Cruise Altitude Selection with Increasing Headwind
A twin-jet is cruising at FL350 with a true airspeed of 450 kt and a fuel flow of 2,400 kg/h total. The forecast shows a headwind of 60 kt at FL350, 90 kt at FL370, and 120 kt at FL390. The aircraft mass is 62,000 kg and the maximum cruise altitude at this mass is FL410. The destination is 1,800 nm away, and the crew has 9,500 kg of fuel remaining, with a required reserve of 2,300 kg. The optimum cruise altitude in still air at this mass is FL370. The crew is considering climbing to FL390 to reduce fuel burn, but the headwind increases with altitude.
1. Calculate the still-air specific range and the ground specific range at FL350, and compare with FL390 using the given winds.
Read the worked answer
At FL350, the still-air specific range is TAS divided by fuel flow: 450/2,400 = 0.1875 nm/kg. The ground speed is 450 - 60 = 390 kt, so the ground specific range is 390/2,400 = 0.1625 nm/kg. At FL390, the TAS is higher, say 460 kt, and the fuel flow is lower, say 2,200 kg/h, giving a still-air specific range of 460/2,200 = 0.2091 nm/kg. The ground speed is 460 - 120 = 340 kt, so the ground specific range is 340/2,200 = 0.1545 nm/kg. Despite the better still-air efficiency at FL390, the stronger headwind reduces the ground specific range below the FL350 value. The crew should stay at FL350 or consider FL370, where the headwind is 90 kt. At FL370 with TAS 455 kt and fuel flow 2,300 kg/h, the ground speed is 365 kt, giving 365/2,300 = 0.1587 nm/kg, still below FL350. The best ground specific range is therefore at FL350 in this wind profile.
2. Determine whether the aircraft can reach the destination with the required reserve at FL350.
Read the worked answer
At FL350, the ground speed is 390 kt. The time to fly 1,800 nm is 1,800/390 = 4.62 hours. The fuel burn at 2,400 kg/h is 4.62 x 2,400 = 11,088 kg. The fuel remaining is 9,500 kg, which is less than 11,088 kg, so the aircraft cannot reach the destination at FL350 without using reserve fuel. The shortfall is 11,088 - 9,500 = 1,588 kg, and the required reserve of 2,300 kg would be infringed. The crew must either climb to a more efficient altitude, reduce speed, or divert. At FL390, the ground speed is 340 kt, the time is 5.29 hours, and the fuel burn is 5.29 x 2,200 = 11,638 kg, which is worse. The crew should consider a lower altitude with a weaker headwind or a fuel stop, and must declare a fuel emergency if the situation deteriorates.
3. Explain how the crew should use the concept of maximum range cruise versus long-range cruise in this situation.
Read the worked answer
Maximum range cruise is the speed that gives the best specific range, usually about 1.316 times the speed for minimum drag, and it is flown when fuel is critical. Long-range cruise is a faster speed, typically 0.99 of maximum range cruise, and it gives about 99 percent of the range with a higher speed and better schedule. In this case, fuel is critical because the aircraft cannot reach the destination at the planned speed. The crew should slow to maximum range cruise to stretch the fuel, accepting a longer flight time. The AFM or performance manual gives the maximum range cruise speed for the mass and altitude. The crew should also consider the wind: if a lower altitude has a weaker headwind, the ground specific range may be better there even if the still-air specific range is worse. The decision should be based on ground specific range, not still-air specific range, and the crew should monitor fuel against the reserve continuously.