Parasite drag and the drag polar

Where drag exists without lift

The zero-lift drag term groups several mechanisms; it does not mean every mechanism is independent of α.

Friction and pressure drag

Skin friction comes from viscous shear on wetted surfaces. Form or pressure drag comes from the pressure distribution, especially separation and the low-pressure wake. Streamlining reduces the pressure-drag component.

Interference drag arises where flows meet, such as wing–fuselage junctions. Cooling flows, protrusions, antennas and exposed undercarriage can contribute additional drag. Configuration determines the baseline.

A useful model has a domain

The simple parabolic polar is CD = CD0 + kCL², with k = 1/(πARe). It combines an approximately constant baseline and an induced term for a stated low-speed configuration.

Do not use one polar unchanged across large Mach changes, flap movement, icing or extensive separation. Near the stall or wave-drag rise, the parabola is an inadequate model.

A configuration penalty at two speeds

Suppose a configuration change adds ΔCD0 = 0.010 on a 30 m² reference area. At density 1.20 kg/m³ and 50 m/s, q is 1,500 Pa and the added drag is 450 N. At 100 m/s, q is 6,000 Pa and the added drag is 1,800 N. The same coefficient penalty produces four times the force when speed doubles.

The added propulsive power is ΔD × V. It grows from 22.5 kW to 180 kW in this comparison, an eightfold change. This is why an apparently modest protrusion or configuration drag term can have a much larger power consequence at high speed even when its coefficient is approximately constant.

Keep CD0 fixed in the laboratory and compare selected points on the parasite curve, then vary CD0 at a single speed. Distinguish changing the flow scale from changing the configuration coefficient. Near extensive separation or a compressibility drag rise, do not insist that the same constant-CD0 approximation remains accurate.

Find the best lift-to-drag ratio

Minimum total drag at fixed weight comes from a trade between parasite and induced terms.

Equal components at the simple minimum

In the parabolic model, minimum drag occurs when CD0 = kCL². Thus CL at maximum L/D is √(CD0/k), and (L/D)max = 1/(2√(CD0k)).

This is a minimum in drag force as speed varies at fixed supported weight, not the minimum value of total CD on the coefficient polar. CD itself is smallest at zero lift in this model.

Turn the optimum into a speed

For a stated load and density, V = √(2L/(ρSCL)). Increasing weight moves the speed for the same optimum CL upward by √weight ratio. The maximum L/D of the unchanged ideal polar stays the same.

Adding drag with gear or spoilers raises CD0 or changes the polar. The optimum coefficient, speed and glide performance all need to be recomputed from that new configuration.

Solve weight and optimum separately

For CD0 = 0.020 and k = 0.050, the optimum coefficient is √0.4 = 0.6325 and maximum L/D is 15.81. At W = 100 kN, density 1.20 kg/m³ and S = 30 m², the corresponding speed is 93.72 m/s. The minimum drag is W/(L/D) = 6.325 kN, divided equally between the two model components.

Raise weight to 121 kN without changing the polar. The optimum coefficient and maximum L/D remain fixed, but speed rises by 10% to about 103.09 m/s and minimum drag rises by 21%. The shape’s aerodynamic efficiency is unchanged; supporting more weight still needs more force and power.

In the laboratory, locate the bottom of total drag rather than the bottom of the induced curve. Verify the equal-component condition at the computed optimum, allowing for slider resolution. If the optimum speed moves outside the displayed range after a parameter change, use the calculated readout and report the chart-domain limit.

Can you explain and apply the mechanism?

Four original questions. Work from the stated facts, then compare your reasoning with the explanation.