Newton's 3rd law & rocket propulsion (detailed explanation)

[Frank Castle]

I had someone ask me how rockets are able to accelerate in space and my initial answer was that the rocket fuel combusts and is heated into an energetic gas, the gas is accelerated out of the back of the rocket (i.e. the rocket exerts a force on the gas), then according to Newton's 3rd law, the gas exerts an equal and opposite force on the rocket resulting in the rocket accelerating in the opposite direction to the gas. Although a simplistic explanation I think this is correct?!
The person wasn't quite satisfied with this answer and wanted more details, such as, what is the gas pushing on in the rocket (by this I think they understand that there doesn't have to be anything external to push on, but they are unsure as to how the gas pushes on the rocket). My follow-up explanation was the following:

Imagine a super simplified model in which the rocket is completely hollow inside, then without any nozzle at the rear end, the pressurised gas on the inside of the rocket would exert equal forces on all internal walls of the rocket. Newton's 3rd law then states that the (rigid) walls of the rocket will exert an equal, but opposite force on the gas and everything will remain in equilibrium (since on average there will be an equal amount of force acting on the left and right walls of the rocket, and the top and bottom walls of the rocket) . Imagine now that we create a nozzle at the bottom end of the rocket, now the situation has changed. The forces exerted by the gas on the sides of the rocket will remain balanced, however, now the top end rocket wall will a force exerted on it, pushing it upwards, but there is now no balancing force acting on the bottom end, since the gas is escaping out of the nozzle. Hence there will be a net force acting on the top end of the rocket, propelling it in the opposite direction to the gas accelerating out of the nozzle at the bottom end.

Would this be a valid explanation or have I made some errors (if so, could someone provide a detailed correct explanation)?!

 

[A.T.]

Imagine now that we create a nozzle at the bottom end of the rocket, now the situation has changed. The forces exerted by the gas on the sides of the rocket will remain balanced, however, now the top end rocket wall will a force exerted on it, pushing it upwards, but there is now NO balancing force acting on the bottom end, since the gas is escaping out of the nozzle. Hence there will be a net force acting on the top end of the rocket, propelling it in the opposite direction to the gas accelerating out of the nozzle at the bottom end.

I think you forgot that highlighted "NO". Otherwise it's a correct explanation an you will find many pictures on the internet visualizing it.

 

[Frank Castle]

I think you forgot that highlighted "NO". Otherwise it's a correct explanation an you will find many pictures on the internet visualizing it.

Ah yes, thanks for pointing that out (I've edited in the correction). Thanks for taking a look for me!

 

[wrobel]

google "variable mass systems equations of motion"

 

[wwoollyyhheeaa]

Bernoulli's theorem says that there will in fact be pressure on the bottom of the rocket case but because the speed of the exhaust is greater there than it is elsewhere, the gas pressure will be lowered compared to elsewhere. Therefore there will be a net force acting along the axis of the rocket.

 

[A.T.]

Bernoulli's theorem says that there will in fact be pressure on the bottom of the rocket case

What is the "bottom of the rocket case"?

 

[Delta Kilo]

In fact large part of the rocket thrust comes from the nozzle. Inside the nozzle the gas expands, cools down and accelerates backwards. Exhaust pressure on the nozzle walls results in net force pushing the rocket forward. Somewhat surprisingly rockets work better in vacuum (where "there is nothing to push against") than in the atmosphere. In the atmosphere, the pressure at the exit of the nozzle (and the size of the nozzle) is limited by the ambient pressure. Vacuum nozzle can be made much bigger to take advantage of every last drop of pressure remaining in the exhaust as it expands into the vacuum.

 

[Frank Castle]

In fact large part of the rocket thrust comes from the nozzle. Inside the nozzle the gas expands, cools down and accelerates backwards. Exhaust pressure on the nozzle walls results in net force pushing the rocket forward. Somewhat surprisingly rockets work better in vacuum (where "there is nothing to push against") than in the atmosphere. In the atmosphere, the pressure at the exit of the nozzle (and the size of the nozzle) is limited by the ambient pressure. Vacuum nozzle can be made much bigger to take advantage of every last drop of pressure remaining in the exhaust as it expands into the vacuum.

Is it correct to say that the gas is heated causing it to expand and accelerate, and because the nozzle is open at one end and closed at the other the expanding gas experiences a force acting on it from the top (unopen) end of the nozzle accelerating it towards the bottom (open) end of the nozzle, and so by Newton's third law, the gas also exerts an equal and opposite force on the top (unopen) end of the nozzle, however there is no such boundary to exert a force on the gas at the bottom end (that would accelerate it back towards the top end and keep the forces balanced), and so it simple accelerates out of the nozzle. The fact that the gas can escape from the bottom end, but not the top means that there is an unbalanced force acting on the top end of the nozzle, thus accelerating the rocket forwards (i.e. in the opposite direction to the accelerated gas escaping from the back (open) end of the nozzle)?!

 

[wrobel]

For which purpose are these lengthy essays? Are you preparing to deliver a lecture in physics for a journalism faculty? It is a completely standard effect which is described by clear equations that are contained in many good books. Why do not you read them?

 

[I Like Science]

The gas pushing the rocket is hydrogen and oxygen combusted together to form carbon monoxide, a toxic gas. Also, what you said about Newton's third law and jet propulsion is 100% correct, so the person needs to be satisfied by your answer

 

[russ_watters]

The gas pushing the rocket is hydrogen and oxygen combusted together to form carbon monoxide, a toxic gas.

Hydrogen and oxygen combusted together form water vapor. Carbon monoxide isn't possible there: you need carbon to get carbon monoxide. And even a hydrocarbon like gasoline or methane produces little or no carbon monoxide if burned properly -- it produces carbon dioxide.

 

[I Like Science]

Hydrogen and oxygen combusted together form water vapor. Carbon monoxide isn't possible there: you need carbon to get carbon monoxide. And even a hydrocarbon like gasoline or methane produces little or no carbon monoxide if burned properly -- it produces carbon dioxide.

Oh... Good to know. But the fuel is liquid hydrogen and liquid oxygen... It is on the NASA website... Thanks for your help russ_watters

 

[Delta Kilo]

Pop-sci description of rocket thrust sprinkled with a few formulas:
https://www.grc.nasa.gov/www/k-12/airplane/rocket.html
https://www.grc.nasa.gov/www/k-12/airplane/rktthsum.html

 

[I Like Science]

Cool... I'll take a look at that now

 

[Frank Castle]

Apologies for my lengthy contributions. I just want to make sure that I've understood the idea correctly.

 

[wrobel]

in physics ideas are expressed by formulas

 

[Frank Castle]

in physics the ideas is expressed by formulas

Yes, I appreciate that, but I like to try and develop an intuition for these things as well instead of simply relying on equations.

 

[wwoollyyhheeaa]

I agree wrobel but understanding is often expressed in words and pictures.

 

[rcgldr]

Bernoulli's theorem says that there will in fact be pressure on the bottom of the rocket case but because the speed of the exhaust is greater there than it is elsewhere, the gas pressure will be lowered compared to elsewhere. Therefore there will be a net force acting along the axis of the rocket.

Bernoulli is violated during the time when chemical potential energy is converted into mechanical energy (and heat), (during the time that the fuel burns).

- - -

In the case of a liquid fueled rocket, one or more pumps have to increase the pressure of the liquids to a bit above the pressure at the rocket nozzle, otherwise the liquids would not flow into the combustion chamber. One way to achieve this is to burn a portion of the fuel in a turbine to pressurize the remaining fuel going into the combustion chamber.