An Automatic Pilot to Make Perfect Loops Varying only Gflyup through the Loop as an Anticipatory System: from Theory to its Implementation

In this paper I define an automatic pilot to make a perfect loop, that is a circumference, making the centripetal acceleration, Gflyup, to vary through the loop and maintaining a constant motor impulse, although it varies a little bit with altitude. I prove that this automatic pilot could be implemented easily in the flight computer of an F16, F15, F18, or in any other aircraft with a GonSetRate \gt 0.62 g/s, which includes low power propeller aerobatic aircrafts. Although its mathematical formulation is very simple, the implementation in the flight computer implies the development of a very accurate numerical simulator to estimate the future values of V and ??, angle of trajectory, based on which is calculated the actual GonSetRate. It is in this sense that this automatic pilot can be seen as an anticipatory system. I prove by simulation it would not be enough and safe to show to the pilot the correct Gflyup through the loop due to the pilot reaction time, the flight computer sample time and the aircraft reaction time..