

#### Geezer

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##### Will rockets accelerate until they run out of fuel?
« Reply #27 on: 05/07/2010 04:03:41 »
A rocket in orbit does not need to do any work (well, hardly any) to travel at constant velocity in orbit.

Power is the rate of doing work. No work, no power.

#### wolfekeeper

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##### Will rockets accelerate until they run out of fuel?
« Reply #28 on: 05/07/2010 04:28:33 »
Whenever a rocket is being accelerated work is being done.

#### Bored chemist

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##### Will rockets accelerate until they run out of fuel?
« Reply #29 on: 05/07/2010 06:52:28 »
Not if that acceleration is to keep it in a circular path at a constant speed.

#### wolfekeeper

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##### Will rockets accelerate until they run out of fuel?
« Reply #30 on: 05/07/2010 15:00:33 »
Ok, you have a point about that at least, but here we're talking about rockets accelerating under their own power.

The rocket power is proportional to speed (from force x distance) but that implies that the rocket's power increases apparently without limit, depending on how fast it happens to be going.

This is an apparent paradox. But of course in physics there are no true paradoxes!

So how can a rocket produce ever increasing power?

(FWIW the early rocket pioneer that discovered this thought that he had broken physics, but later realised what's happening.)

#### wolfekeeper

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##### Will rockets accelerate until they run out of fuel?
« Reply #31 on: 06/07/2010 15:13:52 »
Hint: there's a hidden source of energy, other than chemical energy of the fuel.

#### Geezer

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##### Will rockets accelerate until they run out of fuel?
« Reply #32 on: 07/07/2010 06:51:26 »
Hint: there's a hidden source of energy, other than chemical energy of the fuel.

Yes, well considering when all of this was going on, it would not surprise me in the least to learn that many of the "rocket scientists" thought magic mushrooms were the source of the apparent energy.

At any point in time, f = m.a   Does anyone care about the apparent power?

#### wolfekeeper

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##### Will rockets accelerate until they run out of fuel?
« Reply #33 on: 07/07/2010 14:09:59 »
Actually energy is really important in rocketry.

For example, if you want to go to Mars from the surface of the Earth.

You can either:

a) takeoff, and burn to an extremely high orbit, check things out, then do a burn to go to Mars.

b) takeoff, and burn to a low orbit, check things out, then do a burn to go to Mars.

You should always do b), because in a low orbit you're moving faster and the energy you're making from the rocket burn is higher, even though F=ma is the same. Doing this reduces the amount of propellant you need by several times!
« Last Edit: 07/07/2010 14:12:01 by wolfekeeper »

#### wolfekeeper

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##### Will rockets accelerate until they run out of fuel?
« Reply #34 on: 07/07/2010 14:26:22 »
Anyway, I guess you've given up.

The secret is in the propellant. It has the chemical energy, but it also has kinetic energy. That's the hidden source.

Before it's burnt any kilogram of fuel has:

14MJ/kg of chemical energy
0.5 m v^2 of kinetic energy

At high enough speed the kinetic energy is bigger.

When it gets thrown out the back of the rocket, the kinetic energy of each kilogram ends up as 0.5 * 1 * (v-c)^2

So if, m = 1 kg, it changes by:

0.5 * 1 * (v - c)^2 -  0.5 * 1 * v^2

= 0.5 * ( v^2 - 2 v c + c^2 ) - 0.5 * v^2

= 0.5 v^2 - v c + 0.5 c ^ 2 - 0.5 * v^2

= 0.5 c^2 - v c

The 0.5 c^2 is just 0.5 m c^2 where c is the exhaust velocity- it comes from the chemical energy, that's just the fixed chemical energy (14 MJ/kg - losses) used by the rocket to make the jet, and it's constant. the -vc is more interesting; that's extra energy that's lost by the exhaust, an amount directly proportional to the rockets speed v, and from conservation of energy it all ends up in the rocket; that's where the extra energy you can calculate from W = f x d comes from.
« Last Edit: 07/07/2010 16:19:25 by wolfekeeper »

#### Geezer

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##### Will rockets accelerate until they run out of fuel?
« Reply #35 on: 07/07/2010 18:09:56 »
Ah! Right. As a in f=ma is the amount of acceleration applied to the exhaust relative to the rocket, would f=ma not take the kinetic energy of the propellant into account?

#### wolfekeeper

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##### Will rockets accelerate until they run out of fuel?
« Reply #36 on: 07/07/2010 23:49:10 »
No, it doesn't tell you where the energy ends up. You need to look at the speeds to calculate the kinetic energy, F=ma only gives you the rate of change of speed.

#### Geezer

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##### Will rockets accelerate until they run out of fuel?
« Reply #37 on: 08/07/2010 00:41:36 »
No, it doesn't tell you where the energy ends up. You need to look at the speeds to calculate the kinetic energy, F=ma only gives you the rate of change of speed.

But surely if you knew how fast you were going in the first place, it should be quite straightforward to determine your current speed from the rate of change of speed.

