🔍 /
Home › CFD & Aerodynamics › Optimal L/D & Best Glide

📐 Optimal Lift-to-Drag Ratio

Determine the maximum lift-to-drag ratio (L/D) and optimal cruise angle of attack for aircraft wings.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated
Optimal Lift-to-Drag Ratio Cfd
📊 Solver Telemetry ● ACTIVE
👁️ Views 22
⚡ Solves 18
💾 Downloads 654 📦 Fortran Code 4.4 KB
📅 Released Jun 2026
⏱️ Latency < 1 ms
⚡ TOOLS & REPORTS:
💾 Download Fortran 90
Aircraft Configurations: High-Performance Competition Sailplane Cessna 172 Skyhawk (Light Aircraft) Commercial Wide-Body Jet Cruise Solar High-Altitude Endurance UAV

📥 Aircraft Weight, Polar & Wing Geometry

Mass: 224,338 kg
📖 Optimal Performance Formulae: $$(L/D)_{\text{max}} = \frac{1}{2 \sqrt{C_{D,0} / (\pi e AR)}}, \quad C_{L,\text{range}} = \sqrt{\pi e AR C_{D,0}}$$ $$V_{\text{range}} = \sqrt{\frac{2 W}{\rho S C_{L,\text{range}}}}, \quad V_{\text{endurance}} = \frac{V_{\text{range}}}{3^{1/4}} \approx 0.76\, V_{\text{range}}$$
19.6 : 1
Maximum $(L/D)_{\text{max}}$
740.2 km/h
Best Glide Speed ($V_{\text{range}}$)
562.5 km/h
Max Endurance ($V_{\text{end}}$)
495.4 km/h
Stall Speed ($V_{\text{stall}}$)

⚡ Flight Optimization Regimes Comparison

Operating Regime Optimal $C_L$ $L/D$ Efficiency True Airspeed (m/s) Thrust Req. (N)
Max Range / Best Glide 0.627 19.6 205.6 m/s (740 km/h) 112,288.3 N
Max Loiter Endurance 1.086 17.0 156.2 m/s (562 km/h) 129,659.3 N
Clean Stall Boundary 1.40 - 137.6 m/s (495 km/h) -

