Corona688

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

102 posts in this topic

23 minutes ago, tjt said:

...this makes my brain hurt (in the post workout muscle-soreness way) :)

That's what learning feels like XD

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Thank you @Snark for fighting the good fight

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A really simple way to picture this is to imagine someone playing fetch with their dog:

The man holds his stick at its (non-slobbery) end, and in the throwing motion he applies not only linear force to make the stick fly, but also moment causing it to tumble.
The stick is roughly aerodynamically uniform and tumbles end-over-end. What's significant is that it doesn't rotate around the point where the man's hand was, it rotates around a point roughly equidistant from both ends - it's CoM.

Edited by The_Rocketeer
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12 minutes ago, The_Rocketeer said:

A really simple way to picture this is to imagine someone playing fetch with their dog:

The man holds his stick at its (non-slobbery) end, and in the throwing motion he applies not only linear force to make the stick fly, but also moment causing it to tumble.
The stick is roughly aerodynamically uniform and tumbles end-over-end. What's significant is that it doesn't rotate around the point where the man's hand was, it rotates around a point roughly equidistant from both ends - it's CoM.

Dog saliva is highly slippery and very heavy though and completely changes the aerodynamics. that's why when the stick lands the end closest to the human, and most likely to be grabbed, is inevitably the saliva covered one.

Edited by tjt
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So, if you were thinking about it the wrong way around, I wouldn't feel bad about it. I was, too! The situation reminds me of a Feynman sprinkler, where the answer is immediately obvious everyone, but everyone gets a different answer. Conservation of angular momentum with no torque paths to ground doesn't show up that often, so our intuitions can be ill-equiped for some reason! Where did my original misconception come from? Well.... turns out it was KSP! Or atleast the KSP wiki. In the description for the tiny reaction wheel it says:

The placement does matter for reaction wheels. Generally speaking they can cause some problems if placed far from the center of mass. Imagine you are grabbing that point and rotating it. That is what the reaction wheels will try to do. You'll get offcenter rotation anywhere other then near the COM.

comment by C7, in his blog entry “Updated Information on SAS in 0.21.1

 

In retrospect, it might just be misleadingly ambiguous. I didn't try to scrutinize it or anything, it just sounds like torque works better near the COM, which sounds legit enough. (Except it's not) So for us that had intuition pointing the wrong way, how can we fix it? Well, torques are weird, so instead let's imagine our torque as two forces being applied L distance apart from eachother on a long rod in space (the best kind). In space you spin around the COM, and we can imagine putting these two forces either centered on the COM, or way at the end of the rod.

Torque-Equivalent Forces on a Rod in Spaaaaacetorque_forces.png

For both setups, the red and green points both apply F force and are are L distance apart from eachother. What's the resulting torque?

Torque = Force * radius (from COM)   ...   In the first case, that'll be F*(L/2) + F*(L/2) = F*L, and in the second case it'll be F*3L - F*2L = F*L . Huh. Two very different situations, but the same resulting torque about the COM.

Conceptually why?
    The forces centered on the rod both torque in the same direction and add together but they're quite close. On the other hand, the forces near the end of the rod wind up primarily fighting eachother and torquing the rod in opposite directions. However they're also much further away from the COM, so what little force isn't balanced out is amplified by the long lever arm. Because these two effects balance perfectly (physics :rolleyes:), the net effect of both setups is the same. So apparently angular momentum is conserved. Huh, imagine that :) . I hope that thought experiment helps other people as it did me.

 

 

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The problem with wrong placement or reaction wheels is not magnitude of torque, but structural stress due to its propagation.

 

Let's imagine a station with a central module and several peripheral modules docked around it (let's say the CoM of the station is close to the CoM of the central module). Note also that unless a module docked on the axis of rotation, moment of inertia it adds to the entire station (around the station's CoM) is several times more than the moment if inertia of the module on its own (around its CoM). What happens when you give a command for the reaction wheels to start rotating in some direction

a) Place all the reaction wheels on one of the side modules. The module will first start turning itself, bending the joint and even slightly pushing the rest in the opposite direction, only then due to the torque applied to the docking port the central module starts slowly rotating in the right direction, pulling the other modules and slightly bending those joints

b) Place all the reaction wheels in the central module. In the initial moment it may slightly turn itself, bending the joints. To rotate further it will have to apply tangential force to the peripheral modules (on the entire station scale these forces net zero, of course) to make them move around the center, plus also passing some torque to make the peripherals rotate. The peripheral modules end up slightly bent in the opposite to angular acceleration direction relative to the central module.

c) Evenly distributed torque across the modules. Each module will try turning itself in the right direction, however necessity to actually move the peripheral modules around the center produces produces force on the docking ports that results in the central module having to fight more counter-torque and the peripherals still bending in the direction of rotation.

d) the perfect balance that minimizes bending on the ports has most torque authority in the central module, but also some in the peripherals - this way almost only linear force to make the peripherals move around the center comes through the ports, but the rotational effects are handled on each module minimizing actual flexing.

