NOT A BUG: Reaction wheels don't care where they're mounted

[Corona688]

They ought to and don't.  Center of mass is where they belong and that should be fixed.  Either that, or engines and RCS shouldn't care either.

[Boris-Barboris]

 

[pincushionman]

In a rigid-body system, the system does not care where moment is applied. The locations of the components of a force couple (RCS, fins, engine gimbal) matter very much, but sources of pure moment can be placed pretty much amywhere.

Now, there is a different behavior in elastic systems (like we have). Displacements propogate through the structure in a wave, and of course the locations of components will affect the behavior. However, once these oscillations have been damped out, the end result is the same.

The biggest effect that happens is the instantaneous deflections at the control points get out of phase with the global orientation, which is in turn out of phase with the sources of moment. But that's not unique to pure-moment sources; All other contols suffer from the same effect. And that doesn't mean it's a bug either; it's a consequence of structure that's insufficiently stiff.

Edited August 7, 2016 by pincushionman

[Jovus]

12 minutes ago, pincushionman said:

In a rigid-body system, the system does not care where moment is applied. The locations of the components of a force couple (RCS, fins, engine gimbal) matter very much, but sources of pure moment can be placed pretty much anywhere.

Uhh...what?

I might be misunderstanding you, but this seems really untrue. The placement of control moment gyroscopes is very sensitive, isn't it?

[Kerbart]

On 8/6/2016 at 2:22 PM, Corona688 said:

Either that, or engines and RCS shouldn't care either.

Reaction wheels supply torque. RCS and engines supply force which, when applied from a distance of the COM (the "lever") results in torque. Therefore, it does matter where you place RCS or engines, as it will affect how much torque they will create when running them (which might or might not be the desired side-effect). For reaction wheels it does not matter as their output is direct torque, and not a force.

[Alshain]

Not a bug.  Intended behavior.

[Corona688]

You had me on ignore, remember?  But I'm curious why it's intended.

5 hours ago, Kerbart said:

Reaction wheels supply torque.

So does a wrench of length L with force F.  Where you put the wrench matters.

This is because you get different values of inertia depending on where the torque is applied.  See also mass-centered vs rim-loaded wheel.

KSP doesn't do this, and probably should, as they did their physics homework in most other areas.

Edited August 8, 2016 by Corona688

[Alchemist]

5 hours ago, Corona688 said:

So does a wrench of length L with force F.  Where you put the wrench matters.

This is because you get different values of inertia depending on where the torque is applied.  See also mass-centered vs rim-loaded wheel.

No. Moment of inertia depends on where center of mass and where axis of rotation is, not where torque is applied. When no rigidly fixed axis is provided, a craft in space will rotate around its center of mass, so this question is not an issue.

Plus, you never get pure torque by applying just 1 force. You need 2 or more forces that have 0 vector sum, but are not on the same axis. What matters is not positioning of these forces relative to the center of mass or even the rotation axis, but only relative to each other. The story with force applied to a  wrench has the second force applied by the axis itself, so it matters where you put the first force in relation to the axis.

Reaction wheel provides only torque with no unbalanced force, so positioning doesn't really matter.

Edited August 8, 2016 by Alchemist

[Sharpy]

People still think in terms of Earth. People still can't imagine this being in freefall. People still can't dissociate torque from a support point.

Of course if you apply a wrench to the end of a beam, it will behave differently than if you apply it to the middle. Because besides the torque, you're providing a support. You are forcing the beam to rotate around the wrench, not around its center of mass.

 

Point torque alone is a force very rarely encountered in real life, so we don't have the fundamental intuition to imagine it. You try to imagine a motor with a flywheel? But then the flywheel has considerable mass and inertia, again, acting as a support. You imagine it as a wrench? There's your hand applying a pressure over a lever. Maybe a cross-wrench. But then you still need to make sure to apply the same force to both sides.

Still counter-intuitive.

Anyway, equations make it clear. Calculating momentum acting on any body you take all the forces and distances from the point where you calculate the momentum - but if you have an external point momentum, you just add it, completely regardless of the location.

[sal_vager]

Actually no, there is no bug here, it'd help if people checked things a bit more thoroughly

Here, these pics will explain.

It's been this way for a long time, one of our old member @Kasuha proved this long ago.

[Snark]

On 8/6/2016 at 11:22 AM, Corona688 said:

They ought to and don't.  Center of mass is where they belong and that should be fixed.  Either that, or engines and RCS shouldn't care either.

As numerous other posters in this thread have pointed out, the above is incorrect.  Reaction wheels don't care where they're placed, and they shouldn't.  That's how physics works.

Here's a very important concept, which has been known and well-understood for centuries:

The center of mass of a closed system moves at constant velocity.

This is known as conservation of momentum.  It's why rocket ships have to expend reaction mass in order to move.  If you don't believe in conservation of momentum, then I suggest you read the wiki article, and further references about it, until you do. 

This is why a vessel in space always rotates around its center of mass, unless it's expending reaction mass:  It's a closed system, and therefore, it can't move its CoM.  If it rotated around anything other than its CoM, then its CoM would be moving.

Here's a thought experiment for you.  Imagine if you were correct, and a reaction wheel caused the vessel to rotate around itself rather than the CoM.  You have a 10-meter long ship with a reaction wheel at one end, floating motionless in space.  Its CoM is at x=0m, with the reaction wheel located at x=5m.  The reaction wheel turns on, and over the course of ten seconds, it rotates the ship 180 degrees so that the CoM is now at x=10m.  While it's rotating, the CoM is now moving, where it wasn't, before.  Congratulations!  You have just invented inertialess drive!  You can explore the universe without expending any fuel.  Ships can just fling themselves around with reaction wheels, no fuel necessary!

...No.  It doesn't work that way.

14 hours ago, Jovus said:

I might be misunderstanding you, but this seems really untrue. The placement of control moment gyroscopes is very sensitive, isn't it?

No, you're understanding him just fine.  He's telling you the placement isn't "very sensitive", but rather doesn't matter.  At all.

And he's correct.  (Speaking as a physics major, here.)

8 hours ago, Corona688 said:

But I'm curious why it's intended.

Because it's the physically correct behavior, and your understanding of physics is mistaken.

8 hours ago, Corona688 said:

So does a wrench of length L with force F.  Where you put the wrench matters.

Yes, because you're not just supplying torque.  You're also supplying an external force.

This is a common mental confusion that people run into when trying to think about problems like this.  You're used to thinking about things in terms of a rotating object on a fixed axle, like a car wheel.  The issue is this:  it's not a closed system.  If you have a rotating object mounted on a fixed axle, then the axle is supplying an external translational force to the wheel by holding its center of rotation in a particular fixed place.  And unless you're standing on the wheel, you're supplying an external force, because you're standing on the floor and your connection point with the thing you're turning with the wrench gets linear force transmitted through that.

8 hours ago, Corona688 said:

you get different values of inertia depending on where the torque is applied.  See also mass-centered vs rim-loaded wheel.

Incorrect.  Where the torque is applied doesn't matter.  The moment of inertia of an object depends only on where the center of rotation is.

Your confusion is because you (incorrectly) think that the point of application of the torque is where the center of rotation is.  But it's not.

 

Here's a recent thread in which this entire topic was discussed in detail.  @OhioBob gives some excellent examples to demonstrate:

 

[Corona688]

7 minutes ago, Snark said:

Here's a thought experiment for you.  Imagine if you were correct, and a reaction wheel caused the vessel to rotate around itself rather than the CoM.  You have a 10-meter long ship with a reaction wheel at one end, floating motionless in space.  Its CoM is at x=0m, with the reaction wheel located at x=5m.  The reaction wheel turns on, and over the course of ten seconds, it rotates the ship 180 degrees so that the CoM is now at x=10m.  While it's rotating, the CoM is now moving, where it wasn't, before.  Congratulations!  You have just invented inertialess drive!  You can explore the universe without expending any fuel.  Ships can just fling themselves around with reaction wheels, no fuel necessary!

...No.  It doesn't work that way.

Huh?  I never claimed that it's coM or center of rotation would move in the first place.  If that's what you think I'm claiming, no wonder you think I'm so far wrong.

Edited August 8, 2016 by Corona688

[Snark]

28 minutes ago, Corona688 said:

Huh?  I never claimed that it's coM or center of rotation would move in the first place.  If that's what you think I'm claiming, no wonder you think I'm so far wrong.

