Breguet Range Equation (Jet) Calculator
Solve for range, speed, fuel consumption, L/D or aircraft weights, with step-by-step math, a flight-profile diagram, fuel-weight bar and live range curves.
The Breguet range equation
For a jet in steady cruise at constant speed and constant lift-to-drag ratio, range depends on three things: aerodynamic efficiency (L/D), engine efficiency (thrust-specific fuel consumption, c) and the logarithm of the weight ratio, which captures how much fuel is burned. Because the aircraft gets lighter as fuel is burned, the relationship is logarithmic rather than linear: doubling fuel does not double range.
Wi = Wf · exp( R·c / (V·L/D) )
Wf = Wi · exp( −R·c / (V·L/D) )
| Symbol | Meaning | Units used here |
|---|---|---|
| R | Cruise range | km |
| V | True airspeed in cruise | km/h |
| c | TSFC: fuel flow per unit thrust (kg/h per kgf, same number as lb/h per lbf) | 1/h |
| L/D | Lift-to-drag ratio | dimensionless |
| Wi, Wf | Weight at start and end of cruise (Wf = Wi − fuel burned) | kg |
Worked example
R = (850 / 0.6) × 17 × ln(1.2727) = 1416.7 × 17 × 0.2412
R ≈ 5,809 km
FAQ
Why is range logarithmic in the weight ratio?
Fuel burned early in the flight must also carry the fuel burned later. Integrating dW/W over the weight drop gives ln(Wi/Wf), so each extra kilogram of fuel buys less range than the one before.
What does "cruise-climb" mean here?
Holding V and L/D constant while weight falls requires the aircraft to climb gradually. Real airliners step-climb or fly at fixed altitude, so the equation is an excellent first estimate but not a flight-plan tool.
Does it include climb, descent and reserves?
No. It models cruise only. Subtract fuel for taxi, climb, descent, diversion and reserves to find the weight Wf to use for a mission.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| R | Range | m |
| V | Cruise speed | m/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 range equation is a fundamental performance formula for jet‑propelled aircraft, relating range to propulsion efficiency and aerodynamic efficiency. It is derived from the integration of the energy balance during cruise, assuming constant lift‑to‑drag ratio and thrust specific fuel consumption (TSFC). The equation shows that range increases with higher L/D, higher cruise speed (for a given TSFC), and higher weight fraction (more fuel). It is used in conceptual design to estimate the range capability of an aircraft and to trade off fuel weight versus payload. The equation is also applied to mission analysis and to compare different aircraft designs. Understanding the Breguet equation is essential for aerospace engineers to optimise aircraft for long‑range missions.
Worked example
Breguet Range Equation (Jet) – Two Examples
Real‑World| Parameter | Value |
|---|---|
| V | 230 m/s |
| c | 2×10⁻⁵ s⁻¹ |
| L/D | 17 |
| Wᵢ | 800,000 N |
| W_f | 600,000 N |
| Parameter | Value |
|---|---|
| V | 240 |
| c | 1.8×10⁻⁵ |
| L/D | 18 |
| Wᵢ/W_f | 900000/650000 = 1.3846 |
Common mistakes
- Breguet range equation (jet): R = (V/c) · (L/D) · ln(W_i/W_f).
- Specific fuel consumption c: TSFC (thrust specific fuel consumption) – in 1/s or kg/(N·s).
- L/D: Lift‑to‑drag ratio – use the cruise value.
- Weights: Initial and final weights – both in same units (N).
- V/c: Units: (m/s) / (1/s) = m – gives range in metres.
Applications
The Breguet range equation for jet aircraft, R = (V/c)·(L/D)·ln(W_i/W_f), relates range to cruise speed, fuel consumption, aerodynamic efficiency, and weight fraction. It is a fundamental equation for aircraft design and mission analysis. Engineers use it to size fuel tanks, to estimate the payload‑range capability, and to compare the efficiency of different propulsion systems. The equation shows that range is maximised by flying at the optimum L/D and using an efficient engine (low TSFC). It guides design trade‑offs between weight, drag, and fuel consumption. By applying the Breguet equation, aerospace engineers can design aircraft that meet range requirements while minimising fuel and structural weight.
- Preliminary design and sizing of commercial and military aircraft
- Payload‑range trade‑off studies
- Optimisation of cruise speed and altitude
- Engine selection and SFC targets
- Mission analysis and performance benchmarking
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