📈 Thrust Required & Total Drag Curve vs Airspeed: $D(V)$

Min Drag at $V = 740\ \text{km/h}$
🔍 View Raw GNU Fortran Double-Precision Solver Output 
CD0= 1.60000000E-02
OSWALD_E=  0.8500
AR=    9.2000
RHO= 3.80000000E-01
S= 4.36800000E+02
W= 2.20000000E+06
CL_MAX=  1.4000
K= 4.07045890E-02
CL_RANGE=  0.626958
CD_RANGE=  0.032000
LD_RANGE=   19.5924
V_RANGE=   205.624
CL_ENDUR=  1.085923
CD_ENDUR=  0.064000
LD_ENDUR=   16.9675
V_ENDUR=   156.241
CL_CLIMB=  0.361974
CD_CLIMB=  0.021333
LD_CLIMB=   16.9675
V_CLIMB=   270.617
V_MIN=   137.603
CD_VMIN=  0.095781
LD_VMIN=   14.6167
SENSITIVITY_START
 8.00000000E-03,     27.7079
 8.24242424E-03,     27.2974
 8.48484848E-03,     26.9046
 8.72727273E-03,     26.5283
 8.96969697E-03,     26.1673
 9.21212121E-03,     25.8207
 9.45454545E-03,     25.4875
 9.69696970E-03,     25.1669
 9.93939394E-03,     24.8581
 1.01818182E-02,     24.5604
 1.04242424E-02,     24.2731
 1.06666667E-02,     23.9957
 1.09090909E-02,     23.7276
 1.11515152E-02,     23.4683
 1.13939394E-02,     23.2173
 1.16363636E-02,     22.9742
 1.18787879E-02,     22.7385
 1.21212121E-02,     22.5100
 1.23636364E-02,     22.2882
 1.26060606E-02,     22.0729
 1.28484848E-02,     21.8636
 1.30909091E-02,     21.6602
 1.33333333E-02,     21.4624
 1.35757576E-02,     21.2699
 1.38181818E-02,     21.0825
 1.40606061E-02,     20.9000
 1.43030303E-02,     20.7221
 1.45454545E-02,     20.5487
 1.47878788E-02,     20.3796
 1.50303030E-02,     20.2146
 1.52727273E-02,     20.0535
 1.55151515E-02,     19.8962
 1.57575758E-02,     19.7426
 1.60000000E-02,     19.5924
 1.62424242E-02,     19.4457
 1.64848485E-02,     19.3022
 1.67272727E-02,     19.1618
 1.69696970E-02,     19.0244
 1.72121212E-02,     18.8900
 1.74545455E-02,     18.7583
 1.76969697E-02,     18.6294
 1.79393939E-02,     18.5031
 1.81818182E-02,     18.3793
 1.84242424E-02,     18.2580
 1.86666667E-02,     18.1391
 1.89090909E-02,     18.0224
 1.91515152E-02,     17.9080
 1.93939394E-02,     17.7957
 1.96363636E-02,     17.6855
 1.98787879E-02,     17.5773
 2.01212121E-02,     17.4711
 2.03636364E-02,     17.3668
 2.06060606E-02,     17.2644
 2.08484848E-02,     17.1637
 2.10909091E-02,     17.0648
 2.13333333E-02,     16.9675
 2.15757576E-02,     16.8720
 2.18181818E-02,     16.7780
 2.20606061E-02,     16.6855
 2.23030303E-02,     16.5946
 2.25454545E-02,     16.5051
 2.27878788E-02,     16.4171
 2.30303030E-02,     16.3305
 2.32727273E-02,     16.2452
 2.35151515E-02,     16.1612
 2.37575758E-02,     16.0786
 2.40000000E-02,     15.9972
 2.42424242E-02,     15.9170
 2.44848485E-02,     15.8380
 2.47272727E-02,     15.7601
 2.49696970E-02,     15.6835
 2.52121212E-02,     15.6079
 2.54545455E-02,     15.5334
 2.56969697E-02,     15.4599
 2.59393939E-02,     15.3875
 2.61818182E-02,     15.3161
 2.64242424E-02,     15.2457
 2.66666667E-02,     15.1762
 2.69090909E-02,     15.1077
 2.71515152E-02,     15.0401
 2.73939394E-02,     14.9734
 2.76363636E-02,     14.9076
 2.78787879E-02,     14.8426
 2.81212121E-02,     14.7785
 2.83636364E-02,     14.7152
 2.86060606E-02,     14.6528
 2.88484848E-02,     14.5911
 2.90909091E-02,     14.5301
 2.93333333E-02,     14.4700
 2.95757576E-02,     14.4105
 2.98181818E-02,     14.3518
 3.00606061E-02,     14.2939
 3.03030303E-02,     14.2366
 3.05454545E-02,     14.1800
 3.07878788E-02,     14.1240
 3.10303030E-02,     14.0687
 3.12727273E-02,     14.0141
 3.15151515E-02,     13.9601
 3.17575758E-02,     13.9067
 3.20000000E-02,     13.8539
SENSITIVITY_END
💾 Download .f90 Code

📘 Calculation Methodology: Maximum Aerodynamic Efficiency (L/D)max

Mathematical Model & Theory

The maximum lift-to-drag ratio $(L/D)_{max}$ occurs where parasite drag equals induced drag ($C_{D,0} = C_{D,i}$), defining the optimum cruise condition and minimum glide angle:

$$C_{L,opt} = \sqrt{\pi e AR C_{D,0}}, \quad \left(\frac{L}{D}\right)_{max} = \frac{1}{2}\sqrt{\frac{\pi e AR}{C_{D,0}}}$$
$$\gamma_{min} = \arctan\left(\frac{1}{(L/D)_{max}}\right)$$

Assumptions

  • Parabolic drag polar without shock wave separation.
  • Subsonic attached flow.

Academic References

  1. McCormick, B. W.: Aerodynamics, Aeronautics & Flight Mechanics, Wiley.
  2. Hoerner, S. F.: Fluid-Dynamic Drag.

Worked Engineering Example

Problem Statement:
A glider has $AR = 18.0$, $e = 0.92$, $C_{D,0} = 0.014$. Determine $(L/D)_{max}$ and optimal $C_L$.

Step-by-step Solution:
1. $C_{L,opt} = \sqrt{\pi \times 0.92 \times 18.0 \times 0.014} \approx 0.853$.
2. $(L/D)_{max} = 0.5 \times \sqrt{\pi \times 0.92 \times 18.0 / 0.014} \approx 30.48$.
Final Result:
Maximum efficiency is $(L/D)_{max} = \mathbf{30.48}$ at $C_L = \mathbf{0.853}$.