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PHYSICAL SCIENCE-- 4Ts -- Tempo

Gravity Timing

The three things that determine the qualitative characteristics of your stroke (consistentcy, smoothness, repeatability, eveness of timing, presence or absence of jerkiness or abruptness at transitions, and so on) are: 1) GRAVITY; 2) your putter; and 3) your body. Of these, the most consistent and predictable is GRAVITY. The force of gravity is exactly the same for all objects on earth at the same location, regardless of size, shape, or mass. All objects freefall with exactly the same pattern of motion -- that is, the force of gravity gives all objects the same pattern of acceleration from zero on up.

Did you know that gravity is not exactly the same around the Earth? The actual pull of gravity varies from mountain tops like Everest to low spots like the Dead Sea, on the continents, and under the oceans, and depending upon what density of rocks and other material are inside the mantle. Balls weigh less in Colorado than they do in Miami. But it's close enough for government work all over the Planet (usually under 1% variation).

New Satellites to Map Gravity More Precisely, Warren E. Leary, NY Times, March 19, 2002

NASA Satellite Gravity Map

To test this, take a quarter and hold it above your open palm about six inches and drop it and time the fall until it hits your hand. Now try a dime; now a golf tee; now a golf ball. They all hit your hand at exactly the same time, which can easily be calculated from the physics of gravity as follows:

TIME of fall (in seconds) = Square root of [2 x Distance of fall (in feet) / Accleration due to gravity (in feet per second per second].

The only 3 quantities here are TIME, DISTANCE, and GRAVITATIONAL ACCELERATION. Gravity on earth always accelerates objects towards the center of the earth at the rate of 32 feet per second every second, so after one second a golf ball dropped off the Leaning Tower of Pisa will accelerate from 0 to 32 feet per second; after two seconds, it will have increased its downward speed to 64 feet per second, and so on.

How Fast Do Objects Accelerate To Earth?

The only reason you don't fall down into the center of the earth like into a deep well is that the dirt got there first. Even so, gravity is what makes your body mass"weigh" something. Out in deep space away from the earth's gravity, your body mass would be weightless. So, on earth everything labors under the very constant and exact "hugging" of gravity. If the surface is somehow removed between the object and straight down (by jumping up, getting dropped over the side of a tower, or the surface tilts out of the way a bit), then the constant hugging starts moving the object, adding that motion to whatever other motion is present.

Back to timing: In our eaxample, 6 inches is 0.5 feet. That's the only number you need to see how much time it takes for gravity to move any object down 6 inches. From the formula, TIME = SQR [2 * 0.5 / 32] = 0.177 seconds - a little less than 2/10ths of a second.

This sort of thing can be approached from the opposite direction: how high do you have to drop an object for the fall to take EXACTLY ONE SECOND? From the same formula, just square both sides and rearrange, as follows: TIME(squared) = 2 * Distance / 32, rearranged as DISTANCE = Time(squared) * 32 / 2. Stick in one second and crank out the answer: DISTANCE = 1*1*32 / 2 = 16 feet! In other words, if the object starts at zero from 16 feet high, at the end of one second it will be going 32 feet per second, so over the whole course of the 16 feet, it AVERAGED half that or 16 feet per second.

In terms of tempo, gravity's constant hugging force determines whether your stroke will be smooth or jerky, depending upon how you time it with your body. You just can't escape gravity!

Gravity in the Brain

Every brain on earth is taught timing by gravity all the time. The evolution of all brains has been guided and directed by gravity towards better and better movement control. The human brain for movement is tyhe beneficiary of eons of animal brain refinements in this evolutionary process for the timing of movements of the body and objects in gravity on earth. The brain knows the tempo and timing of gravity better than any other tempo. When astronauts travel into the microgravity of outer space, they have a very difficult time adjusting to the new timing pattern of objects in motion in outer space because this brain awareness of gravity is so deeply fixed in our brains.


