If a key would be massless, a linear speed to velocity conversion seems to be a good construction. But a real key has a mass, that has to be accelerated to reach a given velocity. And acceleration against inertia needs a force F=m*a. That could be an explanation, why I use and prefer my s-shaped curve to the default linear velocity mapping:

Such a shaped curve makes the key virtually "heavier" in the ppp-mp range, where inertia is low, and virtually lighter in the mf-fff range, where F=m*a is stronger. As a result the keyboard response "feels" linearly balanced.

A question could be, whether an s-shaped curve can be derived/calculated somehow from the measured key-speed function and F=m*a. Any ideas or show-stoppers welcome ...

I had an idea to estimate the real speed a pressed key has and how it is related to the midi velocity.

All I needed was a flat piece of wood, a coin and Pianoteq's midi-eventmonitor.

With this wooden "tool" I can press three white keys at the same time. Because a ten eurocent coin is 1.93 mm thick, the note-on event of the key below, here c3, happens a little earlier than note-on of d3. The distance of 1.93 mm divided by this eventtime-difference is a rough estimation of the speed of key c3.

Example:
30729 ms Note On C3 veloc: 75
30736 ms Note On D3

ds = 1.93mm
dt = 7ms
keyspeed = ds/dt = 1.93mm/7ms = 0.276 m/s

This velocity 75 and keyspeed 0.276 m/s are representing one point in the graph. I set a linear trendline in libreoffice, but many other curves would fit, so I'm not sure it is really a linear relationship in the Kawai. I have to test a few more keys because those rubberbubble-contacts are prone for high tolerances.

From midi velocity 60 upwards the method is getting unprecisely. The highest resolution in PTQ's midi-eventmonitor is 1 ms and the faster the keys are pressed, the nearer dt comes to this limit.

Thanks for your interest