Used to be. So there is stickage.

Now the more I talk with manufacturers about this and you go look at the specs

they go zero crossings naah. That's so old school.

No. We don't worry about that anymore.

They can get good enough. And the issue we talked about was stickage.

If you go slow enough all of a sudden you

want to cross zero at a nice spin-off prescribed rate.

Once you get close enough all of a sudden it goes Uhh!

And it basically sticks and then you have to give it enough force to unstick it again.

And It gives you that slight wobble that Kepler really would hate.

You know, so you might have to worry about

zero crossing but they're getting really good with these things now.

So that becomes less of an issue. What are other ones.Ryan?

Russell.

Russell.

De-spinning the wheel?

Momentum management.

That's something we'll keep talking about.

So in the equation we developed you will see,

hey this works. This works infinitely.

But keep in mind these wheel speeds

in the mathematics actually can grow infinitely large.

And in reality you can't do that.

Your wheel will literally fall apart at some point.

It's spinning so fast.

What are other issues that you have with these devices?

The momentum management, it will be true for CMG's and for reaction wheels.

We don't cover much of them in this class the follow on 6010 goes into

way more detail on momentum management because its a whole complexity.

Or CMGCO's singularities if they line up.

Right. Usually comes out of momentum management issues but there are also

controllability problems that sometimes with

these devices you may not be able to produce general torques.

So there's classic CMG singularity that we must about to talk about.

I'm going to show them here but don't go,

We're running out of time doing the details 6010

goes in way more details from this stuff,

but yeah they appear.

But also you basically got this washing machine right,

something that's shaking and rattling and going around.

How balanced is that wheel typically?

Pretty good hopefully.

But is it perfectly balanced?

Right, never. Nothing in life is absolutely perfectly balanced.

So you're actually you know its like having a little imbalanced mass.

And the faster you're spinning you're putting continuously now

a slight shake and disturbance on the craft at the frequency of the wheel.

So if you consider internal modes fuel slosh.

Panels that might be flexing

structural resonances your sense of platform has to be very steady because you want to

stare at the stars with Kepler and it has

a certain natural frequency and if you hit that natural frequency with these wheels,

you might be exciting a little bit more than you want it, you know.

So you have to worry about those things,

so balancing of the stuff.

Modeling in bound in class with an all perfectly balanced.

In modeling one has some current students who are

just not publishing papers in the full stuff.

It's amazing how this little one motor torque equation that takes up this much space,

takes up like a page all of a sudden.

If you do the full model.

So there's some papers, if you're curious I can point you to.

So big benefits, no fuel that's really the biggest thing but also fine tune control.

That's really important if you have to do just

very just a smidgen left you know kind of control.

But there's challenges with all these devices and the mathematics.

So this is typically what they look like this is a very simple reaction wheel,

some of them just basically spinning discs,

a blob of mass, some electronics something that holds it together in case it breaks.

You don't want to smash everything else it becomes a bomb essentially.

So it has to hold itself together as it's a material but with reaction wheels,

the key is this is all bolted down.

I like this picture because it looks kind of beefy you know.

Just remember this wheel is bolted down.

In the mathematics for a reaction wheel we'll always

assume that all those axes are fixed.

The spin axis doesn't,

you know change with respect to the body.

So we have body fixed spin axis.

You can have multiple wheels to generate arbitrary torque.

Each wheel you just get to a torque about the spin axis.

You apply one Newton meter torque.

Then you get a minus 1 Newton meter torque back onto the craft right, at Newton's laws.

You push with one Newton you get pushback back at one Newton.

That's the same principle.

There is no amplification there's nothing to generate

a general three dimensional torque vector.

You didn't have to go this one has to produce 0.2 meter,

this one 0.5, this one 0.3 and you spin them off at particular ways.

Right. And we'll see that in the mathematics.

How do we arrange these,

from a torque command onto wheel speed commands.

But they can saturate.

No wheel can spin infinitely fast and that's a problem.

To apply a torque it has to be spinning up the wheel.

So if you're persistently pushing on the craft like atmospheric drag might do.

And you're holding an attitude that's not in equilibrium with that drag,

you're pushing back with the wheels to hold the attitude.

And that means continuously you're spinning up that wheel more

and more and more and more and at some point it just goes okay,

I'm done. I'm taking off.

We may run into heat issues.

Heat can be an issue as well.

Other ones to look like this.

Here are some ITHACO ones.

These might be very same that was flying on Kepler.

Often look pancake shaped.

Why do these high end wheels often look more like a pancake?

Why not make them skinny, long like a cork bar or something.

But you kind of put the big rod with the wheel out there. What do you think?

Bigger torque.

Sorry?

You have a bigger torque for your speed.

Technically correct because the motor torque,

or whatever that motor produces That's a torque you get back on the craft.

Pressure is on the outside.

The Inertia is the big thing. The bigger,

the more out you put your wheel inertia,

as the wheel mass the bigger the inertia is going to be.

So if you look at 1D rotation where you have

i times the anglular acceleration equal to torque,

the angular acceleration will be smaller.

If you have more inertia.

Right if it's a beefier wheel that means

more inertia and you put the 1 newton meter torque on there.

You're not going to spin up as much.

That means they don't saturate as quickly and that's a nice thing.

You're still storing the same amount of momentum,

torque times time gives you momentum.

So the more momentum we store you will find

every one of these wheels introduces new gyroscopics.

With the dual spinner,

we looked about which wheel speed should we have such that

the gyroscopics actually help us or if you're evil,

don't help you and destabilize it, right.

There's both that you can do with this stuff.

Now we'll see the same effects happening in a general wheel configuration.

All right. So the more momentum you have it makes it really stable.

But if you have to point here and then point over here very

quickly the momentum will work against you.

