Comparison of Trajectory
Tutelman - January 29, 2007
mini-study was provoked by response to my study of launch space
surfaces, and my driver fitting recommendations based on that
study. The accuracy of the Tom Wishon Trajectory Profiler was called
into question. David Bahr in particular suggested that it does not do as good a
good job with drivers as it may with irons.
This motivated me to take a
real-world points in launch space and see how each of several programs
stack up. The programs are:
is the comparison table. Points to note:
Wishon Trajectory Profiler version 2.0.|
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. It can be ordered from Wishon Golf's
this software was develeoped by GolfMechanix and "private labeled" for
Wishon. The same software is available directly from GolfMechanix.
Golf Crafter Trajectory Model version 3.0.|
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.
Adams' Golfball Spreadsheet version 2D.|
is an Excel spreadsheet that Adams used in some research, presented to
the American Society of Mechanical engineers 2/20/2004. You can see his
excellent presentation and download earlier versions of his spreadsheet
at the ASME
This program was intended for driver-type trajectories only; it gives
truly silly results for short irons, and Adams will be the first to
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.
"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.
|Wishon||323 / 9.4||310
/ 7.8||217 / 6.5||226 / 6.8||208 / 6.6||196 / 6.2||204 / 6.4|
|Dupilka||350 / 8.2||327
/ 7.7||226 / 5.9||235 / 6.7||220 / 6.4||205 / 6.0||214 / 6.1|
|Adams||358 / 8.3||333
/ 7.0||212 / 5.4||220 / 6.0||202 / 5.7||189 / 5.3||197 / 5.4|
|OptimalFlight||360 / 8.4||336
/ 7.0||215 / 5.4||222 / 6.1||205 / 5.7||191 / 5.3||199 / 5.5|
most important result is the difference between the program's output
and reality. So the first thing I looked at was the yardage error. I
plotted the error against ball speed, launch angle, and spin. The only
one where there was a visible correlation was ball speed. Here is the
graph of yardage error vs ball speed.
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
- 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 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.
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
- 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.
Shape of the launch spaceCritical
to my work with optimizing drivers is the "shape of the launch space"
-- that is, the shape of the surface when you plot yardage against both
launch angle and spin for a given ball speed. Here are two very
different "shapes" for a ball speed of 124mph (corresponding to a
clubhead speed of about 85mph).
Those are big differences. And those same differences appeared in launch spaces at 100mph and at 200mph ball speeds as well.
- 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
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:
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.
- 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.
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.
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).
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 ObservationsThe Wishon program differed from the other three in a few additional ways:
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.
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.
ConclusionsI no longer trust
the Wishon software for variational analyses. I never really
trusted it for absolute distances, but used it a lot for observing
trends when varying parameters. After this data, I can't trust it with
trends either, because:
- It has a distinct bias with respect to ball speed, so any trend that involves ball speed (directly or indirectly) is suspect.
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.
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
Next StepsThe first of the "next steps" has been to build a program that:
didn't realize that was the next step until Frank Schmidberger
contacted me, having seen a draft of this report, and proposed it. We
collaborated to produce TrajectoWare Drive, which you can download for free from http://www.trajectoware.com.
If you're interested in the subject matter of this report, you will
want to download and try it. Feedback will be welcome; please leave it
on the forum, so others can discuss it as well.
- Gives similar results to those of the OptimalFlight and the Adams spreadsheets.
a flexible and powerful user interface -- a lot more so than can be
accomplished by layering an "application" on top of Excel.
I need to
re-work and re-write my article on optimizing a driver, because I no
longer trust the Wishon software. I will use the TrajectoWare Drive this time. I expect the difference in
the shape of the launch space may produce some differences in the
strategy I recommend.
There may be figures in the Club Design
Notes that also need to be re-worked, though I don't think the verbiage
that goes along with them will require much change.
Finally, if anyone can give me reliable data for lower ball speeds, I would much appreciate it -- and will do the work to see how it fits into the overall conclusions. "Reliable data" means:
Thanks in advance.
- Measured ball speed, spin, and launch angle.
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
- 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.
Information about drive dataThe source for this data is Todd
Kos, except where noted otherwise.
|Long Drive 1||Jason Zuback,
drive #1 at ReMax finals, 2006.|
|Long Drive 2||Erik Lastowka,
Drive #4 at ReMax finals, 2006.|
|Big Tour Drive||Reported drive
of Bubba Watson. Distance measurement not exact.|
|Robot 1||Golf Labs robot
test, made for Golf Digest research article.|
|Robot 2-4||Robot test data - averages - from various sources (GolfWorld, etc.)|
|Bob 1-2||FlightScope Pro measurements in Green Valley, AZ (2700 ft altitude). Source: Bob Barrette.|
2. Settings for the various programsI
used the default conditions for most of the things in each program.
This is especially important for things like the aerodynamics of the
ball. I simply went with the default ball for each program. Here are
the exceptions to that rule of "go with the default".
- 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
- 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.
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.
Last modified July 21, 2007