In the combative arts, it seems logical that punching harder would lead to increased effectiveness. But is this skill trainable, i.e. can things be done that lead to increased punching power?  The authors of “Increasing the Impact Force of the Rear Hand Punch” think so.  They (Turner, Baker, & Miller; Strength and Conditioning Journal, Vol. 33, #6, Dec 2011) identified 5 trainable qualities that influence the impact force of the Rear Hand Punch (RHP):

1. Increase rear leg drive
2. Following the step forward, land with a rigid leg
3. Increase the stretch-shortening cycle (SSC) of the trunk musculature
4. Increase the velocity of the punch
5. Increase the effective mass

To train #1, they recommend using exercises such as the squat, deadlift, & clean, as well as plyometrics. The second attribute (landing with a rigid leg) is meant to increase braking and transmission of forces. Their recommendation is to use plyometrics that emphasize the landing element.  To train the SSC of the trunk, medicine ball training can help with the development of rotational power.  To increase the punch velocity, ballistic exercises such as plyometrics including medicine ball throws and Olympic lifts are recommended.  The key here is ensuring acceleration thru the entire movement. And to increase the effective mass, it is strongly suggested to use pad and bag work that incorporates impact (vs. non-contact sparring or techniques in the air).  
One thing the authors mention is that the punch is initiated by stepping forward.  While this sequence may lead to increased punching power, it is potentially slower and more
telegraphed than when the hand/weapon initiates the movement.  This “true timing” (hand/weapon, then body, then feet) from classical fencing is the ultimate goal in a weapons based system, since the resulting
effectiveness relies on the speed of the movement and impact/piercing of the
weapon as opposed to maximum force.  The opponent can be struck before they’ve even realized that a motion has been initiated, let alone before they have time to respond. 
A subtle point, but one well worth exploring further if you’re a weapons-based player.  
So, back to the punch.  Bottom line is that to increase your punching force, work some fundamental and explosive movements into your training regimen.  Squat, Deadlift,
Clean, Snatch, Plyometrics of many kinds, KBs, Medicine Balls, and Sand Bags would all work great.  Be creative, and as always, have fun.

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