Pendulum Timing

Since a pendulum moves in response to gravity, you can actually use a pendulum to measure gravity! Geologists do this all the time. All it takes is a very precise length of your pendulum and a good stopwatch. With these two squared away, you just let the pendulum swing to and fro and time it as accurately as you can. The math then tells you the force of gravity at that location on the planet. Geologists use this trick to look around for huge oil deposits beneath the surface, because these show up by affecting local gravity measurements. Nowadays, they use satellite gravity mapping, too.

For the physics involved, see this Link:

Using A Pendulum To Measure Gravity

A pendulum is a special case of freefall in gravity -- one where the falling object is swinging on a vine like Tarzan. It doesn't fall straight down, but arcs beneath the pivot where the rope or rod is attached. From the top on one side, like a trapeze artist standing on the platform, gravity is allowed to start to work by releasing the trapeze artist, who leans out off the platform holding onto the trapeze bar. Gravity then starts to accelerate the artist with its perfectly consistent force of acceleration, but the trapeze artist is not free to fall straight down, since the trapeze gear redirects his fall laterally, so he falls in an arcing combination of down and across. The artist speeds up as he arcs down and across, and when he reaches the bottom of the arc, he is traveling as fast as he will ever go. At this point, the trapeze cables prevent any further downward fall (as they have been gradually doing all along). Now, the artist is a moving object who starts to head up and across. How far he gets depends upon where he started from: how high. If there is no loss of energy from air resistance or friction in the trapeze gear, the artist should make it all the way back up on the opposite side and be able to stand on the platform.

In putting, if you construct a well-lubricated putting robot to hold a putter and swivel the putter-arms back to a certain height, and let go, the putterhead will move like the trapeze artist down and through. Starting from zero speed, the putterhead will reach maximum lateral speed right at the bottom, and will then continue up the other side of the stroke to a finish at the same height as the start.

The total time from start to finish and the lateral speed of the putterhead at the bottom (or anywhere else along the way) has been known from physics for centuries. So what DOES set the timing of the pendulum, other than gravity? The only thing that matters for the ideal pendulum is the LENGTH of the rod. The longer the pendulum from pivot to bob, the longer the time from side to side. Now here's the neat part: within a certain range of settings to start with (out to about 20 degrees off vertical), a pendulum with a fixed LENGTH will take exactly the same time from start to finish no matter where you start from to release it. (That's why you adjust the timing of a metronome by sliding the "bob" farther out the rod to get a slower beat.) But the maximum speed at the bottom of these different arcs, though, will increase the higher back the starting position is for that particular length pendulum.

There's one trick, though. In an IDEAL pendulum, where the "bob" is a mass in one single point without extension in space, and the connecting "rod" between bob and pivot is just a fixed line without mass or extension in space, and the pivot has no friction, none of the pendulum's timing aspects depend in the slightest upon the weight or mass of the bob, since all objects freefall the same way in gravity. And for a REAL pendulum, like a clock pendulum in a grandfather clock, taking the mass of ther bob and the mass and shape of the rod into account is necessary, but the end result is close, but always QUICKER than an ideal pendulum. In effect, there is some mass closer to the pivot that is falling along with the bob at the end, and this speeds up the timing of the real pendulum.

So there are two opposite factors: LONGER=SLOWER but REAL=QUICKER.

So the overall timing or tempo of a putting pendulum depends almost exclusively on the length of the system (arms plus putter length out from pivot in your neck area) , while the speed of the putterhead at the bottom of the arc depends on this length and the length or height of your backstroke. Since the length of your arms and putter are always the same, the only factor that determines putterhead speed at impact in this type of stroke is the extent of the backstroke for releasing the freefall into gravity. And since putterhead speed determines the distance the ball will roll on any given green speed, backstroke length determines distance control -- not hit or "muscle memory" or "acclerating through the ball."

In this sort of freefall stroke, the total time from top of backstroke to top of follow-through is your tempo. I say "your" tempo on purpose. Gravity always has exactly the same tempo given a set length of the pendulum. So why isn't your tempo the SAME AS GRAVITY'S? It can be, pretty close.

