The geometry of an aerobatic loop

[Hardy Heinlin]

There might be some misunderstandings among some PSX users regarding the interpretation of the instruments during a 360° vertical loop maneuver.

It's all normal. Let me explain ...

Say, you are on a flight from Rome to Paris.

You're facing Paris. Bank is 0°, pitch is 0°.

Now you start a positive loop: Pitch 10°, 20° ... 80°, 89°, 90°! What happens at 90°?

At pitch 90° there is no bank angle and no longitudinal heading (longitudinal means "refering to the present longitude"). Bank and heading cannot be defined at 90° pitch, just as you cannot define the heading when you are at the Northpole. At the Northpole there are no longitudes. The Northpole is a point.

When you approach and overfly the Northpole, the present latitudes go 88, 89, 90, 89, 88 ... It doesn't go 88, 89, 90, 91, 92. At 90, your heading changes by 180°, i.e. from a north heading to a south heading.

The same happens in a loop at pitch 90°. When you continue the rise of your aircraft nose above 90°, you actually start lowering the nose. So the pitch goes 88, 89, 90, 89, 88 ...

On the way to Paris, when you're doing your loop, and you pass the highest pitch -- 88, 89, 90, 89, 88 -- you will fly back to Rome with the bluebrown side up, and your bank angle is suddenly 180°.

The aircraft will not make a roll motion of 180°. Just your instruments will rotate. Their gyro construction is not infinite. They don't flip the bluebrown side up, they rotate it up (very quickly). And when the heading changes by 180°, the compass doesn't flip either. It rotates by 180° (very quickly).

So you continue your loop and you reach the highest altitude when the pitch is lowered to 0°, while your bank remains 180°. You're still facing Rome.

Then you start losing altitude. The pitch lowers to negative values until reaching -88°, -89°, -90°. When passing -90°, the pitch rises with the same values in reversed order: -89, -88, -87 ...

Also, when passing -90°, your heading and bank again changes by 180°, directly, without a rotational motion of the aircaft. Only the instruments rotate by 180°. And your bank is again 0°, and you're back on the course to Paris.

So you continue your loop and you reach the lowest altitude when the pitch is increased to 0°, while your bank remains 0°. You're still facing Paris. And here's the end of the loop.


Cheers,

|-|ardy

[cavaricooper]

I'm all for unusual attitude recovery training, but are there really people looping the 744?

I love that you are always "thinking" Hardy- normally on plane elevations several orders of magnitude greater than mine.  This forum is ALWAYS educational, and so much more civilized than others.

Best- C

PS- Aaaaaaaah- I just read the post..... even Tex Johnson would draw the line at this

[Peter Lang]

....., but are there really people looping the 744?

Up to now, I never thought about that. But the idea is quite interesting....  

[cagarini]

Thx HH for the rather complete coverage of the "anatomy of a loop the loop" :-)

At another thread, in the "Accessories" board, I addressed this regarding the way VisualPSX ( and I guess XView as well ) deal with the change in pitch, hdg and roll...

This results, from an outside view, in an instantaneous "flip" of 180º in roll as the 90º pitch is reached, either climbing or descending...

Using roll rate as an additional variable in this situation could help avoiding the unwanted "flip" effect...

P.S.: And sorry for having misunderstood this as a flaw in the FDM :-/

[falconeye]

Of course Hardy must show us now a video of a perfect loop with the 747  :mrgreen:

[Hardy Heinlin]

Another common misunderstanding is that the highest altitude of a loop be reached when the pitch is 90°. That's wrong. At 90° you have passed only 25% of the 360° circle.

As I wrote above, after the inital 25% your route goes backwards to where you're coming from. That is, the bank and the heading change by 180°. The blue side is no longer up; it is down now.

When the blue side is down, your bank angle is 180°. Not 0°!

50% of the loop (highest altitude) is reached when your pitch has returned to 0° with the blue side down. Blue side down does not mean 0° bank!

Only after 75% of the loop, the blue side is back up, and the heading redirects to the planned destination.


|-|

[Hardy Heinlin]

In case you wonder why the ND compass makes a little jump by a few degrees during the loop:

This is normal and happens when the ND is in "TRACK UP" display mode (i.e. not in "HDG UP" mode) and the groundspeed increases or decreases through the 80 knot level. Below 80 knots groundspeed, the track and the FPA instruments are set to zero. (At 0 knots groundspeed there is no track and no FPA.)

When the wind is calm and the pitch is +90° or -90°, the groundspeed is zero.

