I wrote this up years ago, April 2009 in Golfweek. As I learned (?) by asking Frank Thomas, everything is variable: depends upon launch angle, humidity, NFL scores the night before, but it's basically 1.7% per 1,000 feet of elevation change, less as the club you hit gets shorter.
Playing distance: or, how far is 175 yards?
By Bradley S. Klein
You're standing over a shot that measures exactly 175 yards on the ground.
For most of us, that's an easy club to pull. An average male amateur might
select a 5-iron. A PGA Tour pro would probably hit a 7-iron or perhaps even
an 8-iron. An average female golfer might go for a 3- wood. The choice
obviously depends upon how far one hits the ball. But it also depends on how
far that 175 yards really is.
Compared to what? If you're playing golf in Denver, the shot will play
shorter than if you're playing in Death Valley, Calif. That's because air is
denser at 300 feet below sea level than at 5,000 feet above and thus offers
more resistance at the lower altitude. So there's more air to penetrate, in
effect, during the duration of the ball's flight when you're closer to sea
level - or under it.
What's the formula for calculating effective distance? Don't ask an engineer.
They'll just give you an engineer's answer. "It depends on launch angle and
spin rate," said Frank Thomas, formerly the USGA technical director and now
proprietor of his own firm, Frankly Consulting, in Chester, N.J. As Thomas
makes clear, effective distance is a function of a series of interactive
factors, including altitude, the vertical climb (or fall) of the shot,
humidity, wind and temperature. Each of these elements exercises a different
effect upon the golf ball's coefficient of lift and drag. Don't have time for
calculating differential equations in the middle of a round? Here's a quick
and dirty guide to figuring out effective distance. Note no. 1: these data
are my own non-linear extrapolations from USGA Research and Test Center
studies of driver distances and represent ballpark estimates at best. As with
everything else in golf, more research is needed.
For altitude, a good rule of thumb is two percent per 1,000 feet of
elevation. Actually, the figure is about 1.7 percent for drivers, probably a
little less for mid-irons given their higher spin rates and launch angles.
But ballpark estimates work well enough, so for each 1,000 feet of elevation
on that 175 yard shot, figure a 3 yard bonus. That means at 5,000 feet above sea level it will play like 160 yards.
Hot air is thinner than cold air, thereby offering less resistance and
allowing greater distance. On drives, the bonus approaches one yard for each
5-degree increment, less than that for a mid-iron. If that shot plays 175
yards at 75 degrees F., it will play about 170 at 115 degrees and 180 at 35
degrees.
Humidity has a much smaller effect on distance than either altitude or
temperature, but it does count, even if it's barely discernible. Contrary to
conventional wisdom, humid air is thinner and drier air is denser. Note no. 2
(to certain TV tournament commentators): the ball actually flies farther in
humid conditions than in arid ones. If folks think the ball travels better
when they play in the desert, that's a function of altitude, not humidity.
Wind is the obvious wild card in any golf game. Interestingly enough, on long
shot (with a lower trajectory), it's effect on roll actually exceeds its
effect on carry. For that 175-yard shot, the effect is about the same, but a
fair number for calculation is +/- one yard for each mile per hour of
head/tail wind. Into the teeth of a 15 mile per hour breeze the shot plays
190; straight downwind it plays 160..
Let's not forget the vertical climb or fall of the shot. We all know downhill
shots travel farther and uphill shots travel less. But how much? This one is
very tough to estimate because it varies so much with the shot trajectory.
Shots with a higher angle of launch (and descent) will be affected less.
Confused? Figure the difference at about 1.5 percent per 10 feet of elevation
change (Note no.3: it helps to be able to eyeball elevation shifts). So,
let's consider a 175-yard par-3. Uphill to a green 30 feet above the tee, the
shot plays 183 yards; downhill to a green 30 feet below the tee, it plays 167.
It's all pretty simple to calculate. Who says golf isn't rocket science?