What is the drag polar equation?

The parabolic drag polar is CD = CD0 + k·CL², where CD0 is the zero-lift (parasite) drag coefficient and k·CL² is the induced drag term. This equation accurately models subsonic aircraft drag over most of the CL operating range.

How is k related to wing geometry?

The induced drag factor k = 1 / (π·e·AR), where e is the Oswald span efficiency factor (typically 0.7–0.95 for conventional wings) and AR is the wing aspect ratio. A higher AR or higher e gives a smaller k and therefore less induced drag.

What are typical values for CD0?

For a clean subsonic jet transport, CD0 is roughly 0.015–0.025. General aviation piston aircraft typically range from 0.025–0.040. Gliders can be as low as 0.010–0.015, while a pod-and-boom UAV might be 0.030–0.060.

What is the minimum drag point?

Minimum drag occurs at the CL where induced drag equals parasite drag, i.e., CD0 = k·CL². This gives CL_md = sqrt(CD0 / k) and CD_min = 2·CD0. The minimum drag speed is the speed at which total drag is lowest.

What is the maximum lift-to-drag ratio?

Maximum L/D occurs at the minimum drag point: (L/D)_max = 1 / (2·sqrt(CD0·k)). This is the most aerodynamically efficient flight condition and corresponds to maximum range for a jet aircraft or maximum endurance for a propeller aircraft.

Does this tool handle compressibility effects?

No. The parabolic drag polar is a subsonic, incompressible model. Near and above Mach 0.6, wave drag increases CD0 significantly and the polar becomes non-parabolic. For transonic analysis, use drag-divergence corrections or more detailed CFD data.

Drag Polar Calculator

Name: Drag Polar Calculator
Availability: InStock
Author: Nham Vu

Enter zero-lift drag (CD0), induced drag factor (k), and a CL value to compute CD from the parabolic drag polar, then plot the full CL vs CD curve.

Drag Polar Parameters

CD = CD0 + k · CL²

Zero-Lift Drag Coefficient, CD₀

Parasite drag at zero lift. Jet transport: 0.015–0.025.

Induced Drag Factor, k (= 1/π·e·AR)

Typical range 0.03–0.12. Lower k = less induced drag.

Query: Lift Coefficient, CL

Compute CD and L/D at this specific CL value.

Polar Range: CL_max

Upper CL limit for the plotted polar curve.

CD at CL = 0.50

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Drag coefficient

Lift-to-Drag Ratio (L/D)

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Max L/D

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Best aerodynamic efficiency

At CL_md / CD_min

— / —

Drag Polar Curve

CL vs CD

Click "Calculate & Plot" to display the drag polar curve.

Typical Drag Polar Parameters by Aircraft Type

Aircraft Type	CD0	k	Max L/D (approx.)
High-performance glider	0.010	0.018	~52
Jet transport (clean)	0.020	0.042	~17
General aviation (piston)	0.030	0.055	~12
Fighter jet (supersonic)	0.014	0.140	~10
Fixed-wing UAV	0.040	0.070	~9

Values are representative approximations for conceptual design. Actual polars depend on wing geometry, Reynolds number, and configuration.

Summary

Enter zero-lift drag (CD0), induced drag factor (k), and a CL value to compute CD from the parabolic drag polar, then plot the full CL vs CD curve.

How it works

Enter the zero-lift drag coefficient CD0 (parasite drag at CL = 0).
Enter the induced drag factor k (often written as 1 / (π·e·AR), where e is Oswald efficiency and AR is aspect ratio).
Optionally enter the maximum CL for the polar range (default 1.8).
Enter a specific CL value to compute the corresponding CD point.
Click Calculate to get CD, L/D, and display the full drag polar curve.
The chart highlights the minimum drag point and the maximum L/D point.

Use cases

Computing drag coefficient at any lift condition during aircraft conceptual design.
Plotting the full drag polar curve for performance analysis.
Finding the minimum drag speed and maximum lift-to-drag ratio for range/endurance optimization.
Verifying drag polar models against wind-tunnel or flight-test data.
Teaching aerodynamics and aircraft performance fundamentals.
Sizing propulsion requirements from known aerodynamic polars.
Comparing polars for different Oswald efficiency factors or aspect ratios.
Supporting UAV and glider performance trade studies.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu