is equal to the weight of the aircraft. As induced drag increases with weight, mass reduction, with improvements in engine efficiency and reductions in aerodynamic drag, has been a principal source of efficiency gains in aircraft, with a rule-of-thumb being that a 1% weight reduction corresponds to around a 0.75% reduction in fuel consumption. Flight altitude affects engine efficiency. Jet-engine efficiency increases at altitude up to the tropopause, the temperature minimum of the atmosphere; at lower temperatures, the Carnot efficiency is higher. Jet engine efficiency is also increased at high speeds, but above about Mach 0.85 the airframe aerodynamic losses increase faster. Compressibility effects: beginning at transonic speeds of around Mach 0.85, shockwaves form increasing drag. For supersonic flight, it is difficult to achieve a lift to drag ratio greater than 5, and fuel consumption is increased in proportion. However, the faster speed inherent to supersonic flight means that the higher fuel burn is counterbalanced by a shorter flight duration. Passenger airplanes averaged 4.8 L/100 km per passenger (1.4 MJ/passenger-km) (49 passenger-miles per gallon) in 1998. On average 20% of seats are left unoccupied. Jet aircraft efficiencies are improving: Between 1960 and 2000 there was a 55% overall fuel efficiency gain (if one were to exclude the inefficient and limited fleet of the DH Comet 4 and to consider the Boeing 707 as the base case). Most of the improvements in efficiency were gained in the first decade when jet craft first came into widespread commercial use. Compared to advanced piston engine airliners of the 1950s, current jet airliners are only marginally more efficient per passenger-mile. Between 1971 and 1998 the fleet-average annual improvement per available seat-kilometre was estimated at 2.4%. Concorde the supersonic transport managed about 17 passenger-miles to the Imperial gallon; similar to a business jet, but much worse than a subsonic turbofan aircraft. Airbus puts the fuel rate consumption of their A380 at less than 3 L/100 km per passenger (78 passenger-miles per US gallon). The mass of an aircraft can be reduced by using light-weight materials such as titanium, carbon fibre and other composite plastics. Expensive materials may be used, if the reduction of mass justifies the price of materials through improved fuel efficiency. The improvements achieved in fuel efficiency by mass reduction, reduces the amount of fuel that needs to be carried. This further reduces the mass of the aircraft and therefore enables further gains