Comparison of Trajectory Programs

Wishon	Tom Wishon Trajectory Profiler version 2.0. Nice GUI on a commercially available program. Has separate modes for launch parameters directly or for impact parameters (which computes launch parameters). This dual-mode interface made it the first choice for this study. Actually, this software was develeoped by GolfMechanix and "private labeled" for Wishon. The same software may still be available directly from GolfMechanix. The link here is where I last saw it, but I had to look for it on their site.
Dupilka	Niblick Golf Crafter Trajectory Model version 3.0. GUI similar to Wishon, and predates it by years. Only has a single mode: impact parameters. In order to use launch parameters, you have to guess a good set of impact parameters and tweak them until it shows the launch parameters you want. This software used to be freely downloadable from Max Dupilka's web site, but he has discontinued it. A newer version is available and Max is allowing it to be downloaded from here.
Adams	John C. Adams' Golfball Spreadsheet version 2D. This is an Excel spreadsheet that Adams used in some research, presented to the American Society of Mechanical engineers 2/20/2004. His excellent presentation and earlier versions of his spreadsheet used to be downloadable at the ASME site; unfortunately is it no longer available. This program was intended for driver-type trajectories only; it gives truly silly results for short irons, and Adams will be the first to admit this.
OptimalFlight	Todd Kos' OptimalFlight. I do not have this software yet, because it requires a later version of Excel than I have on my computer. Todd provided me with its output for the sample launch parameters, so I could include it in the comparison. You can see more about the program at Todd's web site.

• The "Real World" row contains actual, measured carry distances. They are the accuracy standard by which the programs need to be judged.
• All these points involve driver lofts and ball speeds. This study was not interested in how well the programs simulate irons, just drivers.

Results

Yardage error

1. The sample at 121mph is probably a wild data point. All the programs estimated its distance about 17 yards lower than that program's estimate for nearby samples. I'll ignore that sample in the subsequent observations.
2. The Wishon and Dupilka programs had a substantial correlation between ball speed and error. The signed value of the error decreased with increasing ball speed. In more detail:
• The Wishon program was at its most accurate at about 140mph of ball speed, while the Dupilka program was at its most accurate at about 170mph of ball speed.
• At long-drive ball speeds (over 170mph), the Wishon program was way low -- 25- 40 yards off. The Dupilka program gave usable results, within 10 yards.
• At typical golfer ball speeds (120-150mph), the Wishon program gave usable results, within 10 yards. The Dupilka program was 10-20 yards high.
3. The Adams and OptimalFlight programs did well -- inside 5 yards -- for all ball samples except the outlier at 121mph. OptimalFlight usually did a little better, but both gave better than merely "usable" results.

Shape of the launch space

Wishon - The Wishon program produces a launch space that looks like this. It is a chart of carry distance in yards for combinations of launch angle and spin. In order to visually enhance what the graph looks like, I have added color representing the yardage. The redder the color, the longer the drive. The colors go through the spectrum, all the way to violet for short drives. Looking at this chart, we can see: The maximum drive for a ball speed of 124mph is 201 yards. The conditions to attain this drive are 20º of launch angle and 2500rpm of spin. (There is a red circle around the maximum.) The 201-yard point lies on a "ridge" of fairly long distances going diagonally across the chart. The ridge is represented by the black dotted line. Distance decreases in both directions from the maximum, but very slowly.

Adams, Dupilka - This launch space was produced by the Adams spreadsheet, but the Dupilka program creates one very much like it. It is similar to the Wishon launch space in a few ways, but distinctly different also: First, a similarity. At 20º and 2500rpm, the distance is still 201 yards. Another similarity. There is a diagonal ridge of good drive distances. Big difference! 201yd is not the maximum on this graph. Distance continues to increase as you go to higher launch angle and less spin. We have only plotted it to 26º, but it is not showing signs of decreasing again, the way the Wishon plot did. Another difference, and an important one. As we go left along the ridge (to lower launch angles and higher spin), the distance drops off significantly -- much faster than on the Wishon graph. For instance: On the Wishon plot, moving 6º along the ridge, from 20º to 14º, you lose only 2 yards of distance (201 to 199). On the Adams plot, moving the same 6º along the ridge, you lose 11 yards (201 to 190). Not only does the ridge have more variation as you move along it; it is also "sharper". That is, you lose distance faster as you move away from the ridge. This is very visible from the much larger violet areas (lower left and top right) on the Adams chart than the Wishon chart.

