= 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 been found in studies with shot-putters that the resultant velocity increases—and, thus, acceleration and force increase—when the shot is released at an angle of less than 45°.6 To maximize horizontal velocity and minimize "hang time," then, the same goes for you when you "release" yourself as a projectile from the ground. This has to do with air resistance. The higher you launch yourself, the more you are actually held up, to some degree, by air resistance. This is exactly what we don't want. What we're aiming for is to cover as much ground as possible with the least amount of time in the air. You'll have to experiment with this on your own to find what is most efficient for you.
WORK AND POWER
From our discussion of impulse, you know that the impulse is the product of force and time. We can also measure another variable—the distance an object moves when a force is applied to it. The product of this distance and the force is known as work and the equation is:
Work = force x distance
Whenever you step and slide and cover a certain amount of ground, work is being done. Whenever you throw a kick, your muscles contract, producing forces that pull on your tendons and bones. This causes your leg to move through space. Your leg covers a specific distance. That's work.
Crucial to the biomechanics of the martial arts is the rate at which you can do work. We call this power. In layman's terms, we often interchange this with the word force and we will do so in this book, but in "biomechanicspeak," they are two very different things. The equation for power is as follows:
Power, as you can imagine, is very important to us. It doesn't really help us to throw a kick if it's so slow it never reaches the target. Just think of Bruce Lee and how fast he moved his limbs through space. He was power personified.
KINETIC ENERGY
In the realm of biomechanics, energy is defined as the capacity to do work. As you may recall from high school physics, mechanical energy comes in two forms: 1) kinetic energy, which is energy of motion and 2) potential energy, which is energy due to position.
When an object moves, its motion gives it an ability to do work. The movement gives it kinetic energy. If you hit a heavy bag, your moving fist has kinetic energy, the ability to displace the bag. Kinetic energy is determined by an object's mass and velocity. The mathematical equation is:
Kinetic energy = ½ (mass x velocity2)
This equation makes measuring kinetic energy much easier than measuring force, as we often know the mass and velocity of objects. Measuring acceleration is not always so easy.7
In the case of hitting the heavy bag, the equation makes sense. The faster you hit the bag, the more capacity you have for moving it. And the more body weight—or mass—you put behind your punch, the more you'll displace it.
POTENTIAL ENERGY: THE ENERGY OF GOOD FORM
In scientific terms, potential energy is often defined as energy of position. How appropriate! Throughout Bruce Lee's writings, you'll see reference after reference to good form, alignment, position. In the following chapters, we'll be spending a lot of time describing the proper stance, and the mechanics of each technique. Some of this is strategic, of course, but the underlying principle is that we are trying to create the most potential energy without sacrificing efficiency or safety (i.e. mobility, stability, etc.)
There are two types of potential energy that we'll be discussing repeatedly. The first is gravitational potential energy. Elevating objects against gravity requires work. So once an object is elevated, it has additional potential energy. Just as we explained in the case of projectile motion, we want to use gravity to our advantage as often as we can. The equation for this is:
Gravitational potential energy = mass x gravitational acceleration x height
So, in our example of the straight lead and projectile motion, when you push off, you temporarily elevate yourself above the ground. In that airborne position, you have more gravitational potential energy to direct in your punch. This is essentially what Jack Dempsey described as the "falling step." By "falling," you allow gravity to take you downward and into the punch. In his book, Championship Fighting, Dempsey uses the analogy of a sled to explain gravitational potential energy:
"In a sense, the boy and his sled are falling objects. But the slope of the hill prevents them from falling straight down. Their fall is deflected to the angle of the hill. The direction of their weight-in-motion is on a slant. And when they reach the level plain at the bottom of the hill, they will continue to slide for a while. However, the direction of their slide on the plain—the direction of their weight-in-motion—will be straight out, at a right angle to the straight-down pull of gravity."8
We'll