 

Now remember that we aren't usually just making the craft spin - we use that for active attitude control, and here joint flexing can have critical effects. Therefore, the recipe is: ensure that primary torque source is attached to the center as rigidly as possible, select control reference point around there as well, but also give some torque authority to the heavier side modules, especially if the connections flex a bit

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Without reading the whole thread now I'll have to add one more post from the "position of reaction wheels doesn't matter" faction:

 

Our ships are rigid bodies in a Zero-G environment with no atmosphere. They have a center of thrust and a center of mass. The center of thrust, although not being used for that in the game, also applies for RCS. I think we all had that problem that misplaced RCS-thrusters caused problems in docking mode, like drifting out of place in rotation mode and turning unintentionally in translation mode. The reason being the center of thrust of the RCS thrusters wasn't in the exact same spot as the center of mass. That means on one side of the CoT there's more mass than on the other side, causing an unequal acceleration.

 

When we're talkin' about reaction wheels tho, again, our ships are solid bodies. Not only can reaction wheels only apply torque and no lateral force, but no matter where u place them on ur ship, be it in the very tip, directly in the CoM or in the upper left front of a side-mounted fuel tank, they'll always apply the same force to the ship and only make it counter-rotate around the "ball joint" that is kinda formed by the CoM. The reason being the reaction wheel applies the same force all around the wheel. No matter what sector of the wheel u look at, on the opposite sector there's the exact same amount of force, just in the opposite direction. And since the ship that it's supposed to turn is a rigid body the same thing applies if u imagine the CoM to be said ball joint around which the ship rotates. No matter which sector of the ship u look at, there is an exact opposite sector with the exact same mass that is simply shaped a little different. Rotating around the CoM results in the same thing as the reaction wheel rotating around its axis. And while soft bodies do indeed flex when torque is applied to a certain area of them that torque also applies to the rest of the soft body after a while and makes it rotate around its CoM. In a rigid-body ship the flexing is still there, but it's so little that no one would ever notice. Even measuring it would take very very sensitive instruments. Such little movements of flexing also travel through the ship much faster than through a soft body and thus make it look like the reaction happens instantly.

And here comes why the actual POSITION of the reaction wheel can be ANYWHERE aboard the ship: The reaction wheel doesn't induce any other force than torque. It doesn't push the ship like the RCS does. And while torque is applied at a certain area it's still the exact same torque everywhere else on the ship due to it being rigid. Imagine the ship was full of weaker reaction wheels littered throughout its body. The exact same thing. The ship is always gonna turn around the CoM.

 

Looking at the 2.5 meter reaction wheel modules in the game u may have noticed that other than having a cross of struts on one end they're pretty much empty, with the exception of an orange object stickin' into it from one position inside the circle. That's where the reaction wheels would be, not in its center.

Edited by DualDesertEagle
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I'm glad this came up.  I had been obsessing over precise reaction-wheel placement and knowing that I can relax on that and put it where it's convenient or aesthetically-pleasing is a relief.  :D

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15 hours ago, The_Rocketeer said:

A really simple way to picture this is to imagine someone playing fetch with their dog:

The man holds his stick at its (non-slobbery) end, and in the throwing motion he applies not only linear force to make the stick fly, but also moment causing it to tumble.
The stick is roughly aerodynamically uniform and tumbles end-over-end. What's significant is that it doesn't rotate around the point where the man's hand was, it rotates around a point roughly equidistant from both ends - it's CoM.

Of course it rotates about the CoM, I don't see anyone saying different.

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Just now, Corona688 said:

Of course it rotates about the CoM, I don't see anyone saying different.

Then I guess I must be right? Not sure where you're going with this...

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Just that you're answering the wrong question.  If nobody ever said the CoM or CoR moved, "the CoR doesn't move" isn't helpful.

People keep mentioning where the torque comes from, not because it changes the center of rotation (how could it possibly?) but because it seems relevant.  Anyone who's taken introductory physics at this level intuitively knows that the moment changes depending where you apply torque -- which is wrong.  The moment changes depending where it rotates.  And here, unlike all our high school examples, it's not being forced to rotate anywhere but its center of mass, so the lever-effect torque equation does no apply, distances do not matter, etc.

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I don't think I said that it did or didn't move, I just said that it was at the CoM. I also wasn't trying to explain anything, I was simply providing a RL example that people can recognise and associate with the problem. My post was intended to help people realise that they already understand, not to teach them something new.

