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Aerospace
Breguet jet cruise range
Range of a jet in quasi-steady cruise at constant speed, thrust-specific fuel consumption and lift-to-drag ratio in still air, from the initial and final weights.
- Ref
- AER-31
- Rev
- v1
- Field
- Aerospace
- Result
- R [m]
Fuel burn reduces the weight, so range is found by integrating. For a jet with thrust equal to drag, the fuel weight flow is cT·T = cT·W/(L/D), and dR = V dt gives R = (V/cT)(L/D) ln(Wi/Wf) for constant V, cT and L/D. The weight flow cT is fuel weight flow per unit thrust, in 1/s; multiply mass-based TSFC in kg/(N·s) by g₀. It assumes still air and quasi-steady flight.
Range of a jet in quasi-steady cruise at constant speed, thrust-specific fuel consumption and lift-to-drag ratio in still air, from the initial and final weights. cT is fuel weight flow divided by thrust, in 1/s; multiply mass-based TSFC in kg/(N·s) by g0 to get it. Wi ≥ Wf > 0.
Calculator
- Fuel burned, Wi − Wf20,000 N
- Fuel fraction, (Wi − Wf)/Wi0.1667
- Range in kilometres3,039 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 3,038.7 km on 20,000 N of fuel, which is 16.67 % of the initial weight.
- Because of the logarithm, each extra newton of fuel buys slightly more range than the last when burned from a heavier aircraft, so range grows faster than linearly with fuel fraction.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Wf Final weight | 50,000 to 120,000 N | 0 | 1.459e7 | 1.459e7 | +10% | −52.3 % |
| Wi Initial weight | 100,000 to 200,000 N | 0 | 1.155e7 | 1.155e7 | +10% | +52.3 % |
| cT Weight-flow TSFC | 5e-5 to 5e-4 1/s | 1,094,000 | 1.094e7 | 9,845,000 | +10% | −9.09 % |
| L/D Lift-to-drag ratio | 5 to 30 | 1,013,000 | 6,077,000 | 5,064,000 | +10% | +10 % |
| V Cruise speed | 100 to 300 m/s | 1,519,000 | 4,558,000 | 3,039,000 | +10% | +10 % |
Sweep of Final weight
| Final weight (N) | Cruise range (m) |
|---|---|
| 50,000 | 1.459e7 |
| 58,750 | 1.19e7 |
| 67,500 | 9,589,000 |
| 76,250 | 7,558,000 |
| 85,000 | 5,747,000 |
| 93,750 | 4,114,000 |
| 102,500 | 2,627,000 |
| 111,300 | 1,262,000 |
| 120,000 | 0 |
Sweep one variable
Variables and how each one contributes
Cruise range
What the equation gives you. Everything else feeds it.
Cruise speed
The cruise speed, in m/s. Raises the range in direct proportion. Raising it by 10 % (to 220) moves the result by +10 %, from 3,039,000 to 3,343,000 m.
Lift-to-drag ratio
The lift-to-drag ratio in cruise. Raises the range in direct proportion. Raising it by 10 % (to 16.5) moves the result by +10 %, from 3,039,000 to 3,343,000 m.
Weight-flow TSFC
The weight-flow thrust-specific fuel consumption, in 1/s. Lowers the range in inverse proportion. Raising it by 10 % (to 1.98×10−4) moves the result by −9.09 %, from 3,039,000 to 2,762,000 m.
Initial weight
The initial weight at the start of cruise, in N. Raises the range through the logarithm of the weight ratio. Raising it by 10 % (to 132,000) moves the result by +52.3 %, from 3,039,000 to 4,627,000 m.
Final weight
The final weight at the end of cruise, in N. A lower final weight means more fuel burned and a longer range. Raising it by 10 % (to 110,000) moves the result by −52.3 %, from 3,039,000 to 1,450,000 m.
Worked example with the values above
- Weight ratio: Wi/Wf = 120,000 / 100,000 = 1.2; ln = 0.182322.
- Efficiency term: V(L/D)/cT = 200 × 15 / 1.8×10−4 = 1.666667×107 m.
- R = 1.666667×107 × 0.182322 = 3,038,693 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