Asymmetric Flight

[Chesty Morgan]

With a constant heading and the ball in the middle, which is all we have to go on up the front, and assuming wings level, it seems to my little brain that your actual flight path would be away from the live engine (due to the side force generated by the rudder?).

Is it possible to calculate your actual flight path during asymmetric flight?

Assuming still air, balanced flight, fixed thrust and fixed control deflection.


Cheers all

[Mad (Flt) Scientist]

With a constant heading and the ball in the middle, which is all we have to go on up the front, and assuming wings level, it seems to my little brain that your actual flight path would be away from the live engine (due to the side force generated by the rudder?).
Is it possible to calculate your actual flight path during asymmetric flight?
Assuming still air, balanced flight, fixed thrust and fixed control deflection.
Cheers all

I'd say that if you actually did achieve the situation you postulate - wings level, heading constant, no lateral accel - then you would simply fly in straight line - sideforce due to rudder alone doesn't matter for this, its the total net sideforce. If you've found some balance of sideslip and rudder that gives no net sideforce then there's nothing to cause a flightpath deviation.

[NutherA2]

:confused: If only the memory didn't fade with increasing age :ugh: :ugh: :ugh: .............IIRC when an aircraft is in balanced asymmetric flight, with wings level & ball in the middle, it is actually flying with the "dead" engine leading. It certainly flies in a constant direction, but there is a small difference between that direction and the way it is pointing (ie the indicated heading). If I've remembered wrong or expressed it badly, please don't ask for my A2 category back.

[fantom]

Ooh.. get into the 20th century and fly Airbus.
It's called beta-target.

[Mad (Flt) Scientist]

NutherA2 - correct, it'd almost certainly have a bit of sideslip, with the nose not pointing in the direction of flight. But with a steady heading, the track would also be constant, and I understood the OP to be enquiring whether the flight path would be linear (which it would be), not whether it would be aligned with the nose (which barring some strange control positions, it wouldn't be).

With the left engine dead, the good engine creates a yawing moment nose left. So the rudder needs to produce a nose right counter moment. That means right rudder, and so a sideforce the to left, too. To counter that, wings level, needs a sideforce to the right. That has to come from a nose-right sideslip, which does indeed mean that the dead (left) engine leads.

(All assuming no crosscoupling and the rudder at the back!)

[PantLoad]

Chesty,


Take a string and tape it to the nose of the plane...some place where you can see it from your seat in the cockpit. Now, fly around on all engines. Assuming coordinated flight, the string flows with the airflow...straight back.

OK, now shut down (or pull back) an engine. Manipulate the controls such that the string is still flowing straight back. (Zero sideslip...as with all engines.)

Guess what!!!! The ball is not in the center, and with that, in order to hold a constant heading, you need a slight amount of bank into the good engine.

So, now, put the ball in the center with wings levelled with ailerons....and watch what the string does. Oops...it's leaning in the direction of the live engine.

Further, you're trying to climb straight ahead at, say 500 FPM, on one engine. How much power (thrust) do you need to do this with the above-two trials?

Answer: significantly less when the string is flowing straight back. So, when you lose an engine and need to meet a stringent climb gradient....you'll have a better chance of doing so when you don't try to center the ball.

Or, if you're in a Bus, the 'Beta Target' does all this for you...tells you EXACTLY how much rudder you need for maximum performance....assuming flaps extended. (Once you clean up, you're back to the traditional sideslip indication.)


BTW, don't let the CAA see you taping strings to your airplane. They see no educational value in this whatsoever!



PantLoad.....

[Basil]

PantLoad,
So you're saying 'Don't quite centre the ball.' i.e. leaving it out slightly towards the live engine could save the day in an aircraft with marginal performance?

