Lag,
I am not trying to pick on you as I love your insights. BUT…
If mass times acceleration equals force than the force that you refer to above equals ZERO. Constant velocity equals zero acceleration. So no matter how you state it, when acceleration equals zero so does force. You can multiply any amount of mass you want by zero acceleration and still will be left with zero force.
The equation clearly points out that it is maximizing acceleration which should be of primary concern and not velocity. Try this little thought experiment. What has more energy a brick that sits stationary atop a 20 story building or a brick that has fallen off of a 20 story building just before it strikes the ground? Even though the hurtling brick is whizzing along at a frightening velocity and the other is sitting motionless on the roof they both have exactly the same amount of energy. Well not really. The falling brick actually has considerably less energy because air resistance throughout its motion has removed a considerable amount before it will ever reach the ground! The roof ledge is actually “feeling” more force from the stationary brick than the sidewalk will when it is struck by the now “weakened” falling one. This is why people who don’t understand science cannot really understand what is going on in the golf swing. It is “logical” to most people to surmise that the falling brick has more energy, because they cannot differentiate between different types of of the same energy. In this case the stationary brick has more TOTAL energy than the falling one. The one on the roof is all gravitational potential energy and the falling one, (at the exact moment just prior to impact) is all kinetic energy.
But, Tom, you can’t “hit” a golf ball while not in motion! That is absolutely correct. You simply have to shift your perspective to understand what is really IDEAL. The purpose of any method of swinging the golf club, regardless of your golfing religion or methodology, is essentially the attempt to TRANSFER energy into a golf ball in such a way that it will be propelled towards a target as efficiently and accurately as possible.
Why are all of the theories that maximize velocity wrong? First understand that in order to reach maximum velocity, acceleration will also have to be zero. Huh? Well if you are still accelerating you have not reached maximum velocity. Follow the light. But assume that your acceleration has reached its maximum at the moment of impact and your acceleration is now zero. Well, you now have zero force and a maximum amount of kinetic energy. So how will the following collision take place?
Well the ball will absorb SOME of your kinetic energy for the very short time period that is necessary to overcome the ball’s inertia and a very small portion of its deformation energy. So in the best case scenario in this study the ball will absorb an amount of energy equal to its inertia, VERY SMALL AMOUNT OF ENERGY, and the amount of energy needed to deform the ball until its velocity surpasses that of the clubhead WHICH IS DECELERATING BECAUSE there is no FORCE DRIVING the clubhead at all!
Now imagine the scenario that I have been trying to teach some of the less science savvy people here for a while. All the while ripping me to shreds with no understanding of what they are talking about whatsoever. Now we will accept that the same golfer who made the previous swing with faulty science will now make a scientifically correct swing using sound science principles, because he is willing to actually learn something instead of ignorantly defending or sticking with what he does not truly understand. (Lag, this is not in any way directed towards you, but rather some droolers that troll around here!) You were simply the one that drove me to explain why a lot of people around here are absolutely clueless.
So now this same golfer redirects his efforts towards maximizing ACCELERATION THROUGHOUT impact UNTIL AFTER THE BALL HAS LEFT THE CLUBFACE with little concern as to velocity other that there will be SOME simply because we need to “get” to the ball in the first place which requires some motion.
In order for us to maximize acceleration as described above, it follows naturally that we need to actively apply maximum force at the point when the ball is about to leave the clubface. Huh? Mass isn’t changing people. If mass is constant than the famous equation becomes F=kA. k is not going to change. So to increase A requires an increase in F. If we wish to compress the ball as fully as is humanly possible, thereby allowing the ball to absorb as much energy as possible we should have increasing F throughout the entire compression period until the maximum deformation of the golf ball has occured. Note that you would then have a golf ball that ABSORBED AN AMOUNT OF ENERGY EQUAL TO ITS INERTIA PLUS THE AVERAGE FORCE APPLIED THROUGHOUT THE DEFORMATION AND REBOUND PROCESS TIMES DISTANCE TRAVELLED IN THAT TIME, AND THE TOTAL ENERGY OF MAXIMUM DEFORMATION OF THE GOLF BALL. (minus the energy of sound and heat generated during compression of course.) This far exceeds the puny energy transfer of the previous example. I know, you need more proof, right? Do you people want me to hold it for you in the bathroom too?
