Have you ever thought your airline ticket cost too much?

Suppose you're flying from San Francisco (SFO) to New York (NYC). The plane (Airbus 320) carries 189 passengers and has 6 crew members who each make $20 per hour. Assume a minimal model where the only costs of operating the flight are paying the salary of the crew, and paying for fuel. Further, assume that the all the engine does is fight the drag force. If each ticket costs $300, jet fuel costs $0.75 per liter, and the crew is paid for the number of complete hours they work, what percent of your ticket price goes toward the airline's profit?

Assumptions and Details

  • The Airbus has a drag coefficient CDC_D of 13π.\frac{1}{3\pi}.
  • The density of air is ρ=1.275 kg/m3\rho=1.275\text{ kg/m}^3.
  • The plane flies at 511 mph (228 m/s)511\text{ mph } (228\text{ m/s}) from start to finish.
  • The distance from NYC to SFO is 4148 km.4148\text{ km}.
  • The energy efficiency of the jet engines is η=16%\eta=16\%.
  • Approximate the Airbus as a cylinder of diameter 6 m.6\text{ m}.
  • The energy density of the jet fuel is 45×106 J/kg.45\times 10^6\text{ J/kg}.
  • The density of the fuel is 804 kg/m3804\text{ kg/m}^3.
  • The crew is paid for each full hour they work, i.e. if they work 5.2 hrs5.2\text{ hrs} they are paid for 5.5.
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