Analysis of some aspects of weight shifting

Weight shifting is an expression often employed in articles, books, on TV, etc., but rarely hears one a coherent explanation why there is one and what exactly is it doing in a swing. There can be different  styles for weight shifting - a short lateral bump followed by rotation or a cross-lateral slide with minimum and retarded rotation. Or, very little weight shift and simply a rotation of the upper body over a stable lower body. But why have one? What is it doing in a downswing? Is it to inject energy into the downswing? Is it simply for keeping things in balance? Or perhaps simply to give room for the trail elbow in the downswing? Or a mix of all mentioned before?

Above we have been implicitly referring to the obvious cause for weight shifting, i.e., a lateral shifting of the body weight from the trail foot to the lead foot. However is that the only way to shift weight? There is also the rotation of the arms and club which have a considerable weight associated with it and so does the head for only small lateral movements. We will presently look at and analyze causes for weight shifting normally overlooked such as by torquing and by the centrifugal force in the downswing. Scientists will use 'force plates' to measure weight shift. These can be rather sophisticated 3D measuring devices. We will use a mathematical model to derive both the total apparent dynamic weight and the weight shift for a simple model just to show very clearly the weight shift mechanisms at work in a golf swing, due to rotating arms, torque exerted and centrifugal force.

Fig1 shows the model used. It represents a golfer, without being quite a golfer. Its sole purpose is to readily show the mechanisms analyzed. The rotating segment, m2, with  point mass m3, at one end, rotates around a fixed pivot on the main body, m1. The arm starts to rotate from  the vertical position, see Fig 3, and is acted upon by a constant torque. For static conditions the total weight, as measured under both 'feet' by force plates would be simply the sum of the gravitational weight of the three masses, m1, m2 and m3. However, for dynamic conditions, when any acceleration occurs, there will be, by definition, inertial forces coming into the act  and they will show up at A and B as a weight shift and a change in overall weight..

m1 = 1 kg,  m2=11 kg,   m3 =100 kg,   width = 0.5 m,  height = 1.50 m,  length of rotating segment 1 m. Torque = 30 Nm.

As soon as the arm starts to rotate there will be a centripetal acceleration and hence a centripetal force and therefore a centrifugal force operating on the pivot point. The vector sum of the centrifugal force and the gravitational force is shown in Fig 3, whereas the associated horizontal and vertical force components are given in Fig 4.
The torque and the linear force acting on the pivot change the effective weight measured at A and B. As one can see from Fig 5, even for a very simple model, it is quite a complicated matter.

Initially, with the arm starting to rotate from the vertical position, it is primarily the active torque and angular acceleration playing a role. There is a symmetrical weight shift, an increase towards the lead foot and an equal decrease for the lead foot. The total weight however remains the same. As the angular velocity increases the centrifugal force starts rapid stealing the show. There is an interesting 'unweighting'  taking place during the first quarter. The black dotted vertical lines represents the two horizontal positions of the rotating segment, whereas the red one represents the bottom vertical position. Notice that for these two horizontal positions the total weight does not change but there is nevertheless a substantial weight shift occurring. Also note that the weight shifting effect rapidly increases as the angular velocity increases. Our  little robot is in effect starting to topple over when t = 0.78 sec.

Above is an good illustration of the complexity of the golf swing as soon as it analyzed scientifically. Somebody using force plates to analyze real golf swings has to cope with a very complex problem at hand indeed. Instead of our very simple 2D model he has to struggle with a very complex 3D model in which there are also real lateral and vertical and twisting body motions taking place. To work backwards from the measured data to the golf swing is an extremely hazardous task since virtually anything in the swing can lead to changes both in overall weight and in the weight shift as measured by the force plates. The only way out is to have numerous detailed video sequences to supplement the force plate measurements.

Usually when referring to weight shift in a golf swing one does not have in mind the factors analyzed above but rather the shifting of the lower body towards the target prior to impact. So let's also a have brief look. One possible model for the golf swing is a kinetic chain having  progressive lesser mass, from proximal to distal, leading to the possibility of efficient velocity multiplication. If subdivided into ever smaller segments one would end up with a whip. We all know a whip to be an extraordinary efficient velocity multiplier, breaking the sound barrier at its tip.

It is important to note that a heavy object can acquire, even at modest velocities, an appreciable amount of kinetic energy. In a kinetic chain the kinetic energy is passed down the line by having the bigger segments successively slow down. In a down swing however there is not much time and hence the bigger parts better get their act together as soon as possible to be able to transfer an interesting amount of kinetic energy down the line before impact. So hence it is not a bad idea to look for body motions from the very start which are efficient for acquiring and transmitting kinetic energy.

A fact usually overlooked is that the body motions to be really energy efficient have to slow down to be able to let kinetic energy flow to the distal part. At the driving range you can often see enthusiastic groups of young males generating very large amount of energy, usually throwing them completely off balance but yet not generating really much clubhead speed. They have not learned to sequence their motion properly and are wasting a considerable amount of energy.

One attractive lower body motion is whipping very briskly  the lower trail side towards the ball, as done by Tiger Woods. It can be done with lots of vigor and yet due to the resistance encountered it does not last long, hence ideal for efficient kinetic energy transfer. Another interesting option is the 'sitz' move taught by old timer Joe Norwood - a short sudden jolting downward motion of the body, for only a spit-second duration.

mandrin