Calculator Inputs
Example data table
| Mode | AR | k | CL | CD0 | Estimated e | CDi | Total CD |
|---|---|---|---|---|---|---|---|
| Direct from k | 9.50 | 0.0410 | 0.600 | 0.0220 | 0.8175 | 0.0148 | 0.0368 |
| Drag polar | 10.20 | 0.0375 | 0.700 | 0.0200 | 0.8324 | 0.0184 | 0.0384 |
| Geometry estimate | 8.80 | 0.0448 | 0.550 | 0.0240 | 0.8089 | 0.0135 | 0.0375 |
These values illustrate typical calculator behavior for preliminary wing analysis.
Formula used
1. Induced drag factor relation: k = 1 / (π × AR × e)
2. Oswald efficiency from k: e = 1 / (π × AR × k)
3. Drag polar method: CD = CD0 + kCL², so k = (CD - CD0) / CL²
4. Lift coefficient from flight condition: CL = W / (q × S), where q = 0.5ρV²
5. Induced drag coefficient: CDi = CL² / (π × AR × e)
6. Total drag coefficient: CD = CD0 + CDi
The geometry mode applies an empirical preliminary-design estimate using aspect ratio, sweep, and taper ratio. Use direct drag-polar data whenever measured or validated data is available.
How to use this calculator
- Select a calculation mode based on your available aerodynamic data.
- Enter aspect ratio directly, or let the calculator derive it from span and wing area.
- Provide k for direct mode, drag coefficients for drag polar mode, or sweep and taper for geometry mode.
- Optionally enter weight, speed, density, and area to derive lift coefficient and force outputs.
- Press Calculate Efficiency to show the result above the form.
- Review the result table, Plotly graph, and engineering notes.
- Use the CSV and PDF buttons to export the calculated summary.
FAQs
1. What does Oswald efficiency measure?
It measures how closely a real wing approaches the ideal elliptical lift distribution. Higher values usually mean lower induced drag for the same lift and aspect ratio.
2. What is a typical range for e?
Many practical subsonic wings fall roughly between 0.70 and 0.90. Very efficient designs can exceed that range, while compromised geometries may fall lower.
3. When should I use direct k mode?
Use it when you already know the induced drag factor from testing, simulation, or trusted aerodynamic literature. It is the most direct way to compute Oswald efficiency.
4. When is drag polar mode better?
Choose drag polar mode when you know total drag coefficient, zero-lift drag coefficient, and lift coefficient at the same condition. It back-calculates k and then derives e.
5. Is geometry mode exact?
No. Geometry mode is a preliminary estimate for concept studies. It is useful early in design, but measured or validated aerodynamic data should replace it later.
6. Why can CL be derived automatically?
If weight, air density, speed, and wing area are known, the calculator can compute dynamic pressure and infer the lift coefficient needed for steady flight.
7. What does the graph show?
The graph shows induced drag coefficient across a lift coefficient range. When zero-lift drag is available, it also plots estimated total drag coefficient for comparison.
8. Why export CSV or PDF?
Exports help document design studies, compare cases, share results with teammates, and preserve calculated metrics for reports, reviews, or further optimization work.