Except that that's exactly what you're claiming, though you may not realize it.

You're claiming that a ship should rotate around its reaction wheel rather than around the center of mass, yes?

If I've misunderstood you, it's because your original statement was rather vague, and most of the many people who post about this issue (because they're under the same misconception) tend to think that.  If that's not what you mean, then what exactly do you mean when you say "reaction wheels should care where they're mounted"?

Specifically:  What exactly do you think the physical behavior should be, that's different from what is now happening?

The only other thing I can imagine that you might mean, is that you think the reaction wheels should turn the ship more slowly if they're not mounted at the center.  But this is also  incorrect.  If you look at the equations for angular acceleration, you'll find that all that matters is the amount of torque, and the moment of inertia.  There's nothing in that equation that talks about where the torque is applied, because it doesn't matter.

The moment of inertia does depend on the center of rotation.  But that will always be around the center of mass, if you're talking about a closed system.

You mention that a wrench works better based on its placement, and that's true.  But not because the moment of inertia of the wheel changes-- it's because the torque changes, because you're generating torque by applying an external force via a lever arm, and increasing the lever arm increases the force.  In the case of a reaction wheel, they apply a fixed amount of pure torque.  The placement doesn't matter, there's no lever arm to contend with here.

In case you don't want to take the word of a physics major, or of the many other people who have posted in this thread, here are a few references to demonstrate that the moment of inertia of a rotating body depends on the center of rotation and not where the torque is applied (emphasis added for clarity):

http://www.engineeringtoolbox.com/moment-inertia-torque-d_913.html
"Moment of Inertia of a body depends on the distribution of mass in the body with respect to the axis of rotation"

http://physics.about.com/od/physicsmtop/g/MomentOfInertia.htm
"The moment of inertia of an object is a calculated quantity for a rigid body that is undergoing rotational motion around a fixed axis. It is calculated based upon the distribution of mass within the object and the position of the axis, so the same object can have very different moment of inertia values depending upon the location and orientation of the axis of rotation."

https://www.britannica.com/science/moment-of-inertia
"Moment of inertia, in physics, quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of a torque (turning force). The axis may be internal or external and may or may not be fixed. The moment of inertia (I), however, is always specified with respect to that axis"

...There are plenty of others, those are just a few.

For reaction wheels to "care" about where they're placed, then either you'd have to assert that their placement changes where the center of rotation is, or you'd have to assert that it changes the moment of inertia of the ship.  Neither of those is the case.

[Corona688]

18 minutes ago, Snark said:

Except that that's exactly what you're claiming, though you may not realize it.

You're claiming that a ship should rotate around its reaction wheel rather than around the center of mass, yes?

No.  If that's what you think I'm claiming, no wonder you think I'm so far wrong.

18 minutes ago, Snark said:

Specifically:  What exactly do you think the physical behavior should be, that's different from what is now happening?

Should a torque 9 miles from the center of mass be as efficient?

18 minutes ago, Snark said:

The moment of inertia does depend on the center of rotation.  But that will always be around the center of mass, if you're talking about a closed system.

This may be my misconception...  So the resultant change in angular speed has nothing to do with the distribution of mass around the torque?

18 minutes ago, Snark said:

You mention that a wrench works better based on its placement, and that's true.  But not because the moment of inertia of the wheel changes-- it's because the torque changes, because you're generating torque by applying an external force via a lever arm, and increasing the lever arm increases the force.  In the case of a reaction wheel, they apply a fixed amount of pure torque.  The placement doesn't matter, there's no lever arm to contend with here.

But moment is related to where you push, no?  Not exactly separable.

[Snark]

7 minutes ago, Corona688 said:

Should a torque 9 miles from the center of mass be as efficient?

Yup, assuming your ship is 9 miles in radius.

A linear force wouldn't.  If you had an RCS thruster 9 miles from the CoM, it would be enormously more effective than one at the CoM.  But a reaction wheel doesn't care; physically, it's a different beast entirely.

7 minutes ago, Corona688 said:

This may be my misconception...  So the resultant change in angular speed has nothing to do with the distribution of mass around the torque?

Correct.  The distribution of mass matters, yes, but it matters around the axis of rotation, not around where the torque is applied.

