[SveinJo]

The formula is not hard (physics), but finding the correct numbers to insert into the formula is not easy (laboratory work).

The formula for the top repeat rate is that it is proportional to the square root of <the spring stiffness> divided by <the angular momentum of the key>. The angular momentum depends mostly on the pad size and the distance from the pivot.

Usually, the best spring stiffness is found by trial and error (engineering).

 

[SveinJo]

When I get up to a very fast speed, like 325 bpm in 8th notes, I find that my scales going downward come out fine and is easy. Now on the other hand, when I try and play going up the scales are not even at all and in many cases some notes dont even speak.

This just means that your fingers are stronger than the springs (going down, your fingers push the keys down; going up, the springs push the keys up).

An instrument such as the recorder (no springs or pads, just your fingers) will play just as fast in both directions.

 

[SveinJo]

what about the length of the levers? the distance from the hinge to the finger touch in relationship with the hinge to the pad cup? all those angles and lever/pivot distances?

All these distances and masses are part of the calculation of the angular momentum.

A visual demonstration of angular momentum: Have you ever seen an ice skater making a slow pirouette with the arms stretched out? And suddenly spinning much faster when they pull their arms close to the body? What they are doing is reducing the angular momentum and since the rotational energy is the same, they rotate faster.