Propeller Range (Breguet)
Breguet range for a propeller aircraft: range grows with propeller efficiency, lift-to-drag ratio and the fuel-weight fraction.
Formula
Variables
Example
η=0.8, high L/D and fuel fraction extend range substantially
How it works
This relation estimates how far a propeller aircraft can fly before its weight drops from fuel burn, assuming it flies efficiently and steadily. It comes from balancing thrust against drag while accounting for the fact that a propeller converts engine power to useful thrust with efficiency \(\eta\), and that a higher lift-to-drag ratio means less thrust is needed to support the airplane in level flight. The logarithmic term appears because each small amount of fuel burned changes the aircraft’s weight, so range depends on the cumulative effect of losing weight from \(W_0\) to \(W_1\), not just the total fuel amount linearly.
When to use it
Use this for long-range propeller-driven aircraft when estimating cruise range from aircraft performance data, especially in preliminary design or mission analysis. It is most appropriate for steady, level cruise under roughly constant \(L/D\), propeller efficiency, and fuel consumption conditions.
Worked example, step by step
Given: \(\eta = 0.82\), \(c = 0.50\,\text{hr}^{-1}\), \(L/D = 14\), \(W_0 = 12{,}000\,\text{kg}\), \(W_1 = 9{,}000\,\text{kg}\) Step 1: Compute the weight ratio. \(W_0/W_1 = 12{,}000/9{,}000 = 1.3333\) Step 2: Take the natural logarithm. \(\ln(1.3333) \approx 0.2877\) Step 3: Compute the performance factor. \(\eta/c = 0.82/0.50 = 1.64\) Step 4: Multiply by \(L/D\). \((\eta/c)(L/D) = 1.64 \times 14 = 22.96\) Step 5: Compute range. \(R = 22.96 \times 0.2877 \approx 6.61\) If \(c\) is in \(\text{hr}^{-1}\) and cruise speed is built into the form used, the result is a range factor; in the common mission-analysis form this corresponds to about \(6.61\) hours-equivalent of cruise distance scaling, which would be converted using the appropriate cruise speed. Numerically, the key result is \(R \propto 6.61\) for these inputs.
Common mistakes to avoid
- Using fuel mass directly instead of the weight ratio \(W_0/W_1\); the formula needs the logarithm of the ratio, not fuel consumed alone
- Confusing propeller efficiency \(\eta\) with engine efficiency or using a value greater than 1
- Plugging in inconsistent units for specific fuel consumption \(c\) and expecting the range to come out correctly without checking the unit system
Did You Know?
For propeller aircraft, best range is flown at the speed for maximum L/D — unlike jets, which fly faster.
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