The change in angular speed does depend on the distribution of mass around the center of rotation, which has nothing to do with where the torque is applied.  A ship with most of its mass concentrated near the CoM will be more nimble to rotate than a ship that has the mass mostly out at the ends.

The change in angular speed also depends on the amount of torque.  I think what may be confusing you is that you're conflating "place where the torque is applied" with "place where force is applied."  They're not the same thing.  If you're generating torque by exerting a linear force on it-- say, by using an RCS thruster to turn a ship, or using your hand on the rim of a wheel to turn it-- then it matters where you apply that force.  Because torque = force times distance, and a bigger lever arm gives you more torque for the same amount of force.

But a reaction wheel isn't exerting torque by applying a linear force to a lever arm from the center of ship's rotation.  It's applying pure torque, which is something you don't generally experience in everyday life and therefore your "common sense" isn't parsing it correctly.

7 minutes ago, Corona688 said:

But moment is related to where you push, no?  Not exactly separable.

No.  Not even slightly.  Again, you're conflating things.  Don't feel bad, it's a common misconception and you're in lots of good company. 

Amount of torque matters relevant to where you push, if you're generating torque by "pushing", i.e. exerting a linear force.  Reaction wheels don't do that.

Moment doesn't matter where you push, or where torque is, or anything else except 1. mass distribution of the object, and 2. the center of rotation.  I'm telling you that as a physics major, or if you don't want to take my word for it, see all the references that I link to in my previous post.

[Corona688]

OK, one final question then.

Are KSP reaction wheels breaking traditional physics by applying "pure torque"?  Or is this how a reaction wheel on a space telescope would really act?

[Snark]

8 hours ago, Corona688 said:

Are KSP reaction wheels breaking traditional physics by applying "pure torque"?  Or is this how a reaction wheel on a space telescope would really act?

Oh, they're breaking it all to heck, but not in a way that matters to your question. 

They are flagrantly violating the law of conservation of angular momentum.  However, I didn't mention it here, because it's not germane to the question you originally posted.  KSP could model reaction wheels actually realistically (which it doesn't), or it could model them as magical infinite sources of angular momentum (which breaks the laws of physics, and which is what it does)... but either way, the placement of the reaction wheel wouldn't matter and all of the above arguments would still hold.  If you're putting a real reaction wheel on a real space telescope, then no, it doesn't matter where you put it.  Presumably you'd put it as far from the sensitive optics as possible to minimize vibration or what-not, but that's an engineering issue, not a physics one.

Real-world reaction wheels do apply "pure torque", just as KSP wheels do.  The difference is that a real-world reaction wheel is a small, finite "storage battery" for angular momentum that can only hold a certain amount, whereas KSP reaction wheels are a magical infinite source/sink, like a battery that can run forever without needing to charge it.

The way a real-world reaction wheel works is this:  Suppose you have a ship floating in free space, totally motionless (no rotation at all).  The net angular momentum of the ship is zero; nothing's moving.  It's pointing north, and you want it to point south.  How do you do it?

Well, there are a couple of ways.  One would be to use RCS thrusters.  You shoot off a quick squirt of monopropellant, imparting some angular momentum to the ship; it starts to rotate slowly, and has nonzero total angular momentum while it's rotating.  (It got that angular momentum by expending reaction mass.  If you ask "where did the angular momentum come from?", it came from the high-velocity exhaust gas leaving the RCS thrusters.)  When the ship gets to its desired final orientation, you now have to expend another burst of monopropellant to stop it, and return its angular momentum to zero.

But there's another way:  you can use a reaction wheel.  You start up an electric motor that rapidly spins the reaction wheel in one direction, thus giving it a chunk of angular momentum.  Action-and-reaction causes the ship itself to start rotating in the opposite direction.  The total angular momentum of the system is unchanged:  it was zero before, and it's still zero while the ship is rotating.  That's because the angular momentum of the spinning wheel is precisely equal and opposite to the angular momentum of the rotating ship, so they cancel out.  Of course, the ship is much more massive and has a much bigger radius than the reaction wheel does, which means its moment of inertia is hugely bigger, so of course the ship rotates much more slowly than the wheel does.  Maybe the wheel is spinning madly at 5,000 RPM, but the ship takes a full minute to turn 180 degrees.  When the ship reaches its desired orientation, you simply put the brakes on the wheel and bring it to a halt... and that stops the ship, too.  No high-tech monitoring or sensors are needed:  it's dead simple, because the law of conservation of angular momentum has got your back.  As long as you didn't expend any reaction mass during the process (thus giving you net angular momentum), and as long as you started with no net rotation, then simply braking the wheel to a halt is guaranteed to render the rotation of the ship perfectly motionless.

