AOA and Banking

Hi there

 

I have this question in my head for a few days and can't seem to find the answer....hopefully somebody here can help.

 

In an aileron only turn, let's say a 30' bank, the nose will drop and the airspeed will increase. An "equilibrium" will be found where the rate of descent does not increase any more but the plane is still descending. (hope I said all that right).

 

Question

If you wanted to now do a level 30' bank, you would have to use some elevator and pull a 1.15g bank. As you are using elevator, you are increasing your AOA and thus increasing drag: What is the mathematical relationship between bank angle and AOA? Or is there one?

 

 

I know I'm missing something(s) but I can't put my finger on it....I'm guessing it has something to do with drag due to inclination but I'd like to know more about this (hard data ie. formula). Is it as simple as 30' bank means 30' change in AOA (doubt that)?

 

Any how...hope somebody can sort me out on this...

If you wanted to now do a level 30' bank

That's a level turn, not just bank, unless you throw in enough opposite rudder to keep the nose from yawing, which throws more complications into the problem.

 

And no, it's not as simple as your question might indicate, since there are numerous variables and it's not a 1:1 relationship (perhaps roughly proportional?). The one thing you can really say is that, for a level turn, the steeper the bank, the more lift is needed, therefore the more G's and the greater the AoA, thus more induced drag. Typical max AoA on aircraft is around 17º to 18º, thus ready to stall at that point. A 60º banked level turn needs a 2G pull.

 

I'd suggest you hunt through the Aviation Formulary, which has all manner of math related to aviation, both aerodynamics and navigation. There might be something there for you. Or perhaps some of the Wikipedia articles would have what you need.

When you say the following: 'If you wanted to now do a level 30' bank, you would have to use some elevator' this is not the case, or rather not the only thing you could do. Yes, you could do that, but it's not typically what one should do, which is of course to increase thrust a little to compensate for the lift vector having changed, so that there is a surfeit of lift available to counter the weight.

 

Naturally, with thrust, drag, light and weight all in equilibrium, your aeroplane will fly along at a constant speed and altitude as these forces directly oppose one another, but stick in 30 degrees of bank and now a large percentage of what was opposing the weight and keeping you level is now being vectored off to one side, causing a slipping sideways skid, so it isn't just the wings changing their lift vector we have to consider, the fuselage is now blocking airflow to the wing on the outside of the slip and the side of the fuselage into the oncoming airflow is causing vastly greater form and skin drag too, not to mention the horizontal stabiliser, elevator rudder and tailfin also being affected by matters.

 

All this of course is where flight simulators go a bit cack in comparison to flying a real aeroplane, since you can use things such as feedback through the stick from elevator buffet to know when you're pushing the AoA a bit too far when you are flying an aeroplane for real. Without a motion platform or some other system to provide that feedback, a flight sim cannot convey any of that stuff to us and it is a big omission to the experience of flight sims. Maths is great for working out the technical side of what wings and airframes whould be doing, but it can only take you so far, especially when such calculations are often made in isolation of where they will be applied in reality.

When you say the following: 'If you wanted to now do a level 30' bank, you would have to use some elevator' this is not the case, or rather not the only thing you could do. Yes, you could do that, but it's not typically what one should do, which is of course to increase thrust a little to compensate for the lift vector having changed, so that there is a surfeit of lift available to counter the weight.

 

I'll have to disagree with that statement. In all my years of teaching people to fly, I never once tried to have them substitute power for elevator back pressure (besides, precision would be difficult to achieve). And if you look at the FAA's pilot handbook, you'll see that back pressure is the proper way. And how would you add power in a glider?

