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In order to be able to reasonably approximate the forces on
the
C-130 a few assumptions must be made. For the purposes of this I am
going to assume that the mass of the plane does not change during the
take-off. This is untrue as the airplane is likely burning multiple
gallons of AN-8 every minute, each one weighing 6.8 pounds. However the
duration of the take-off run is fairly short, and relative to the mass
of the entire plane very little mass is actually being lost. I also
assume that the plane operates without air resistance. This is not the
case since the plane is very large and moving through air, there will
be a some amount of resistance. Comparitively speaking, the air
resistance should be small compared to the friction between the plane
and the runway, and the work required to move the mass of the plane and
payload. Lastly I will assume that the normal force on the plane
decreases steadily, due to the increasing lift from the wings. In order to estimate fuel burn, I make the assumption that the engines are ideal, burning all fuel and converting it all into thrust. The engines are quite loud, and very hot, so we are certain this is not exactly the case. I will use the following numbers for calculations: Take off speed: 185 km/h Weight of the plane + Cargo: 70,000 kg Co-efficient of friction between the ski and ski-way: .04 Take-off distance: 5 km Energy in 1 gallon of AN-8(Almost same thing as JP-8): 42.8 MJ/kg Next |