Thats a new use for a bowling ball! Actually what happens is that the moment of inertias go up. You can write a big hairy equation that defines a steady state flat spin and in it is included the moments of inertia of the airplane about the 3 body axes. Increasing his yaw and pitching moment of inertia by one bowling ball, along with a move aft shift in CG, put him over the edge.

He would have been better off balancing with a higher weight closer to the CG. The moment of inertia is a direct function of mass and the square of the length. The link below gives the methods of determining several common moments of inertia. The fuselage is like the first one. For an irregular body like a fuselage with motor, person, construction and bowling ball you would do each piece separately.


http://www.physics.uoguelph.ca/tutor...e.inertia.html