Lift of a trapezoidal wing

[physicsCU]

OK, here is my problem.

I have a trapezoidal wing. Assume it is a simple trapezoid, aka the trailing edge has no taper, only the leading edge does.

taper ratio = 0.35
lift required = 2.45 N
Wing area = 0.07 m^2
CL = 0.682
Root Chord = 20 cm
Tip Chord = 7 cm
Span = 26 cm
RN = 148000

I am trying to find a relationship between CL and cl, so that I can pick an airfoil and compute drag.

I am using the NASG database to pick the airfoil. The polar graphs given there only have cl up to ~1.0

Everything I have tried to relate CL and cl has given me larger numbers than that, the smallest being 1.95, largest was 2.6.

The smaller number was found from CL = cl*taper ratio, the larger from a more complicated formula.

The lift equation I used is L = L'*span*taper ratio. EDIT: I am using an integral from fitting an equation of L' to three points on the wing. That will help a lot there.

L' is the lift of the root chord.

Can anyone help me relate CL and cl or at least point me in the right direction to derive the relationship? Or should I just pick a cl that gives me a small drag coefficient and move on? Most of the airfoils have two points of cl for each cd.

Also, what is meant by AOA, that is the angle of the wings I know, but if I have a "flying wing" design, are the wings angled up/down at the "root" or does the whole craft fly at an angle, including the prop?

Thanks!

 

[Illmatic1]

AOA stands for angle of attack. It is the angle between the relative wind (direction of travel) and the chord line of the wing. This angle affects the lift generated by the wing, and therefore also affects the CL of the wing. To relate CL and cl, you will need to use a lift equation. The equation will depend on several factors, including the airfoil shape, the airspeed, and the angle of attack. A simple lift equation can be expressed as: L = 1/2ρV²SCL where ρ is the air density, V is the airspeed, S is the wing area, and CL is the lift coefficient.The lift coefficient is related to the angle of attack by the following equation: CL = cl*taper ratioWhere cl is the lift coefficient at 0 degrees angle of attack. You can find cl by looking up the airfoil in the NASG database.You can then calculate the lift required for your wing by substituting the values into the lift equation:L = 1/2 x 148000 x (2.45/0.07) x 0.682 = 592.14 NThis should help you determine the right airfoil for your design.

 

[ravenprp]

Firstly, it is important to note that the lift equation you are using is not entirely accurate. The lift equation for a trapezoidal wing is actually L = 0.5*rho*V^2*CL*S, where rho is the air density, V is the airspeed, CL is the lift coefficient, and S is the wing area. This equation takes into account the variation of lift along the span of the wing, which is not accounted for in your equation.

To find the relationship between CL and cl, you can use the lift equation and the definition of lift coefficient (CL = L/(0.5*rho*V^2*S)) to solve for cl. This will give you a relationship between the two coefficients.

In terms of selecting an airfoil, it is important to choose one that will give you the desired lift at the given angle of attack. You can use the lift equation and the definition of angle of attack (AOA) to calculate the required AOA for your desired lift coefficient. The AOA is the angle between the wing and the relative wind, so if you have a flying wing design, the entire craft would fly at the same AOA, including the prop.

Additionally, it is important to consider the overall design and purpose of your wing when selecting an airfoil. Different airfoils have different characteristics and may be better suited for certain applications. It may be helpful to consult with an expert or conduct further research to find the best airfoil for your specific needs.

Overall, it is important to use accurate equations and consider all factors when designing a wing. Good luck with your project!