In my previous post I discussed gathering some data from the Airbus A319. I want to look into this a bit more, and consider some of the forces involved. Starting with takeoff and looking here I find that the standard maximum takeoff weight of the aircraft is 64,000 kilograms and that its range at that takeoff weight is 3391 kilometers. There are several variants of the aircraft but I'll assume that the figures cited are correct. There were no empty seats on the plane but Wolfram Alpha tells me that the distance from New York Laguardia to Chicago O'hare is 1180 kilometers so I assume that a partial fuel load was carried. The maximum fuel capacity was found here to be 24,210 liters or 24.21 m^3, which, at 804 kg/m^3, has a mass of 19,465 kg. I'm going to speculate that the aircraft carried 2/3 of its maximum fuel capacity, which should meet FAA regulations and United's standard operating procedures, for a weight savings of 6,488 kilograms.
So we're contemplating an aircraft with a mass of about 57,512 kg. and an average "mid roll" acceleration of about 3.4 m/s^2 by my data. So, as usual F=m*a, and the force the engines are applying is 195,500 Nt or about 44,000 pounds of force. This is, for the two engine aircraft, 22,000 pounds per engine. I've checked various sites and determined that the specific aircraft was likely the A319-131 model with IAE 2500 series engines with thrust rated in the 25,000 pound force range. Thus, the data is clearly on the right track. I do so love it when that happens.
How about stopping? The aircraft from Chicago O'hare to John Wayne Airport in Orange County was also an Airbus A319, presumably another "dash 131" as they say in aviation. Since it was also full and traveled a considerably larger distance, I'll assume that it started at 64,000 kilograms. Here I find that my flight took 3 hours, 42 minutes, or 3.7 hours. I find here that, as an estimate, the A319 burns maybe 5,000 pounds mass or about 2,270 kilograms of fuel per hour so I estimate that the aircraft burned 3.7*2,270 kilograms from its 64,000 starting weight to land weighing 55,600 kilograms.
Touching down at 90 knots (I suspect this is actually a bit slow) or 46.3 m/s, the airplane has a kinetic energy of 0.5*55600*46.4^2 or 59,850,000 joules. It stops braking at 10 knots or 5.14 m/s and then has about 734,000 joules of kinetic energy (non-intuitively, not that far from my Land Rover LR3 HSE at 55 m.p.h.). The brakes have dissipated (that is, turned into heat) about 59,000,000 joules in about 27 seconds. This equates to a rate of energy dissipation of 59,000,000/27 or 2.19 megawatts. They are actually assisted in this disspation by burning jet fuel in a process called "reverse thrust" but in the end, that's the kinetic energy that is dissipated. Of course, braking is an extraordinarily efficient process for turning kinetic into thermal energy, slowing the plane down by reverse thrust is much less efficient but, in the end, it's all turned into dispersed thermal energy.
Next post: Integrate again for length of takeoff and landing roll.
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