Spinning - can anyone explain moments of inertia ?

[mungo_55]

Hi,

For my sins I am doing the long brief for my FI test on spinning, and I am trying to get to grips with the moments of inertia involved.

I've read a definition which says an object's moment of inertia about an axis describes how difficult it is to change its angular momentum about its axis.

So for an aircraft I think the idea is - if you are looking at the fuselage, an aircraft with a long heavy fuselage is harder to get moving around its C of G (ie. in pitch) than one with a short light fuselage. So the long heavy fuselage has a greater moment of inertia. But once the long, heavy fuselage has started moving eg. because of aerodynamic forces in the spin, it is harder to stop it moving, because its inertia is greater. I think this gives it more rigidity as well,when looking at the gyroscopic moments involved.

Am I along the right lines here, or barking up the wrong tree ?!

Any help much appreciated.

Mungo

[gijoe]

Mungo,
Let's have a go...

Imagine a big horizontal disc lying on the floor with a pin in the middle to spin on. It is a heavy disc so is hard to get going.

You use X amount of energy to get the disc going and this is a perfect process (unlike real life) and all of the energy used is transferred to the disc.

The energy is stored by Inertia, which as you said is the unwillingness of an object to change it's momentum, which in another non-real environment would mean that the disc would continue spinning for ever on it's pin until something stops it, and transfers that stored energy (brakes = resulting heat etc).

So the Moment of Inertia bit is the total sum of the inertia of all of the smaller parts of the big disc acting about the centre.

(Think Moment = Turning force about the pin)

Here's the clever bit...

Imagine that the big disc is instantly replaced by a smaller disc but the new smaller disc in our 'perfect' and 'instantaneous' process retains all of the Inertia that the big disc had.

To keep the same amount of energy the disc would have to spin much faster given the momentum ( = weight x speed) , or
Moment of Inertia, that the original big disc had spread over a smaller area from the centre point.

So what?

Go to a kid's playground. Get on the roundabout and get it going whilst leaning back out of the roundabout. Then pull yourself in and the roundabout will speed up because it will want to maintain the same amount of inertia about the rotating point.

This is a great practical demonstration of Moment of Inertia.

I think you need to be careful about what is caused by Moment of inertia and aerodynamic forces in a stalled situation, which is what a spin is after all, but
I hope that this gives you the idea about M of I.

G :ok:

[Dan Winterland]

Or the 'standard' CFS analogy of the ice skater spinning on the tip of one skate. She brings he arms in and speeds up. It's because (as explained so well by gijoe) the mass of her arms are now close to her body, but they want to move at the same speed, so her body rotates faster.

"So that Bloggs, is why the spin accelerates when you move the control column forward".

[gijoe]

Absolutely.

The stored inertia energy is put closer to the centre of rotation when cc goes forward and so things speed up to keep the total M of I the same.

Mungo, are you happy with this?

G;)

[hugh flung_dung]

The ice-skater analogy is the simplest for people to understand. If you want a full description of what's going on in a spin I can send you a scan of the relevant parts of AP3456 if you let me have your email address in a PM.

There's a good description here: http://en.wikipedia.org/wiki/Moment_of_inertia

HFD

(edited to add link)

[mungo_55]

Thanks for the replies, I appreciate your time.

I think I'm getting there..... Half the battle is understanding enough to be able to ask the right question !

I understand the analogies with the roundabout and the ice skater. You say that the energy stays the same if you make the distance from the axis smaller (eg. the person moving into the roundabout). So I take it the Energy = Weight x Distance x Speed. By reducing the distance, the speed must go up to keep the energy the same (the weight doesn't change). But this is the Energy, right ? Is the Moment of Inertia just the Weight x Distance part ?

I'm trying to get from this kind of understanding to understanding how aircraft would vary from each other in spins based on the weight of eg. their fuselage and their dimensions ie. the length of the fuselage in this case. It seems an aircraft with a long heavy fuselage would have a greater moment of inertia in the pitching plane (big weight x big distance) than one with a shorter lighter fuselage.

And I think (but I aint sure) that this moment in the pitching plane has to be looked at against the moment in the rolling plane (based on the weight and length of the wings), to see which is dominant. I think from there maybe you can look at whether gyroscopic precession of yawing / rolling forces is likely to have anti-spin or pro-spin effects.

I have to admit there is one diagram I don't fully understand which is one of a Tucano, nose low in a apin, and the explanation says the inertia moment in pitch causes a flattening of the spin in the yawing plane.

How I wish I'd listened more in my Physics lessons....

[cavortingcheetah]

:hmm:

If AP 3456 is the Air Force manual dealing with spinning, amongst other things, there was a good description in there of the A/B ratio and, if memory serves, the X/Y ratio - at any rate, another important one. Therein may lie the secrets for which you search?:)

['India-Mike]

I would thoroughly recommend any of Darrol Stinton's books on aeroplane design. The spinning parts are very well explained. However, they're engineers' books and so not worth your while buying. Get a copy through local library just for the spin parts.

[Dan Winterland]

The subject is covered very well in the instructional film, 'The Spin Explained'. Produced by SSVC, it's shown to all RAF students and is very very good. Unfortunately, if you ask SSVC for a copy, it's very very expensive.

['India-Mike]

Dan

Who's SSVC? And quantify 'very expensive'. Sounds worthwhile

[chornedsnorkack]

An important thing to consider:

Rotational energy is actually NOT conserved in the roundabout case - it does not have to be!

Angular momentum is conserved even without conserving rotational energy.

Think about it. When you are not rotating, you can extend and retract your hands without any opposing forces. But when you are rotating, the centrifugal forces will push your hands out and resist retracting them.