What is gravity's tempo in putting? It depends upon the length. In fact, a "meter stick" pendulum was formerly the defined as the length of a 1-second pendulum: how long it takes a pendulum 1 meter long (39.37 inches) to swing from side to side (1.0035 seconds). The physics is expressed in the formula: TIME (side to side) = Pi * SQR [Length/Gravitational Acceleration]. In this case Time = 3.14 * SQR [1 meter / 9.8 meteres per sec. per sec.] (National Institute of Standards & Technology -- historical definition of meter.)

What is the length of a typical putting "system" of arms plus putter? For a six foot male, the center of the palms take hold of the putter handle about two feet out from the pivot area in the neck (check this by holding a yardstick against your neck), and since the hands are part-way down on the 35" standard putter, the putterhead ends up a total of about four and one-half feet (54 inches) away from the neck. This is a pendulum length of 4.5 feet. If you construct an IDEAL pendulum 4.5 feet long, gravity gives it a timing period from side to side of 1.18 seconds, no matter how far back the backstroke goes (within a certain range of about 1.5 feet back). A REAL pendulum is a little quicker, as the shape and masses have an effect. For a rod 4.5 feet long built like a "meter stick", the quicker timing means the REAL pendulum takes only about 80% of the time of the IDEAL pendulum (or 1.22 times faster). The REAL pendulum 4.5 feet long takes about 0.96 seconds. Compared to a meter stick, the real putting system is longer (and therefore slower) but real with mass in the arms (and therefore quicker). When all is said and done, these two counter factors almost cancel out, and a meter stick and a putting system that is 4.5 feet long act about the same for timing or tempo.

So a meter stick takes 1 second, and a longer real pendulum does too, just about (0.96 seconds). The significance of this is that if you use a totally relaxed pendulum stroke powered solely by the freefall of gravity, without any contribution from muscle hit, your putter will have a gravity tempo of about 1 second from side to side. Every single time! The total time for the stroke from start to top of backstroke, and from there across to the finish will be about twice that long. So a gravity tempo for a hitless pendulum freefall stroke is "one potato, two potato" from start to finish, with impact on "two."

If you want to observe this first hand, just grip the top of your putter handle between the thumb and index fingertips and let the putter swing like a pendulum from side to side. It doesn't matter how far, really. The back-and-forth motion should take roughly the same time -- about one second from side to side. Nice and slow and even and consistent and repeating. Nothing you can do with a "hit" stroke can get this smooth and consistent. To see a pendulum demonstration, pop up this Java Pendulum.

Heartrate Timing

A typical relaxed heart rate for an adult male in good health is about 72 beats per second. For most of us, a heartbeat defines a moment for us as about 8/10ths of a second. A finely conditioned endurance athlete, on the other hand, might have a heartrate closer to 60 beats per minute, or one each second. There is usually a disparity between a golfer's heartrate and his putting tempo, so that the heartrate is faster than a good putting tempo. In addition, anxiety and pressure and adrenalin make the heart race faster, so your tempo gets harder to identify. Ideally, you would like to have your heartrate match your putting tempo, so a good heartrate target ought to be about 60 beats per second.


Breathing Timing

Your cardio-pulmonary system of oxygen intake and oxygen conversion and carbon monoxide expulsion determines your breathing rate and your heart rate. Usually, there is a normal ratio between the number of heart beats and the number of breaths per minute -- about 15 breaths for every 60 heart beats (1:4, or four heart beats for each breath). This ratio has a big influence on how the body is using oxygen (and producing carbon monoxide as a byproduct). If the breathing is too fast for the heart's moving the blood into the body, there is too much oxygen in the blood and not enough carbon monoxide. If the heart is outracing the breathing, the blood gets oxygen-thin and builds up excess carbon monoxide. In either case, your brain will not be functioning optimally. Breathing control is how you get a handle on anxiety, pressure, and adrenaline to calm your heartrate and get your body closer to your optimal tempo. Breath control has been the foundation for most eastern meditative practices for millennia, including yoga and zen. "Deep abdominal breathing" is a western stress control relaxation technique that works on the same principle of coordinating the cardio-pulmonary system. One of the most important features to know about this is the benefit of controlled exhalation. This is where the timing control is found.

