How should Reaction Wheels work?

[Red Iron Crown]

lol. physics. The moment of inertial is minimum around an axis that passes through the CoM, so it's "harder" to get the object to rotate around an off-CoM axis. also, if there isnt a fixed axis (the center of rotation isnt pinned to an infinitely heavy object) the object u wanna rotate off-centre will move away on a spiral trajectory as the centripetal forces are off-centre too, aka its far better to place the RW into CM. its an other question that KSP (and unity) doesnt calculate these forces fight.

Link does not apply. An object in freefall can only spin about an axis that passes through the CoM when torque is applied.

[michaelsteele3]

They should be round and they should spin and they shouldn't blow up for no reason like in a Michael Bay movie. Then I'm happy

[Tuareg]

Link does not apply. An object in freefall can only spin about an axis that passes through the CoM when torque is applied.

yes, it very much does apply. rotation around the CM will be a derived rotation not equal with the rotation if the torque is applied at the CM directly

[Red Iron Crown]

yes, it very much does apply. rotation around the CM will be a derived rotation not equal with the rotation if the torque is applied at the CM directly

Perhaps I misunderstand what you're trying to say. It seems to me that the angular momentum accumulated by the reaction wheel must be exactly offset by angular momentum of the craft, because of the conservation of angular momentum. Given that the wheel spun up to a defined RPM has a fixed angular momentum, how can the rotation applied to the craft be different if it's in a different spot?

[Tuareg]

Perhaps I misunderstand what you're trying to say. It seems to me that the angular momentum accumulated by the reaction wheel must be exactly offset by angular momentum of the craft, because of the conservation of angular momentum. Given that the wheel spun up to a defined RPM has a fixed angular momentum, how can the rotation applied to the craft be different if it's in a different spot?

instead of trying to make a physics study i made a simulation in unity. 2 "crafts" behind each, each has 5 standard cube object with weight 1. the craft in front has the torque applied to the central (black) cube, the craft behind has the same torque applied on the last cube... watch them rotating. if you dont get it, watch it again

(its still uploading, but i have to leave)

[Red Iron Crown]

instead of trying to make a physics study i made a simulation in unity. 2 "crafts" behind each, each has 5 standard cube object with weight 1. the craft in front has the torque applied to the central (black) cube, the craft behind has the same torque applied on the last cube... watch them rotating. if you dont get it, watch it again

I see the effect, but I don't get why it's different.

[Renegrade]

Not quite. Spacecraft aren't fighting gravity to stay at the same altitude, the baseball bat is. I'm struggling to think of an earth analogy because it would have to rotate about the CoM while being torqued from any point about a vertical axis (no gravity), but RIC's statement should be atleast approximately right (I can't be bothered doing the math right now -.-)

I was imagining my example in space (I know, kinda weird for a stuff-in-your-garage example). Also, you could imagine it as all occurring in the horizontal plane, and ignoring any gravity-related torques when you're holding it from the end (when you hold it around the CoM for the first part, that will prevent gravity-induced torques).

That difference is due not to the torque applied being different, but the different polar moment of inertia when rotating it on a different axis. If you suspend the bat on a string so the axis is always the same, the same torque applied will create the same rotation regardless of where along its length it is applied.

Err what do you mean, by a string? Also polar coordinates are just a myth, to frighten young children with . Go light on the terminology, it's been more than two decades since I've been in anything like a physics class.

I've actually physically performed my experiment (only with a broom, I'm not sure if I have my baseball bat anymore, it hasn't been in the field for at least thirty years~) as described above. In the initial part, I put my hand under the CoM, and rotated my wrist clockwise/counterclockwise, which resulted in the ends swinging fairly easily in a horizontal arc back and forth. In the second part, I held it from the far end (away from the bristles obviously), briefly familiarizing myself with the gravity-induced torque so I could ignore it for the rest of the test. Now, in order to make the shaft rotate with the same angular velocity, I had to really crank in a great degree more of torque.

Now I'm not saying it's impossible to turn something from a point not on the CoM (or at least, the .. Axis..of...mass? My test proved it is POSSIBLE), just that it's harder.

