Torque wheel positioning

[mabarry3]

So, I've been going over torque and its relationship to angular velocity in my physics course, which led to a few questions about the physics of KSP in relation to where I should put my torque wheels on a vessel. I would've posted this in the science lab area but my overall question ties back into gameplay. Sorry if this has been brought up numerous times before, I kind of suck with the search function.

(It also doubles as a check to make sure I understood my physics class! )

So, given that a force that changes angular velocity is more effective when it is farther away from the axis of rotation on the object you're trying to rotate, would that mean that torque wheels for pitch and yaw (or roll, if your torque wheels are to the right/left of CoM rather than the normal up/down of a vertical rocket) movement are more effective the further away from the CoM that they are?

In addition, can torque wheels "cancel each other out" by being placed on symmetrically opposite sides of the CoM or does the game automatically invert how the torque wheels rotate based on its position to the CoM?

Or, does the KSP model not care? And, of course, the last possible answer: is my understanding of torque and gyroscopic rotation total crap?

Edited November 5, 2015 by mabarry3

[Gaarst]

While torque depends on distance to centre of mass, concluding that putting reaction wheels further away from the CoM should be better is wrong, at least IRL, not sure how KSP handles this.

Torque is defined by the application of an external force about a fixed centre, defined by:

t = r x F

Note that here, letters in bold are vectors, and "x" the cross product, in terms of magnitude, you'll get:

t = r.F.sin(A) where A is the angle between r and F.

r is the distance vectore from the centre of rotation to the point of application of the force, and F is the force vector itself.

This means that for a given force vector you should put your RCS the furthest you can from your CoM for maximal torque, to get r as high as you can.

For reaction wheels though this is different: reaction wheels use the principle of conservation of angular momentum.

A mass starts spinning inside the wheel, and as no external force is applied the total angular momentum of the ship must be conserved, therefore the ship starts spinning in the opposite direction.

Then, for maximum efficiency, the reaction wheel must be placed as close as possible to the natural centre of rotation of the ship: its centre of mass.

Note that in KSP, reaction wheels are completely OP, and therefore physics show their limits pretty fast with those.

Edited November 4, 2015 by Gaarst
Clarifications

[Empiro]

In KSP, I also don't believe that where the SAS units are placed has any effect on their effectiveness.

[Kerbart]

Torque is indifferent to the location. We tend to think it is because when applying torque through a force, the effectiveness of that force increases with the distance to the fulcrum. But pure torque can be applied anywhere to an inflexible body with exactly the same result. Theoretically, for the effectiveness of delivering torque itself doesn't matter if your torque wheels (whose output is torque, not force) are at the top, bottom or center of your station.

However, your ship or station is not inflexible. The less bendable material you put between the torque wheels and the center of rotation, the less your bending losses will be (which will merely result in parts swaying back and forth instead of being applied to the rotation). For that reason you want your torque wheels placed as close to the center of mass (so there's less material to bend), and not connected on external docked parts (as docking ports are extremely flexible).

[sdj64]

This post has nothing to do with landing gear, OP is talking about SAS wheels, if I'm not mistaken?

It might make sense that you should put SAS as far from the COM as possible, since Torque = Force * Distance. But the wheels just produce torque, not force, so I'm not sure. In that case it's best to put them on your COM because at that axis, your ship's rotational inertia is least (you learned about the Parallel Axis Theorem, right?).

In short, I don't really know. You should try it out. RCS, however, should be as far from the COM as possible but symmetric, since it produces a force not a torque.

[Kerbart]

(...)In that case it's best to put them on your COM because at that axis, your ship's rotational inertia is least (you learned about the Parallel Axis Theorem, right?).

Not really. Torque = Moment of Inertia × Angular Acceleration, just like Force = mass × acceleration. Note the complete absence of "distance to fulcrum" in the formula. It doesn't matter where you apply torque. Apply torque, and things start rotating (unless restrained). The amount of rotation (speed) depends on the moment of intertia and the amount of torque, and nothing else. The reason you want to be close to the COM is to reduce bending (for obvious reasons), not to "maximize" the effect of torque (unless you consider it "maximizing the effect by reducing the losses due to bending")

We hardly ever create torque otherwise than applying a set of forces that are offset along a distance, and that is what causes the confusion.

[Snark]

In answer to the OP's post:

No, it doesn't matter where you put your reaction wheels, at least not in terms of the overall behavior of your ship as a rigid body. Exactly the same effect no matter where they go. This is true IRL, and I've experimentally verified it in KSP.

(It may "matter" in the sense of causing issues with floppy ships that can bend, but that's a different issue and I gather is not really what you were asking about.)

If you have multiple reaction wheels in KSP, their effect adds up. It doesn't matter where they are relative to each other, or whether they're facing in the same direction. They will never "cancel each other out".

[mabarry3]

Thanks for all the answers guys. KSP definitely makes more sense (at least to me) when I look at the stuff in terms of the underlying physics behind everything. Makes significantly more sense when I think of the torque wheels not being an external force on the "system".

