Research notes:
physics of drum strokes
http://acoustics.org/pressroom/httpdocs/155th/dahl.htm
~60-75N peak force
http://www.sofiadahl.net/pdf/DahletalForumAcusticum2011.pdf
peak forces ranging from 1.8 to 106.8 N
strike velocity ranging from 1 to 10m/s
(interesting f~v² relationship between velocity and force)
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.416.3669&rep=rep1&type=pdf
this one’s good. they stuck a piezo crystal and accelerometer on the end of a drumstick
mmm data
So, the drum stick is moving at 10m/s and decelerates to 0 in 3ms. That’s 3333m/s²
If the contact force is 100N, that means the effective mass of (drumstick+residual effect of drummer’s arm) is 100/3333 = 0.03kg - which is in the same ballpark as the weight of an actual drumstick (about 50g)
That’s good. It means the drummer’s arm is not pressing on the drum - it’s just a fast moving bit of wood, free to rebound. All I have to do is accelerate 30g of wood to 10m/s as quickly/easily as possible.
So now I can make a quick spreadsheet so I can figure out what sort of solenoid I’m going to need. Let’s assume a 50% duty cycle - ie, every other 8th of a 180bpm beat. That’s 80ms. Assuming 1/2 that time is needed to make the hit (the other half for returning from it), I need a solenoid with…
7.5N, 20cm throw.
or, to make the hit in only 4ms
75N, 2cm throw.
These are outside the limits of physics and my budget respectively.
Someone check my sums, but I think there has to be a lever to get the required acceleration.