Heavy Air and the Golfball

[David Davis]

Brent,

Hey I asked. It's a logical answer even if it reads a bit like shakespeare to someone of my meager intelligence. In fact, I did not misquote the anonymous member, who by the way was quoting another member that did all the research. It didn't make sense to me so I argued it but this was in vain. Now with your permission I would like to copy paste your response and pass it on. I do not need to quote the source but the result might be that I will be passed on the details of the expert directly to continue the debate. Which I don't mind at all :-)

Thanks for the explanation.

Can you make an education guess at how much further (in meters or yards) a ball flies due to the better aerodynamics in warm air compared to cold air assuming a 200 meter tee shot is being considered? Not including roll of course.

[Brent Hutto]

Schmidt was the all time Expo-killer.

Mike Schmidt, I assume you mean. Just for any Philly guys happening by, I'll share this OT recollection.

Some time in '85 or '86 me and a buddy drove up from D.C. to the Vet for a Wednesday afternoon game between the Phillies and the Braves. Both teams were cover-your-eyes awful and there were a couple thousand people in the stands, if that.

Schmidt was the entire Phils offense that day, pretty much. I think he hit a solo homer, maybe a base hit and a walk then in the bottom of the 7th he made a diving grab of a line drive, saving a run from scoring. Played like a Hall of Famer, unlike the other 19 guys playing that day.

Top of the next inning he comes to bat with a man in scoring position, takes a couple pitches then grounds out to end the inning. If there were 2,000 souls in attendance, then at least 1,900 of them roundly booed Mike Schmidt for making that out. You gotta love those Philadelphia sports fans.

[Kirk Moon]

Ancillary question #1:

I would imagine that in foggy conditions the presence of liquid water in the air would have a negative impact on ball flight and distance, primarily due to mechanical considerations (loss of kinetic energy of the ball due to impact with semi-stationary liquid water particles in flight, deposition of liquid water on the surface of the ball in flight.) 

Any data on the effect of fog on distance? 

Ancillary question #2: 

Could pressure changes result in a phase change from water vapor to liquid water (i.e. fog) on the back side of the golf ball when a rapidly moving golf ball flies through extremely humid air?  Since the phase of water in the air is, at least in part, a function of air pressure (higher pressure = higher water vapor carrying capacity, lower pressure = lower water vapor carrying capacity.)  Seems possible that the low pressure area behind the ball might have low enough pressure to allow for a transient phase change from water vapor to liquid water (just like those pictures you have probably seen of fighter jets with water vapor clouds around parts of the wing where pressure is very low). 

Would drag on the ball increase if a phase change were occurring on the back side of the ball while it was in flight?  Are there combinations of air temperature and humidity where such a phase change might occur in real life out on a golf course?

[Matthew Petersen]

I just read an article about Furnace Creek Golf Club in Death Valley where they are 214 feet below sea level, the lowest golf course on earth, they claim. They stated that the ball flies 10 yards or so less on an iron shot. Any thoughts?  The superintendent said when temperatures reach 123 degrees he sends the guys home because it is just too hot! Gotta hate those days when it just hits 120.

10 yards less as compared to? And what length of an iron shot?

240 feet of positive elevation certainly doesn't equate to that much change in distance. Some guys don't even see that much change at several thousand feet of difference.

I do.

I play golf in Utah at 4500-5000 feet and my 3 wood is easily 40-50 yards longer compared to playing in the bay area...near sea level.

Even my 9 iron is a good 20 yards longer at elevation.

That's fairly typical for that much elevation. But 5000 feet is 20x more than the elevation difference of Furncae Creek (240 feet negative). So by that logic, if anything, players should see a yard or two of difference in distance (shorter) at FC. No one would notice that.

[Steve Lang]

   Its the human feel of moisture... that's heavy

First consider the atmospheric pressure at elevations
Site Atm. Pressure:            
El, ft   psia      El, m   mm Hg   mbar
-200   14.80      -61   765   1021
0   14.70      0   760   1013
200   14.59      61   755   1006
700   14.33      213   741   988
1200   14.07      366   728   970
1700   13.82      518   715   953
2200   13.57      671   702   935
2700   13.32      823   689   918
3200   13.08      976   676   902
3700   12.84      1128   664   885
4200   12.60      1280   652   869
4700   12.37      1433   640   853
5200   12.14      1585   628   837
5700   11.92      1738   616   822
6200   11.70      1890   605   806
6700   11.48      2043   594   791
7200   11.27      2195   583   777
7700   11.06      2348   572   762
8200   10.85      2500   561   748
8700   10.65      2652   551   734

Applying a little pv=nrt and vapor pressure of water, one can see that warm air can carry a lot of moisture and how much density of air is affected by elevation, , what a drag... at sea level.. or below