The intuitive error you refer to is actually one of the many relevant points that is subtly addressed by my post - there's a change in my scenario from a situation in which the lever-effect does apply - the man twists the stick as he throws it - to a (nearly) closed system in which it tumbles like a ship in orbit - it flies through the air. Contracting the lever-effect situation into a single moment of torque (the point of release), this becomes mathematically identical to using a reaction wheel on a craft in orbit.

Edited by The_Rocketeer
Removed confrontational phrasing

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There IS a fundamental difference if the reaction wheels are off center.

Just as the man throwing the stick -- there is a reason he grabs the stick out of center. That's exactly the reason he *throws* it, because the torque is off center, it causes the center of mass to be flung around the point where torque is applied (his hand), resulting in a circular movement, which is translated in a forward movement once the torque is removed (result: Stick is thrown further).

If he were to do the same thing in the center of the stick, it would just twirl the stick around in his hand and it would go nowhere.

I can understand why it's not simulated as such in KSP, because it would be very difficult to simulate.

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28 minutes ago, Stoney3K said:

There IS a fundamental difference if the reaction wheels are off center.

Just as the man throwing the stick -- there is a reason he grabs the stick out of center. That's exactly the reason he *throws* it, because the torque is off center, it causes the center of mass to be flung around the point where torque is applied (his hand), resulting in a circular movement, which is translated in a forward movement once the torque is removed (result: Stick is thrown further).

If he were to do the same thing in the center of the stick, it would just twirl the stick around in his hand and it would go nowhere.

I can understand why it's not simulated as such in KSP, because it would be very difficult to simulate.

It's not "simulated" in KSP because it would be wrong. Spacecraft in vacuum will always, always rotate around the CoM, unlike the stick where you change the center of rotation to wherever it is gripped. Applying pure torque cannot move the CoM of a spacecraft by a millimeter.

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Just now, Red Iron Crown said:

It's not "simulated" in KSP because it would be wrong. Spacecraft in vacuum will always, always rotate around the CoM, unlike the stick where you change the center of rotation to wherever it is gripped. Applying pure torque cannot move the CoM of a spacecraft by a millimeter.

Splitting hairs here, but that's not a property of a vacuum, but a property of a spacecraft that is not connected to anything else. If an off-center reaction wheel were to result in a translational movement, it would violate the law of conservation of momentum (and it would be a propellantless rocket engine).

It still remains very counter-intuitive because it means you can stick a million reaction wheels on one end of a 50 meter long girder with a fuel tank on the other end, and the ship will rotate around the center of it.

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1 minute ago, Stoney3K said:

Splitting hairs here, but that's not a property of a vacuum, but a property of a spacecraft that is not connected to anything else. If an off-center reaction wheel were to result in a translational movement, it would violate the law of conservation of momentum (and it would be a propellantless rocket engine).

It gets more complicated anywhere other than vacuum. Interaction with atmosphere can cause some forces to appear that translate the craft.

1 minute ago, Stoney3K said:

It still remains very counter-intuitive because it means you can stick a million reaction wheels on one end of a 50 meter long girder with a fuel tank on the other end, and the ship will rotate around the center of it.

Agreed, I am one of the ones for whom it took several people explaining to be convinced (in a thread similar to this one). :) 

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One thing I didn't get before reading this thread and the wiki on reaction wheels: sounds like there are actually four or more spinning thingies inside each of those cylinders we snap into place in the game called "reaction wheels."

It seems less counter-intuitive when I consider that.

Edited by Diche Bach
fix link

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17 hours ago, Diche Bach said:

One thing I didn't get before reading this thread and the wiki on reaction wheels: sounds like there are actually four or more spinning thingies inside each of those cylinders we snap into place in the game called "reaction wheels."

It seems less counter-intuitive when I consider that.

Actually, turns out there are zero spinning thingies inside those cylinders we add to our craft, because they're just polygon models that exude magical torque from nowhere.  I'm not being pedantic, here-- it's very relevant, because KSP reaction wheels are very unrealistic, in one very important way:  they violate the heck out of conservation of angular momentum, even though they obey conservation of linear momentum.  :wink:

That particular unrealistic aspect of their operation, however, is irrelevant to this thread.  They're unrealistic in that they create torque from nowhere.  Other than that (which I realize is kind of like saying "other than that, Mrs. Lincoln, how did you like the play?", but please bear with me, here), they're modeled realistically, in every way that is germane to the discussion in this thread.  Whether they conserve angular momentum or not has nothing to do with "does placement matter?"  Placement doesn't matter, whether they work like IRL reaction wheels or whether they magically create torque from nowhere.  Torque is torque.  Once you've got the torque, it behaves in certain ways, which is why placement doesn't matter.

