# How to calculate drag of a flat rectangular surface at given area, air density, airspeed and angle of attack?

I'm a complete noob in aerodynamics, and I'm trying to calculate the drag of a rectangular flat area, given the air pressure / density, area, angle of attack and airspeed. I've read this question, but it is about calculating the drag for two rectangular areas, whereas I need it for one area, and I couldn't derive a formula for one area. Can you please help me with this ?

I need this to get the drag of cowl flaps extended at an angle between 0 and 20 degrees for a FlightGear model.

• You’ve got a lot more to consider than just flat plate drag in determining the overall change in drag due to opening cowl flaps. The whole airflow through the engine compartment changes. And because the cowl flap is not just a flat plate in the free stream but has some sides and is attached to the fuselage and has air flow from the engine compartment moving over the upper surface the flat plate drag equations are just a small part of it.
– Jim
Oct 16 at 17:11
• There's quite a variety of cowl flaps, which aeroplane are you modelling? Oct 18 at 5:11
• @Koyovis Cessna 182 S/T and Cessna P210N Oct 18 at 13:07

Simply using the generic drag equation will get you within the ballpark required for FlightGear.

$$D = C_D \cdot \frac{1}{2} \rho V^2 \cdot A$$ with $$C_D$$ the flat plate drag coefficient and A being a reference area of your cowl flaps. The data for the correct Reynolds number is best used, with $$Re = \frac{\rho V \bar{c}}{\mu}$$ with $$\bar{c}$$ = mean aerodynamic chord and $$\mu$$ = kinematic viscosity of air. The Re uses the wing geometry to determine if the flow is laminar or turbulent, which has a large influence on the drag calculation.

So calculating additional drag for air density $$\rho$$ of 1.1 kg/m$$^3$$ (function of altitude) and airspeed of 150 m/s, we would get: $$D = C_D \cdot ½ \cdot 1.1 \cdot 150^2 \cdot A = 12,375 \cdot C_D \cdot A [N]$$. Now the only thing we need to do is look up the $$C_D$$ and determine reference area A in [$$m^2$$], and this is where things get a bit more challenging.

Note that we're calculating additional drag. When the flap is fully retracted and aligned with the cowling, additional drag is zero. Pull the flap open and extra drag is created - it will be less than bluff body drag, since the cowl flap opens to expel exhaust gases which prevents some of the pressure drag from occurring.

To keep things simple, we can use bluff body aerodynamics with the front projected area as our reference A. For instance an airfoil $$C_D$$ of 0.045, with projected area of 0.002 * sin$$\alpha$$ [m$$^2$$]. $$\alpha$$ is the deflection angle of the flap.

The exhaust gas expelled behind the cowling flap prevents much of the pressure drag from happening, like in an airfoil where the flow gently foils back into the afterbody. Without the exhaust gas the $$C_D$$ would be higher, more that of a bullet. How much more depends on a whole lot of exhaust gas pressure parameters. Values of between 0.05 and 0.3 seem could be taken.

• Oh, looks like you're not familiar with piston engine aircraft ! ;) Cowl flaps are not situated on the wing, but rather they are used to open / close a small hole in the engine cowling. In high performance situations such as takeoff or enroute climb they are opened to increase the airflow going through the gnine cowling and past the engine to have better cooling. In cruise and descent they are closed to reduce drag. Oct 16 at 12:36
• Have edited to use the more streamlined shapes of airfoil and bullet. Oct 20 at 13:09