Not really. Torque = Moment of Inertia × Angular Acceleration, just like Force = mass × acceleration. Note the complete absence of "distance to fulcrum" in the formula. It doesn't matter where you apply torque. Apply torque, and things start rotating (unless restrained).

Question about this - isn't moment of intertia mr^2, where r is the distance between the axis of rotation and the location of the applied force? So isn't "distance to fulcrum" indirectly in that formula?

[Snark]

Question about this - isn't moment of intertia mr^2, where r is the distance between the axis of rotation and the location of the applied force? So isn't "distance to fulcrum" indirectly in that formula?

Nope. The R term in the formula for moment of inertia refers to where the mass is relative to the axis of rotation. It has nothing to do with where torque is applied.

Put more concretely, the moment of inertia of your ship (for a given axis of rotation) depends only on the overall mass distribution of your ship. It has nothing to do with where any reaction wheels may be located.

Edited November 4, 2015 by Snark

[mabarry3]

Ah, okay; that seems to have been the primary source of my confusion, since that misconception hasn't mattered yet thus far in my work with torque and rotation in class.

Thanks again for all the help.

[paul23]

Not really. Torque = Moment of Inertia × Angular Acceleration, just like Force = mass × acceleration. Note the complete absence of "distance to fulcrum" in the formula. It doesn't matter where you apply torque. Apply torque, and things start rotating (unless restrained). The amount of rotation (speed) depends on the moment of intertia and the amount of torque, and nothing else. The reason you want to be close to the COM is to reduce bending (for obvious reasons), not to "maximize" the effect of torque (unless you consider it "maximizing the effect by reducing the losses due to bending")

We hardly ever create torque otherwise than applying a set of forces that are offset along a distance, and that is what causes the confusion.

Nitpicking: but putting mass (for example the reaction wheels) away from the line of rotation does increase the (mass) moment of inertia around that axes. - quadratic in fact.

Edited November 5, 2015 by paul23

[Laie]

One more small thing: ships in (stock) KSP are not exactly rigid bodies. Concentrating all torque at one end can, at worst, lead to visible bending (Kasuha made a few demos using toroidal tanks, but I can't find the pictures atm).

For the sake of wobblies, it's preferable if you can distribute the torque evenly across your vessel. Then again, reaction wheels tend to be among the more sloppy parts and having them in the middle of the stack can make matters worse. Choose your poison.

[Snark]

One more small thing: ships in (stock) KSP are not exactly rigid bodies. Concentrating all torque at one end can, at worst, lead to visible bending (Kasuha made a few demos using toroidal tanks, but I can't find the pictures atm).

For the sake of wobblies, it's preferable if you can distribute the torque evenly across your vessel. Then again, reaction wheels tend to be among the more sloppy parts and having them in the middle of the stack can make matters worse. Choose your poison.

Depends a lot on the shape of the ship. Unless you're really going nuts with lots of reaction wheels, for most "reasonable" ship designs they don't generate enough torque to seriously bend the ship. The concern about reducing "bendiness" is not about torque wheel placement, it's about keeping the ship as stiff as possible. Everywhere that you have two parts joining in a stack is a spot that can bend, and you want to minimize the number of such spots in the middle of the ship where it matters the most. Since reaction wheels are short little things, they've got two interfaces (top and bottom) where bending can happen. So usually the strategy for making the ship as stiff as possible is to put all your longest components (usually fuel tanks) in the middle, and leave the short items (reaction wheels, stack-mounted batteries) out at the ends.

Another thing to bear in mind is that the PID tuning of SAS in KSP is pretty rudimentary. It's possible to get ship designs where SAS sets up a resonance that magnifies wobble more and more. This happens because the "sensor" is on the control-from-here point (your command pod or probe core, usually), whereas the "effector" is located where the reaction wheels are. If those things are far apart from each other, so that applying a torque at the reaction wheel takes a long time to be felt at the control-from-here point, it's easier to get into one of those destructive resonances. TL;DR: if wobble is a concern, you usually want your reaction wheels fairly close to your probe core or command pod to minimize this problem.

[paul23]

Another thing to bear in mind is that the PID tuning of SAS in KSP is pretty rudimentary. It's possible to get ship designs where SAS sets up a resonance that magnifies wobble more and more. This happens because the "sensor" is on the control-from-here point (your command pod or probe core, usually), whereas the "effector" is located where the reaction wheels are. If those things are far apart from each other, so that applying a torque at the reaction wheel takes a long time to be felt at the control-from-here point, it's easier to get into one of those destructive resonances.

Quick: make up a system of differential equations, do a la place transform and reduce the reactive strength in such a way that all the important poles are on the left side of the plane.

[mhoram]

As a reference: a while back it was also experimentally established that the position does not matter.

http://forum.kerbalspaceprogram.com/threads/75916-If-something-has-an-SAS-torque-of-20-what-does-that-actually-mean

[steuben]

Quick: make up a system of differential equations, do a la place transform and reduce the reactive strength in such a way that all the important poles are on the left side of the plane.

If you're going to do that you might as well give up on PID and start using the heavier controllers, like "sliding mode"...