How to Make the World's Longest-Spinning Top

In this video I briefly discuss how spinning tops really work and how to design them to spin for as long as possible.
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Glossary (technical jargon translation):
Statically unstable:
Small disturbances cause it to fall over when stationary
Dynamically stable:
Small disturbances won’t cause it to fall over when moving
Rotational kinetic energy:
Embodied energy due to rotational motion (RKE = ½Iω^2)
Gyroscopic stability:
Extension of newton’s first law (F=ma) to rotational motion (T=Iω ̇).
The higher the moment of inertia and angular velocity of an object, the
more torque is required to turn it.
Precession:
A special kind of motion observed when a rotating object experiences an
external torque (in this case due to the lateral displacement of the centre
of mass). The top falls ‘sideways’ in a direction perpendicular to the
applied torque. (Q=jω)
Negative feedback loop:
The further from equilibrium, the stronger the correcting force
Corrective torque:
A moment (T=Fd) turning the top upright
Critical speed:
The lowest angular velocity before the top topples
Mechanical battery:
Kinetic energy is stored and dissipates like a battery
Moment of inertia, I:
Equivalent of mass for rotation (I = ∫r^2 dm)
Angular velocity, ω:
Speed of rotation e.g. rotations per minute
Breaking torque, T:
A torque acting to slow down the rotation of the top
Analytical solution:
A solution derived with algebra
Numerical optimisation:
A best solution found with computers using recursive formulas
Viscous centrifugal pumps:
Air taken in from top/bottom and expelled as a central thin disc
“Basic” model:
An interactive formula where the inputs are spinning top variables and
the output is the predicted spin time
Summary of Fundamental problem:
Assuming final energy is approximately 0 (fair assumption), we want to maximise starting energy and minimise power loss. However both of these increase with mass, radius and angular velocity. This is a complication and means there exists an optimal mass, radius and angular velocity which is neither a minimum nor maximum.
Tops shown in this video:
W/Mg top by @pliertops (0:27)
Cu top by @billetspin (0:55)
and various of my own tops @hipertops including 2 members of the Quasar series (0:00), (1:40)