Sea Level, Dry Air
temp, F   40   60   80   100
temp, C   4.4   15.6   26.7   37.8
pres, mmHG   760   760   760   760
% RH.    0   0   0   0
% Vol. Mois   0.00%   0.00%   0.00%   0.00%
mw   28.979   28.979   28.979   28.979
acf/lbmol   364.807   379.411   394.015   408.619
lb/ft3   0.079   0.076   0.074   0.071


Sea Level, 50% Relative Humidity
temp, F   40   60   80   100
temp, C   4.4   15.6   26.7   37.8
pres, mmHG   760   760   760   760
% RH   50   50   50   50
% Vol. Moist   0.41%   0.86%   1.71%   3.21%
mw   28.861   28.729   28.483   28.050
acf/lbmol   364.807   379.411   394.015   408.619
lb/ft3   0.079   0.076   0.072   0.069


Sea Level, 85% Relative Humidity
temp, F   40   60   80   100
temp, C   4.4   15.6   26.7   37.8
pres, mmHG   760   760   760   760
% RH   85   85   85   85
% Vol. Moist   0.70%   1.47%   2.91%   5.45%
mw   28.778   28.554   28.136   27.399
acf/lbmol   364.807   379.411   394.015   408.619
lb/ft3   0.079   0.075   0.071   0.067


4700 Ft elevation, 0% relative Humidity
temp, F   40   60   80   100
temp, C   4.4   15.6   26.7   37.8
pres, mmHG   640   640   640   640
% RH   0   0   0   0
% Vol. Moist   0.00%   0.00%   0.00%   0.00%
mw   28.979   28.979   28.979   28.979
acf/lbmol   433.209   450.551   467.893   485.235
lb/ft3   0.067   0.064   0.062   0.060


4700 Ft elevation, 50% relative Humidity
temp, F   40   60   80   100
temp, C   4.4   15.6   26.7   37.8
pres, mmHG   640   640   640   640
% RH   50   50   50   50
% Vol. Moist   0.49%   1.03%   2.03%   3.81%
mw   28.839   28.682   28.390   27.875
acf/lbmol   433.209   450.551   467.893   485.235
lb/ft3   0.067   0.064   0.061   0.057


4700 Ft elevation, 85% relative Humidity
temp, F   40   60   80   100
temp, C   4.4   15.6   26.7   37.8
pres, mmHG   640   640   640   640
% RH   85   85   85   85
% Vol. Moist   0.83%   1.74%   3.46%   6.48%
mw   28.740   28.474   27.978   27.103
acf/lbmol   433.209   450.551   467.893   485.235
lb/ft3   0.066   0.063   0.060   0.056
 
Looking at equation for drag forces on a body below.. given the coefficient of drag, velocity, and frontal area of ball are constant, drag is proportional to density of fluid (air)..  drag goes down, ball should go farther, though lift is also reduced as temps go up and elevation goes up...

from http://www.engineeringtoolbox.com/drag-coefficient-d_627.html

Drag force can be expressed as:

   Fd = cd 1/2 ρ v2 A         (1)
 
where
   Fd = drag force (N)
   cd = drag coefficient
   ρ = density of fluid
   v = flow velocity
   A = characteristic frontal area of the body

The drag coefficient is a function of several parameters like shape of the body, Reynolds Number for the flow, Froude number, Mach Number and Roughness of the Surface.    (These are normally determined experimentally)

[Tim Gavrich]

By the way, this bit of physical reality is one reason some armchair golf pundits oughtn't be so alarmed to see that Tiger hit an 8 iron 190 yards back at Congressional a few weeks ago.

Why so? I don't see where you're going with that Tim.

I'm certainly not calling anyone out; I was just annoyed to hear a lot of people (on the radio, around the golf course, etc.) following the lead of the seemingly shocked announcing crew when they heard that Tiger hit that club that distance, because no one bothered to explain that the ball goes farther when it's hot and humid (to say nothing of Tiger having a downhill lie, hitting to a firm green).

[Doug Siebert]

Interestingly enough I was informed by a member of the R&A something similar about 3 weeks ago. They had done extensive research and came to the conclusion that even temperature change does not affect the distance or flight of a ball. Something I just can't imagine. I always seem to hit so much further when it's warm and dry as apposed to the normaly cool wet condition we are use to here.

It's hard for me to accept that it's only due to me being more limber and loose when it's warm. No physics experts out there?

I'm not sure how they could have done such invalid research, did they hire creation scientists to do it?  It is elementary physics that warmer air is less dense, and the ball goes further in less dense air.  This is the same reason why it goes further at elevation, and why it goes further in humid air (though the difference between 0% and 100% humidity at 70*F is only about 270 feet in elevation or 5 degrees temperature change, so the effect of humidity is small)  If it was the warm golf ball cold weather golfers would keep warm balls in a thermos and switch them every hole

The reason why golfers think the ball goes shorter in humid air is 1) it "feels" thicker so it makes logical sense, 2) high humidity is more likely near the ocean (so lower elevations) and in wet areas (less roll) and 3) humidity is more noticeable when the air is still, so people's internal distance benchmarks aren't misled by shots hit with the wind