I'm going to go back and re-read my previous post to make sure I didn't leave out any words now~

[Red Iron Crown]

Err what do you mean, by a string? Also polar coordinates are just a myth, to frighten young children with . Go light on the terminology, it's been more than two decades since I've been in anything like a physics class.

I've actually physically performed my experiment (only with a broom, I'm not sure if I have my baseball bat anymore, it hasn't been in the field for at least thirty years~) as described above. In the initial part, I put my hand under the CoM, and rotated my wrist clockwise/counterclockwise, which resulted in the ends swinging fairly easily in a horizontal arc back and forth. In the second part, I held it from the far end (away from the bristles obviously), briefly familiarizing myself with the gravity-induced torque so I could ignore it for the rest of the test. Now, in order to make the shaft rotate with the same angular velocity, I had to really crank in a great degree more of torque.

Now I'm not saying it's impossible to turn something from a point not on the CoM (or at least, the .. Axis..of...mass? My test proved it is POSSIBLE), just that it's harder.

I'm going to go back and re-read my previous post to make sure I didn't leave out any words now~

I'm meaning does the bat (or broom, or other asymmetric object) rotate around the same point in both of your tests? I.e. if the pivot point is your wrist, having the CoM further away affects how much the object resists rotation.

[Tuareg]

I see the effect, but I don't get why it's different.

well, it will not be a scientific explanation just some common sense.

explanation 1: when you apply torque off center (if are taking granted that the free-falling object will rotate around its com) the effect rotates the object is not the torque but the force created by the torque on an arm (im sure its not the perfect word but blame my English, sry )

explanation 2: when you rotate something at its com, the centripetal forces are equal, they don't do work so they use no energy (i guess i don't have to explain the diff between force, work and energy), when you rotate around an off center axis, the centripetal forces are off and they make the object move along a spiral path (this is not modeled in unity, or at least i've never built anything big enough to make the effect visible). if you would stop applying torque after a quarter round the object would fly away. if you keep rotating and there would be no centripetal forces (mass-less object) the craft or object would rotate around the axis the torque is applied. now put the 2 effects together and you will see that when centripetal forces equal out that movement they do work and so use energy. but energy is not created or lost, that energy comes from the torque. (in reality a free falling object rotated off center does rotate perfectly around its com only when you stop applying the torque and its rotating free, until that its center moves on a tiny elliptical spiral based on the starting resultant force. im not sure if im clear.)

Edited February 18, 2015 by Tuareg

[Superfluous J]

The angular momentum of a closed system must remain 0. I can't see how, if the two 1-mass cubes have the same "spin" inside them in Unity (I'm assuming this is an abstraction), the two 5-mass conglomerations of 5 cubes can't also have the same spin.

Are those sets of cubes nailed down? Or is the 1-mass spinning cube actually 1 mass unit and then you added a 1 mass unit spinny ball inside it, making it actually 2 mass units?

Something is wrong with the simulation, I think. I'm no physicist and I'm not saying you're trying to trick us, but this seems impossible to me. I'd be much more comfortable with a real world test, though I'm having trouble coming up with one. The closest I can come up with is a free spinning wheel (like a bicycle tire) with something motorized attached to it, and a counterweight exactly equal to the motorized attachment so you can keep the mass of the system equal and the center of mass on the axle. Move the motorized part (and its counterweight) back and forth on a spoke of the wheel and record the rpm of the wheel as it's spinning up. Do it 3-5 times each way and compare the data.

[/always preferred experiments to deduction]

[Renegrade]

I'm meaning does the bat (or broom, or other asymmetric object) rotate around the same point in both of your tests? I.e. if the pivot point is your wrist, having the CoM further away affects how much the object resists rotation.

It rotates around the source of the torque (which is roughly the axis of my arm). In space, I'd imagine such a system would try to rotate around the CoM, but I'd imagine that would reduce the acceleration even further (like... sqrt.. or.. square.. or so..)

[KSK]

The angular momentum of a closed system must remain 0. I can't see how, if the two 1-mass cubes have the same "spin" inside them in Unity (I'm assuming this is an abstraction), the two 5-mass conglomerations of 5 cubes can't also have the same spin.

