Lift vs Lift Coefficient Calculations

[cad2blender]

Ok guys I got a question that has been bugging me for a while. Lets say that an airplane is flying at at velocity of 200 ft/s and I want to calculate the amount of lift produced, so :
Airplane:
(W)weight 5000 lb
(V)velocity 200 ft/s
(r)density 2.37x10-3 slugs/ft^3
(S)Wing Area (S ref) 1000 ft^2

Now if we plug these values in into the Cl equation:

Cl=W/(1/2*r*V^2*S)

we get Cl=0.1054

Ok now we plug that into the Lift Equation:

L= 1/2*r*V^2*S*Cl

We get 4,995.96

I know that the airplane is NOT capable of level flight, since lift is less that weight, but these number are just made up. Now lets increase the velocity to 400 ft/s (all other things being equal) Cl is now 0.0263 and Lift produced is now 4986.48, Lift as decreased as velocity increased. Here's the funny part if you fire up Foilsim or any other airfoils analysis program if you increase velocity lift also increases! What is up with that? according to the calculations lift should decrease as velocity increases. This explains hypersonic aircraft or AA missiles they have TINY wings they do not need to create as much lift since they are going so fast. So question still remains, why is my calculations not agreeing with the software?

Anyone?

EDIT: The airfoil has a slight camber and has a AOA of 0 degrees

[kcaldwel]

Can I see your license to drive that calculator and computer?

First, you are doing mathematical operations, rounding off the result (improperly I might add), and then reversing the mathematical operation and not getting exactly what you started with - surprise.

Second, the airfoil is not at a zero lift angle of attack, or it wouldn't be making any lift, regardless of speed. A geomertical zero angle of attack with a cambered airfoil will still have the airfoil making lift. You are arbitrarily deciding that the lift is still 5000 lbs. and the AoA is the same. Foilsim and the other programs know that if the speed increases, and the angle of attack stays the same, the lift will increase.

Kevin

[pmackenzie]

I know that the airplane is NOT capable of level flight, since lift is less that weight, but these number are just made up. Now lets increase the velocity to 400 ft/s (all other things being equal) Cl is now 0.0263 and Lift produced is now 4986.48,
Anyone?



Have you ever heard of rounding errors?

Take your first equation

Cl=W/(1/2*r*V^2*S)

and plug it into the second one

L= 1/2*r*V^2*S*Cl

= 1/2*r*v^2*S*W/(1/2*r*V^2*S)

= W

Surprise!

L=W is the assumption made in deriving the equations. It is called steady state level flight.

Any difference you got is just due to the precision of your calculations, not some mysterious aerodynamic effect.


Clear?

Pat MacKenzie