Asparagus staging causing rotation? Weigh in here!

[jf0]

On 2/1/2016 at 1:05 AM, K^2 said:

Doesn't matter. SomeGuy123 summarized it already. For angular momentum of the rocket to change, something must carry it away. Unless exhaust itself is angled and/or rotating, you can't come up with any sort of internal piping that will cause the rocket to rotate. This is no different than trying to accelerate a rocket without having some sort of an exhaust. Just like linear momentum, angular momentum has to go somewhere.

For the angular momentum of the rocket plus fuel.

If you had a circular pipe filled with fuel with a pump on it, floating in space and you turned the pump on so the fuel started circulating in the pipe, the whole contraption will start rotating in the opposite direction. Conservation of angular momentum is correct, but an even more obvious way to look at it is that the pump pushes on the fuel, and the fuel pushes back on the pump with the same force.

If you had two fuel tanks say arranged 180 degrees apart around a rocket and you simply pumped fuel from one to another, fuel leving one tank would push on that tank/pump and give an opposite push when it slowed down as it fills the second tank, so the net force on the rocket/tanks/pump arrangement is zero. But I think things would be different if the fuel did not all decellerate in the second tank, as would happen in asparagus staging, there is still a net flow out of the second tank. The flow does not completely decellerate or diffuse in the second tank so there is some net force on the rocket.

 

Quote

Let's do some more mental gymnastics.  Consider the following geometry:

The two tanks hold fuel, with the bottom tank feeding an engine.  The top tank feeds the bottom tank by pumping fuel through two helical pipes.

When the engine is burning fuel, what happens?  Does this thing spin on its axis?

This thing wont spin, provided the flow through the two spirals is the same because one is on the opposite direction to the other. If only one spiral carried fuel, I think there would be a net torque. But I think it would depend very strongly on how diffused the flow of fuel becomes into the second tank. Imagine simply chopping off the second tank and letting the fuel out the end of one spiral: I think we all agree it would spin then. Now imagine the second tank starts empty (hollow sphere with a nozzle on the bottom) If all the jet of fuel from the spiral went through the middle of the tank out the nozzle with out hitting the walls of the tank, I think we can still agree the thing would spin. Now what if the second tank has fuel in it? How much does the fuel flow from the top tank become diffused as it enters the bottom?

Bottom line is in principle, yes asparagus staging (pumping fuel around) will cause a force on the rocket. But it could probably be eliminated by diffusing the flow into the second tank, or more likely gimbaling engines...

[Steel]

So the way I see it, simplifying the setup to 4 external tanks and one central one with no rocket engines (also spherical cows in a vacuum e.t.c), the only way a torque can be produced is if the two external tanks on one side of the craft are producing a net force when pumping fuel from one to the other

In this case can anyone explain how this:

Produces a net force?

 

Edited January 9, 2016 by Steel

[jf0]

32 minutes ago, Steel said:

So the way I see it, simplifying the setup to 4 external tanks and one central one with no rocket engines (also spherical cows in a vacuum e.t.c), the only way a torque can be produced is if the two external tanks on one side of the craft are producing a net force when pumping fuel from one to the other

In this case can anyone explain how this:

Produces a net force?

 

Imagine a pump where the arrow is, imagine the second tank is missing at first. The fuel exiting the pump pushes back on the pump with the same force the pump is pushing on the fuel (this is really just like how rockets produce force anyway, so we know that works...) so in this case there is definitely a force.

When the second tank is there, initially the same force pushes back to the left on the full tank. When the liquid hits the opposite wall of the empty tank,or diffuses into any liquid already in the tank, it creates an equal force to the right, so in 'steady state' there is no net force, but initially there will be a force.

What I was trying to explain in my last post was: now imagine a hole in the right-hand side of the right-hand tank: some of the pumped liquid will simply 'go straight through', some will hit the walls of the right-hand tank/or mix with fuel aready in the tank. Then in this case the force is not perfectly balanced - some momentum is carried by the fuel leaving the system. In asparagus staging we aren't just pumping from one full tank to an empty one, we are pumping from one tank into another and simultaneously draining fuel from the other. The actual forces produced would depend on the geometry of the tanks and the piping and exactly how the flow of liquid occurs in the tanks. In asparagus staging (or any rocket for that matter), it is not a closed system (fuel leaves the tanks and out the rocket nozzel!), so momentum/forces does not necessarily need to be conserved/balanced.