Are those sets of cubes nailed down? Or is the 1-mass spinning cube actually 1 mass unit and then you added a 1 mass unit spinny ball inside it, making it actually 2 mass units?

Something is wrong with the simulation, I think. I'm no physicist and I'm not saying you're trying to trick us, but this seems impossible to me. I'd be much more comfortable with a real world test, though I'm having trouble coming up with one. The closest I can come up with is a free spinning wheel (like a bicycle tire) with something motorized attached to it, and a counterweight exactly equal to the motorized attachment so you can keep the mass of the system equal and the center of mass on the axle. Move the motorized part (and its counterweight) back and forth on a spoke of the wheel and record the rpm of the wheel as it's spinning up. Do it 3-5 times each way and compare the data.

[/always preferred experiments to deduction]

Yes, I'm not really understanding what point the video is trying to make. The front craft (with the reaction wheel in the centre) - I get that. It's symmetrical so the rotation axis passes through the com. Reaction wheel spins one way about that axis, ship spins the other way about the same axis. Net angular momentum zero. But I can't figure out how the second craft works at all. How is it still managing to spin about it's centre?

[Red Iron Crown]

But I can't figure out how the second craft works at all. How is it still managing to spin about it's centre?

It rotates around its CoM, as it must. The angular momentum from the wheel must go somewhere, so the whole thing rotates.

[Crzyrndm]

Yes, I'm not really understanding what point the video is trying to make. The front craft (with the reaction wheel in the centre) - I get that. It's symmetrical so the rotation axis passes through the com. Reaction wheel spins one way about that axis, ship spins the other way about the same axis. Net angular momentum zero. But I can't figure out how the second craft works at all. How is it still managing to spin about it's centre?

Unless I'm completely mistaken, the "torque" being applied is actually a rate of change of angular momentum of an object. To conserve angular momentum, the entire body must change it's angular momentum to equal and opposite the angular momentum being stored in the black block. This causes it to rotate, and the rotational axis of a free floating body is its CoM.

However, that still doesn't explain why the rate of ang. acceleration differs. That in my mind violates conservation of ang. momentum (if you move the black block from the outside to the center and spun it down completely, you would still have a rotating body). Guess it's time to break out the pencil and paper...

Edited February 18, 2015 by Crzyrndm

[Tuareg]

the problem is that you all take the laws like given things. it doesnt happen like that because it must, it has a reason behind. the law is there to be used on higher level without the need of deducing the entire low level problem again and again. saying it rotates around its com because it must is like saying there is a god because why not...

The angular momentum of a closed system must remain 0. I can't see how, if the two 1-mass cubes have the same "spin" inside them in Unity (I'm assuming this is an abstraction), the two 5-mass conglomerations of 5 cubes can't also have the same spin.

Are those sets of cubes nailed down? Or is the 1-mass spinning cube actually 1 mass unit and then you added a 1 mass unit spinny ball inside it, making it actually 2 mass units?

Something is wrong with the simulation, I think. I'm no physicist and I'm not saying you're trying to trick us, but this seems impossible to me. I'd be much more comfortable with a real world test, though I'm having trouble coming up with one. The closest I can come up with is a free spinning wheel (like a bicycle tire) with something motorized attached to it, and a counterweight exactly equal to the motorized attachment so you can keep the mass of the system equal and the center of mass on the axle. Move the motorized part (and its counterweight) back and forth on a spoke of the wheel and record the rpm of the wheel as it's spinning up. Do it 3-5 times each way and compare the data.

[/always preferred experiments to deduction]

there is no mistake or cheat, not nailed down they are 2 copied "crafts" just the cubes are in different order. no other objects at all and it is right as it is, it SHOULD work like this. the law say only it will rotate around its com, not that it will rotate with the same speed...

Edited February 18, 2015 by Tuareg

[Red Iron Crown]

the problem is that you all take the laws like given things. it doesnt happen like that because it must, it has a reason behind. the law is there to be used on higher level without the need of deducing the entire low level problem again and again. saying it rotates around its com because it must is like saying there is a god because why not...

