Calculate Lift Coefficient

[Cpt. A380]

I'm trying to figure out what's the lift coefficient of an A320. What I'm doing is the following: during cruise, the lift is equal to the weight of the aircraft (mg) so that I used the cruise table taken from the FCOM to get the speed, the wing area is known (122.6 m^2) and I calculated using an online tool (http://aero.stanford.edu/stdatm.html) the air density at FL290 (29000ft):

http://i.stack.imgur.com/l9g9N.png

The result is that the lift coefficient is 0.03029. Is it right for the assumptions given above? Next, if I want to relate the Cl with the Angle of Attack, what is the formula and the procedure? Thank you for your help.

[JABBARA]

Capt. A 380
I do not think it is so easy practically calculate CL with simple arithmetic. This is because every component of airplane (e.g fuselage) has effect on resultant aerodynamic force.

But just one contribution: L=W is incorrect,
The correct one is : L=W+Td,

What is Td?
I can describe it as the downward lift force created by Horizontal Stabilizer to equalize the moments about CG to zero. In another word, it is the downward force to create a counter moment to balance the moment created by wing.

[Wizofoz]

Jabbara,

I don't agree with that. Lift is the sum of all vertical forces on the aircraft, and in cruise is equal to weight. Yes, the wing has to produce extra lift to over come the downforce of the tail (in most aircraft- some models actually have a lifting tail), but total lift is the sum of these.

Co-efficient of lift refers to the whole airframe, not just the wing, so entering values to the equations L=C 1/2 RHO V^2, with the assumption that in cruise L=W is valid as far as I can see.

[ManUtd1999]

You're method seems sound but the answer you have is too low. Conversion of TAS from kts to m/s perhaps? I ran through it and got Cl = 0.3 ish.

As a first approximation, CL = Cl_alfa * AoA, where Cl_alfa is a constant dependent on aerofoil and wing geometry. Good luck finding any accurate numbers for the A320, but I think Cl_alfa = 5-6 rad^-1 is the rough range.

As others have pointed out, this method gives the effective "whole aircraft" Cl. To get the Cl for the wing in isolation and a true AoA much more detail regarding the tailplane, fuselage lift contribution etc etc would be needed. As a rough approximation though it shouldn't be too far out.

[Owain Glyndwr]

Check your units.
As Man.Utd said, for the conditions you cite the overall CL is 0.27
m - kg
g - m/sec squared
rho - kg/ m cubed
TAS - m/ sec
Area - m squared

Depending on CG the tail lift will be in the range 2 to say 8% of the total so the wing lift will be that much higher. To get an exact value you need detailed aerodynamic information that is almost never published.

The aoa will depend on flap setting and Mach number, but again needs unpublished detail. As a ballpark figure use aoa = 10 times CL (aoa in degrees)

[JABBARA]

To get an exact value you need detailed aerodynamic information that is almost never published
I totally agree


Hi Wizofoz
Lift is the sum of all vertical forces on the aircraft, and in cruise is equal to weight. Yes, the wing has to produce extra lift to over come the downforce of the tail
I agree, I mean the same.

some models actually have a lifting tail This is mostly correct for naturally designed unstable fighter jets (but to be controlled only by FBW), not for Transport Category Airplane

Co-efficient of lift refers to the whole airframe, not just the wing, I agree, I mean the same

Of course I agree with the equation "so entering values to the equations L=C 1/2 RHO V^2, but "S" is missing.

But my knowledge of Flight Mechanics tells me here: L is always bigger than W. As below.




http://i1222.photobucket.com/albums/dd499/Jabbara1/CG%20effetct%20and%20Lift.jpg (http://s1222.photobucket.com/user/Jabbara1/media/CG%20effetct%20and%20Lift.jpg.html)[/IMG]





At the end, I am not an expert, I may be missing something. if correct me I will be happy.

Thanks

[phiggsbroadband]

If you are counting in the tailplane component, then you could also include the upward thrust from the engines. This depends upon their alignment, and will increase at slower speeds as AoA increases (towards say +14 deg.).

[Owain Glyndwr]

Thrust contribution

Yes in principle, but in cruise T/W around 5 or 6%, aoa around 1/15 radian, vertical component of thrust only about 0.4%W - negligible compared to other contributions