The more stable it is the harder it is sometimes to move it.

That's what stability gives you.

But that's why these things are flat.

We have so much mass they give you 10 kilograms the

best you can do is a ring of 10 kilograms all the way out.

In reality you need something around it to hold it together.

You need some thin spokes to hold it together.

You need enough stiffness so these things don't vibrate like crazy

or you know start having other modes that get excited.

So there's always a tradeoff but you do like as much mass as possible out.

That gets you the most inertia for the mass that you're allocated for this device.

Good if you look inside you can see it's basically this.

Most of the mass is out here.

This one happens to have a flat but it's

a very thin kind of thing that comes out, they have certain shapes.

This is all for structural purposes.

You're looking at resonances,

trying to make it a hyper stable wheel.

You don't want this thing to beat off balance washing machine thing.

So a lot of effort goes into that and they're getting really good these days.

And there is always some electronics that drives it.

Some of them are analog. Many of them,

some of the cool ones I've seen from Germany these days are digital.

You just basically give it a command and it does everything, tracks it's friction,

tracks it's zero crossing,

tracks its heat, if it gets too hot it automatically cuts down.

So there are some really nice what they call smart

reaction wheels that we've seen there too.

You can find those on the web. Honeywell makes also,

they are a huge reactionary manufacturer that make up a lot of these devices.

Now Control Moment Gyroscope look very similar.

Same pancake. That means we've got a spinning disk.

We want as much inertia as possible and there's

still a motor in here actually that controls the wheel speed,

because in fact none of these devices launch start up like with the dual spinner.

Once you're in the craft it's all bolted down,

and once you're up there you have to figure out how

do I now spin up this whole system. All right.

So with a CMG, what's different from a reaction wheel,

a reaction wheel, Ideally you'd like to have around

zero speed ish or at least a low speed.

The higher the speed you will see from

a motor torque equation and we've seen the work energy principle already.

It will cause more power be required. So we want the speeds low.

With a CMG, we want a high speed because the thing

that drives us here is not the motor torque actually but the gyroscopic effect.

I'm assuming you've all done this experiment with the bicycle wheel you spin it up,

right, and then you tilt it and you get this weird kick in another direction right.

That's really the gyroscopic effect because if you

spun it up like this you get momentum vector sticking out.

When you tilt it, you've changed the momentum,

changed momentum is torque.

So that's actually going to spin you about this other orthogonal axes.

Right. That's what we're taking advantage of.

So these should be spinning at a,

you know 5000 10000 RPM.

Some of the smaller ones are going way more than 10000 even,

it's a very high need to be very very balanced very carefully designed.

Immediately, that means more money for one of these devices.

But you have a motor that gets you to that speed and then holds it roughly at that speed.

But then there's a second motor here that's

the new part that allows that spinning wheel now to be Gimbaled.

That's what they call the gimbaling angle.

How much and as you Gimbel it if this is your spin axis of the wheel,

as we Gimbel about this,

you know you're changing the spin axis now relative to the body.

So when we do these derivatives there will be body relative derivatives in CMG.

All right. For a reaction wheel, those are not there.

So the big benefit here too and you'll see in the mathematics is actually the

torque amplification small input torques

allow you to get a large torque back on the thing.

So that small input really what you're taking advantage of is

the gyroscopic that happens so the faster the wheel is spinning.

The bigger the gyroscopic will be for that input and

you can put in one penny and get a dollar out of it so to speak, you know.

And that's why it's great if you have huge things to move, very big satellites.

It might take huge reaction wheels to move them but you

can do it way better with a CMG device

or at the space station it actually uses

double gimballed CMG clusters to kind of hold their attitude and do stuff.

And double gimballing has some benefits,

momentum absorption capability but most

of the devices you see are like this single gimballed,

they have a single axis not a double,

you know, gyrating axis.

That makes it even more complicated.

So drawbacks, definitely mechanically more complex.

Controls are definitely much more complicated.

You will see in the equations of motion and we go from

variable speed CMG to our classic CMG and

a classic CMG just holds the wheel speed

constant versus variable allows you to go all over the place.

It doesn't simplify it much.

It's still really complicated to just just really complicated.

You know, the good down to reaction wheels it becomes actually quite doable.

So the mathematics is def,

it's trickier, singularities we're mentioning.

You're getting a Torque that's orthogonal to this axis and

the spin axis and so that third axis actually varies with time.

So depending on what you're doing you can get these things to

line up in a plane which is a singularity you're talking about.

And if it controls as I need a torque out of that plane you just can't produce that.

And that's the gimble lock,

kind of a consideration.

So we'll see hints of that in the mathematics that come up some singularities.

So good how did they look. They're not.

You don't typically fly one device so you have clusters of CMG's,

often four with clusters of four.

The nice thing is you can.... Each wheel has momentum.

Each wheel is spinning let's say 10000 RPM,

that's an easy number and you can align them in such a way that two wheels are

pointing out so the outward parts cancel the upwards part add up.

The other two wheels are pointing downwards in the other direction where

the total momentum of the fourth CMG cluster is zero normally,

And that's nice because having zero momentum means I stay agile.

The momentum I have like we saw with the dual spinners,

you get very very stable but it also means you

become more lethargic it takes a huge effort to

drag all that momentum through space that takes a huge torque to do that.

So people like this for agility purposes.

You can do the same with reaction wheels but you need more than three.

You can do it with four reaction wheels,

tetrahedron configurations where you can set up

a system that has a nominal zero momentum device.

So again so there's whole lectures we can do on how to configure these things.

But that's kind of what they look like in clusters.

We'll typically in class,

you'll see my pictures being mimics of this one,

the pyramid CMG cluster.

Also popular configuration for reaction wheels.