[John H Watson]

Another common misunderstanding is that the highest altitude of a loop be reached when the pitch is 90°. That's wrong. At 90° you have passed only 25% of the 360° circle.

This is assuming the aircraft doesn't stall prior to reaching 90deg.

The real aircraft may survive such manoeuvres, but can the real instrumentation handle these? We know traditional mechanical gyros can topple if they are not designed for aerobatics, and I've even seen the real ISFD* return to not-quite-straight-and-level after being at the extremes (requiring a quick realignment).

The 744 gyros are also self levelling (so don't spend too much time inverted or it will get really confusing).

Rgds
JHW

*simulated by pulling the ISFD from the instrument panel without depowering

[Hardy Heinlin]

This is assuming the aircraft doesn't stall prior to reaching 90deg.

Sure. My comments refer to an ideal 360° circle.


|-|


P.S.: The slow, long-term self-correction by gravity in the gyro systems is also modelled in PSX. But this works only when you are approximately in level flight, i.e. within ca. +/- 10° bank or pitch respectively. If the angles are greater, the system cannot correct itself. On a long-range flight around half of the globe, ending with an opposite attitude with regard to the takeoff position (and referring to outer space), the flight time is long enough to keep the slow self-correction intact, i.e. the groundspeed is low enough.

[Hardy Heinlin]

Hi all,

just to avoid any confusion ...

The above discussion refers to 10.0.4 and previous versions.

I just noticed in 10.0.5 that the aircraft will smoothly roll by 180° when passing +90 or -90 pitch. This is an aerodynamic effect, not an instrument effect, and: I didn't program this intentionally. It's a side effect of these items:

0.5.0013.
0.5.0017.

In 10.0.6, later this year, I'll eliminate this unwanted effect -- but only for very steep pitch attitudes.


Cheers,

|-|ardy

[cagarini]

So... now you're playing aerobatics with PSX....    

[Hessel Oosten]

May be we really can expect barrel roll and looping demo's by Hardy some day.
[size=8](Of course with 3 engines off...).[/size]

It can be performed with a jet aircraft, in real life

Google for the name of the famous (Boeing 707) pilot "Tex Johnson" or look here:

https://www.youtube.com/watch?v=Ra_khhzuFlE

Hessel

[jb747]

I had an ex member of the USAF Thunderbirds fly my sim awhile ago.  He could roll it but stalled when attempting the loop.  Another friend, an instructor in the B744 for UAL said you can loop it but have deploy some flaps to make it all the way over.

You can also land it on a carrier.

Who'd have thought.

Cheers,

Jon

[frumpy]

I doubt it would be possible to slow down the 744 on a carrier

[jb747]

I agree.  You could "land it" but not stop it.  No tailhook

[martin]

I doubt it would be possible to slow down the 744 on a carrier

Perfectly possible. The carrier just has to go at about 120 kn or so. Which in turn is no problem if utilizing e.g. a typhoon providing a tailwind of 100 kn or so.

It all adds up.

Cheers,
Martin

PS
Come to think of it, do we have a physics trick question here??

Assume a super-nuclear carrier is really going at 120 kn, typhoon or no.
The 744 speed at touchdown is, say 140 kn.
Will she, after touchdown, really roll down the carrier deck at a leisurely relative 20 kn (i.e. speed relative to the deck)?

Actually, didn't they do something like this once, by landing a Cessna on top of a speeding car?

[Britjet]

In one of my old rw sims we did exactly this. There was a model carrier moored in HKG. Harbour and if you set the sim wind straight down the carrier deck at about 90 kts it was perfectly possible to land and stop.

The real giggle came for a subsequent takeoff - you actioned  the "position freeze" ( Hardy is considering this one, I know) and power up. At Vr we released the POS Freeze - it was quite dramatic!

Peter

[Hessel Oosten]

http://m.youtube.com/watch?v=pUdzVnZBaoY

Hessel

[Hardy Heinlin]

The tailwind will not help, Martin, it will not only increase the groundspeed of the carrier, but also the groundspeed of the aircraft. So the carrier must move on its own while the wind is calm, or the planet must provide headwind (not tailwind) while the carrier is stationary, or a mix of both conditions :-)


Cheers,

|-|ardy

[martin]

So the carrier must move on its own while the wind is calm

True. So, super-nuclear carrier it is, no typhoon.
[size=8](Unless it is one of those dreaded GLTs (ground layer typhoons) which reach up to but not above the altitude of a carrier deck. Triggered by big icebergs breaking through the circumfence, falling off the edge of the world, and thus creating a sudden vacuum.)[/size]

Thanks to Hessel, too, for the link!

Cheers,
Martin