Drag Polar Calculator
With C_D0 = 0.025, AR = 8 and e = 0.8, flying at C_L = 0.5 gives a drag coefficient of 0.037434; the best L/D of about 14.2 comes at C_L ≈ 0.71.
0.0374339799290543
Full answer, then cut to fewer decimals (not rounded):
- 0.0374339799290543
- 0.037433979929054
- 0.03743397992905
- 0.0374339799290
- 0.037433979929
- 0.03743397992
- 0.0374339799
- 0.037433979
- 0.03743397
- 0.0374339
- 0.037433
- 0.03743
- 0.0374
- 0.037
- 0.03
- Lift-to-drag ratio C_L/C_D
- 13.35684854
- Induced drag factor K = 1/(πeAR)
- 0.04973591972
- Induced drag coefficient KC_L²
- 0.01243397993
- Maximum L/D = 1/(2√(C_D0 K))
- 14.17963081
- C_L for maximum L/D = √(C_D0/K)
- 0.7089815404
- C_L for minimum power √(3C_D0/K)
- 1.22799205
- C_L for jet maximum range √(C_D0/3K)
- 0.4093306832
Step-by-step solution
- K = 1 ÷ (π × 0.8 × 8) = 0.04973591972
- C_D = C_D0 + KC_L² = 0.025 + 0.04973591972 × 0.5² = 0.03743397993
- (L/D)max = 1 ÷ (2√(C_D0 K)) = 14.17963081 at C_L = 0.7089815404
Drag Polar Formula
C_D = C_D0 + K C_L², K = 1/(πeAR)
(L/D)max = 1/(2√(C_D0 K)) at C_L = √(C_D0/K)
Worked Example
C_D0 = 0.025, AR = 8, e = 0.8 at C_L = 0.5:
- K = 1 ÷ (π × 0.8 × 8) = 0.04973591972
- C_D = C_D0 + KC_L² = 0.025 + 0.04973591972 × 0.5² = 0.03743397993
- (L/D)max = 1 ÷ (2√(C_D0 K)) = 14.17963081 at C_L = 0.7089815404
Induced drag factor K = 1/(πeAR): 0.04973591972 · Induced drag coefficient KC_L²: 0.01243397993 · Maximum L/D = 1/(2√(C_D0 K)): 14.17963081 · C_L for maximum L/D = √(C_D0/K): 0.7089815404 · C_L for minimum power √(3C_D0/K): 1.22799205 · C_L for jet maximum range √(C_D0/3K): 0.4093306832
GATE tip
Remember the sequence of optimum C_L: jet range √(C_D0/3K) < max L/D √(C_D0/K) < propeller endurance √(3C_D0/K). The speeds run the other way.
More Airplane Performance Calculators
-
Lift Equation Calculator
L = ½ ρ V² S C_L
ρ air density, V true airspeed, S wing area, C_L lift coefficient; drag uses C_D the same way
Example: A 16.2 m² wing at 60 m/s and C_L = 0.5 at sea level: Lift L = 17860.5 N.
-
Breguet Range Calculator
Jet: R = (V/c)(L/D) ln(W₀/W₁)
propeller: R = (η/c)(L/D) ln(W₀/W₁); jet endurance E = (1/c)(L/D) ln(W₀/W₁)
Example: A jet at 850 km/h, L/D = 16, TSFC 0.6 per hour, burning from 70 t to 55 t: Range R = 5466.34 km.
-
Stall Speed Calculator
V_s = √(2W / (ρ S C_L,max))
in a turn V_s√n; manoeuvring speed V_A = V_s√n_max
Example: An 1100 kg aircraft with a 16.2 m² wing and C_L,max = 1.6 at sea level: Stall speed V_s = 26.0667 m/s.
-
Take-off Distance Calculator
s_LO ≈ 1.44 W² / (g ρ S C_L,max T)
lift-off at 1.2 V_s; drag and rolling friction neglected (Anderson)
Example: An 1100 kg aircraft, 16.2 m², C_L,max 1.6, 3 kN thrust at sea level: Ground roll s_LO ≈ 179.381 m.
Frequently asked questions
Why is maximum L/D where induced and parasite drag are equal?
Minimising C_D/C_L = C_D0/C_L + KC_L gives C_D0 = KC_L²: at the optimum the two drags match.
Which C_L gives best range and endurance?
Propeller aircraft: max L/D for range and √(3C_D0/K) for endurance. Jets: √(C_D0/3K) for range (max √C_L/C_D) and max L/D for endurance.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Drag Polar Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/drag-polar-calculator/
IEEE
Scientific Converters, "Drag Polar Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/drag-polar-calculator/