Calculating Lift-Drag Ratio of a Wing Under Flight Conditions

[marv]

Homework Statement

"The lift gradient of a wing under actual flight conditions is 0.1179 per degree. Calculate the lift-drag ratio of the wing with an angle of attak of 3 degrees?"

Given is:
altitude=5000 m
velocity=225 m/s
wing area S=149 m2
wing span b=34.5 m
span efficiency factor e1=0.82
Cd (profile drag coefficient) at 3 degrees=0.0062.
ρ∞=0.736 kg/m3
p∞=5.41*10^4 Pa, T∞=255.7 K
cp=1008 J/kg*K

Homework Equations

I don't exactly know which equation to use, that's the whole point of my question. You might can use a=dCl/dalpha = a0/(1+(a0/pi*A*e1)). Note that everyting in the equation is in radians. Maybe you can calculate Cl with this equation, and as you know Cd (given) you can calculate the L/D ratio.

The Attempt at a Solution

I've tried several things like the lift gradient equation a=dCl/dalpha=a0/(1+(a0/pi*A*e1), is I can calculate the aspect ratio A (S/b^2). A=35.4^/149≈0.231. I also know the span efficiency factor e1, as this is given (0.82). The fact is that I don't know if this equation is right.
The other thing I know, is that the equation for lift drag ratio is L/D = Cl/Cd. Am I right to say that we know Cd? This is 0.0062. Then we only have to calculate the lift coefficient, but I don't know how to do that without the lift given or the mass of the aircraft. (as the equation is L=Cl*(0.5*ρ*V^2)*S.

Can anyone help me with this problem?

 

[munster]

You need both Cl and Cd to get the ratio. Look at the question again - you are given the lift gradient. What exactly is this 0.1179 that increases for every degree? Can you thus figure out the corresponding value at 3 degrees? For Cd, you need the total drag, which is the sum of profile drag and induced drag. 0.0062 is only the profile drag. If you know the equation for induced drag, the information provided is enough to answer the question.

 

[manish_mech]

i cannot figure out the value at 3 degree ?
is it simply 3*0.1179 or we have to look at some graph
please help me !

 

[rcgldr]

Cl should be 3 * 0.1179. Cd normally refers to the sum of profile and induced drag, but the problem uses it as Cd (coefficient of profile drag). Assuming that the problem statement is only defining profile drag, then as posted, you'll need a formula to determine induced drag.

 

[manish_mech]

total drag = profile +induced drag
=: 0.0062 + CL^2/pi*A*e1
=0.0062+ (3*0.1179)^2/p1*7.988*0.82
=0.0062+0.0060795
=0.0122795
then Cl/Cd = 0.3537/0.0122795
=28.804
this is what i got ...but answer is not correct
Is there any mistake ?
thanks in advance!