Calculating Airplane Drag

The drag of the airplane can be calculated through the drag of the various components.

The calculation starts with the non dimensional drag coefficient (C_D) of the various components. Once the aircraft C_D is known, the drag is then obtained by scaling with the free stream dynamic pressure and the wing reference area.

For the calculation of the drag coefficients

• If a wind tunnel model exists then the overall drag coefficient (and maybe the component drag coefficient can be obtained through testing
• The history of design within the company (aircraft manufacturers) will provide good estimates
• In this course, and for preliminary design some simple models are used to estimating the drag coefficient

Simplified Drag Calculations

There are essentially three significant types of drag (or drag coefficients) for calculations

Parasite Drag : the penalty the object must suffer just to move through the fluid. It is sometimes called the zero lift drag. There are two important components to parasite drag

Skin friction Drag - the friction is estimated through the shear stress at the surface. This is usually applied in the region the fluid is still attached to the object. Since the shear stress varies with distance from the stagnation point, an average value is used. It is computed through estimating the skin friction drag coefficient (C_f ). From previous discussion, this coefficient depends on the type of flow (laminar/turbulent) and can be calculated based on the Reynolds number. Once the coefficient is known, the shear stress is calculated over the entire wetted area (the area over which fluid is in contact with the flow).

For the wing

The factor of 2 is for top and bottom surface. f_cur is a factor for increase in area (about 2 %) due to curvature. NOTE: (i) We are really not concerned with the type of airfoil at this stage

(ii) skin friction drag calculations are based in the wetted area (S_wet) but the parasite drag coefficient (like all other aerodynamic coefficients for the aircraft) is based on the reference area (S)

Pressure Drag : The pressure drag is due to flow separation. This cannot be known until an actual design exists. In that case usually wind tunnel or other such sources will provide the information. In the preliminary design, for general aviation in normal flight conditions we will assume a 50 % drag increase (of the skin friction drag) due to pressure drag. This correction factor (referred to K_p) is a strong function of thickness Mach number.

Therefore we can compute the total parasite drag as

We can obtain similar information for the fuselage, horizontal tail, and vertical tail.

The parasite drag for the engine is usually provided by the manufacturer.

The wing and the fuselage parasite drag is typically 75 % of the total parasite drag of the plane

The engine drag can be assumed to be 20 % of the drag of the plane

Induced Drag : The induced drag is calculated from the induced drag coefficient and is generated by the wing only. The formula is same as the one we saw earlier.

Wave Drag: The wave drag is the effect of compressibility. There is a sharp rise in the drag coefficient at the Mach number close to 1. Once again corrections are based on actual design.

In the paper design project we will only consider parasite and induced drag and ignore wave drag computation. We will discuss wave drag under compressibility effects.