I would treat your body as a pinned support (your feet), rotating about a point. You know your body weight and your center of gravity is the point in your lower back that is 55% of your overall height (measuring from your feet upwards).

Using that, you can get the resultant loads on your toes (pivot point) and your hands.

For instance, I am 190 lbs and 6' (72") tall. My center of gravity is going to be 39.6" from my feet.

Free body diagram is below:

|------------|----------|

Toes 39.6 COG 32.4 Arms

The toes are the pivot point.

Using equations of equilibrium, Ftoes + Farms - Body weight = 0

So, FToes + Farms = 190 lbs

Using a sum of moments about the toes, Farms x 72 - Body weight x 39.6 = 0

Therefore, Farms = 104.5 lbs (ie, your arms are taking 104.5 lbs of your body weight).

One hp = 180 lbs x 181 ft/min = 32580 ft-lbs/min

My arms are probably close to 26" long. Let's assume that I do one complete pushup every 3 seconds. Therefore, I will be moving 104.5 lbs through 26" of travel every 3 seconds (we will assume that you freefall on the downward motion).

26" is 2.1666 ft. We do that 20 times per minute, so total travel will be 43.333'.

So, you'll be moving 104.5 lbs x 43.3 ft/min, or 4528.3 ft-lbs/min.

A ratio of 4528.3/32580 gives 0.14.

Ergo, you will require .14 hp to sustain 20 pushups per minute, in my case. Substitute your own numbers as needed.