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Breguet Endurance Equation (Jet)

Endurance is how long a jet aircraft can stay in the air on a given amount of fuel. This equation is similar to the range equation but focuses on time instead of distance. It depends on fuel consumption, aerodynamic efficiency, and the weight ratio. A jet maximises endurance by flying slowly at high L/D, unlike range which prefers a faster speed. For example, a surveillance aircraft loitering over a target wants maximum endurance, not maximum range.

Written by the Vorzep Team

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Breguet Endurance Equation (Jet) Calculator

Solve for endurance (time aloft), TSFC, L/D or aircraft weights, with step-by-step math, a loiter-pattern diagram, a weight-vs-time curve and live endurance charts.

E = (1 / c) · (L/D) · ln(Wi / Wf)
Aircraft presets (illustrative values)
Solve for
Fuel & time metrics
Sensitivity: effect of +1% in each input on endurance
ENDURANCE (E)
—h
Step-by-step solution
Loiter diagram (constant L/D, aircraft gets lighter as fuel burns)
Aircraft weight vs time
Endurance curves

The Breguet endurance equation

Endurance is the time an aircraft can stay airborne on a given fuel load. For a jet at constant L/D, the fuel flow is proportional to drag, so time aloft depends on aerodynamic efficiency (L/D), engine efficiency (TSFC, c) and the logarithm of the weight ratio. Unlike range, endurance does not depend on speed, so the best endurance comes from flying at the speed that gives maximum L/D (minimum drag).

E = (1 / c) · (L/D) · ln(Wi / Wf)
Wi = Wf · exp( E·c / (L/D) )
Wf = Wi · exp( −E·c / (L/D) )
SymbolMeaningUnits used here
EEndurance (time aloft)hours
cTSFC: fuel flow per unit thrust (same number as lb/h per lbf)1/h
L/DLift-to-drag ratiodimensionless
Wi, WfWeight at start and end of loiter (Wf = Wi − fuel burned)kg

Worked example

c = 0.6 1/h, L/D = 17, Wi = 70,000 kg, Wf = 55,000 kg
E = (1 / 0.6) × 17 × ln(1.2727) = 1.6667 × 17 × 0.2412
E ≈ 6.83 hours

FAQ

Why doesn't speed appear in the equation?

Endurance is time, not distance. At constant L/D, thrust equals drag, so fuel flow depends on weight and L/D, not on how fast the aircraft moves. Speed only matters for range.

How do I get maximum endurance?

Fly at the speed that gives (L/D)max, which for a jet is the minimum-drag speed. This is slower than the speed for best range, which is why holding patterns use lower speeds.

Does it include climb, descent and reserves?

No. It models steady loiter only. Subtract fuel for taxi, climb, descent and reserves to find the weight Wf to use.

Variables

Symbol Quantity Unit
E Endurance s
c Specific fuel consumption 1/s
L/D Lift-to-drag ratio
W_i Initial weight N
W_f Final weight N

What it means

The Breguet endurance equation is analogous to the range equation but for loiter or endurance. It shows that endurance is inversely proportional to TSFC and directly proportional to L/D and the logarithm of the weight ratio. This is important for surveillance, patrolling, and search‑and‑rescue missions. Unlike range, endurance does not depend on speed (assuming constant L/D and c). In design, endurance is maximised by minimising fuel consumption and improving aerodynamic efficiency. The equation is used to estimate time on station and to size fuel tanks for loiter missions. Understanding endurance is crucial for mission planning and for aircraft with high loiter requirements.

Worked example

Breguet Endurance (Jet) – Two Additional Examples

Real‑World
Scenario: A jet has c = 2×10⁻⁵ s⁻¹, L/D = 17, Wᵢ = 800,000, W_f = 600,000. Find endurance.
ParameterValue
c2×10⁻⁵ s⁻¹
L/D17
Wᵢ/W_f800000/600000 = 1.333
1E = (1/c) × (L/D) × ln(Wᵢ/W_f) = (1/2e-5) × 17 × 0.2877 = 50,000 × 17 × 0.2877 = 244,500 s = 67.9 hours
Result 67.9 hr ✓ Very long
Scenario: c = 1.8×10⁻⁵, L/D = 18, Wᵢ = 900,000, W_f = 650,000. Find endurance.
ParameterValue
c1.8×10⁻⁵
L/D18
ln(Wᵢ/W_f)ln(1.3846) = 0.3254
1E = (1/1.8e-5) × 18 × 0.3254 = 55,555 × 18 × 0.3254 = 325,400 s = 90.4 hours
Result 90.4 hr ✓ Exceptional
Key insight: Endurance = (1/c)·(L/D)·ln(Wᵢ/W_f) – high L/D and low TSFC maximise time aloft.

Common mistakes

  • Breguet endurance equation (jet): E = (1/c) · (L/D) · ln(W_i/W_f).
  • c: TSFC in 1/s – endurance in seconds.
  • L/D: At maximum endurance condition (usually at minimum drag).
  • Weights: As above.
  • Endurance vs. range: Endurance maximises time aloft, range maximises distance.

Applications

The Breguet endurance equation for jet aircraft, E = (1/c)·(L/D)·ln(W_i/W_f), gives the time an aircraft can remain in flight (endurance). Endurance is critical for loitering missions, surveillance, and maritime patrol. It shows that endurance depends on engine efficiency (c), aerodynamic efficiency (L/D), and the weight ratio. Engineers use this equation to design aircraft for long‑duration missions, to select engines with low specific fuel consumption, and to plan fuel for holding patterns. Unlike range, endurance is maximised by flying at the speed for minimum drag (which may differ from best range speed). By understanding endurance, aerospace engineers can optimise designs for time‑on‑station requirements.

  • Design of surveillance, reconnaissance, and patrol aircraft
  • Holding pattern fuel planning and loiter performance
  • Engine selection for minimum fuel consumption at loiter
  • Optimisation of flight conditions for maximum time aloft
  • Mission effectiveness analysis for UAVs and manned aircraft

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  • Published July 10, 2026
  • Last updated October 22, 2026