I was not saying the flaps would be used to initiate the loop but in synchrony with the elevator itself. I have used flaps and the elevator together on model aircraft for loops and it worked ok. The flaps seem to help smooth the curve until the plane is upside down and returning back towards...
I think the domain on theta needs to be limited after the reflection to [3pi/2,pi/2] or [0,pi] depending on how the graph is to be visualized. One quadrant is needed for the line entering the loop and the second quadrant representing the loop itself.
I looked up rose curves and polar equations for r^2 =a^2sin2theta. If the equation for that that curve was modified slightly and reflected on polar graph paper, that curve looks similar to your sketch. The line of the curve heading downward could represent the plane's angle of attack and...
Which control surfaces are changing at the beginning of the loop? I can see the loop occur if a change in the tail sections elevator moves upward and occurs at a rate that prevents the plane from stalling. Is the plane's flaps involved as well to generate the loop?
i need help with this question too, But I believe a lot of our science involving time began as qualitative and resulted in quantitative concepts that are now proven mathematically and depend on time. Time is qualitative from the standpoint that we have not figured out how to move things (i.e...