Glossary term
Breguet Range Equation
Cruise range model relating speed, fuel consumption, lift-to-drag ratio and fuel weight ratio for aircraft mission screening.
Definition
modelThe Breguet range equation is an aircraft cruise range model that relates range to speed, fuel consumption, lift-to-drag ratio and initial-to-final weight ratio.
For a jet-aircraft cruise segment with approximately constant speed, thrust-specific fuel consumption and lift-to-drag ratio, the Breguet range equation estimates ideal still-air range from a logarithmic fuel-weight term. It is a segment screening model, not a flight plan. Climb, descent, wind, reserves, step climbs, speed schedule, engine rating, installation effects, alternate routing and operational constraints must be added separately.
The Breguet range equation estimates the ideal cruise range of an aircraft segment from speed, fuel consumption, aerodynamic efficiency and weight ratio. A common jet-aircraft screening form is:
where R is range, V is true airspeed, c is a weight-specific thrust fuel consumption parameter in consistent units, L/D is lift-to-drag ratio, and W_i/W_f is the initial-to-final weight ratio for the cruise segment.
The logarithm is important. Range does not increase linearly with fuel because fuel also contributes to the initial weight that must be carried. A larger fuel fraction helps, but its marginal benefit depends on speed, fuel consumption, aerodynamic efficiency and the mission segment.
Engineering Role
The Breguet range equation is useful for early aircraft mission screening, reserve sensitivity, fuel-fraction trade studies and sanity checks on performance claims. It connects propulsion efficiency, aerodynamic drag and fuel planning in one compact model.
It is not a dispatch calculation. A real mission must include climb, descent, taxi, alternate, holding, reserve, wind, routing, step climb, temperature deviation, air-traffic constraints, payload, unusable fuel, engine deterioration and the approved performance basis.
The equation is also sensitive to units. If c is in \text{s}^{-1}, V/c has units of length. If fuel consumption is given in other forms, such as \text{kg/(N s)}, \text{lb/(lbf h)} or power-specific fuel consumption, the equation must be converted before use.
Worked Example: Cruise Range and Operational Derating
A preliminary cruise segment uses:
| Parameter | Value |
|---|---|
| True airspeed, V | 230\ \text{m/s} |
| Weight-specific fuel consumption, c | 1.8\times10^{-4}\ \text{s}^{-1} |
| Lift-to-drag ratio, L/D | 16 |
| Initial-to-final weight ratio, W_i/W_f | 1.22 |
| Operational derating for reserve, routing and wind | 12\% |
| Route distance to screen | 3400\ \text{km} |
First compute the logarithmic fuel-weight term:
Substitute:
Therefore:
The initial fuel fraction implied by the weight ratio is:
or about 18.0\% of initial cruise-segment weight, before considering reserves and non-cruise fuel.
Apply the operational derating:
Margin against the route distance is:
Engineering comment: the ideal Breguet value looks comfortable, but the usable margin is much smaller after operational derating. A mission release would still need wind, alternate, holding, temperature, climb, descent, payload, engine deterioration, fuel policy and route constraints.
Distinction from Related Terms
The Breguet range equation is not thrust-specific fuel consumption. Fuel consumption is one input to the model. Its units and operating condition must match the range equation.
The Breguet range equation is not specific excess power. Specific excess power describes climb and acceleration energy rate at a condition; Breguet range describes ideal cruise distance over a fuel-burning segment.
The Breguet range equation is not the rocket equation. Both use logarithmic mass or weight ratios, but aircraft range depends on aerodynamic lift-to-drag ratio and propulsion fuel consumption, while rocket delta-v depends on exhaust velocity and mass ratio.
The Breguet range equation is not a flight plan. It omits reserves, winds, routing, climb, descent, speed schedules, air-traffic constraints and regulatory requirements unless they are added outside the equation.
Validation and Common Mistakes
A defensible Breguet calculation states the segment, speed reference, altitude, Mach number, L/D basis, fuel consumption basis, installed or uninstalled engine data, weight ratio, reserve treatment, wind treatment, unit convention and uncertainty.
Common mistakes include:
- using ground speed instead of true airspeed inside the still-air equation;
- mixing fuel consumption units without conversion;
- using sea-level or static fuel consumption for cruise;
- applying one L/D value across climb, cruise, descent and off-design Mach number;
- treating the ideal range as usable mission range without reserves or wind;
- forgetting that \ln(W_i/W_f) grows slowly as fuel fraction increases;
- comparing Breguet range values without stating payload, reserve policy and segment boundaries.