Drag Force⚠ unverified
Aerospace / Aerodynamics · Aerodynamic drag force
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| CD | CD | — | 0.03 | Drag coefficient |
| rho | ρ | kg/m^3 | 1.225 | Air density |
| V | V | m/s | 50.0 | True airspeed |
| S | S | m^2 | 20.0 | Wing area |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| drag | D | N | Drag force |
The science & history
Understanding the Parameters
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Drag coefficient $C_D$ — the sum of two parts: parasite drag $C_{D0}$ (skin friction + pressure/form drag, roughly constant, Parasite Drag) and induced drag $C_{Di} = C_L^2/(\pi\,AR\,e)$ (the price of making lift, Induced Drag). The total drag polar is $C_D = C_{D0} + C_L^2/(\pi AR e)$.
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Airspeed $V$ — drag scales with $V^2$ at fixed $C_D$, but there is a twist: to hold lift as speed drops, $C_L$ must rise, which raises induced drag. So total drag has a minimum at some speed and rises at both lower speed (induced) and higher speed (parasite) — the classic drag curve.
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Air density $\rho$ and area $S$ — as for lift, drag is referenced to dynamic pressure and the same wing area, keeping $C_L$ and $C_D$ on a common basis for the drag polar.
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Why it matters — $D\times V$ is the power required; minimising drag (maximising Lift-to-Drag Ratio) is the central goal of efficient flight.
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.