Golf is one of my lifes obsessions and recently I have started delving into the physics of it. There is however, one thing i could never find any information on. First the backgroud: The most important factor in golf for distance is of course ball speed. Ball speed seems to depend on the the angular momentum transferred to the ball from the club. Angular momentum itself seems to depends on the angular velocity (+ a little bit of linear velocity of the swing) and the moment of inertia (MOI) of the club. The transfer of course also depends on other variables generally simplified as the coefficient of restitution (COR). For those who like equations: \(v_{b} \propto \left (L_{c} + \rho_{c} \right )\cdot c\) \(L_{c} = \omega _{c}\cdot I_{c}\) \(I_{c}=\int r^{2}dm_{c}\) So my problem is that most equations for calculating ball speed (if you can even find any decent ones) only include the clubhead mass in their equations and ignore the momentum of the shaft. In fact it has become quite standard in golf to ignore the shaft as can be seen by the lighter and lighter graphite shafts made every year. For example,15 years ago most professionals were playing with 120g shafts. Nowadays you can get shafts as low as 40g in weight. Now I understand that the clubhead contributes far greater to the MOI term, but surely you cannot completely ignore the effect of shaft momentum on ball speed right? My quesion is, how would you go about calculating the effect of shaft weight on ball speed (assuming other variables such as clubhead velocity remain constant)?
i dont think the weight of either matters because the weight is not attributing to the force the ball is hit with. the persons strenght overrides the weight factor, if the club were freefallling onto the ball then it they would make a difference. an example is if the head alone were propelled and struck the ball with no club or human swinging a club then the ball would travel at the same speed, the difference here is that there is no follow through after the club hits the ball, this is the swing. the thing here is that the club is merely a handle connecting the person exerting the energy and the head making contact. actually the weight of the head is inconsequential as well because it is the hardness and rigidity that is impacting on the ball. since this is harder to measure then an alternative is to weigh it and call it a day.
The person's strength matters in that you need strength to propel the club with velocity. The higher the clubhead speed, the further the ball goes. Anyone will tell you that the weight (mass in fact) matters. Just imagine hitting a golf ball with a very light plastic driver. Do you think the ball would go as far? No, if the ball is lighter than the clubhead, the ball will travel faster than the club - even if nobody swings it. Follow through makes no difference to the ball speed. The time the club spends in contact with the ball is milliseconds. Anyone will tell you that the clubs momentum is the important thing. Again, just think of a plastic club
The person's strength matters in that you need strength to propel the club with velocity. The higher the clubhead speed, the further the ball goes. Anyone will tell you that the weight (mass in fact) matters. I am not disagreeing with you, but trying to figure this out from another perspective. My first paragraph states that the persons strength is the primary factor. It is the source of the energy and is needed for guidance. The strenght of the person has to remain the same for each test so we are not trying to prove anything new here. Just imagine hitting a golf ball with a very light plastic driver. Do you think the ball would go as far? But that is why is stated rigidity is the main factor. Combined with the stenght of the person and the rigidness of the club then that cancels out the weight of the club. To a certain extent anyway. an example is if the head alone were propelled and struck the ball with no club or human swinging a club then the ball would travel at the same speed, No, if the ball is lighter than the clubhead, the ball will travel faster than the club - even if nobody swings it. Sorry, what i was implying is the clubhead striking the ball whilst not attached to anything. Trying to get a visualization of the energy from the head alone, striking the ball at the force it would if attached to a club and then a human. ball-clubhead-club-human. Would it be the same either way? Follow through makes no difference to the ball speed. The time the club spends in contact with the ball is milliseconds. So doyou think it is the weight of the club or the strength and style\ability of the person swinging? You probalbly will say both and could be but is it only, at that point, the momentum? The initial impact has the greatest energy, then after that it a loss of energy from the standpoint of the human and the club. Anyone will tell you that the clubs momentum is the important thing. Again, just think of a plastic club I doubt anyone will agree with me, but that is how i see it. Any computer data to refer to?
First: The issue is exchange of ordinary momentum, not angular momentum. Second: I am not sure that momentum exchange is the only (or even the important) issue here. High speed photography shows the ball distorted from a sphere into a pancake shape which rebounds to its original shape after leaving the club face. I think there is a trade-off between combined weight of the Club head/shaft & the velocity of the club head at impact. The more weight, the more momentum exchange for a given club head velocity at impact. However, the more weight, the more resistance to developing high velocity at impact. I would guess that a tall slim person might be better off with lighter clubs, while a short more muscular person might do better with heavier clubs. My intuition suggests to me that shaft weight is less important than club head weight. Hence, designers attempt to get more weight into the club head & less in the shaft. I suspect that nobody attempts to design clubs based on precise application of the apppropriate laws of physics & the mechanics of materials. Note that the latter is probably critical here: Both the elastic (& other) characteristics of the ball & the elastic (& other) characteristics of the club face are important. It might not be possible to design clubs based solely on the application of the laws of physics, mechanics, & aerodynamics. In the final analysis, actual data based first on swing machines & later on humans using the clubs will be more important than the application of the laws of physics & mechanics of materials. I do not think it is known how to get precise results using the pertinent equations. I suspect that the swing machines might not be the final arbiter of the worth of a design: The use of a club by a golfer might be a better indication. BTW: I suspect that the design of clubs should probably be different for touring pros & duffers, but the duffers would not be willing to use any club too much different from those used by the professionals. I have often wondered if a club designed more like a hammer or a mallet might be more effective than the current club designs. There are historical reasons for the basic shape of a golf club, which were initially made entirely of wood. The first ones were made from a single piece of wood. Initially, a piece of the trunk & part of a limb was used as the starting point in the making of a club. This was done so that the grain of the wood followed the general shape of the club. Later, trees were planted to initially grow out horizontally from a cliff face. The tree truck would turn to a vertical direction as it grew. This resulted in the grain being ideal for the making of a golf club. Using modern materials, an entirely different shape might be ideal but ignored due to habit & the traditional resistance to radical changes in design, which might require a lot of practice before the new design performed better than the traditional design.