#### wolfekeeper

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##### Will rockets accelerate until they run out of fuel?
« Reply #38 on: 08/07/2010 01:20:12 »
Pretty much, but only if you know the speeds at some point (and if the accelerations are known to sufficient accuracy).

The thing is that energy and forces are fundamentally different things, albeit related by numerous equations.

#### Geezer

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##### Will rockets accelerate until they run out of fuel?
« Reply #39 on: 08/07/2010 04:11:43 »
Pretty much, but only if you know the speeds at some point (and if the accelerations are known to sufficient accuracy).

The thing is that energy and forces are fundamentally different things, albeit related by numerous equations.

Quite so. It is not so easy to convert energy into something useful. If it was easy, we might not find ourselves in the pickle that we seem to have created.

#### yor_on

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##### Will rockets accelerate until they run out of fuel?
« Reply #40 on: 06/09/2010 16:57:50 »
ah, the fuel?

How do you differ between its kinetic energy and the chemical?
Doesn't the kinetic energy include all energy that leaves the exhaust?

This one was a tricky one.
==

Thinking of it, what about those exhausts we all leave at times, bringing those vitamins into the air, uplifting the general temperament of our guests and loved ones, especially after a good long dinner?

Chemical energy that too me thinks? As well as kinetic..
So, will the same formula apply there?
« Last Edit: 06/09/2010 17:00:47 by yor_on »

#### wolfekeeper

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##### Will rockets accelerate until they run out of fuel?
« Reply #41 on: 06/09/2010 18:16:20 »
Quote
How do you differ between its kinetic energy and the chemical?
It's the kinetic energy before you burn it. You can tap into that, as well as the chemical energy, which is a constant amount independent of speed.
Quote
Doesn't the kinetic energy include all energy that leaves the exhaust?
No, there's heat energy as well (although at a microscopic level this is largely kinetic energy, but it's relative to the bulk flow which has overall kinetic energy).

A rocket nozzle extracts a lot of that heat, but about 30% is still left over.

#### yor_on

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##### Will rockets accelerate until they run out of fuel?
« Reply #42 on: 06/09/2010 21:39:02 »
Okay thanks Wolfe, I'm not sure I get it still, the difference between chemical and kinetic energy I mean. You mean that it have a 'potential' kinetic energy before getting burned, well, as I think about it, although I won't promise I do, think, that is :)

To me kinetic energy is all those atoms, molecules etc, bouncing around in that chamber as the chemical reaction takes place, burning at a furious rate, throwing them out from the only opening they will find, the exhaust.

But I can see that you consider it two processes, one chemical consisting of a certain energy in itself, and the other one kinetic, getting a boost by the speed of the rocket. How exactly do the speed influence the kinetic energy? It's not like a jet where you can get more oxygen the faster you fly, right? So, where does that extra energy comes from?

« Last Edit: 06/09/2010 21:40:36 by yor_on »

#### wolfekeeper

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##### Will rockets accelerate until they run out of fuel?
« Reply #43 on: 06/09/2010 23:10:23 »
In physics, you always pick a frame of reference. It's usually a good idea to pick the centre of mass frame or the 'zero momentum frame' which is usually the same thing.

In rockets the best frame is usually the one that the rocket takes off from. In that frame, the overall momentum of the rocket is zero at all times (if you include the fuel, and less obviously the exhaust, which you must for the energy/momentum conservation to work out properly).

So the rocket starts going and lobs the exhaust one way, and goes off in the other direction.

At any time the energy of each kilogram of anything is 0.5 m v^2, but m=1, so it's simply 0.5 v^2.

So the kinetic energy of the fuel BEFORE it is burnt is 0.5 v^2, and the potential kinetic energy is just a constant on top.

The maths does work out if you use any other frame, but you have to be a lot more careful.
« Last Edit: 06/09/2010 23:12:09 by wolfekeeper »

#### yor_on

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##### Will rockets accelerate until they run out of fuel?
« Reply #44 on: 06/09/2010 23:47:50 »
Thanks, i have a distinct feeling I will need to come back to this one and reread it all :) I should get some sleep first too I think. "In rockets the best frame is usually the one that the rocket takes off from." And that would be the launch pad in this case, right? I really liked the sound of the 'zero momentum frame', I mean it, it made me think :) And that's a hard thing for me.

"energy/momentum conservation" you say, and that the best frame then would be a 'still' one for that to 'balance out' sort of. Would you say that all uniformly moving frames are 'still' 'zero momentum frames'? As that momentum will be impossible to define inside a black box? Anyway, It made a sort of sense to me. But for the rest I will need to think harder, a lot I'm afraid.. I think I need to start with looking into "energy/momentum conservation" and see how that is expressed, and if i can understand it. Can't say my math is that polished :) But I will look at it, as long as it doesn't attack, that is..

Never trust math that bites back.
But first some sleep :)

Thanks again Wolfe.

#### The Naked Scientists Forum

##### Will rockets accelerate until they run out of fuel?
« Reply #44 on: 06/09/2010 23:47:50 »