Angle of Attack rule of thumb

[Fergal20]

Hello there,

Does anybody know of any rule of thumb to calculate the angle of attack for a light aeroplane, given that you know the pitch angle, airspeed, and vertical airspeed?

The reason I ask is that I'm designing a flight simulator for college and I'm having difficulties calculating the angle of attack.

Thanks in advance for any help;)

[Tinstaafl]

In level flight the AoA will equal pitch angle (referenced to the longitudinal axis) +/- angle of incidence.

Using RoC/RoD & TAS you can determine flight path angle.

Flight path angle could then be compared with pitch angle referred to above to then derive AoA.

[Mad (Flt) Scientist]

If you are building a simulator, do you mean you are deriving the aerodynamic data from flight test - in which case you need a way to measure or deduce angle of attack - or are you building the simulation code (equations of motion, etc.) and have a defined aerodynamic data set.

If the former you are going to have a problem with the data you have because you don't know what the local wind is. Therefore you have two parameters measured relative to the air mass (airspeed and vertical airspeed) and one in the earth axis reference (pitch attitude). If you can't relate the air mass to the earth (wind) then you will have to guess and that will cause potentially large errors.

If you are building equations of motion then you're asking a different question. But again the attention to detail of the reference frames is vital - you can easily make the aircraft unstable/unflyable without careful maintenance of the references.

Let us know which it is...

[Tinstaafl]

I figured motion of the air mass won't be a problem since it's a parameter that must be entered into the sim.

[Mad (Flt) Scientist]

Originally posted by Tinstaafl
I figured motion of the air mass won't be a problem since it's a parameter that must be entered into the sim.

That was why I asked what the prupose of the question was.

If Fergal is building the equations of motion for a sim then he/she should not be using 'rules of thumb'. You need to get the equations spot on or all kinds of nonsense will result. And every single parameter required is available, since you're running a 6dof simulation. So you can use the precise definition for every parameter, be it alpha, beta, whatever.

Having set a class of some 20 people to do pretty much similar to thay job (build a simple 3dof model with defined aerodynamics) and seen a good 75% of a fairly smart class get tripped up by various axis/EoM issues, including mis-calculation of alpha, with the resulting aircraft models being hideously unstable, close is simply not good enough for this kind of work.

Whereas rules of thumb may well be 'good enough' for derivation of the aerodynamic characteristics, depending on what you're after - a level 'D' qualified sim has a much tighter definition of 'good enough' compared to a fixed base visual systems test-bed, for example.

Waiting for guidance....

[Tinstaafl]

Good point. Now I'm really curious about it...

[DustDevil]

Fergal20, i think you have'n the good point of view in the problem. to make a flight model, you do not have to find out Angle of attack.

AoA is just angle resulting of composition beetween Vxy (Vairtotal projected on {XY} plane), and Vz (still in the airplane coordinates). More exaclty it is : arctan(Vz/Vtotal).

To make your plane flying, You just have to compute forces : P, aerodynamics, inertial applied on your planes, => accelerations => speeds in planes coordinates and if you want to, then you can compute AoA and SideSlip angle ( wich is in arcTan(Vy/Vx) ).

Hope this help :)

[Mad (Flt) Scientist]

Posted by DustDevil
To make your plane flying, You just have to compute forces : P, aerodynamics, inertial applied on your planes, => accelerations => speeds in planes coordinates and if you want to, then you can compute AoA and SideSlip angle ( wich is in arcTan(Vy/Vx) ).

Be very careful how you do that!

In particular you cannot use the speeds in aircraft axes for the purpose of deteriming the motion. Because the aircraft axes are themselves in motion, and are not an inertial reference system. So the standard equations of motion cannot be applies in that axis system.

If you just stay in aircraft axes your model will be unstable in pitch.

[DustDevil]

Mad Scientist,
i agree that in a theoric way, standard motion equation shoudn't be used in airplane axis system. But in a real time numeric-model, with a rate of min. 30 updates/sec ,i feel that the reference system's motion is really slight and doesn't really matter. for me, a good solution is :
- compute aerodynamic forces in aerdynamics reference (x on airspeed vector, y in airplane xy plane, z direct)
- compute inertial forces in the local (airplane) reference x longitudinal axis, y right wing...
- compute weights in terrestrial reference. (xy horizontal, z upward)
when it is done, transform all in airplane local reference and apply Newton Law.
I'have already wrote some code with that and plane's behaviour was correct.
However, i hadn't efficient means to quantify the error caused by the reference problem that you had pointed out. :p

[Mad (Flt) Scientist]

Dustdevil

The problem comes if you are carrying the velocities to the next time step in a moving axis system. If you do that then you are violating a number of laws of physics.

Example:
Aircraft in level unaccelerated flight, angle of attack zero (for simplicity).

Introduce a perturbation in vertical velocity (down). This causes a small increase in alpha, which for a stable aircraft causes a nose down pitching moment. The aircraft pitches down, so reducing the angle of attack because the velocity stays pointed slightly below the horizontal and now the nose is also below the horizon.. Depending on the aerodynamics/inertia you'll then get SPPO and Phugoid motion in some combination - just like you should.