That's how real-world reaction wheels work.  There are a few different variations of how they're constructed.  Some are pure "reaction wheels" that simply do exactly what I said.  Some, which need to exert much bigger torques for rotating large spacecraft, work a bit differently by having a rapidly spinning "gyroscope" mounted on gimbals, and then using big motors to muscle the axis of the the wheel around (I think that's what the space shuttle did, for example).  But the fundamental physical principle of conservation-of-angular-momentum is the same.

Note that if you have a ship that's already rotating, it's impossible to use reaction wheels to stop it.  Well, you could, if the ship were rotating very slowly to start with... but that would leave you with a saturated reaction wheel that's spinning rapidly in a direction that you don't want to go, and no way to stop it without starting the ship spinning again.  Similarly, there's no way to take a motionless ship and make it spin faster and faster.

It may help to think of it by analogy:  Your rocket ship is a house, and its unwanted angular momentum is like trash that's scattered around the house.  The reaction wheel is a fairly small trash can that's inside the house.  You can clean up the house, up to a point, by picking up the trash and putting it in the trash can.  But you can only do that just so much, because the trash can is going to fill up pretty quickly.  And once it's full, there's no way to empty it without just taking all the trash out of it and scattering it around the house again, putting you back where you started.

That's not how KSP reaction wheels are modeled.  In KSP, a reaction wheel is a magical, infinite source of torque that comes from nowhere.  In the preceding analogy, it's like having a trash can where the trash magically disappears when you put it into the can.

I don't begrudge that lack of realism, since I think it keeps things simple and helps with game playability, which is why I don't yell about it in the forums despite being physically unrealistic. 

Anyway, that's why real-world spacecraft always have some sort of RCS thruster system, even if they also have reaction wheels:  because there's no way to adjust the net angular momentum of the ship without spending reaction mass.  Reaction wheels IRL are good for adjusting the ship's orientation, but not its net rotation.

[Corona688]

8 hours ago, Snark said:

Oh, they're breaking it all to heck.  They are flagrantly violating the law of conservation of angular momentum.  However, I didn't mention it here, because it's not germane to the question you originally posted.  KSP could model reaction wheels actually realistically (which it doesn't), or it could model them as magical infinite sources of angular momentum (which breaks the laws of physics, and which is what it does)... but either way, the placement of the reaction wheel wouldn't matter and all of the above arguments would still hold.

Oh, I know they break it, but apparently not in this particular way.  Thank you.

[Jovus]

@Snark I think we have different definitions of "doesn't matter," and that's our confusion.

I agree that reaction wheels shouldn't cause a spacecraft to rotate around anything other than their CoM, regardless of the placement of the reaction wheels.

However, their placement (specifically, their orientation) does determine how they apply their torque. Most obviously, if you don't line up your reaction wheels with principal axes of the spacecraft, you're going to have to change your control algorithm to avoid inducing unwanted rotation. And a set of reaction wheels or control moment gyroscopes need to be placed on the spacecraft in such a way that they can constructively interact.

But as for where - locationally - on the body? I agree in principle that it doesn't matter. Of course, for actual engineering problems it does, because you don't want to break structures by applying too heavy a load to something delicate.

 

For anyone curious about specifics in real world spacecraft, here's a paper: http://mae2.nmsu.edu/~asanyal/Sanyal_res/AGNCSpacecraft.pdf

 

ETA: None of this really matters for KSP. I'm perfectly happy calling the Advanced In-line Reaction Wheel (or whichever) a black box the engineers put together with appropriate bits and control algorithms to orient my spacecraft however I want it.

