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Aerospace
Breguet propeller cruise range
Range of a propeller aircraft in quasi-steady level cruise with constant propeller efficiency, power-specific fuel consumption and lift-to-drag ratio.
- Ref
- AER-32
- Rev
- v1
- Field
- Aerospace
- Result
- R [m]
For a propeller aircraft the fuel weight flow is cP times the shaft power, and the power is thrust times speed over propeller efficiency, so the range integral gives R = (ηp/cP)(L/D) ln(Wi/Wf), independent of speed. Here cP is fuel weight flow per unit shaft power, in N/J or 1/m; multiply mass-based consumption in kg/J by g₀. Propeller efficiency, cP and L/D are held constant.
Range of a propeller aircraft in quasi-steady level cruise with constant propeller efficiency, power-specific fuel consumption and lift-to-drag ratio. cP is fuel weight flow divided by shaft power, in 1/m; multiply mass-based consumption in kg/J by g0. Wi ≥ Wf > 0. Range does not depend on speed in this model.
Calculator
- Fuel burned, Wi − Wf2,000 N
- Fuel fraction, (Wi − Wf)/Wi0.1667
- Range in kilometres2,188 km
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The aircraft flies 2,187.9 km on 2,000 N of fuel, 16.67 % of the initial weight.
- The range does not depend on cruise speed in this model, but the best L/D condition is the best-range speed for a propeller aircraft (the minimum-drag speed).
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Wf Final weight | 5,000 to 12,000 N | 0 | 1.051e7 | 1.051e7 | +10% | −52.3 % |
| Wi Initial weight | 10,000 to 20,000 N | 0 | 8,318,000 | 8,318,000 | +10% | +52.3 % |
| cP Weight-flow power-specific consumption | 3e-7 to 2e-6 1/m | 875,100 | 5,834,000 | 4,959,000 | +10% | −9.09 % |
| L/D Lift-to-drag ratio | 5 to 30 | 911,600 | 5,470,000 | 4,558,000 | +10% | +10 % |
| ηp Propeller efficiency | 0.5 to 0.95 | 1,367,000 | 2,598,000 | 1,231,000 | +10% | +10 % |
Sweep of Propeller efficiency
| Propeller efficiency | Cruise range (m) |
|---|---|
| 0.5 | 1,367,000 |
| 0.5563 | 1,521,000 |
| 0.6125 | 1,675,000 |
| 0.6687 | 1,829,000 |
| 0.725 | 1,983,000 |
| 0.7813 | 2,137,000 |
| 0.8375 | 2,290,000 |
| 0.8937 | 2,444,000 |
| 0.95 | 2,598,000 |
Sweep one variable
Variables and how each one contributes
Cruise range
What the equation gives you. Everything else feeds it.
Propeller efficiency
The propeller efficiency. Raises the range in direct proportion. Raising it by 10 % (to 0.88) moves the result by +10 %, from 2,188,000 to 2,407,000 m.
Lift-to-drag ratio
The lift-to-drag ratio in cruise. Raises the range in direct proportion. Raising it by 10 % (to 13.2) moves the result by +10 %, from 2,188,000 to 2,407,000 m.
Weight-flow power-specific consumption
The weight-flow power-specific fuel consumption, in 1/m. Lowers the range in inverse proportion. Raising it by 10 % (to 8.8×10−7) moves the result by −9.09 %, from 2,188,000 to 1,989,000 m.
Initial weight
The initial weight, in N. Raises the range through the logarithm of the weight ratio. Raising it by 10 % (to 13,200) moves the result by +52.3 %, from 2,188,000 to 3,332,000 m.
Final weight
The final weight, in N. A lower final weight means more fuel burned and a longer range. Raising it by 10 % (to 11,000) moves the result by −52.3 %, from 2,188,000 to 1,044,000 m.
Worked example with the values above
- Weight ratio: Wi/Wf = 12,000 / 10,000 = 1.2; ln = 0.182322.
- Efficiency term: ηp(L/D)/cP = 0.8 × 12 / 8×10−7 = 1.2×107 m.
- R = 1.2×107 × 0.182322 = 2,187,859 m.
Assumptions and limits
- Steady flight along a straight path at constant speed, with L/D and specific fuel consumption held constant.
- Still air, and weights taken at the start and end of the cruise segment.
Common mistakes
- Using mass-based fuel consumption directly in a weight-flow equation, which needs g₀.
- Using range formulas for a changing L/D without averaging.
- Treating a still-air glide ratio as the ratio over the ground in a headwind or tailwind.
Statistics and uncertainty
Climb, glide and Breguet results are quasi-steady estimates. Range from the Breguet equation is typically good to 5 % to 10 % for long cruise legs, and worse for short missions where climb and descent are large, or in wind, which the formulas ignore.
Where it is used
- Planning range, fuel, and glide-back or engine-out decisions.
- Comparing the efficiency of aircraft designs.
Maths you need
- Lift-to-drag ratio: L/D, the glide ratio
- Specific fuel consumption: fuel flow per unit thrust or power
- Weight fraction: the ratio of final to initial weight