keflex

The Pokedex entry says that “Machamp can launch 1000 punches within 2 seconds.”

Machamp’s height is 5’03”, which is 1.6002m. Assuming that’s from head to foot, then, by inspecting pictures of it, its arm is about 1m long.

A punch is a full extension and retraction of the arm, meaning one punch must make Machamp’s fist travel 2m.

Given four arms, a single arm must punch 250 times per second to make a total of 1000 punches. 250*2m = 500m/s, the speed a single arm must average whilst punching to achieve that rate.

As for acceleration, the punch must average 500m/s over a distance of 1m, starting at 0m/s. Assuming a constant acceleration, the final velocity of a punch would have to be 1000m/s.

0 to 1000m/s in 0.008 of a second. That’s an acceleration of 125 000m/s/s.

Now for force. Since F = m*a and we know the fist’s acceleration (a), we’ll find the fist’s mass. m = density*volume, so its density and volume must be found. Idealizing the fist as a cube with sides 1/5 its arm’s length, its volume is 0.008m^3. Machamp’s mass is 130kg and it’s volume - approximated as a cylinder with height 1.6002m and radius 0.6m - is ~1.81kg/m^3. Thus, the fist’s mass is 0.008*1.81 = ~0.015kg.

That gives a force of 0.015*125 000 = 1875N.

Assuming that Machamp’s arm is a uniform material and idealising with a cross section similar to its fist - 0.04m^2 - that would make the compressive strength required to endure the force of acceleration 1875/0.04 = 46875kPa = ~47MPa.

The ultimate compressive strength of structural grade concrete is less than 21 MPa.