Sanskrit for Om Sound

A slow, even, steady exhalation is worth its weight in gold for centering your timing. All buddhist meditative chanting is voiced by steady control of exhalation.

The OHMM sound of transcendental meditation is the same - controlled exhalation. Humming a tune is the same.

Sensory Timing

Sensory processes are phenomena in time. For example, vision works in this fashion: light reflects off an object a certain distance from the eyes; light travels at the speed of light (186,000+ miles per second) through the eyeball to the nerve endings at the back on the retina; there the light energizes the chemicals of cones and rods and a chemical reaction later fires the nerves; the nerves then send their impulses along into the brain in a combination of chemical and electrical reactions; the brain wiring routes the impulses into different areas of the brain until it "recognizes" the shape and undertsands its identity and location in space. Touch and body-sense from position signals in joints and muscles also take time.

For example, in baseball, the pitcher's plate on the mound is located 60.5 feet from the back of home plate (MLB Diagram). Pitchers in The Show typically throw the ball at velocities topping out at about 90 mph. Assuming the average velocity of the ball from pitcher's release to contact with bat is this full 90 mph, the actual distance is probably closer to 58 feet as the pitcher leans into the throw beyond the plate. 90 mph is the same as 132 feet per second. A baseball covers those 58 feet in less than 0.5 seconds (58/132 = 0.44 seconds). Once the batter commits to swing, it takes about 0.3 seconds for the brain to move the arms and swing the bat to the contact position. That means the batter has to commit after only 0.2 to 0.3 seconds of the pitcher's release of the ball, at which point the ball has already come 25 to 40 feet of the way to the bat. If the mound were much closer or pitchers able to throw the ball much faster, the batter wouldn't stand a chance! He's already at the limits of perceptual timing as it is. The lesson is that visual processes need about at least one-quarter of a second to register the cues necessary for hand-eye coordination. Slower is definitely better.

The same is ture for slamming on the breaks in an emergency stopping of your car. The reason the State makes tailgating illegal is because the time required for our perceptions to register and prompt action make it necessary that we stay far enough back behind other cars to give ourselves time to see the emergency and stop our car. The faster the two cars are traveling, the greater the separation distance required by our reaction time: one car length for every ten miles per hour of speed. At 60 mph, six car lengths is about 100 feet. The cars would be traveling at 88 feet per second at that speed, so 100 feet of separation allows you just a little over 1 second to see and react to trouble. Of that 1 second, the first 0.3 of it is seeing and moving the foot to the brakes. The other 0.7 of it is for the brakes to take hold and slow the car quickly. Again, the minimum reaction time to see and react is about 0.3 seconds.

Every time the body interacts with the world, the process takes time, sometimes faster and sometimes slower. But there are minimal timings and optimal timings. The time it takes the eye to look from one object to a different object at a different distance and then reshape the lens to focus at the new distance is usually about 1 second (faster for kids than for adults). Also, visual attention takes time to shift from one location to another (Time Course of Visual Attention). The time it takes for the inner ear to settle down after turning the head to look at something off to your side is roughly the same, depending upon how fast you turn your head. Visual memory, spatial memory, and working memory all last only so long -- generally not over about 7-8 seconds without special mental effort to refresh the memories. So there are both minimum times for perceptions and movements, and maximum times for perceptions to retain potency and value in structuring the movement.

All these timing factors have to be respected in optimal putting. You simply cannot have help from your eyes to correct a stroke midway through if the stroke is too quick for the eyes to register the path of the stroke. And your sense of the target's location and mental imagery or visualizations won't do you any good unless you make use of them before they fade.


