My last post, Magnitude of Force to Change Direction or Stop a Moving Object, appealed to readers for technical information concerning the amount of force required to deflect a moving object (e.g. a punch). That appeal is still current, for the time being.
I'm working on Okazaki and Stricevic's 'Principles of Motion' in The Textbook of Modern Karate, that they say is helpful to understand in order to deal with a punch a kick. The second principle is:
To stop an object's motion requires a force greater than the one that set the object in motion. This has special relevance to blocking techniques when the objective is to arrest [(stop)] an attack.
An exploration of the concept of blocking techniques in the martial arts requires a chapter, so, I will only focus on the above PoM.
Firstly, Okazaki and Stricevic leave out one vital piece of information when explaining their second PoM. Force has magnitude, direction, and point of application. The direction of a force applied by a blocking technique has to be applied in the opposite direction to motion of the object/opponent's attacking body part in order to stop its motion. That is an important but often overlooked detail when many distinguish blocking techniques into two types: hard-soft, arresting-deflection, blocks-deflection, direct-indirect, etc.
Secondly, magnitude. Okazaki and Stricevic suggest more force is required to stop a moving object/opponent's attacking body part, than was needed to start it in motion. I initially thought that this might not be true; that only an equal an amount of force as that needed to initiate motion in an object was required to be applied in order to stop that object. In fact, I thought that if you applied more force to an object in motion than was applied to initiate its motion that it would cause the object to move in the direction of the greater force, e.g. backward. What do you think? Sounds reasonable.
As is so often the case in developing the theory in my book, I didn't rely on my assumptions/opinions and went in search of an authoritative answer to this question. I didn't find one per se, however, I was able to develop one from an equation for how much force is required to start an object in motion.
Force can be calculated by the equation change in momentum divided by time. Momentum is calculated as the product of mass and velocity. Force is measured in Newtons (N). What force is required to get a 10 kg object moving at 12 m/s in 5s?
Momentum at start = 10 x 0 = 0 kg m/s
Momentum at end = 10 x 12 = 120 kg m/s
Change in momentum = 120 - 0 = 120 kg m/s
Force = change in momentum/time = 120/5 = 24 N
How much force is needed to stop the above object in motion nearly instantaneously, say in 1s?
Momentum at start = 10 x 12 = 120 kg m/s
Momentum at end = 10 x 0 = 0 kg m/s
Change in momentum = 0 - 120 = -120 kg m/s
Force = change in momentum/time = -120/1 = -120 N
The time was chosen for an instantaneous stopping action. The negative value reflects force applied in the opposite direction. Five times as much force as initiated the motion of that object/attack is required to to be applied to stop that moving object/attack in that time frame.
This equation is also used to describe Impulse and explain how increasing the time that force is applied decreases the average amount of force required to stop an object. E.g. pulling your hands back as you catch a moving ball.
Now, working on how much force is required to deflect a moving object. Anyone?