Now keep track of velocity in aircraft axes, not earth azes and try again. It's all the same until...
aircraft pitches nose down. As the aircraft reference rotates so do the velocities in that axis system and the angle of attack does not reduce. Aircraft happily bunts over into the ground!

If you are handling all the transformations between axes correctly then it's ok to use whichever are convenient for the item concerned. But you have to have a set of inertial axes somewhere.

[DustDevil]

Mad Scientist,
Entirely agree with your explanations. I didn't mention above the important step which have to be done at each updates :
- project plane-relative velocity in terrestrial reference system
- updating plane angular positions.
and on the next step,
- project terrestrial-relative speed on the new plane axis reference,
- on this new reference, compute accelerations and speed
- project plane-relative velocity in terrestrial reference system
etc... etc...
So i use terrestrial system as an intermediary reference system beetween each plane axis change.And this steps are necessary to avoid stability problems you described.

Concerning aerodynamic forces computations : i have used simple equations 0.5*rho*V2*S*C on different parts of my plane, computing local airspeed and angle of attack for each parts. It seem to work well in low speed. But there are limitations such as :
- compressibility effect, when mach number become high
- interferences of airflow beetween parts.
- probably others that i didn't think about
:confused:
Does someone know others way to do that, or correction for this ?

[Mad (Flt) Scientist]

Wow, DustDevil.

You're computing local flow velocities and angles for each aircraft component??? I have to ask why?

We certainly don't bother with that kind of detail for commercial/engineering sims. Just use a single alpha/beta/speed definition, consistent with the means used in flight test for data derivation.

Are you doing local flow calculations using panel methods or similar - I'm intrigued.

[DustDevil]

Mad Scientist
I simply divided my plane into several part. for example 8 parts for each wings, etc... then i compute local airspeed for this part, wich is very easy, since i know :
* the velocity of center of gravity,
* COG-relative position of the part and
* angular velocity around plane axes (wich crosses at approx. COG).

local aispeed of the part is just the addition of G-airspeed + airspeed due to plane angular velocity. then i compute local alpha and beta for this part. and forces applied with my home-made equation. for example, during plane roll, difference of alpha beetwen left wing and right wing give the roll stability, and the same for pitch stability due to difference beetwen wing alpha and stab alpha. The same method has been used for X-plane flight simulator, with probably more accurate calculation than mine.

[BOAC]

What's the betting Fergal is beginning to wish he hadn't asked? :D

[John Farley]

AoA is just angle resulting of composition beetween Vxy (Vairtotal projected on {XY} plane), and Vz (still in the airplane coordinates). More exaclty it is : arctan(Vz/Vtotal)

Isn't it interesting how AOA is viewed by different people.

As a pilot I view it as the be all and end all of using lift.

[Mad (Flt) Scientist]

DustDevil, that's one hell of a complicated and computing intensive approach to the aerodynamic modelling issue.

Obviously it's working for you, but the normal approach is to model the aerodynamics of the whole aircraft, or at most the tail off and tail off aircraft, and use aerodynamic derivatives to capture the effect of roll rate, yaw rate, etc.

You could even use the kind of methodology you describe to determine the derivatives (although its normal to use flight matched data) but if you do the flow analysis/derivative determination first then you can skip that step for all subsequent similar events.

For example, if I want to make the roll damping behaviour correct, I can do as you do and calculate local angles of attack along the span, derive a lift distribution (although that's by no means a trivial exercise) and determine the rolling moment. But if I do that calculation for a matrix of possible values of alpha, beta, roll rate, etc, I should be able to derive a simple relationship between rolling moment and roll rate. It then makes sense to use that relationship in my simulation, rather than recalculate it every time step.

What are you using to determine the forces on, say, one of the sections of wing? Having determined local flow velocities, how are you coming up with the forces? To be honest, unless you are folding in some kind of CFD methodology - and how you keep the sim real-time by doing that I wouldn't know - then you just seem to be doing a lot of work for no significant increase in accuracy.

(By the way, my background is Stability and Control / Flight Simulation, so I'm used to simulations for training and for engineering design.)

[DustDevil]

Mad Scientist, Thank you for this explanations, a bit complex for me however. My background is ...heu...i'm an informatic student and light aircraft pilot.
:O

Essentially for my own pleasure, i'm working on an airbus a320 simulation and flight model is one of my problems, because of its lack of accuracy.

I used this method of computation because it's the only solution i found. To determine lift produced by a section of a wing, once local alpha and beta are known :
i compute Cz as a function of alpha, thanks to a graph Cz=f(alpha) for the corresponding A320 wing section that i found on the doc of a commercial flight simulator (don't know if it is reliable).

with the Cz, i can calculate lift with following equ :
0.5 * airdensity * (local airspeed^2) * Cz, with a correction for beta angle, due to the sweep of the section. And the same for Drag.

Tuning some datas in the Cz = f(alpha) relation in my programs gave me stall speeds and airpeed/alpha relationship near of the real aircraft but not entirely sastifying.