Brainwave Timing

The awake brain has a gross level of electrical activity that shows up as a beta wave, meaning the brain's electrical activity is pulsing overall at about 14 cycles or pulses each second. The awake brain basically buzzes all day. The brain when the eyes are closed or in the dark, when the person is very relaxed and not working on anything mental or physical, operates in an alpha mode of about 6 pulses each second. Specific stimuli, like the cocking of a pistol hammer, set off a quick beta burst. Other patterns are theta for sleep or hypnagogic drowsiness and delta for deep sleep. Newborn infants spend a lot of time in theta, as this promotes learning at that stage of development.

One of the more interesting aspects of brain waves is the notion of "entrainment." Entrainment is the collective organization of brain waves both in their timing and in their spatial arrangement in the brain. For example, the brain stem contains a group of nerve cells (the inferior olive) that sends a steady pulse into the cerebellum of about 40 cycles per second (40 Hz). This pulse organizes the array of Purkenje cells inside the cerebellum so that they can time body movements, sort of like the atomic clock for the body's train schedule. Another pulse, also around 40 Hz, courses across the cerebrum's cortex, and this pulse is thought to help organize and integrate separate mental processes like vision, body-position, and action planning and execution.

External stimuli like sound waves and light waves come in certain frequencies, and these auditory and visual pulsations affect the brain and help "entrain" certain mental states. That's how the meditative mantra works, and why Baroque music is more relaxing than Hip Hop. It's also how the daily phases of sunlight and darkness enter the eyes and activate brain chemicals for arousal and mood. In the morning, the growing light of dawn comes through our eyelids and stimulates a knot along the optic nerves. This knot, the suprachiastic nucleus, registers the brightness of the light and signals other parts of the brain to send wake-up juice (serotonin) into the brain, to take over for the day shift from the nighttime's melatonin. Imbalances in this system, from sleep deprivation or becoming out of sync with the daily pattern of sunrise and sunset (as happens with jet lag), affects mood and arousal level. The same mechanism underlies the Winter Blues for light-deprived residents of the far north, or Seasonal Affective Disorder (SAD), and light therapy is a well-recognized and accepted treatment.

Brain wave training and therapy is becoming an accepted part of advanced medical practice. It currently is used regularly at the Sloan Kettering Institute, Harvard, and other preeminent medical institutions around the world. In addition, a growing field is neurofeedback, wherein brain wave training is used for such problems as Attention Deficit Disorder, and is increasingly being used in sports performance enhancement. (E.g., Brain.com).

The brain is seen today less in terms of a fixed network of computer circuitry and more in terms of a symphony of independent but cooperative centers of oscillation and resonance. The brian is made for action, and that means perceiving and moving in time. Hence the brain makes us part of the action of the world through its timing processes. Because of these neural mechanisms, sound patterns and light patterns can be used to help optimize athletic performance by encouraging appropriate timing and levels of arousal, focus and coordination.


Movement Timing

Tempo in putting is the total time the movement in the stroke takes from beginning to end. Tour pros have been timed, and pros like Nick Price and Chip Beck have tempoes of about 2 full seconds. price was timed at 1.85 seconds, and beck at 1.92 seconds. Because the putting stroke really has two distinct movements (back and then down-and-through), the critical part of the stroke that matters most for timing is the down-and-through stroke. This part of the stroke is roughly half of the total, so a down-and-through stroke timing is somewhere around 1 second from top of backstroke to end of follow-through, or a little quicker. A tempo of 1 second is the same as 60 beats per minute. A tempo of 0.8 seconds is 75 beats per minute. Since the gravity tempo is about 1 second, any movement tempo quicker than this requires some "hit" in the stroke to move the putter faster than gravity alone moves it. To check how the various tempoes feel, use this computer metronome and experiment with settings between 60 and 75 beats per minute. Java Metronome.

