There is a championship golf course in the development where I live. I played solely at this course for 7 years, playing once or twice a year at other courses. When I moved here, I always played 18 hole rounds of golf. After about a year, most of my new friends only played 9 hole rounds and I became a 9-hole golfer. Then I found out that being a "9-hole" golfer tended to make one an outcast at the course. Feelings were strong against the 9-holers. That and the system we have for obtaining tee times caused me to look at other courses in the area. At this course, one can obtain a tee time 7 days in advance. In order to obtain a morning tee time, 7 days hence, one had to go to the golf pro shop, generally one to one and one-half hours before the shop opened and get in line. This meant going to the course at around 6 AM. I stopped doing this when the process became unruly and loud words and near fisticuffs broke out about one's position in line. I joined a group of players who played at many different courses within a 75 mile radius of our development. I thoroughly enjoyed playing at the different courses and was happy with the attitude of the golfers within the group. We played for fun, but we also looked at ways to improve our game.
I found that just comparing my scores from course to course was not a good indication of the status of my game. I read a lot of material on handicaps, handicap differential and handicap index. I looked at the course rating and course slope of the various courses I played at and I developed a handicap calculator for my personal use, which provided the exact same information as the USGA calculators. The major difference was that my calculator used the Microsoft Excel program in association with macros to do the calculations, which can be accomplished on your home computer, and all the data was visible for my analysis. All one needed to do was enter your score and the course you played at to determine your handicap differential and index. This allowed me to more accurately determine how I played that day. A score of 95 at a difficult course might be better than a score of 88 at a less difficult course.
While I just enjoy the game of golf, I developed a curiosity about the physics of golf, since my profession prior to retirement was as a research physicist. Again I did a lot of reading on this subject, developed some programs for performing the necessary calculations and changed my equipment as a result. The net result was a noticeable improvement in my game. I thought I might share some of this physics with you.
The first thing I did was to take some golf balls that I was using and measure their weight and diameter. I was convinced that the Slazenger ball I used was lighter and smaller. Well it wasn't. All the balls weighed 1.62 ounces, about 45.9 grams, and had a diameter of 1.68 inches, about 42.7 mm. I used the following formula to determine ball speed , knowing the swing speed:
Velocity of ball = Swing Speed x (1+e/1+m/M)
- e= effective measure of momentum transfer, range = ( 0.67 to 0.8 )
- m = mass of ball, 1.62 oz.
- M = mass of clubhead, nominally 7 oz.
The saying goes as such: "You drive for show and putt for dough". Truer words were never spoken. Never-the-less, everyone wants to obtain a long drive, provide a good show, and a lot of emphasis is placed on the driver club. Three factors are of interest in this club. The first is the length of the shaft. If you buy a driver off the shelf, the length of the shaft today will most likely be 45 inches. This is generally too long for most golfers. The average shaft length of PGA tour golfers is 44.5 inches. I am only 5'7" tall, and getting shorter by the day. I found that a shaft length of 42.5 inches gave me a club that I was comfortable handling. As a result, I was able to increase my swing speed by 10 %. This is important, since swing speed is the one most important factor in determining drive distance. I still have a rather slow swing speed, comparatively, but I am fairly consistent in ending up on the fairway with my drive. I have tried to increase my swing speed. This resulted in the ball going into the rough or the woods. Nothing can ruin a golf score more than constantly having to recover from an errant drive.
The next important factor is "launch angle", which is influenced by the loft of the driver head and by your swing mechanics. Golfers with high swing speeds, such as the PGA pros whose average swing speed is 115 mph and some pros, notably Tiger Woods, attain speeds of 130 mph, can use a driver loft as low as 10 degrees. Most golfers have swing speeds under 100 mph, and the swing speed decreases as one ages. In my group, I doubt that anyone has a swing speed above 95 mph. My swing speed is less than that figure. Thus, I performed research to determine an optimum launch angle for my swing speed. Using equations of motion and other data found on the internet, I was able to generate a series of curves describing the path of the ball as a function of time for various swing speeds and various launch angles. I used swing speeds of 62 mph, 75 mph, 83 mph, 100 mph and 125 mph and calculated distance as a function of launch angle. I kept other factors, such as spin rate, temp, wind etc., constant. The results are interesting. At the lower swing speed, I calculated a 20 % increase in drive distance by increasing the launch angle from 10 degrees to approximately 15 to 18 degrees. At the higher swing speed, the calculations indicated that the drive distance increased 10 % by increasing the launch angle from 10 degrees to approximately 12 to 15 degrees. Assuming that ones swing mechanics are such that your swing is fairly level, this all translates to club loft. What it says to me is that for us older golfers with slower swing speeds, we should be using a driver with a loft of the order of 15 degrees. For those with higher swing speeds, the loft should be of the order of 12 degrees, never less than that, unless you are in the same class as a PGA pro. See my calculations on the next page. Link is at the bottom of this page.
I found the chart shown below on the internet which pretty much agrees with my calculations. From the chart, the optimum loft angle for a swing speed of 80 mph is about 16 degrees. At 16 degrees, drive range is 180 yds and at 10 degrees it is 150 yds. The optimum loft angle for a golfer with a swing speed of 100 mph is 12 degrees. At 12 degrees, driver range is 240 yds and at 10 degrees it is 220 yds.
When I first started looking at this problem, there were no drivers in our retail outlets with lofts greater than 10.5 degrees. Recently, manufacturers are beginning to understand the importance of club head loft and there are more clubs available in the retail market in the 12 to 15 degree loft range. I recently purchased an Adams driver with a club head loft of 13.5 degrees and I believe Calloway has a high trajectory driver with a 15 degree loft. We have several long drivers in our group; one of them uses a 4-wood as his driver. I'm sure that club has a loft greater than 15 degrees.
Let me first say, before I summarize, that none of this makes any difference if one has poor quality of contact. Okay let's summarize:
- The most important factor in increasing driver range is swing speed. The technology has been working towards that end. Titanium has allowed manufacturers to make lighter clubs. Shafts come in a variety of flex. Balance is generally achieved between the weight of the club head and the shaft.
- The next factor is launch angle. The slower your swing speed, the more loft you want. For most golfers, club head loft should never be less than 12 degrees. Retail outlets have launch monitors to help you pick the proper club.
- Finally, one needs to have a good quality of contact, always trying to hit the ball with your club's sweet spot. Work on your swing mechanics.
While I have not said much about the other aspects of the game, I did say that "one drives for show and putts for dough". Practice on the putting green can lower your score. The other factor is applying good course management to your game. I've found that one errant or misplaced shot can cause many more errant shots.