 

but stick in 30 degrees of bank and now a large percentage of what was opposing the weight and keeping you level is now being vectored off to one side, causing a slipping sideways skid,

And there's no such thing as a "slipping sideways skid" -- you're either skidding (too much rudder in same direction as ailerons) or you're slipping (cross controlled) or you're properly coordinated. The effect you were trying to describe is part of why airplanes have a rudder, which when properly used will eliminate that effect. But the actual effect which happens when only the ailerons are used for adding bank is that the aircraft actually turns* (that's what the vertical fin is for, just like the fletching on an arrow), though it is sloppy and uncoordinated -- the ball will move to the side -- and you can even feel it in the seat of your pants (in an aircraft or full motion sim). The rudder is there to correct for this.

 

So a proper turn will have all three controls used in a coordinated turn such that the ball is centered, the aircraft maintains altitude, and there is a slight loss of airspeed (due to increased drag).

 

feedback through the stick from elevator buffet to know when you're pushing the AoA a bit too far when you are flying an aeroplane for real.

That buffeting feedback won't necessarily be there in all aircraft, though you CAN feel the controls get mushy as you slow down, and you can even feel the sloppiness in your seat.

 

Maths is great for working out the technical side of what wings and airframes whould be doing, but it can only take you so far, especially when such calculations are often made in isolation of where they will be applied in reality.

 

I whole-heartedly concur -- you don't fly an aircraft by mathematics -- math is for designing aircraft. Flying the aircraft requires that computer in your head to evaluate many things at once -- feel, hearing and sight -- to make constant small corrections in a time frame that leaves no time for math and no time for the computed math to be interpreted to get a response. Do that and you'll be 30 minutes late for the crash.

 

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*When applying aileron with no rudder applied, the nose actually yaws the opposite direction for a moment, then catches up in a very sloppy turn. This is due to adverse yaw, that is, the downgoing aileron adds drag, pulling that wind back a tad, causing the yaw. Adding a proper amount of rudder pressure with aileron eliminates this problem.

TY Inuss for your reply.

 

I think you've touched on where my little brain has been and expanded on it a bit...that AOA doesn't care if you are in a bank or not. The fact that (in my example) you are in a 30' bank (while maintaining level flight) is almost irrelevant. The airflow over the wings is now starting to load them up and as you said, will eventually stall just as is if you pulled a hard Gee climb while level...same result...just the size of the envelope changes.

 

Still doesn't help with an exact(sic) formula/relationship but I think a few hours in DCS might help me ballpark a "rule"...

 

I've had a super long day and barely can keep my eyes open so I'll reply to the other two posts in about 10-12 hours.

 

Thanks again....more in a bit....

I'll have to disagree with that statement. In all my years of teaching people to fly, I never once tried to have them substitute power for elevator back pressure (besides, precision would be difficult to achieve). And if you look at the FAA's pilot handbook, you'll see that back pressure is the proper way. And how would you add power in a glider?

 

Well, in a glider of course the Earth's gravitational pull and the energy potential granted by your height above the ground is your 'engine', so like everyone else who flies gliders, I add 'power' by sticking the nose down. Thus more often than not when in a thermaling turn, easing up on the back pressure is the way to not only control the rate of turn but also the speed, which in turn then also has an effect on the radius of the turn. But here the similarity ends with the OP's example because when doing that in a glider, one is less concerned with a specific rate of turn of course and more concerned with centering in the source of lift so that regardless of the speed your aeroplane is going down at, the air mass it is doing that in, is going up at a faster rate. Well, that and looking out for other gliders which are in the same thermal of course, sometimes they get pretty close.

Well, in a glider of course the Earth's gravitational pull and the energy potential granted by your height above the ground is your 'engine',

True, of course, and what is true for the controls in a glider is true for controls in a powered aircraft. Substituting throttle for elevator in a turn is poor flying. Granted that if you are attempting to maintain the exact same airspeed in a turn that you must either add throttle or allow a slight descent, but while it can be done it's a poor way to build your mental image of control usage -- it's better in that case to add the back pressure then adjust power slightly, readjusting elevator (actually, once you're experienced the two come together).

