Cruise performance
The cruise problem
Cruise performance answers: how far, how fast, how much fuel. Key speeds are maximum range speed (best specific range, the tangent from the origin to the power-required curve) and maximum endurance speed (minimum power required, lower speed). For a jet, specific range is best near the speed for maximum lift-to-drag ratio, adjusted for wind. A tailwind favours a slower cruise speed; a headwind favours a faster one. Long-range cruise (LRC) trades a little speed for a useful fuel saving.
Altitude, temperature and wind
As altitude increases, true airspeed for a given Mach number increases, but engine thrust falls. The optimum cruise altitude balances these; too high and the aircraft cannot hold speed, too low and fuel burn is high. Temperature above ISA reduces thrust and increases fuel flow. A trap is the crossover altitude where a climb at constant indicated airspeed changes to constant Mach. Another trap is the wind effect: a headwind reduces ground speed and specific range, so the range in still air overestimates actual range.
Worked example and rule of thumb
An aircraft burns 2,400 kg/h at a true airspeed of 440 kt, so specific range is 440/2,400 = 0.183 nm/kg. With a 40 kt headwind, ground speed is 400 kt, so specific range falls to 400/2,400 = 0.167 nm/kg, about 9% worse. With 8,000 kg of usable fuel, still-air range is 8,000 × 0.183 = 1,464 nm, but into the headwind it is 8,000 × 0.167 = 1,336 nm. Rule of thumb: a 10% change in ground speed changes range by about 10%.