Breguet Range Equation
Breguet Range Equation
The Breguet range equation is the foundational tool aircraft designers use to estimate how far an airplane can fly on a given fuel load, tying together propulsion efficiency (specific fuel consumption), aerodynamic efficiency (lift-to-drag ratio), and how much of the aircraft's weight is burned off as fuel during cruise. Because range depends logarithmically on the weight ratio but linearly on L/D and inversely on fuel consumption, aircraft designers get more mileage improving aerodynamic efficiency or engine economy than by simply carrying more fuel, since extra fuel itself adds weight that must also be carried and burned.
The Breguet range equation is R = (V/c)*(L/D)*ln(W1/W2). where V_cruise is cruise true airspeed, c_sfc is the engine's specific fuel consumption (fuel weight burned per unit thrust per unit time), LD_ratio is the cruise lift-to-drag ratio, and W_1 and W_2 are the aircraft weight (or mass) at the start and end of cruise.
Inputs
V_cruise := 230 m/s=230 m/s
c_sfc := 0.00015 s^-1=1.5e-04 Hz
LD_ratio := 15=15
W_1 := 80000 kg=80000 kg
W_2 := 65000 kg=65000 kg
The V/c term is effectively how far the aircraft travels per unit fuel weight burned, the L/D ratio scales that by aerodynamic efficiency, and the log of the weight ratio captures how the aircraft gets progressively lighter (and thus more fuel-efficient) as fuel burns off.
R_range := (V_cruise/c_sfc)·LD_ratio·ln(W_1/W_2)=4.78e+06 m
Results
A range on the order of several thousand kilometres from this weight fraction and L/D is consistent with a medium-to-long-haul transport aircraft. Because range depends on the natural log of the weight ratio, carrying more fuel gives strongly diminishing returns on range — this is precisely why long-range aircraft are so sensitive to structural weight and why every percent of L/D improvement or SFC reduction is aggressively pursued by designers.
Assumptions & limitations
- Steady, level cruise flight at constant L/D and specific fuel consumption.
- Does not include climb, descent, taxi, or reserve fuel segments.
- Assumes no wind (still-air range); headwind/tailwind would adjust the result.
- c (specific fuel consumption) treated as constant over the whole cruise segment.