 

Look at it how you wish, for yourself, but please don't espouse that method to others. One reason (among others) is that any simmer who takes flying lessons after practicing that in the sim for a while will have a bad habit that his instructor will have to break, thus extending the time and cost of learning to fly. Another reason is: Why learn to do it different in a powered aircraft than what you do in a glider? This creates a very dangerous situation where someone thinks power but happens to be in a sailplane, thus (at best) delaying proper response for a moment. And what about in a jet where thrust is delayed after adding power -- do you get in a situation where you are playing catch up?

So I think I "figured it out"...mostly thanks to something you hinted at when you said "Typical max AoA on aircraft is around 17º to 18º"

 

In a 30' bank, you are going to lose approximately 13% of lift and your nose will drop until the point where your speed is creating more lift. If you want to avoid the nose-drop bit and make a level turn (without touching rudder/power) then your option is to apply elevator which increases your AOA.

 

As you increase the AOA, you are increasing the lift coefficient. As you pointed out, this will happen up to the 17'-30' range depending on plane type. But what I also pieced together is that the increased lift coefficient rises at a non-linear rate so that while level, a wing might be a "1" and at 1-degree AOA but a "2.5" at 2-degrees of AOA. ie, there is a sweet-spot where AOA will produce the most lift but that sport is unique to each plane.

 

So what does that mean? I don't think there is a formula for this one (and that's why I couldn't find one). The AOA just needs to be raised to the point where that 13% loss of lift (from above) has been counteracted. Some planes that might be at 5' AOA while others maybe 8'.

 

Thanks!

 

ps. I totally agree with the whole "knowing and doing are not the same" philosophy. I will never fly as IMO to do that, you need to be an excellent multitasker of which I am not. I'm a firm believer however that to truly know something, you need to know the numbers behind it (or as much as possible) first.

The lift-curve slope in most airplanes is linear, up to the area where stall is approaching - the slope only changes if you deploy flaps or LE devices. In any case, the lift-curve slope is dependent on the wing design - and therefore different for different airplane designs.

 

When you say a level turn, I think you mean a level constant speed turn - in that case yes, you have to add power to maintain a given desired speed because of increased induced drag caused by a higher angle of attack.

 

Finally, if you DO have the lift-curve slope for a given airplane, the change in AoA for a given angle of bank at a given airspeed could be calculated. Getting the slope curve data is not very easy in most cases, not generally available but could be deduced from flight testing.

When you say a level turn, I think you mean a level constant speed turn - in that case yes, you have to add power to maintain a given desired speed because of increased induced drag caused by a higher angle of attack.

For level AND constant speed, yes, you are correct. But that wasn't indicated before. And thanks for clarifying some of what I was trying to get across to the OP -- nicely done.

 

I'm a firm believer however that to truly know something, you need to know the numbers behind it (or as much as possible) first.

 

For my view, at least, I'd modify that to say "know how it works." Too often the math for some of these things is WAY beyond me, since I've not gone beyond some basic calculus, and that is too many years ago. But understanding how it works is good.

 

OpusTheFowl, one thing you might do is to get a copy of Stick and Rudder by Wolfgang Langewiesche, a superb book on the art of flying from a pilot's point of view, but it also often contrasts that with how an engineer would look at it. Very worthwhile reading -- a LOT to learn. Available at Sporty's Pilot Shop, among other places.

And, in the end - once again, you should still think of the truth in a constant speed turn; pitch controls airspeed, throttle controls rate of descent or climb. If you do not take that as an absolute, you will really get in trouble at very low airspeeds, where the high drag changes drastically with very small changes in AoA/airspeed. For math majors, the induced drag curve is "asymptotic" with decreasing AoA/KIAS.

Thanks for the added input. Just to clarify, my example was not for a constant speed but rather a level turn and new issues that creates...added throttle is the obvious solution to this issue but my initial question was the relationship between the bank angle and increased AOA (without touching anything else).