[NutherA2]

Basil,
Pantload is quite correct, a small angle of bank towards the live engine results in a slight reduction in overall drag, hence an improvement in performance; I think you'll find that most Pilots' Operating Handbooks for American manufactured light twins recommend 5° bank in their Emergency Procedures.
On older design military jets (Meteor, Canberra etc), where pilots' leg strength was a limiting factor in determining Critical Speed in asymmetric flight, banking towards the live engine was an important factor in retaining control in marginal circumstances.
I believe the only reason for teaching "wings level & ball in the middle" is that this is the simplest technique for keeping the aircraft in balanced flight. "a little bank and the ball out a bit" needs a bit more finesse and a beady eye on the compass to achieve the same end.

[Chesty Morgan]

Thanks for your responses chaps.

I was aware that your Track made good (TMG) would be towards the dead engine, and would be linear assuming a constant heading (sorry didn't make my question very clear).

With the predefined criteria in my first post, would it be possible to work out your actual TMG or, for want of a better word, drift, towards the dead engine? Is there a formula you can use or is it a case of working up a vector diagram for a defined example?

[Mad (Flt) Scientist]

With the predefined criteria in my first post, would it be possible to work out your actual TMG or, for want of a better word, drift, towards the dead engine? Is there a formula you can use or is it a case of working up a vector diagram for a defined example?

You basically need to solve for the trimmed sideslip. That means you need to know various control and stability derivatives.

If you ignore all rolling and pitching behaviour, then:

CY=CY-beta*beta+CY-dr*dr
CN=CN-beta*beta+CN-dr*dr+CN-engine

Where:
CY-beta is derivative of sideforce coef with sideslip
CN-beta is derivative of yawing moment coef with sideslip
CY-dr is derivative of sideforce coef with rudder
CN-dr is derivative of yawing moment coef with rudder
CN-engine is Yawing moment coef due to OEI condition
and
beta=sideslip
dr=rudder angle
(working everything in coefficients; alternatively you can dimensionalise it all, it works out the same in the end)

Now, for trim, CN=CY=0, and you know everything except beta and dr, so you have two simulatanoeus equations and two unknowns. Easy-peasy.

(In reality of course, things like yaw due to ailerons, roll due to sideslip, lift changes due to sideslip and alpha-sensitvity of many of the terms make it a much bigger problem, and one that can only be solved iteratively...)

Once you have beta, you have the difference between track and heading (assuming zero wind).

[PantLoad]

Basil,

Yes, that's exactly what I'm saying. Because centering the ball creates more drag... The airplane is going sideways...to a large degree. Again, you can see this with the string on the nose of the aircraft.

In light twins, where single-engine performance is a joke, that additional drag (from centering the ball) will kill you with virtually 100% certainty.

FAA certification allows for a maximum of 5 degrees bank...typically, this will require the ball be about half in/half out. You'll get better performance (best climb...or least descent).

Mad (flt) Scientist is very correct. In fact, in the Bus, that's what they call it...the Beta target. (Again, this applies with flaps extended. Once you clean up for your final segment climb, the wedge is exactly like 'the ball' in a conventional aircraft.)

It's fun to experiment with a light twin (don't shut down the engine, though...just set power for 'zero thrust'). And, while you're at it, play with Vyse. You'll find that it can vary quite a bit depending on weight and density altitude.

I strongly recommend, however, that when you're 'playing', don't play with Vmc. Unfortunately, not many multi-engine drivers understand how easily they can get into trouble (i.e. flat spin) when doing this. Hardly no one teaches anymore the relationship of Vmca and stall speed and what causes the twin (on one engine) to spin.


PantLoad

[one dot right]

With the ball in the middle,on on donk, the thing flies sideways.full stop.period.the end!

[Basil]

Yes, I recollect the bit about bank away from the dead engine in manuals but they didn't make the point about the slip indicator very well.
Wish someone had told me all that before I flew the Varsity and Aztec. (Perhaps they did and I was gazing out the window that day)
Fortunately never got into a situation where it would have been a situation saver; only real EF in Aztec was in flight.