Standard pitcher's arm acceleration while throwing

[Johnny101]

For a standard base ball pitch what is the range of pitcher's arm acceleration while throwing I am trying to get it with accelerometer and I am getting 80 ms-2?

 

[BobK]

Let's see. The entire arc of the arm is probably something like 2m (the entire body moves forward as well as the arm going from pointing backward to pointing forward, so 2m is a reasonable guess.

Assuming uniform acceleration (this will not actually be true, but for a back of the envelope calculation it should give us something close to the average acceleration)

We have two equations, one for the velocity, and one for distance travelled that we can solve. We write each in terms of the time it takes to make the pitch, which we call t.

v = a * t = 90mph = 40 m/s

So

(1) a * t = 40

And we know the distance traveled over time t is:

x = 1 /2 a * t^2 = 2

(2) a * t^2 = 4

Now solve the (1) for t and we get

t = 40 / a

Substitute it into (2)

a * 40^2 / a^2 = 4

40^2 / a = 4
40^2 = 4 a
1600 = 4 a
400 = a

So I get 400 m/sec^2

Bob

 

[BobK]

After doing my calculation, I did an internet search and found this article:

http://www.science20.com/science_20/science_baseball_what_fastest_pitcher_can_throw-51797

It claims the acceleration is something like 40g which is 40 * 9.8 = 392 m/s^2

So I guess I done good.

They also estimate that it takes 0.11 sec to make the picth, which is comparable to what I got (0.1 sec). And, get this, that it take 3HP over that 0.11 sec to move the ball + the body. No wonder their arms have to be packed in ice after throwing 100 pitches!

Bob

 

[BobK]

Anyone up for calculating what it takes to kick a football (= soccer ball in American) the length of the field?

Bob