By the way, there is a maximum movement speed. If a musical composer were to write a violin concerto for Paganinni to play, or a piano piece for Mozart to play, the fastest notes he could write would be about 12 notes per second, and probably a lot less. Try tapping your index finger on a table as fast as you can and count "one mississippi" to see how many taps you can jam into one second! If you have a palsied tremor in your hand, your hand will shake at about 8 to 10 shakes per second (8-10 Hz). The shaking results from the breakdown of our normal control, so old age in effect "unmasks" our underlying reality. A healthy athlete would have a shake like this if his brain were not in good working order, and partially that's what Parkinson's Disease is -- a brain in which the normal circuitry for controlling this underlying shakiness wears out. Some people believe the "yips" can be traced to a similar wearing down of similar circuits. These maximum movement times don't matter much in putting unless you have the shakes, but it may be important to know that our smoothness is not really the normal situation, but is the result of constant controlling work done by our brains.


Biological Clocks and Rhythms

 

BioRhythm Calculator

Relation to Touch and Targeting

Touch (distance control for a specific green, putter, and ball) and Targeting are critically dependent upon Tempo. Without a sense of stable, repeating Tempo, one has imprecision in movement interaction with the environment. Tempo, in a manner of speaking, is the "grid" within which we map the environment for Targeting and by which we imagine and generate movement with reference to these targets (Touch). If the "grid" of latitude and longitude is not relatively fixed and known, navigation is difficult and lacks accuracy.

The importance of Tempo to Touch and movement control should be fairly obvious, and the connection to Targeting more nebulous. Everyone appreciates the importance of good timing in precise motion control, but it's harder to see how Tempo underlies Targeting. The Targeting here is not simply "seeing" a target, or not even "knowing where" the target is located. Targeting here means building a physical relationship between the target and the body for purposes of action (in putting, rolling the ball across the surface into the hole). This sort of Targeting requires a mental preview of the action -- like Jack Nicklaus' "movies" of the putt or other golf shot -- and this is an imagining in 4 dimensions, the fourth being TIME. For the purposes of putting, all the physics boils down to the Classical Physics of motion, which is the change of location in TIME. The brain needs to imagine the desired motion of the ball, but first it needs to clarify what the desired motion ought to be. This is the process of Targeting that sorts out variations of motion and fixes the one motion that then becomes the intented motion. One can simply look at the green surface and imagine a ball rolling across it in a given pattern of speed and "watching" how the ball takes the break of the surface contour, and then imagining variations with different speeds or paths.

At this level, Targeting is concerned with the motion of the ball, and not the motion of the body to produce the motion of the ball. Tempo is what integrates these two components into the desired putt motion with proper Touch. If you have a stable Tempo, then your imagining of the body movement is simplified and clear: make a stroke that conforms to the Tempo. For this reason, ALL putting body motions are the same stroke, except for the amplitude of the backstroke. The "choosing" of the appropriate backstroke (Touch) comes solely from Targeting. That is, the Touch is produced automatically from accurately imagining how the body movement will roll the ball (Targeting in the second sense) and by getting this sense in tune with the intended motion of the ball across the surface (Targeting in the first sense). Tempo integrates Targeting for Touch. Because of this, putting boils down to: Target well and putt with Touch by adhering to a good Tempo.

Relation to Technique

Technique is the combination of behaviors (perceptions and movements) in Targeting and Stroking. The putt is not comprised of separate, distinct behaviors, such as "plump bobbing," "logo alignment," "face alignment," "practice stroke," "last look at the target," and so forth. The putt is a segment of time in the game of golf when the intention of rolling this ball into that hole is put into action. The behaviors that the golfer engages in during this segment of time should be productive and helpful ones, but by far most of the behaviors of golfers on the greens today are chaotic and conflicting. Optimal putting requires taking the TIME of this segment on the green and structuring it so that the perceptual and movement behaviors engaged in are well-considered, effective, and mutually enhancing. So optimal putting is all about sequencing peceptual and movement processes in time during the action of the putt in light of how these processes work best and work best together, for purposes of rolling the ball into the hole. As guitarist Brian Mullen says, "It's all in the ty-MING." Technique is the well-considered timing of perceptual and movement processes in the action of the putt.

 

Updated Wednesday, September 10, 2008 3:36 PM

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