Edited August 8, 2016 by Jovus

[Tyko]

I'm still not visualizing this. If I'm reading the above commentary correctly it's saying that it doesn't matter where the reaction wheel is placed. this is so counterintuitive that I'm going to need an example...here it is

I have a 1 kilometer long rod of homogeneous, perfectly stiff material. It's CoM is exactly in the center. If I have 1 reaction wheel module, my intuition tells me that placing it exactly in the center of my kilometer long rod is going to give me the "most ability to rotate the rod for the least effort"*. If I'm reading the above info though it sounds like I can turn it just as effectively if I place my single reaction wheel module all the way at one of the end of the rod.

(* I intentionally avoided using specific technical terms here because I didn't want to screw up how I used them. I hope my plain English wording gets my point across)

Edited August 8, 2016 by tjt

[Snark]

4 minutes ago, tjt said:

I have a 1 kilometer long rod of homogeneous, perfectly stiff material.

Okay.

4 minutes ago, tjt said:

It's CoM is exactly in the center.

Still with ya.

4 minutes ago, tjt said:

If I have 1 reaction wheel module, my intuition tells me that placing it exactly in the center of my kilometer long rod is going to give me the most turning ability for the least effort.

In this case, your intuition-- and I mean this in the nicest way-- is flat-out dead wrong. 

Doesn't matter where you put it.  Result will be the same.

Don't feel too bad-- lots of people get sucked into the same mental trap.  It's a common problem.  This is about the Nth time I've needed to explain it... and the pattern tends to be the same every time:

• Person says <wrong thing about reaction wheels>
• Various people (including me) explain <right way to think about it>
• This seems so patently ludicrous to the OP that they're certain that everyone must have misunderstood <wrong thing>.  So the OP reiterates, with a slightly different approach to try to make themselves more clear.
• Everyone patiently explains, again, no we're not misunderstanding you, we understood you fine, you're just wrong.
• Repeat N times.

...it happens again and again.  It's hard for me to blame anyone for having trouble with it-- this is one of those cases where our everyday "common sense" experience is so different from what actually happens that it's really hard for folks to believe that it doesn't work the way they think.

 

4 minutes ago, tjt said:

If I'm reading the above info though it sounds like I can turn it just as effectively if I place my single reaction wheel module all the way at one of the end of the rod.

Yes, you are reading it absolutely correctly.  That was the impression I was trying to convey, and I'm glad that I have succeeded in this attempt. 

[Tyko]

I really appreciate your patience...one more try...I'm holding a marching band baton in my hand...one of those 4 foot long metal ones that they spin and throw in the air. I want to spin it. I hold the baton in the exact center and I apply rotation with my wrist - I would expect the baton to rotate on it's CoM, which is also where I'm applying the rotational force and the baton spins.

If I hold the baton near one of the ends and twist my wrist, the force my wrist is applying isn't aligned with the CoM of my baton. Its trying to spin at its CoM and my wrist is trying to spin it from the end. I have to exert a lot of effort to move it at all.

It's not that same

[sdj64]

Reaction wheel placement does not matter from a rigid body dynamics perspective.  A torque applied to a rigid body makes it act the same regardless of where the torque is applied.  This is exactly what @Snark and others have been saying.  In real life and with small, low part count ships in KSP, it's a fair assumption to treat the ship as a rigid body.

But as KSP players we've all experienced "wobbly" or "floppy" rockets - not exactly a rigid body.  From a stress and bending perspective, where the torque is applied matters very much.  Putting your reaction wheels near the center of mass minimizes bending stresses in a large ship.  Torque at the ends will cause a long ship with many joints to bend more easily.  This post above shows how it works in KSP.

[Snark]

20 minutes ago, sdj64 said:

But as KSP players we've all experienced "wobbly" or "floppy" rockets - not exactly a rigid body.  From a stress and bending perspective, where the torque is applied matters very much.  Putting your reaction wheels near the center of mass minimizes bending stresses in a large ship.  Torque at the ends will cause a long ship with many joints to bend more easily.  This post above shows how it works in KSP.

^ Yes, this.  Wobbling is another matter entirely. 

20 minutes ago, tjt said:

I really appreciate your patience...one more try...I'm holding a marching band baton in my hand...one of those 4 foot long metal ones that they spin and throw in the air. I want to spin it. I hold the baton in the exact center and I apply rotation with my wrist - I would expect the baton to rotate on it's CoM, which is also where I'm applying the rotational force and the baton spins.

