Aviation Calcs

Breguet range

Breguet Range and Endurance Calculator

The classical Breguet equations for cruise range and endurance at constant lift-to-drag ratio. For a jet, range is (V / ct) (L/D) ln(Wi/Wf) and endurance is (1 / ct) (L/D) ln(Wi/Wf). For a propeller airplane, range is (η / c) (L/D) ln(Wi/Wf) with a unit identity that yields nautical miles from an SFC in lb/(hp·h).

Airplane type

Any consistent weight unit is fine — only the ratio Wi/Wf matters.

A TSFC of 0.5 lb/(lbf·h) is 0.5 per hour. Typical cruise values are often in the 0.5–0.7 /h band for older turbojets and lower for high-bypass turbofans — use the engine’s book.

Range

—

Advertisement
Ad slot — 728×90 desktop / 320×100 mobile

Jet Breguet equations

For a jet (or turbofan) cruising at constant true airspeed and constant thrust-specific fuel consumption ct,

R = (V / ct) (L/D) ln(Wi / Wf)
E = (1 / ct) (L/D) ln(Wi / Wf)

With V in knots and ct in 1/h (lb of fuel per lbf of thrust per hour), R is in nautical miles and E is in hours. A worked check: 450 kt, ct = 0.5 /h, L/D = 16, Wi/Wf = 1.2, gives R ≈ 2,625 nm and E ≈ 5.83 h.

Propeller form

For a propeller airplane the fuel flow is referred to power, not thrust. With propulsive efficiency η and a power-specific fuel consumption c in lb/(hp·h),

Rnmi = 325.87 (η / c) (L/D) ln(Wi / Wf)

The factor 325.87 is 1 hp·h expressed as nautical-mile-pounds (550 × 3,600 ft·lbf / 6,076.12 ft). Endurance at a stated constant speed is then range divided by that speed. The best-endurance condition for a propeller airplane is not, in general, the same speed as best range; this page reports the constant-speed identity you entered.

Sources

Breguet; Anderson, Introduction to Flight (Breguet range and endurance); NASA Glenn Beginner’s Guide; FAA Pilot’s Handbook of Aeronautical Knowledge (range and endurance, qualitative). For trip fuel with VFR/IFR reserves, use the fuel planner.

Frequently asked questions

What weights should I use for Wi and Wf?

Wi is the weight at the start of the cruise segment you are analysing, Wf the weight at the end of that segment. Taxi, climb, descent, and legally required reserves are usually kept out of this ratio and added separately.

Does wind appear in the Breguet equation?

Not in the still-air form used here. A headwind reduces the ground range relative to the air-range this page reports; a tailwind increases it. Endurance (time) is unchanged by a steady wind.

Why is jet endurance independent of speed in the formula?

Because, at constant TSFC and constant L/D, fuel flow is proportional to thrust, and thrust equals drag, which equals weight / (L/D). Speed cancels in the endurance integral. Range then brings speed back in as R = V E. In reality TSFC and L/D both vary with speed, so there is still a best-range Mach.