Dear Larry,
With the caveat that I don't really know the full swing stuff, here goes:
In your example all things were equal, but you didn't spercify what speed the robot is set, and clubhead speed at impact and thus the initial ball speed makes all the difference in optimum launch angle and hence club loft. For each different golfer's swing speed, there is a different combination of loft, launch angle, and backspin rate that maximizes carry and roll.
There is a big difference in pro driver shots and amatuer driver shots, and it relates mostly to the ball's initial speed. A typical pro ball leaves the tee at about 170 to 220 mph, while a good amateur speed is 150 to 200 mph. In the aerodynamics of how the golf ball combines speed, drag, spin, and lift through the air, there is a "threshold" speed that allows a "boring" shot. In a "boring" shot, the speed is sufficiently high that the drag on the ball is significantly reduced, and thus the ball will fly farther. This "boring" shot is within reach of most pros and very few amateurs. When you can hit a "boring" driver shot on a regular basis, your use for backspin is lessened. Backspin is mostly due to loft, and the higher the backspin the less sidespin, so high backspin flights stay on line better. That's why wedge shots are straighter than 2 iron shots.
At amateur speeds, not attaining the "boring" speed, golfers have more drag and so get relatively less distance for each mph of swingspeed. The tradeoff of more sbackspin and straighter shots pays better dividends. The tour player relies more on technique to keep sidespin out of the shot and so does not need all that much backspin or loft on the driver.
The driver's loft is only one (main) factor in the launch angle that the drive shot starts off. The other main factor is angle of attack, or how the driver head is moving thru the impact area. A downward blow imparts more backspin, and a level to upward blow gets the lofted face more flush to the launch angle, so there is more energy transfer in the desired direction but less backspin. You can vary the effective loft and hence the launch angle of your shots to suit the need, within a certain range.
While it is true that a "boring" and lower trajectory has greater roll on the same flat landing area of the course, the sorts of trajectories that amateurs need have curves that end up allowing rolls after carry that aren't that much different. For pros, there is a big difference in roll from a low trajectory and a high trajectory. For amateurs, total distance is maximized by a more-or-less high trajectory anyway, and the choices between more backspin and less backspin via loft don't change the roll all that much. Pros also like the lower trajectory more because it sends the ball under the wind, whereas a high trajectory is susceptible to variation due to head winds, tail winds, and side winds. When there is a good tail wind, a pro with an 8 degree driver will increase his angle of attack upwards so the launch angle is higher to allow the ball to benefit more from the tail wind.
Golf club manufacturers study these relations of launch angle, speed, and spin intensely, and they also make the balls with dimple patterns and cover / core properties to allow for different performance and trajectory combinations, mostly depending upon swing speed. For example, Titleist has a Launch Monitor [
http://www.titleist.com/t_7675.htm] with which they have gathered tens of thousands of combinations for golfers at all levels and swing speeds. In general, the amateur needs a higher launch angle and more backspin than a pro. Calloway has a ball dimple design that it claims aids "low speed lift" late in the ball flight to help keep the ball aloft in the dropping phase of the flight and thus maximize carry and impact angle for greater roll [
http://www.callawaygolf.com/glossary/browse.asp?displayRange=H-N].
There is a very nice computer animation [
http://simscience.org/fluid/red/golf.html] that allows you to plug in swing speeds and lofts and see a plot of the ball's flight trajectory, with a readout of the total distance. The speed range varies from 30 meters per second to 80 meters per second (roughly 75 mph to 200 mph). The author uses these typical numbers (in meters):
Amateur drive: Launch velocity = 60 m/s [155 mph]; Rotational speed = 2500 rpm; Launch angle = 9 degrees, Yields 187.05628 meters (204.6 yards carry).
Professional drive: Launch velocity = 70 m/s [180 mph]; Rotational speed = 3500 rpm; Launch angle = 6 degrees, Yields 218.66062 meters (239.0 yards carry).
At these spin rates and speeds, you can plot all launch angles and compare carry distances. The pro carry distance increases marginally from 5 degrees to 12 degrees launch angle, and then starts declining. The range of carry is 5 degrees = 217.1 meters [237.4 yards] to 12 degrees = 221.9 meters [242.6 yards] - only a five yard difference. Roll depends upon the angle of impact and the surface tilt and hardness -- AND the height from which the ball is descending and its component of forward speed. For a steep impact into normally hard flat fairway, roll is typically about 15% of carry. For lower impact angles, carry may get as high as 20% to 25%. Thus a 242.6 yard shot that landed with a low trajectory might get an extra 50 yards of roll, whereas the standard trajectory would roll about 35 yards (extra total distance of about 15 yards). So the angle of impact can just about double the roll distance, over the usual range of impact angles. Thus, roll can be increased a lot, while launch angle does not increase carry all that much. In the trade-off between launch angle and total distance, it is probably well worth it to give up some carry distance for more roll with a slightly lower trajectory, so long as you have enough swing speed.