If I hold the baton near one of the ends and twist my wrist, the force my wrist is applying isn't aligned with the CoM of my baton. Its trying to spin at its CoM and my wrist is trying to spin it from the end. I have to exert a lot of effort to move it at all.

It's not that same

Yes, and you are absolutely correct.  It's a lot harder to waggle it when you're holding it at one end.  This is precisely the example that trips up so many people.

The problem is this:  In your holding-the-baton-at-one-end example, you're moving the center of rotation.  The baton is rotating around one end, not around its CoM.  That increases its moment of inertia, so it's harder to waggle.

When you grip the baton in the center and waggle it, you're exerting pure torque.  (Let's say you're doing this in free-fall, so we don't have to talk about the muscular effort you're exerting to lift its weight.)

When you grip the baton at one end and waggle it, you're not only exerting torque.  You're also applying a linear force by holding your arm rigid and not allowing that end of the baton to move.

So you're comparing apples and oranges.  Here's a better example to demonstrate the it-doesn't-matter principle:  Hold the baton at one end.  But don't hold your arm rigidly stationary and waggle the baton around that end as a pivot point.  Instead, move your arm in a semircle, so that the center of the baton stays stationary while you move one end back and forth.  Guess what?  It just got a whole lot easier!  It got as easy, in fact, as it was when you were holding the baton in the middle.  (Well, okay, not quite as easy, since now you're moving the mass of your arm back and forth, but you know what I mean).

When a reaction wheel is placed at one end of a ship as opposed to the middle, it doesn't rotate the ship around the reaction wheel.  It rotates the ship around its CoM, which is where the ship will rotate regardless of where the reaction wheel is placed.  That's why the reaction wheel placement doesn't matter in this instance.

If you were rotating the ship, not with a reaction wheel, but rather by mounting the ship on a fixed axle, and having an electric motor on that axle to rotate the ship... in that case, yes, it would matter where you put the axle on the ship, and it would be best to put the axle so that it goes through the middle of the ship.  That would be your baton-waggling analogy.

[Tyko]

2 hours ago, Snark said:

^ Yes, this.  Wobbling is another matter entirely. 

Yes, and you are absolutely correct.  It's a lot harder to waggle it when you're holding it at one end.  This is precisely the example that trips up so many people.

The problem is this:  In your holding-the-baton-at-one-end example, you're moving the center of rotation.  The baton is rotating around one end, not around its CoM.  That increases its moment of inertia, so it's harder to waggle.

When you grip the baton in the center and waggle it, you're exerting pure torque.  (Let's say you're doing this in free-fall, so we don't have to talk about the muscular effort you're exerting to lift its weight.)

When you grip the baton at one end and waggle it, you're not only exerting torque.  You're also applying a linear force by holding your arm rigid and not allowing that end of the baton to move.

So you're comparing apples and oranges.  Here's a better example to demonstrate the it-doesn't-matter principle:  Hold the baton at one end.  But don't hold your arm rigidly stationary and waggle the baton around that end as a pivot point.  Instead, move your arm in a semircle, so that the center of the baton stays stationary while you move one end back and forth.  Guess what?  It just got a whole lot easier!  It got as easy, in fact, as it was when you were holding the baton in the middle.  (Well, okay, not quite as easy, since now you're moving the mass of your arm back and forth, but you know what I mean).

When a reaction wheel is placed at one end of a ship as opposed to the middle, it doesn't rotate the ship around the reaction wheel.  It rotates the ship around its CoM, which is where the ship will rotate regardless of where the reaction wheel is placed.  That's why the reaction wheel placement doesn't matter in this instance.

If you were rotating the ship, not with a reaction wheel, but rather by mounting the ship on a fixed axle, and having an electric motor on that axle to rotate the ship... in that case, yes, it would matter where you put the axle on the ship, and it would be best to put the axle so that it goes through the middle of the ship.  That would be your baton-waggling analogy.

As usual, you're awesome Snark...I totally wasn't considering that my feet being planted on the ground and holding my arm rigid introduced a bunch of other forces...this makes my brain hurt (in the post workout muscle-soreness way)

Edited August 8, 2016 by tjt