 

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On 08/08/2016 at 1:55 PM, tjt said:

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.

Just to make things a bit more complicated, it doesn't matter where you place your magical torque factory reaction wheels only if the module is either massless (which would make generating real life torque a bit... difficult), or didn't alter the assembly's moment of inertia. In other words, by adding a reaction-wheel-mass to the rod, you're actually changing the assembly's moment of inertia. Depending on it's geometry and mass, placing it at the end or in the middle would make a difference if the resulting moments of inertia aren't the same.

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This may be unrelated, but, what makes a long thin spacecraft take longer to build up rotational speed? Or does it just seem that way because all my long spacecraft are generally much heavier than my short ones?

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11 minutes ago, String Witch said:

This may be unrelated, but, what makes a long thin spacecraft take longer to build up rotational speed? Or does it just seem that way because all my long spacecraft are generally much heavier than my short ones?

Polar moment of inertia, or in layman's terms, resistance to turning. Imagine a barbell with weights at the very ends resting on your shoulders and try to turn, it's pretty difficult. Now imagine those weights are moved as close to your body as they can be, suddenly it's much easier to turn. Even though the total mass is the same, the former case has a higher polar moment of inertia.

Simply put, the more the mass is concentrated near the CoM, the easier it is to turn. The more it is moved away from the CoM, the harder it becomes to turn.

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1 minute ago, String Witch said:

This may be unrelated, but, what makes a long thin spacecraft take longer to build up rotational speed? Or does it just seem that way because all my long spacecraft are generally much heavier than my short ones?

Moment of inertia. For the same mass, a longer object will have more moment of inertia (proportional to square of the length, if the mass distribution along the length stays the same). 

Note that for a system of point-masses (and you can always split something into small enough chunks and then integrate them) the moment of inertia is calculated as the sum of these masses, each multiplied by the square of its distance to the rotation axis.

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23 minutes ago, String Witch said:

This may be unrelated, but, what makes a long thin spacecraft take longer to build up rotational speed? Or does it just seem that way because all my long spacecraft are generally much heavier than my short ones?

Think of it a little like this:

It takes time for a given force to move a given mass a given distance.

Assuming the mass is the same, long thin craft travel more distance than short fat craft when they rotate, because their extremities move around in a bigger circle. So, if the force applied to turn them is the same, it will take more time for them to complete one whole turn. The variables here are distance and time, so the term for expressing them is speed. If you wanted the speed to be the same, you would need more force or less mass.


Any good?

Edited by The_Rocketeer
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On 24.8.2016 at 2:06 PM, Stoney3K said:

There IS a fundamental difference if the reaction wheels are off center.

Just as the man throwing the stick -- there is a reason he grabs the stick out of center. That's exactly the reason he *throws* it, because the torque is off center, it causes the center of mass to be flung around the point where torque is applied (his hand), resulting in a circular movement, which is translated in a forward movement once the torque is removed (result: Stick is thrown further).

If he were to do the same thing in the center of the stick, it would just twirl the stick around in his hand and it would go nowhere.

I can understand why it's not simulated as such in KSP, because it would be very difficult to simulate.

U are missing something there, which is the fact that the stick still rotates around its center of mass when it's flying trough the air. U can even see that by throwing a stick urself. As u throw it the center of rotation is in ur wrist, so actually not even in the stick itself. But as soon as u let go u'll notice that as the stick is moving through the air it's spinning evenly like the propeller of a plane, just around another axis. Now add a weight to one end of the stick so that the center of mass lies roughly at the position where the weight is. Then grab the opposite end with no weight on it an throw the stick like that. Now is the stick still spinning evenly or is it spinning around the point where u added the weight? Both is true actually, even tho 1 end of the stick spins much further out than the other. The reason for that is that the stick with the weight on it is now spinning around their shared center of mass.

And now I've got something for u to try out in KSP: make a ship that consists of a long I-beam in the center and equally heavy "pods" on its ends, one of them containing a reaction wheel. Make absolutely sure the pods are the exact same mass, clip lighter parts into them if u have to.

Now send it to LKO either using a rocket or hyperedit, whatever u prefer, and  make sure it's decoupled from the rocket with nothing left of it. Wait until the rocket has drifted away a few meters and then start yawing or pitching using the reaction wheel. Of course it's gonna rotate around the center of the I-beam.

 

Now do the same thing again but this time make 1 pod significantly heavier and the other just the reaction wheel itself. I promise u it's gonna spin roughly around the heavier pod, not around the center of the I-beam, not around the reaction wheel.

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