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.

Parameter	Value
c	2×10⁻⁵ s⁻¹
L/D	17
Wᵢ/W_f	800000/600000 = 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.

Parameter	Value
c	1.8×10⁻⁵
L/D	18
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

Breguet Endurance Equation (Jet)