Jeet Kune Do. Teri Tom
long do we apply force to an object to maximize force production?
Let's use the equation for Newton's Second Law and for acceleration, we'll use the average acceleration. This is the initial velocity (vj) (which in the case of our punch is when the hand starts moving towards the target) minus the final velocity (vf) (the velocity at impact) divided by the time duration of force application:
Remember Newton's Second Law is expressed as:
Force = mass x acceleration
If we substitute average acceleration into the equation, we have:
Multiply both sides of the equation by the time interval:
Force x time interval = mass x (final velocity — initial velocity)
This product of force and the time interval is what we call impulse and is expressed as:
Impulse = Ft
What does this have to do with JKD? In Bruce Lee's words, this is what we'd call the equation for "snappiness." You'll see quite a few references to snappiness in Lee's writings, as he was distinguishing between a forceful punch and a push. If your hand stays in contact with the target too long, it becomes a mere push.
This is why: from the equation, you can see that force is inversely related to time. The more time spent during force application, the less force is required to cause a change in momentum. When you throw a punch, at some point, you are going to have to stop and retract the hand. When you stop your fist, this is a change in momentum. The time that it takes for you to change that momentum is inversely related to the amount of force required to make that change.
A good example would be that of the shoulder roll versus running straight into a punch. To decrease the amount of force coming your way, you roll with a punch. You move in the same direction with the punch to increase the amount of time you're in contact with it. This lessens the impact. On the other hand, say you run into a punch. It takes a lot less time, and therefore, a lot more force, to stop you in your tracks. I wouldn't recommend trying this one out.
Another example would be the difference between training gloves and fight gloves. Training gloves have a lot more padding. This lessens the impact of punches because it takes more time to for your fist to connect with its target. Fight gloves, have less padding and therefore require less time to change the momentum of your fist, and less impact time means a greater force is required to change that momentum.
In general, Bruce favored a punching depth of about 2—4 inches past the target. This was just enough to penetrate the target without devolving into a push:
"All punches should end with a snap several inches behind the target. Thus, you punch through the opponent yet end the punch with a snap." 4
This goes for all punches and not just straight ones. Even with angular punches like hooks and uppercuts, you move straight through the target for only a few inches before leaving the target with a tearing motion as your hand continues to travel along its angular path.
PROJECTILE MOTION
In discussions of martial arts technique, you hear a lot about torque, force, mass, acceleration, and stability. But you never hear about projectile motion. Yet this is a concept central to most JKD techniques, and it has to do with footwork. A projectile is any object that has been thrown or dropped into the air and once in the air, the only force acting on it, barring significant air resistance, is gravity. A lot of the time in JKD, the projectile is you! Every time you push step or push off, you are momentarily—even if it's only for a millisecond—in the air. Your toes might still be barely touching the ground, but the majority of your body weight is airborne. Every time you throw a straight punch, and almost any time you throw any punch, your body itself becomes a projectile giving you more force production by allowing you to throw your body weight into it.
So let's look a little closer at projectile motion. Once you've thrown an object—in this case, your body—into the air, that's it, you cannot change directions in midair. The only force acting on you at this point is gravity, which we know to have an acceleration of 9.81 m/s/s downward or —9.81 m/s/s.
I won't bore you with the derivation of the equations for projectile motion, but there is an excellent explanation of it in McGinnis' Biomechanics of Sport and Exercise for those of you who are interested.5
For our purposes, just knowing what the equation is for vertical velocity of a projectile should be enough:
Where:
Now, if you look at this equation carefully, it should look familiar. Remember from algebra class:
y = mx + b
It's that trusty parabolic equation where —9.8 m/s/s is the slope of the line. Again, we won't go into all the mathematical details here. Just know that whenever you push off or launch yourself into the air, even if it's just for a fraction of a second, your body is following a parabolic pathway. And at any point on that path, you have both a vertical and horizontal velocity. The horizontal displacements for each time interval, by the way, are equal, creating that symmetrical parabolic path.
What does all of this have to do with JKD? Well, first we mentioned footwork. There are three things that determine what kind of parabola we have: time spent airborne, peak height, and horizontal distance covered (also known as horizontal displacement). In his discussions of footwork, Bruce stresses the importance of small steps. The reason? You'll be able to shift direction much faster. Yes, there's even an equation for this:
Horizontal displacement = initial horizontal velocity x flight time
So you can see the bigger your step, the longer time you spend in the air. And remember once you've launched yourself into the air, you are at the mercy of gravity. You cannot change your direction until you come back down. So the less push off you give yourself, the less time you'll spend in the air, and the less distance you'll cover—small steps. There will be times, of course, when the situation will call for you to cover greater distance with your footwork, but in general, keep those steps small and controlled.
Projectile motion is not only used to explain shiftiness, though. It's a law that is central to punching power. As you'll see in our discussion of the punches, when you push off with the back leg, you always want to hit the target before your front foot hits the ground. The reason is easily explained by projectile motion. Remember, force is a product of mass and acceleration. Acceleration is a change in velocity. At any point on the projectile parabola, you have both a vertical and horizontal velocity, and you are accelerating towards the ground. If you wait until you stop and hit the ground, you will no longer be accelerating towards the target. You no longer have a velocity in the direction of the target and you've missed out on using all the body weight that gravity was pulling on. How are you going to produce force for that punch now?
If you do hit the target before you and your front foot land, you take advantage of throwing all your body weight into the punch. You have both horizontal velocity and gravity on your side. You're accelerating, baby.
With footwork, with or without an accompanying punch, it's best to minimize your time in flight so that you will stay close to the ground and mobile. So how high should you push off? It's