Friday, September 10, 2010

Kinetic energy of flight 175

The kinetic energy (KE) of a moving object is given by the formula

E = 1/2 m * v2

Where, in the case of flight UA 175:

  • m is the mass of the plane: That is, empty mass plus fuel load plus passengers, their baggage, and additional cargo. AA 11 was a Boeing 767-222, which has an operating emtpy weight of 80,130kg and a maximum take-off weight of 142,880kg. Maxium fuel capacity is 63.216l (see Specs at ZAP16.com). Maximum range is 7,300 km. Flight UA171 had 168 passenger seats, but only 56 passengers (33% capacity), plus 9 crew members. 65 people, weighing on average 70kg, have a mass of 4,550kg. For each, luggage, food, drinks and other supplies of 20kg may be added, or 1,300kg. It was scheduled to fly from Boston to Los Angeles, a distance of about 46% of its maximum range. Wikipedia, quoting NIST, states that it carried about 38,000l of fuel - about 60% of maximum fuel capacity, by the time of impact. Jet fuel has a specific weight of about 0.8 kg/l, so 38,000l fuel is about 30,000kg. The total mass of the plabe was thus at least:
    m = 80,130kg + (4,550+1,300)kg + 30,000kg = 115,980kg
    (empty weight + passengers + fuel)
  • v is the velocity of the plane at impact, which was estimated by NIST as 545mph or 243m/s

Using these estimates, the kinetic energy of flight AA11 works out as

Ekin = 1/2 * 115,980kg * (243m/s)2 = 3.42 * 109J

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