Other Observations

• For ball speeds above about 135mph, the Wishon program gave significantly higher hang time estimates for the ball flight. For lower ball speeds, Dupilka gave almost as large a hang time as Wishon, and both significantly higher than Adams and OptimalFlight.
• I made it a point to observe the peak height of the trajectory for some of the samples. The Adams, OptimalFlight, and Dupilka programs had very similar heights, but the Wishon program predicted that the ball flew significantly higher, usually about 20%. This probably strongly related to the higher hang time.

Conclusions

• It has a distinct bias with respect to ball speed, so any trend that involves ball speed (directly or indirectly) is suspect.
• It gives a different shape of launch space from that of the other programs. This fact is true at several ball speeds, including some where the Wishon program clearly does not predict distance well. So I trust the other programs more. It would seem that the Wishon software has other biases beyond just ball speed, because ball speed was held constant in each of these plots of launch space.
• Note that there is no data on ball speeds below 120mph. That is a shortcoming of the study. It is possible that the Wishon program might actually be more accurate than the others for low ball speeds. There is no trend to indicate that this is true, but it can't be ruled out completely yet.

Next Steps

• Gives similar results to those of the OptimalFlight and the Adams spreadsheets.
• Has a flexible and powerful user interface -- a lot more so than can be accomplished by layering an "application" on top of Excel.

• Measured ball speed, spin, and launch angle.
• Measured carry distance (total distance, too, if you have it). I am not interested in the data if the distance was computed by the launch monitor rather than actually measured. But the measurements don't have to be "paced off"; they can be radar or laser measurements, such as Trackman supplies.
• Other environmental info, such as altitude (if not at sea level), wind speed and direction, and temperature.
• Preferably several (4-8) similar hits, so wild data points can be identified and ignored.

Appendices:

1. Information about drive data

2. Settings for the various programs

• Altitude / air density - All the programs have "sea level" as their default. Some of the data were taken at significant altitude. The way I accounted for this in the programs was:
• Wishon: set the altitude directly with a control in the program.
• Dupilka: set the altitude directly with a control in the program. Dupilka's control also shows the fractional pressure density, compared to sea level. I copied this number down.
• Adams: this program takes barometric pressure in inches of mercury. I used the fraction copied from the Dupilka program, and multiplied it by the default pressure from the Adams program. I plugged the result back into the air pressure box in the Adams program.
• Other atmospheric conditions - All programs allow adjustment for temperature. It was set the same for all programs. While it might not have been exactly as the conditions for the real-world strike, (a) none of the strikes were under extreme conditions, so it would not matter much, and (b) it should affect all the programs the same in the error induced. No wind was reported for any of the strikes, so none was cranked into those programs that deal with wind. That may have been oversight on the part of the person reporting the data, but it is the best we can do with the data. However, it might account for the one wild data point, where all programs reported a considerably lower-than-reality carry distance.
• Launch conditions - All the programs except Dupilka start with launch conditions (ball speed, launch angle, and spin). Dupilka only allows impact conditions (clubhead speed, loft angle, attack angle, clubhead mass). It does provide launch conditions as output. So I "tweaked" the Dupilka program for each data point, to get it so the input impact conditions resulted in the desired launch conditions.
• Other default parameters:
• Adams has a tee height that defaults to one yard. I set it to zero, to match what the other programs do.
• Dupilka, having been written in 1999, has a COR of less than the currently-allowed 0.83. I increased it to 0.83 using a control provided in the program. This is really a non-issue anyway, since it is an impact condition; as long as the launch conditions were tweaked to be right, it doesn't matter what the COR is.