As you understand, this method is the only one possible for me because of the lack of aerodynamic datas about the aircraft, or flight-matched datas. didn't understand your remarks about real-time (CFD methodoly ??). Real time is ensured by use of clock's access functions of my PC.

Your explanations about use of matrix to find relationship beetwen flight parameter is very interesting.
but it's probably very memory-expensive, isn'it ? i mean: for your example you d have a lot if parameter to derive rool damping ( AoA,roll rate, all wing control surface's positions etc... ). Would you know where i could find this type of datas ?

[timzsta]

Just sat the ATPL Principles of Flight exam today! All the above is way over that level. I will try to give you some basic numbers and facts that may be of use.

AoA is defined as the angle between the chord line (a straight line joining the leading edge and trailing edge) and the relative airflow.

For a typical light aircraft in the cruise phase of flight (for a Cessna 152 lets say IAS of 90 knots) the aoa will be of the order of 4 degrees. This is fairly typical for many aircraft.

The wing off course is not set in a direct line along the aircraft longitudinal axis but is inclined at an angle called the angle of incidence. Hence a 737 cruises with around 2.5 deg nose up (aircraft pitch angle) but the wing is probably about 4 deg aoa. Hence why in the cruise you feel like you are walking uphill when going from row 10 to the forward toilet (because you are!) and hence the No 2 cabin crew, who will be at the rear, has bigger muscles than the No1 and No 3!

The wing will stall at an aoa of approximately 15 degrees.

The wing of typical light aircraft is not symmetrical, the upper surface has greater curvature then the lower, so as to increase the pressure differences and generate more lift. This is called camber. Hence at 0 deg AoA a light aircraft wing will produce a small amount of lift. Typically zero lift is produced at a small negative AoA on such an aerofoil, of the order of -3 to -4 deg.

As you increase the angle of attack of the wing it produces more and more lift, and the centre of pressure moves forward. Max lift is just before stalling AoA. At stall AoA the lift drops sharply and the centre of pressure moves back aft (those causing the nose to drop and help you to recover from the stall).

The lift equations is as follows :
Lift = Coefficient of lift x 0.5pv2 x S

p = pressure, v2 = velocity squared, S=surface area of the wing

Coefficient of lift is harder to define, but is basically to do with the shape and design of the wing and increases with an increase of AoA.

Hope thats of benefit, e-mail me at [email protected] if you want any more help.

[Mad (Flt) Scientist]

DustDevil

Are you sure its a Cz-alpha (CL-alpha?) plot for the section? Might it not be the Cz-alpha for the whole plane? That would be more useful to a commercial sim company - since they won't be doing it the way you are doing it. If it is the overall aircraft lift-curve characteristic, use it as that, it'll save a lot of problems.

If you want to get a better feel for what the aerodynamic derivatives of the aircraft should be, these are often discussed in textbooks. Babister has a section on predicting derivatives, I'll look it up tomorrow at work.

Actually, there aren't that many parameters you have to consider, once you apply a bit of engineering judgement and remove the minor effects - most axes of motion can be adequatelyu described with 3 or 4 derivatives, stored as tables of a hundred or so numbers each. It sounds a lot, but not having to redo the local flow angle calcs at every time step is a huge saving in computational overhead, and memory isn't the bottleneck usually. If the tables of numbers bog things down you can sometimes base one parameter on another - for example, pitching moment, drag and lift contributions of the tail are all basically just a function of tailplane lift (to a first approximation) so you can neglect the tail drag and Cm0 terms and just use the lift, especially if you aren't going for super accuracy.

If you can get access to something like ESDU or Roskam, there's a wealth of impirical data in those (and things like them). If not then making some fairly simple assumptions about section lift characteristics can get you a way along.

My reference to real-time was in the context of using CFD (computational fluid dynamics) to calculate the local flow for each set of conditions. That would be a horrendously complex thing to do - it's done for things like aircraft/store release calcs, where the aerodynamic interaction is important, but not in real-time AFAIK. You're doing it in a very simplified way by using the section lift characteristics.

[DustDevil]

Mad Scientist
I used Clift-alpha and Cdrag-alpha curves. This datas come from Xplane simulator, wich looks like MS Flight Simulator, but more realistic in plane modelization. Xplane enables user to create its own flying machine : use predefined airfoil, engine, dimension of fuselage... Xplane analyse aerdynamic and physical behaviour of your creation and then you can fly with. That's why Xplane uses this method of computing independant elements of plane for flight model.

I will try to study in details aerodynamic derivatives of aircraft, and know more about empiric datas. In particular independance beetwen flight parameters, wich is very mysterious for me. I also looked at aircraft 's aerodynamic websites listed in "useful websites reference " thread. there are a lot of polar curves on http://www.nasg.com/afdb/list-airfoil-e.phtml, but don't known wich has been used for airbus a320, and if there are on this site. A lot of work for me now !

Fergal20, if you are interested, i could email you pseudo-code or the flight model part of my program in C++. you can email me at
[email protected] .