But can’t the strong guy develop a lot more kinetic energy than acceleration? Well, let the same strong guy do both swings shall we? We will assume that he is not losing any significant mass during the swing, but he could sure write a good diet book if he could, and we will assume that no parts of the golf club fly off during the swing so that mass will remain constant as well. The only change in mass to the entire system will take place while the golf club is physically in contact with the whopping ounce and a half golf ball.
First we will look at the guy who would be able to apply all of his force at the optimal time so that it would all be converted to kinetic energy prior to impact. The kinetic energy guy would apply his energy at the point where it would maximize velocity when the clubhead would just start to make contact with the ball. Basically he would have allowed sufficient travel distance of the club to occur after applying his force so that it could absorb maximum kinetic energy. The maximum that he could convert into the club would what remained by subtracting the kinetic energy of everything else withing the machine. Namely, all of the kinetic energy of his body must be subtracted from the total energy available to be transferred to the club. So we will assume that this guy has the greatest timing in the world and pulled off the feat of complete energy transformation and transfer of the energy that remains after his body has been taking into acount into the club. He will then accomplish transferring the kinetic energy lost by the club through impact, which will only be equal to the inertia of the ball and the defomation energy that accumulated until the ball surpassed the velocity of the club head. Remember that this approach demands that the clubhead lose velocity throughout the impact with and compression of the golf ball, physics demands it!
So in essense we have a guy with his veins sticking out of his head trying to maximize velocity and only converting about 2/1000 of his maximum force into kinetic energy. Remember he has converted his maximum force into giving the whole system kinetic energy. Think about his mass versus the club and you should get a figure similar as that above.
Now let’s look at the smart guy. Instead of wasting his maximum force to create maximum kinetic energy he chooses instead to use the very minimum force necessary to place the system in a state of perpetual increasing acceleration. How is this done? Well if you look at yourself at the top of the swing and notice how the segments have “separation” meaning different angular position within the rotational movement of the system. Ideally, you would provide only the necessary force necessary to accelerate your torso enough to keep these “separations” constant or growing until the ball leaves the clubface. Why is this so important Tom? Well to decelerate segments of the body in any way requires considerable energy to be directed away from our goal of putting energy into the ball. The more energy that is wasted applying force to decelerate segments the less that is available when it matters, during compression of the ball. “But my body slows down all by it self.” No, it does not. Your body must expend as much energy to decelerate something as it did to accelerate it in the first place. Period. So understand that deceleration of any kind is throwing away energy by the bucket load! In simplest terms, EVERY SEGMENT OF THE BODY MUST CONTINUE TO ACCELERATE AT A RATE HIGHER THAN OR EQUAL TO THAT OF THE CENTER OF MASS OF THE CLUB IN ORDER TO MAXIMIZE ENERGY TRANSFER WHILE COMPRESSING THE BALL. Only in this way is it possible to actually add the average force being supplied by you in addition to the loss of the balls inertia and deformation energy during the compression phase! So how much of an energy differentce are we talking about here?
Well you could wrap a rope around your waist and tie the other end to known masses. When you just reach a mass that will not allow you to rotate your torso during your “transition” move you can approximate you that force by multiplying that mass times the friction coefficient between the two surfaces. That will give you a decent approximation of the maximum force you are capable of. If you then multiply this force by the maximum deformation of the golf ball ball that you usually use, (this represents the distance travelled while compression takes place before the ball rockets off the clubface) This will approximate the energy you place into the golf ball in addition to the that possible by the most idealized kinetic energy swing.
If you take the above force that you are capable of and convert it entirely into kinetic energy of the whole system (you and the club), subtract your body’s kinetic energy and then multiply that figure by the ration of mass of you versus the club you will see how pathetic that energy is in comparison to what you found earlier.
That puny amount is what the other guys rely on most. And only a very tiny amount of that is ever absorbed by the ball. Whatever.
Tom