Practical Math: How to Take a Punch - Try this video version that is less than 3 minutes! (VIDEO ELECTIVES)
Taking a punch is all about transfer of momentum. The momentum from the fist hitting you will be transferred to your body unless you do something about it. A fist travels with a specific velocity, v, towards you, with a mass, m. The product of the mass and velocity (mass times velocity) is the momentum (p = mv). When the fist hits your body, it slows or stops, but the momentum from the fist approaching you needs to go somewhere (m1v1 = m2v2 here, m1 and v1 are the mass and velocity of a fist, while m2 and v2 are the mass and velocity of the target of the punch). That somewhere is typically into your tender flesh.
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Since your body is absorbing all of the momentum of a flying fist, you want to change that momentum as slowly as possible; or, more accurately, over as great a time as possible (m1Δv1 = m2Δv2 this says that the change in momentum is preserved. Since mass isn’t changing, it’s the change in velocity that’s preserved). In order to do this, you either need to make your body very soft (think additional layers of clothing), or travel with the punch.
Since you’ll rarely have the opportunity to dress for a fight, let’s focus on traveling with the punch to gradually reduce the transferred momentum.
In order to travel with a punch, it helps to figure out the direction of the punch, and to start moving the impact area of your body when the punch comes (m1Δv1= m2Δv2 since velocity has both a value and a direction, rolling with the punch means that you slowly change the velocity of the fist without getting any momentum transferred in an unexpected way). Let the punch lightly contact you, and then roll with it as the puncher follows through. If you can move initially with the speed of the punch, and then gradually slow down, the transfer of momentum will happen over a greater period of time, and the impulse will remain low.
And that’s the best way to take a punch.