Edited January 9, 2016 by jf0

[Val]

The way I see it, you move an amount fuel a certain number of degrees around the center of the rocket.

The rotation created by this can never be greater than the angle the fuel is moved and will in practice always be smaller.

How big that angle is depends on the ratio of moment of inertia between the fuel moved and the rest of the rocket.

I calculated an arbitrary example using the geometry of my illustration above.

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In general, given an object of mass m, an effective radius k can be defined for an axis through its center of mass, with such a value that its moment of inertia is

where k is known as the radius of gyration

• I set k for the center stage as 1 and the aspargus tanks to 2.
• I set the mass of the center stage to 100 and each of the 4 aspargus tanks to 25.

The mass of 2 aspargus tanks is moved: 2 x 25 x 2² = 200 inertial moment

Inertial moment for the remaining rocket: 100 x 1² + 2 x 25 x 2² = 300

That gives a ratio of 200/300 = 2/3

The fuels angle of movement is 90^o which means the rocket rotates 2/3rds that in the opposite direction: 60^o

Note: There are several things the above doesn't take into account, like liquid fuel in the centerstage wouldn't rotate with the rest of the rocket like a solid, which the above assumes.

TL;DR In summary. Aspargus staging creates a small jolt when fuel starts flowing, which starts a rotation, and another opposite jolt that stops the rotation, when the fuel stops flowing.

There's no net force while the fuel is flowing, unless the rate of flow changes.

The size of the rotation will never exceed the angle that the fuel is moved around the center axis.

Edit: As far as I can tell the above is not affected by the fact the the moved fuel is also spent and removed from the rocket.

Edited January 9, 2016 by Val
Typos + clarification

[Val]

I forgot to mention, my example above assumes there's only an engine on the center stage. If there's also engines on the asparagus stages, then the rotation will be smaller.

I also didn't consider the ice skater effect of the fuel being moved in towards the center. I'm not able to research it properly right now, but I think it can be considered like this: Simultaneously as the fuel movement above, the fuel mass of the second pair of asparagus stages is being moved from r=2 to r=1.

This will lower the moment of inertia for the rest of rocket from 300 to (100 + 2 x 25) x 1² = 150

Halving the moment of inertia means the angular velocity has to double to keep angular momentum constant.

Which I guess means the rotation could get as big as 120^o in my example. 

And I'm unsure about the effect of the spent fuel. If that needs to be subtracted from the moment of inertia then it drops to 100 and the angular velocity is triple the first estimate, potentially increasing the angle to 180^o

[HebaruSan]

Anyone have access to any of the detailed planning documents for the Shuttle? If the gist of the discussion here is correct, then there should (might?) also have been some torque generated by the fuel lines from the external tank to the orbiter, depending on how they were aligned. It wouldn't have been the roll torque of asparagus in that case, but rather a bit of pitch torque, if the endpoints weren't colinear with the center of mass. If that's the case, then some engineer or other ought to have calculated its magnitude and discussed methods of dealing with it (such as keeping the launch clamps attached while the SSMEs warm up, which they did anyway). Similarly we might notice either a pitching motion or attitude jets firing when the ET runs out, if there is video of that stage occurring. I respect the physics and math abilities of everyone here, but I think NASA's design process was probably more resistant to easy errors of intuition that we might make.

[magnemoe]

12 hours ago, HebaruSan said:

Anyone have access to any of the detailed planning documents for the Shuttle? If the gist of the discussion here is correct, then there should (might?) also have been some torque generated by the fuel lines from the external tank to the orbiter, depending on how they were aligned. It wouldn't have been the roll torque of asparagus in that case, but rather a bit of pitch torque, if the endpoints weren't colinear with the center of mass. If that's the case, then some engineer or other ought to have calculated its magnitude and discussed methods of dealing with it (such as keeping the launch clamps attached while the SSMEs warm up, which they did anyway). Similarly we might notice either a pitching motion or attitude jets firing when the ET runs out, if there is video of that stage occurring. I respect the physics and math abilities of everyone here, but I think NASA's design process was probably more resistant to easy errors of intuition that we might make.

I don't think you get any, fuel accelerate out of tank by the pump but fuel flow is then directed downward and the bend would cancel the rotation.
This can be tested easy in the shower or better with an stronger water beam. the way the tubing is arranged has no impact, just the direction of the water at the end.

You get static push, an bend will have to be strong enough to absorb the force generated then redirecting the fuel.