Breguet Range Equation
Maximum range of a jet aircraft from speed, efficiency, L/D and fuel fraction.
Formula
Variables
Example
A higher lift-to-drag ratio and a lighter engine both directly stretch an aircraft’s range.
How it works
This equation estimates how far a jet can fly on a given amount of fuel by combining speed, engine fuel efficiency, aerodynamic efficiency, and the change in aircraft weight as fuel is burned. It comes from balancing fuel flow against the aircraft’s need for thrust: at steady cruise, the jet must keep producing enough thrust to overcome drag, so better lift-to-drag ratio, lower fuel consumption, and a larger starting-to-ending weight ratio all increase the distance flown. The logarithm appears because the airplane gets lighter as fuel is used, so each additional kilogram of fuel does not contribute equally to range.
When to use it
Use this for long-range cruise estimates of jet aircraft, especially when comparing how changes in speed, aerodynamics, or fuel load affect maximum range. It is most useful in aircraft performance analysis, preliminary design, and mission planning under steady-level flight assumptions.
Worked example, step by step
Given: V = 230 m/s c = 0.60 1/hr L/D = 18 W_i = 70,000 kg W_f = 50,000 kg Step 1: Find the weight ratio W_i / W_f = 70,000 / 50,000 = 1.4 Step 2: Take the natural log ln(1.4) = 0.3365 Step 3: Compute V/c V / c = 230 / 0.60 = 383.33 m Step 4: Multiply by L/D (383.33)(18) = 6900.0 m Step 5: Multiply by ln(W_i/W_f) R = 6900.0 × 0.3365 = 2321.9 m Final answer: R ≈ 2.32 × 10^3 m = 2.32 km (Note: if c is given in 1/hr and V in m/s, units must be made consistent before using the formula; in practice, aircraft problems often use c in 1/s or convert speed to match.)
Common mistakes to avoid
- Using the fuel mass directly instead of the logarithm of the initial-to-final weight ratio
- Mixing units for speed and specific fuel consumption, which gives a meaningless range
- Applying the equation to climb, descent, or highly non-steady flight instead of steady cruise
Did You Know?
The Breguet range equation shows why airliners cruise high and light — and why efficient engines extend range so much.
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