Which means that when you are retracting weight, you are doing work to increase your energy of rotation!

Also, note that a plane has three moments of inertia: in roll, yaw and pitch. Those depend on the airplane construction AND loading.

Planes with heavy engines in nose or tail, near roll axis, have small roll moments of inertia. Planes with engines far outboard have large roll moments of inertia.

A plane might have very different moments of inertia at exact same weight and CoG! Imagine a plane nearly empty of payload and with a lot of fuel for a long ferry flight - it has a lot of weight far from roll axis in wing tanks, but little weight away from pitch axis. Now load the same plane with heavy payload and limited fuel for a short hop - the roll moment of inertia is small, but pitch moment of inertia may be big because of weight in nose and tail!

[mungo_55]

thanks for the further explanations and the tips on books. The explanation of how moments of inertia can be changed by chornedsnorkack is a useful one for my brief I think. Ta !

I tried looking for Darrol Stinton's books in the Dorset Libraries catalogue, but no joy unfortunately. My FI instructor may well have AP3456 so I might try and track that down. Anybody read 'Anatomy of a Spin' by John Lowery? Looks like a short but affordable book.

[BigEndBob]

Local park as what i can only describe as a mini vertical roundabout.
Vertical tube rotating on a shaft with four set of foot rests and handles to hold on to.

Jump on, lean out then spin yourself round.
Then pull yourself to the centre and hold on for dear life!
The forces in your arms have to be experienced to believed.

So when an aircraft recovers from a spin there must be similiar forces trying to pull it apart! those poor wing roots!

[Dan Winterland]

SSVC = Services Sound and Vision Corporation. www.ssvc.com or type SSVC into google. They produce a lot of military training films and the unclassified ones are available for purchase. Unfortunately, they don't have a catalogue online so you have to know what you are looking for. When the Tucano came into service, they produced 'the Spin Explained' and 'The propeller explained'. Both are execllent. The spin film explains the moment of inertia very well, but it excells in explaining the gyroscpic effects which are more significant than you would expect.

To quantify 'very expensive', this question arose on pprune some years ago, I e-mailed SSVC and they quoted a price. I seem to remeber it was in excess of a hundred quid!!!!! Their pricing plicy may have changed, so it may be worth asking the question again.

[hugh flung_dung]

The trap with briefs (to FIEs and to studes) is that if you start going into too much detail there's a serious risk of causing confusion, waffling and being caught out by the "and why's that?" question. My suggestion would be to keep it simple. Does the stude need to understand MoI? - almost certainly not! I had to learn about it many years ago and have never consciously used the knowledge since.
Think about what the stude needs to know in a spin brief:

Why...

stall+yaw=wing_drop=autorotation;
Autorotation+Differential induced drag+gravity=spin;

Recognition...

Low speed (stalled), high rate of descent (dangerous), high rate of yaw (but we tend to notice the roll and this can be confusing so must be ignored)
Spin characteristics depend on mass distribution as well as engine RPM and energy at entry, and many other things. The aircraft achieves a balance between gyroscopic and aerodynamic forces, it's a stable condition that will not self-recover (OK some types will but that's not the message)

Avoidance...
Spin avoidance is easy: don't stall. If you must stall then avoid doing so with yaw present. If you do stall and get to the incipient spin stage just centralise everything and the autorotation should stop (recover from whatever the aircraft is now doing); if it doesn't stop go to the recovery technique.
Recovery...

Power and aileron will have varying effects so simplify the situation by taking-off the power and centering the ailerons
In SEPs (big weight at the front) the yaw rate tends to flatten the spin (whirling a weight on the end of a string) and therefore increases the angle of attack further, so use full rudder opposite to the yaw indication to reduce the yaw rate. Pause for this to have some effect (a second or so) - but the aircraft is stalled so this alone will not lead to recovery
Unstall the aircraft by moving the stick progressively forward (ailerons neutral) until the spin stops. Then centralise everything and recover from whatever the aircraft is now doing. Note that as the aircraft starts to recover the roll rate will increase slightly - same as an ice skater.

Considerations...

If the elevator is not held back until the appropriate point in the recovery the roll rate may increase (ice skater) and lead to a delayed recovery - quickly going back fully pro-spin and starting again with the correct sequence will give a standard recovery
If you're confident of your facts you could discuss precision, advanced and inverted recoveries but you don't want to risk adding confusion so I'd suggest holding this back unless asked - unless this is an aeros spin brief
If asked anything for which you don't know the answer say: "I don't know the answer to that but I'll find out and get back to you the next time we meet"



I hope this helps.

HFD (waiting flor flak)

[gijoe]

Mungo,

You've got the O-Level (Mine!), A Level, BSc, MSc and Phd answers all on one thread.

I hope our combined efforts helped. :ok:


G

[mungo_55]

They certainly did ! Thanks again. I have found myself looking at all sorts of stuff eg. angular momentum, what radians are, and found myself being pleasantly interested. The section from AP3456 was kindly emailed to me and that, together with these posts and Wikipedia (very useful for physics definitions) have all helped.

[porridge]

I have a long brief I prepared for my FIC approval on spinning which covers the moments of inertia etc.
If anyone work like a copy of it (it is in PDF format) send me an PM with your email address and I'll forward a copy.

[djpil]

Thanks porridge.
Same offer from me too for anyone who wants my notes on "basic" spinning and a ppt slideshow.
However, there is some excellent stuff online at Bill Crawford's website (http://www.flightlab.net/download.html) although too much detail for basic piloting briefing.
All I say about MofI's is that the whole aeroplane behaves like a gyroscope - nose down aerodynamic pitch balanced by nose up gyroscopic forces.

(just got my Grade 1 instructor rating with spins as the test brief)