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The trick is to find the right racing line that best balances the tradeoff between the distance flown and speed of the aircraft.

Much like a formula car race, the rules specify what aircraft can be flown. Most pilots fly a modified Zivko Edge 540 (Version 2 or 3), manufactured by Zivko Aeronautics in Oklahoma. The Edge 540 is a 300 hp single place aerobatic aircraft. All aircraft use the same model engine and propeller, and no modifications may be made to them. Some modifications may be made to the aircraft aerodynamics, induction, and cooling systems.

Unlike most other air races, such as the Reno race, the Red Bull races are designed to be aerobatic, with rapid maneuvering and acceleration levels up to 10 g. For a pilot, it’s not obvious how to minimize the time it takes to complete a run through such a track. Turning as tightly as possible near each gate can reduce the total distance traveled, but a tight turn requires a high load factor (lift divided by weight), which in turn produces greater drag and thus slows the airplane. Larger radius turns produce less drag, and so don’t slow the aircraft, but increase the distance traveled. The trick is to find the right racing line that best balances the tradeoff between the distance flown and speed of the aircraft.

OPTIMAL CONTROL THEORY The problem of how to fly an aircraft around a racetrack as fast as possible is an example of an optimal control problem. The history of optimal control theory stretches back more than 300 years to the solution of the brachistochrone problem (to find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip from one point to another in the least time) but interest in optimal control theory in engineering, especially aerospace engineering, ballooned in the 1960s, fueled in part by the Cold War and the space race, and enabled by the advent of modern digital computing. To formulate an optimal control problem, one needs three things: a model of the dynamics of the system of interest, the performance objective to be minimized, and any constraints on the problem. For the air race problem, we use a simplified dynamic model of the aircraft flight mechanics that captures the performance of the airplane and, of course, the performance objective is to minimize the time around the track.

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AEROASTRO 2015-2016

MIT AeroAstro annual magazine 2015-2016Aeroastro 2015 16  

Annual magazine review of MIT Aeronautics and Astronautics Department research and educational initiatives.

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