Gathering The Data
Hang a target of a known weight from the ceiling; for example, a 100 kg punching bag.
Set up a video camera with a known frames per second speed -- 30 fps is typical -- to observe the bag.
Put a backdrop behind the bag in line with the camera that has 10 centimeter stripes, alternating between white and dark gray.
Turn on the camera and punch the bag. After each punch, make sure the bag is put at rest before the next punch. Repeat this step multiple times.
Calculating The Force of the Punch
Review the film footage, advancing one frame at a time. Most digital cameras and digital video editing software allows you to advance video footage one frame at a time. Determine how far the bag moves from each punch in one frame. Repeat this for as many frames as you can, summing the distances and dividing by the number of frames used. This will give you the average distance moved per frame.
Multiply the average distance in meters moved per frame by the number of frames per second your camera records. This is the velocity the bag moves in meters per second.
Multiply meters per second by the weight of the bag. You will have calculated the total force delivered to the bag by the punch, in kilogram meters per second, which happens to be one newton.
Wrap the surface of the martial artist's hand in athletic tape, and press lightly into a sponge; the water will temporarily mark the surface of the tape. Cut the moistened part of the tape off; this will be a proxy for how much surface area struck the bag. Measure this piece of tape -- if it's 5 cm by 8 cm, for example, it has 40 cm^2 of surface area.
Divide newtons of force from step 3 by square centimeters of impact, then divide by 10,000. This yields the pressure in pascals.