The Speed of the Overhand Throw

Humans are the only species capable of throwing overhand fast and on target. (Location 2881)

when we unwind, the arm rotates like a spring in the opposite direction with incredible speed. In professional baseball pitchers, this rotation can be nine thousand degrees per second, the fastest motion recorded in the human body. (Location 2906)

Definition of 1 degrees per second = 1/360 Hz. Degrees per second is a variant of the angular velocity unit. One hertz frequency is equal to turning a full circle (360°) in one second , 1 Hz = 360 deg / s

http://conversion.org/frequency/degrees-per-second/

$9000/360 = 25hz$

One hertz is equal to 60 rpm, since there are 60 seconds in a minute

https://www.google.com/search?q=hertz+to+rpm&oq=hertz+to+r&aqs=chrome.2.69i57j0i20i263i512l2j0i512l7.7993j0j7&sourceid=chrome&ie=UTF-8

$25 * 60 = 1500rpm$

$R * RPM = Miles/Minute$

What is $R$(revolution of the wheel -- circumference) in the human arm?

$c = 2pir$

The typical wingspan to height ratio is right around 1. Those with ratios greater than 1 would be considered to have long arms in relation to their body.

so one of my arms is roughly 40% of my height of 6ft = $72 * .4 =28.8 in$

$28.8 * 2 * pi = 180.95in$

$180.95in = 0.00285590278mi$

so $.0028 * 1500 = 4.2 miles/min$

$4.2 * 60 = 252mph$

252 miles per hour feels like a lot, I may have fucked up my maths somewhere.

Another cause of the 100-mph ceiling owes to this: the amount of torque needed to throw in excess of the century mark is greater than the amount of force the ulnar collateral ligament (the elbow ligament Strasburg tore) can withstand before giving out, according to tests Fleisig has done on cadavers. When a pitcher cocks his arm, where it is turned back to the point where the palm is facing toward the sky, there's about 100 Newton-meters of torque on the arm, which subjects the arm to the same amount of stress as if the pitcher had a 60-pound weight hanging from his hand in that position, Fleisig says.

From that cocked position, the arm snaps forward to its release point in 0.03 seconds, and at its peak speed, an elite pitcher's arm rotates at upward of 8500 degrees per second. If that single instant of speed could be maintained, then a pitcher's arm would spin around 24 times in a second.

https://www.popularmechanics.com/adventure/sports/a6063/how-the-105-mph-fastball-tests-the-limits-of-the-human-body/

Yes, a human can throw a baseball at around 110 MPH. The pitcher's ability to throw a fast ball is based on their genetics and muscle strength. There are many pitchers who can reach 105 MPH or even faster, but the record for the fastest pitch ever thrown is held by an anonymous American pitcher who hit 108 MPH in 2011.

https://www.metroleague.org/what-is-the-fastest-a-human-can-throw-a-baseball/

…As Alexander points out, you can attain these high speeds using leverage. A typical fast bowler's arm is around a meter long from the shoulder joint to the cricket ball, and the rules demand the arm be kept straight during bowling. Dividing the speed by the circumference of the circle traced by the arm give the rotation speed as one rotation in 140ms, which isn't superhumanly fast. It's certainly faster than I can manage, but then I'm not paid millions of pounds per year to play cricket!

https://physics.stackexchange.com/questions/33326/can-human-hand-move-at-a-speed-rate-like-this-baseball-pitch-or-is-it-just-the-s