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Drag Force⚠ unverified

Aerospace / Aerodynamics · Aerodynamic drag force

Parameters

InputSymbolUnitDefaultDescription
CDCD0.03Drag coefficient
rhoρkg/m^31.225Air density
VVm/s50.0True airspeed
SSm^220.0Wing area
OutputSymbolUnitDescription
dragDNDrag force

The science & history

Understanding the Parameters

Derivation (Approaching a Proof)

By the same dimensional-analysis argument as lift (Lift Force), the drag force must be dynamic pressure times reference area times a dimensionless coefficient:

$$D = q\,S\,C_D = \left(\tfrac{1}{2}\rho V^2\right)S\,C_D.$$

The construction defines $C_D$, which is then decomposed physically. Parasite drag comes from viscous skin friction and flow separation and is largely independent of lift. Induced drag is the streamwise component of the tilted lift vector caused by wingtip downwash (Downwash Angle); lifting-line theory gives $C_{Di} = C_L^2/(\pi AR e)$. Adding them yields the drag polar

$$C_D = C_{D0} + \frac{C_L^2}{\pi\,AR\,e},$$

the single most useful relation in aircraft performance.

Dimensional check. $D = \tfrac12 C_D\,\rho V^2 S = (\text{–})\cdot(\text{kg}/\text{m}^3)\cdot(\text{m}/ \text{s})^2\cdot\text{m}^2 = \text{N}$ — a force, as required.

History and Development

The drag equation and its coefficient decomposition are, like lift, products of Prandtl-era aerodynamics. The split into parasite and induced drag — and the realisation that induced drag is an unavoidable consequence of finite-span lifting wings — reshaped wing design toward high aspect ratio and clean surfaces. The drag polar $C_D = C_{D0} + kC_L^2$ underlies every range, endurance, climb, and glide calculation in aircraft performance.

Related Concepts: Lift Force, Parasite Drag, Induced Drag, Lift-to-Drag Ratio, Dynamic Pressure, Downwash Angle

Notes: $C_D = C_{D0} + C_L^2/(\pi AR e)$ (drag polar): parasite (Parasite Drag) + induced (Induced Drag). Total drag has a minimum vs speed. Thrust $= D$ in level flight; power required $= DV$. Same $q$, $S$ basis as Lift Force.

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