However, for lower swing speeds, more roll comes from the ball descending from a higher height of the trajectory. A ball falling from a higher elevation gains more energy from the acceleration of gravity for the longer drop time, so when it hits the hard ground it bounces farther. There are "rolls" and then there are "rolls." What is happening at the higher swing speeds is that the ball hits the ground with more forward speed still in it, even though with less energy due to gravity since it drops from a lower height. These balls "bound" along and the "bounce" is not that much. For slower swing speeds, the "bounce" is more important for roll distance. Unfortunately, for slower swing speeds, since the carry is not that much, a higher percentage of a small carry doesn't mean all that much more total distance.
The amateur carry distances range from 184.3 [201.5 yards] to 187.1 [204.6 yards] meters over the launch angles 10 degrees to 15 degrees, and then start declining. The impact angles of these shots is not all that different, probably around 40 degrees or so, with roll being about 15% of carry. Hence, since carry only varies by 3 yards and is not that great anyway, an amateur is not gaining all that much in roll by lowering trajectory (a maximum roll gain of only 1 or 2 yards).
Golf Tips Magazine has an article about fitting for drivers and reports these recommendations from Titleist for swing speeds:
Clubhead
Speed Loft
Recommendations
< 70 mph 16 degrees or more
70-80 mph 12-15 degrees
80-90 mph 11-12 degrees
90-100 mph 10-11 degrees
> 100 mph 10 degrees or less
[
http://www.golftipsmag.com/content/pastissues/2001/apr/drivers.html].
TaylorMade reports the following example of combinations:
For example, a shot with an initial velocity of 120 mph combined with a six-degree launch angle and a 2,000 rpm spin rate will produce a shot that flies on a low trajectory and travels 155 yards. Meanwhile, a shot with an initial velocity of 120 mph but a 14-degree launch angle and 3,000 rpm spin rate will fly on a high trajectory and travel 205 yards. The higher launch angle produced a higher initial trajectory, while the higher spin rate generated extra lift, keeping the ball in the air longer.
[
http://www.taylormadegolf.com/global/technology/t_ball_Flight.asp].
In addition, weather conditions and wind and ball selection all influence total carry and flight trajectory. Here's a nice illustration of wind effects by Ken Tannar: Wind and the Golf Ball [
http://members.tripod.com/ktannar/id20.htm]. he also discusses weather conditions: Weather Affects Ball Flight [
http://members.tripod.com/ktannar/id21.htm].
Picking a low-spin ball for distance might make you more susceptible to slices and hook, so it's a trade-off in light of your swing speed and skill level. This GolfWeb article ought to help with ball selection: Golf balls: Sorting out what's right for you By Ted Johnson GolfWeb Equipment Columnist [
http://services1.golfweb.com/library/johnson/johnson961120.html]. In the book Strictly Golf Balls (1998), the author prints test results for numerous balls depending upon swing speed, always using the same 10.5 degrees loft in the driver and four types of balls -- 1. distance/durability, 2. feel/istance/durability, 3. spin/feel/durability, and 4. spin/feel/balata
At 80 mph, the maximum total distance is 197.1 yards (type 3 ball) at 12.1 degrees launch angle and 173.5 mph ball speed. The full range of distances is from 185 to 197.1 yards, at launch angles from 11.2 to 12.54 degrees, and ball speeds from 167.38 to 175.78 mph. Roll is about 10% of carry.
At 90 mph, the maximum total distance is about 229.83 yards (type 1 ball) at 10.9 degrees launch angle and 195.27 mph ball speed. The full range of distances is from 215.5 to 229.83 yards, at launch angles from 10.0 to 11.14 degrees, and ball speeds from 187.54 to 198.22 mph. Roll is about 15% of carry.
At 100 mph, the maximum total distance is about 248.83 yards (type 1 ball) at 10.2 degrees launch angle and 211.73 mph ball speed. The full range of distances is from 230.33 to 248.83 yards, at launch angles from 8.85 to 10.8 degrees, and ball speeds from 205.23 to 214.85 mph. Roll is about 8% of carry.
The clubhead design choice for locating the center of gravity in the head alters ball flight trajectory. A lower center of gravity reduces backspin for a more "boring" shot. The Ping Tsi Tec "Bounder" driver incorporates this sort of physics [
http://www.scoregolf.com/columnists/showarchive.cfm?article=268].
And finally, shaft characteristics can alter ball flight trajectory. Harrison Sports Golf Shafts designs a shaft that lowers the trajectory even with a higher loft, thus allowing the backspin to keep the ball in line but provide greater roll upon landing and keep the ball beneath the wind more [
http://www.harrison.com/hs_designs_lowlaunch.htm]. The company also has a neat animation of the added roll [
http://www.harrison.com/launch_anim.htm].
When all is said and done, one launch angle does not fit all golfers. Golfers with greater skill at avoiding sidespin and with faster swing speeds can afford a lower trajectory, get more roll, and get an unfair advantage from "boring" aerodynamics. Golfers with less skill at avoiding sidespin and with slower swing speeds benefit more from a higher trajectory, benefit less from going for extra roll, and need higher rates of backspin to keep the ball on line. The standard advice that amateurs use 11 to 12 degrees of loft in their drivers, and that pros use 8 to 10 degrees of loft is pretty accurate in general. And forget what the pros use! Play your own game.
Cheers!
Geoff Mangum
Putting Theorist and Instructor
The PuttingZone.com
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