**NB: Edited the text below to make it clearer and add the effect on AMI.**

I have no experience with throwing tops. How does the top's curvature affect its play -- not just in theory, but in practice? (By "curvature" here, I mean the curvature of the top's silhouette in a plane containing its "axis" of symmetry.)

For example, let *z* track "height" along the axis, and *r*(*z*), the perpendicular "radius" from the axis to the silhouette at height *z*. Then the silhouette is just a graph of *r*(*z*) vs. *z*. If *T*(*z*) tracks string tension at the top as the string leaves height *z*, then the driving axial torque *Q*_{d}(*z*) applied to the top grows with radius:

*Q*_{d}(*z*) = *T*(*z*) *r*(*z*)

Hence the silhouette shapes the driving torque curve *Q*_{d}(*z*), which in turn limits release speed. The aerodynamic braking torque *Q*_{a}(*z*) opposing the driving torque also grows with *r*(*z*), but at an even faster rate. Hence the net axial torque (ignoring tip friction) at height *z* during spin-up is

*Q*(*z*) = *Q*_{d}(*z*) - *Q*_{a}(*r*(*z*)) = *T*(*z*) *R*(*z*) - *Q*_{a}(*z*)

To accelerate the top to release speed, this net torque has to work against the top's axial moment of inertia (AMI), which depends on the shape of *r*(*z*) and grows very roughly with the square of mean radius.

When integrated over the appropriate height range, are any of the net effects noticeable in play?