Heh, fair enough. It must because all our empirical observations indicate that torque applied to a free floating object results in rotation about the CoM.

there is no mistake or cheat, not nailed down they are 2 copied "crafts" just the cubes are in different order. no other objects at all and it is right as it is, it SHOULD work like this. the law say only it will rotate around its com, not that it will rotate with the same speed...

So where does the leftover angular momentum go?

[Crzyrndm]

Just so I can get things straight in my head... (thinking of it as torque gets somewhat confusing)

Units of angular momentum are: kg * m² / s

Rate of change of angular momentum is the derivative wrt time: kg * m² / s²

SI units for kg are: N * s² / m

Substituted: N * s² * m² * m^-1 * s^-2

Simplifying: N * s^{(2 - 2)} * m^{(2 - 1)}

Finally: N * m => Torque

Rate of change of angular momentum of an object == torque applied to that object

By conservation of angular momentum, the apparent torque on the parent body should not depend on the location in which the angular momentum is being stored or released

So where does the leftover angular momentum go?

That is exactly my question...

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saying it rotates around its com because it must is like saying there is a god because why not...

Can be defined at a lower level if required... (ie. here be two force vectors acting upon an object of mass m...)

Edited February 18, 2015 by Crzyrndm

[KSK]

It rotates around its CoM, as it must. The angular momentum from the wheel must go somewhere, so the whole thing rotates.

Still trying to get my head around this.

We're assuming that the reaction wheel block has the same mass as one of the structural blocks, so the CoM doesn't change when you shuffle the blocks around? Otherwise the second craft wouldn't rotate about it's centre in the same way that the first craft does.

Then we're applying a torque to one 'arm' of the cross by spinning up the reaction wheel. But we're applying that torque about an axis that doesn't appear to intersect the CoM at all. I get that the thing has to rotate about it's CoM (or more accurately, it seems intuitively correct and I'm prepared to take it on faith lacking the maths to prove it for myself ). Is the simulation correct? Will the cross then start rotating in the same plane as before?

Edit. But if the reaction wheel block has the same mass as one of the structural blocks, then shuffling the blocks around not only keeps the CoM in the same place (dead centre) but also keeps the moment of inertia, about the centre axis, the same. So assuming that we're spinning the reaction wheel up to the same speed in each case, why do the two craft spin at different speeds if the relevant moment of inertia remains unchanged and the net angular momentum remains unchanged?

*scratches head*

Edited February 18, 2015 by KSK

[Crzyrndm]

Then we're applying a torque to one 'arm' of the cross by spinning up the reaction wheel. But we're applying that torque about an axis that doesn't appear to intersect the CoM at all.

You're applying a torque to change the angular momentum stored within the reaction wheel (motor torque driving the shaft). That torque itself doesn't effect the main body, the local change in angular momentum it produces does. Try to not think of it as forces and arms/levers

[Tuareg]

Just so I can get things straight in my head... (thinking of it as torque gets somewhat confusing)

Units of angular momentum are: kg * m² / s

Rate of change of angular momentum is the derivative wrt time: kg * m² / s²

SI units for kg are: N * s² / m

Substituted: N * s² * m² * m^-1 * s^-2

Simplifying: N * s^{(2 - 2)} * m^{(2 - 1)}

Finally: N * m => Torque

Rate of change of angular momentum of an object == torque applied to that object

By conservation of angular momentum, the apparent torque on the parent body should not depend on the location in which the angular momentum is being stored or released

That is exactly my question...

- - - Updated - - -

Can be defined at a lower level if required... (ie. here be two force vectors acting upon an object of mass m...)

you really think physics is that simple you can just say "Rate of change of angular momentum of an object == torque applied to that object"?

huhhh. its far more complex. im long years ago out of this kind of math, i've learnt these things about 20 years ago, but still, it's a shame to read something like this.

"Moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration about an axis of rotation."

"Notice that rotation about different axes of the same body yield different moments of inertia."

at least read wiki pls.