I disagree, I think that rigidity is not very important compared to mass. If you take a very light, hollow but rigid clubhead and then take a cluhead with the same rigidy but much more mass, if swung at the same speed - the ball speed will be faster off the heavy head. Simple momentum. Yes, basically, what I am saying is that given a clubhead striking a ball with no shaft and one with a shaft (and ignoring any indirect push from the arms), the club-shaft system will have more angular momentum and ball speed will be greater. The problem is, how much more angular momentum?
No, the amount of momentum the clubhead has at impact from a torque exerted by the human body is calculated using the angular momentum equation (because there is no linear force acting on the club). Of course there are other factors but these are taken care of in the COR term as I have explained in the initial post. Of course, but we are keeping other variables constant as I state in the first post. I would guess that a tall slim person might be better off with lighter clubs, while a short more muscular person might do better with heavier clubs. What about the opposite where the tall person has a heavier club but is able to generate quite a significant club speed anyway since he might use longer clubs? Might be better to use heavier clubs? Yes but my problem is quantifying it. Can we get an equation to calculate ball speed base on the whole club and not just clubhead? Again, this can be simplified by the COR term. This term can actually be measured to make things even more simple. We should be able to use a robot (e.g. look up "Iron Byron") to be able to test our equations against reality and see how they compare. This is true, duffers tend to use shafts that are too still and lofts that are too low for their swing speed. The hammer or mallet would need some kind of loft to get the ball airborne! I wouldn't say ignored completely - there are some crazy shapes out there now!
When I suggested a hammer or mallet design, I was not suggesting that the face be flat exactly like a hammer or mallet. The following from somebody's post is obviously true. The point I was trying to make is that there is torque at impact with the current club design, tending to twist the club face from a square impact. A hammer or mallet design would allow the impact surface to be centered on the shaft. Of course you would want the basic shape of a head to be a cylinder with the impact surface having loft. Duffers might have a lot of trouble with such a design, but the touring pros would have no problem due to an impact surface with a smaller surface area than that of current clubs. BTW: It is well known that the younger players use very stiff shafts which sacrifice some distance for increased control & consistency. As a player loses club head speed with age & gains in swing consistency, he does better with a more flexible shaft. There is a "crack the whip" effect with a more flexible shaft, but it is harder to control. A young touring pro gets so much club head speed with a stiff shaft that he would not want to give up any control in order to get more speed. Hogan & Nicholaus gave up distance for accuracy. Both were capable of hitting farther than they usually did in tournament play. In the few driving competitions he entered, Nicholaus drove 300-325 yards, but seldom drove further than 280-290 in a tournament. I suppose, but am not sure, that Woods can drive farther than he does in a tournament. Maybe he also gives up some distance for more accuracy. It does seem to me that Hogan in particular missed fewer fairways than Woods & other modern golfers. I think the same was true for Nicholaus. I wonder if the courses of yester-years made it more difficult to recover from a missed fairway in the Hogan to Nicholaus era. Perhaps the clubs Hogan & Nicholaus used resulted in more erratic shots at distances beyond 280-290 yeards. Perhaps the courses in their era seldom required hitting farther. Hitting a 325 yard drive would not be a good idea if there is a dog-leg at about 260 yards & a wooded area or a lake at 290 yards.
Calculate the inertial momentum of shaft+clubhead and then use the conservation of angular momentum. I don't know much golf but probably you can use the point where you hold the club as the axis of rotation of the club.
So you are saying that the ball speed is directly proportional to the inertial momentum of the whole club?
You can model the shaft as a stick of mass m that rotates on an axis through its end (approximately), with the club head of mass M at the end of the shaft rotating about the same axis. The total moment of inertia is: \(I = \frac{1}{3}mL^2 + ML^2\) where L is the length of the shaft.
Weight is important. We are talking about an exchange of momentum, after all, and if you understood the equations for that, you'd realise the significance of weight. Common sense or experience should also lead you to the same conclusion, or have you never wondered by drivers are bigger and heavier than putting wedges? Clearly you have never played golf. You don't whack a ball with all your might, you try to have a nice, consistent easy stroke. Accuracy goes awry if you tense up and start whacking.
Maximizing inertial momentum with given overall length and total mass will give you very light shaft and heavy head.
And how does the clubs total moment of inertia relate to ball speed? Make the experiment very simple. 3 drivers made of the exact same material (so COR is the same) and a golf ball. The experiment takes place in a vacuum (so disregard air resistance etc.) Take club1 with a MOI of 2 kg.m^2, club2 has a MOI of 3 kg.m^2 and club3 has a MOI of 4 kg.m^2. ball is 0.05kg and clubhead speed for both clubs is the same at 50m/s. is this enough input to calculate ball speed in each case?
By the way, feel free to add your own numbers in for any other variables as long as they are kept the same for all 3 scenarios. I am only interested in how MOI affect ball speed. For example you could set COR to 0.8 which is the maximum allowed by the USGA.
no i never polayed golf. i said weight was not an issue because the weight is only a pound or two, if that, and the persons strength and force of momentum exhibited by the swing obliterates any factor of weight from the club. iow's it cancels it out/
It is true that the weight of the club also affects the velocity with which it can be swung. But that is why I said assume clubhead velocity remains constant in the OP
