Drag Force on Aircraft: Types and Equation

Drag is one of the four forces of flight. In steady level flight, engine thrust equals drag and lift equals weight. Every reduction in drag means less thrust, less fuel and longer range, so drag prediction and reduction run through every stage of aircraft design.

The drag force equation

The drag equation used throughout aerodynamics, as given by Anderson and by NASA Glenn Research Center, is:

$$D = \tfrac{1}{2}\,\rho\,v^2\,S\,C_D$$

• ρ air density (1.225 kg/m³ at sea level in the standard atmosphere).
• v true airspeed.
• S reference area, normally the wing planform area.
• C_D drag coefficient, which depends on shape, angle of attack (through lift), Reynolds number and Mach number.

The product ½ρv² is the dynamic pressure q, the same term that appears in the lift equation explained in how wings generate lift. Drag and lift are simply the two components of the total aerodynamic force, measured parallel and perpendicular to the relative wind.

Types of drag force on aircraft

Parasite drag

Parasite drag is all drag not associated with producing lift. The FAA Pilot’s Handbook of Aeronautical Knowledge divides it into three kinds:

• Form (pressure) drag: caused by flow separation and the pressure difference between front and rear of a body. Streamlining keeps the flow attached and reduces it.
• Skin friction drag: shear stress in the thin boundary layer on every wetted surface. It depends on wetted area, surface roughness and whether the boundary layer is laminar or turbulent.
• Interference drag: extra drag where components meet, such as the wing to fuselage junction or a strut to wing joint. Fairings and fillets reduce it.

Parasite drag is expressed through the zero lift drag coefficient C_D,0, which is roughly constant at a given Mach number, so parasite drag grows with v².

Induced drag

A finite wing produces lift by creating higher pressure below than above. At the tips, air flows around from the high pressure side to the low pressure side, forming wingtip vortices. These vortices create a downward flow (downwash) over the wing that tilts the local lift vector backward. The rearward component is induced drag. Anderson gives its coefficient as:

$$C_{D,i} = \frac{C_L^2}{\pi\,e\,AR}$$

where AR = b²/S is the aspect ratio (span squared over wing area) and e is the span or Oswald efficiency factor. Long, slender wings with high aspect ratio produce less induced drag, which is why gliders and long range airliners have them.

Wave drag

As an aircraft approaches the speed of sound, local flow over the wing becomes supersonic and shock waves form. Shocks cause a large pressure rise and can separate the boundary layer, adding wave drag. The Mach number at which drag starts to rise sharply is the drag divergence Mach number. Swept wings, thin airfoils and supercritical airfoil sections delay it, which is why jet airliners use swept wings.

The drag polar and total drag

Combining parasite and induced drag gives the drag polar, the relation between C_D and C_L for the whole aircraft:

$$C_D = C_{D,0} + \frac{C_L^2}{\pi\,e\,AR}$$

Because parasite drag rises with speed and induced drag falls, total drag has a minimum. Anderson shows that minimum drag, and so maximum lift to drag ratio, occurs where the two are equal, C_D,0 = C_D,i, and that:

$$\left(\frac{L}{D}\right)_{max} = \frac{1}{2}\sqrt{\frac{\pi\,e\,AR}{C_{D,0}}}$$

Flying at the minimum drag speed gives the best glide ratio, and for propeller driven aircraft Anderson shows that maximum range is obtained at maximum L/D. Minimum power required occurs at a lower speed, where induced drag is three times parasite drag.

Download diagram (WebP)

Worked example: drag force on a light aircraft

At cruise, parasite drag is about four fifths of the total, so cleaning up the airframe pays off most. At low speed, as in climb or approach, induced drag dominates.

Key formulas for drag force

Reducing drag force

• Streamlining fuselages, nacelles and landing gear fairings to delay separation.
• Retractable landing gear and flush rivets to cut parasite drag.
• High aspect ratio wings and winglets to reduce induced drag.
• Laminar flow airfoils and smooth, clean surfaces to reduce skin friction.
• Swept and supercritical wings to raise the drag divergence Mach number.
• Fairings at wing roots and strut joints to cut interference drag.

Engine installation drag also matters; the intake and nozzle design of turbofan and turboprop engines is shaped with this in mind. For small rotorcraft, body and arm drag limit forward speed, as discussed in how a quadcopter flies.

Drag force interview and viva questions

1. What are the main types of drag on an aircraft? Parasite drag (form, skin friction and interference drag), induced drag from producing lift, and wave drag near and above the speed of sound.
2. Why does induced drag fall as speed increases? At higher speed the wing needs a lower lift coefficient to carry the same weight, and induced drag depends on the square of the lift coefficient.
3. At what condition is total drag a minimum? Where parasite drag equals induced drag, which also gives the maximum lift to drag ratio and the best glide.
4. Why do gliders have long, slender wings? A high aspect ratio reduces the induced drag coefficient, which is inversely proportional to aspect ratio.
5. How do swept wings reduce drag on jet airliners? Sweep, together with thin and supercritical airfoils, delays the drag divergence Mach number, so wave drag rises at a higher speed.