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You're applying a torque to change the angular momentum stored within the reaction wheel (motor torque driving the shaft). That torque itself doesn't effect the main body, the local change in angular momentum it produces does. Try to not think of it as forces and arms/levers

thats entirely wrong, all the rules we are talking about are derived from simple forces and arms

Edited February 18, 2015 by Tuareg

[stevehead]

Reaction wheels are too overpowered and I think they should be nerfed at higher difficulty settings. With how reaction wheels are currently, they greatly reduce the importance of other control / torque generation methods that are actually more realistic to some degree (rocket gimbaling, RCS, control surfaces). I use a module manager config that globally nerfs my reaction wheels to 5% effectiveness, and along with RCS, I think I found a good balance; it's actually nice to have a need for RCS outside of translation and have reaction wheels for fine tuning control and very basic stabilization. Keep the current reaction wheels (or slightly nerf them) for "easy" difficulty.

[Crzyrndm]

"Moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration about an axis of rotation."

Angular momentum = Moment of Inertia (MOI) * Angular velocity

Angular Acceleration = Torque / MOI

d(angular momentum)/dt = MOI * d(Angular Velocity)/dt

" = MOI * Angular Acceleration

" = MOI * Torque / MOI

" = Torque

Momentum and acceleration both depend on MOI so it ends up as a non-factor. You can also see it clearly if you use Nms (Newton meter second) as the unit of angular momentum instead of kgm²s^-1(Find torque here, notice angular momentum right above it).

In linear mechanics this would be: F * t = m * v (or rather the integral of force wrt time and dv, but lets keep it simple)

Substituting for rotational equivalents: Torque * t = MOI * angular velocity

thats entirely wrong, all the rules we are talking about are derived from simple forces and arms

The basic principle at play here is conservation of momentum. You can extrapolate that out to a pair of linear forces acting on a body, but it's much less intuitive to do so.

EDIT

I would love to be proven wrong here because otherwise KSP is probably violating conservation of momentum *again*

EDIT2

Approaching this from a slightly different direction using the Unity simulation:

If a torque is applied for x seconds, and then reversed for x seconds, the final rotational velocity of the body should be exactly the same as the initial rotational velocity.

If a torque is applied for x seconds to a block on the end of the arm, and is then swapped with the center block (no change in linear momentum or angular momentum) and then reversed for x seconds, what is the final rotational velocity? The unity simulation poses that it will be non-zero while conservation of momentum poses that it will be zero.

Finally, apply two exactly opposing torques anywhere on an object. Physics states that all forces are in equilibrium and no acceleration can be present while the Unity simulation may imply that there is a torque remainder (ok, I doubt that Unity has this wrong. It's more likely something in the MOI that is inconsistent, but if this fails...)

The simulation doesn't add up to what I understand of the physics involved. Explain the discrepancy, please.

---

Edited February 19, 2015 by Crzyrndm

[Renegrade]

Actually I strongly suspect in this situation, the 'missing' inertia does something weird like move the CoM or is dissipated as heat as the offset mounted RW flexes the craft.

I wonder if a physical rig could be constructed to test this empirically? An obvious construction would be a disk mounted horizontally on a low friction axle, with sub-wheels mounted above the axle, and towards the edge.. but the axle would represent a really hard-fixed, unmoving CoM and an absolute reference frame. To remove that, you'd have to change it such as the disk was sitting on a low-friction surface...

Still, no matter how I visualize it, I'm having trouble seeing the non-CoM mounted wheel having equal (or less) moment of inertia than the CoM-mounted one.

(By the way, building such an affair would not be too difficult. A reaction wheel is just a flywheel, and we wouldn't need the same precision that a satellite or telescope would. Just a simple two speed motor: go, and stop)

[Tuareg]

snip

nicely ignored the second part of what i wrote. try to forget your formulas, just read the sentences together with some common sense:

"Moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration about an axis of rotation."

"Notice that rotation about different axes of the same body yield different moments of inertia."

it means: rotating an object around different axes need more torque to reach the same angular velocity.

not complicated...

[Red Iron Crown]

it means: rotating an object around different axes need more torque to reach the same angular velocity.

not complicated...

What is not clear to me is why the larger object would rotate around a different axis. Can you elaborate?