What does a golf ball weigh?And why?
Dave
Tutelman 
June 28,2017
Yes, it weighs just under 46 grams. You probably knew that.
Here are the details of why it does, and how much under 46
grams.
Why would we expect it?
The Rules of Golf say that the ball
must not exceed 46 grams in weight. Well, it's a bit more precise than
that. "The weight of the
ball must not be greater than 1.620 ounces avoirdupois (45.93 g)."
But 46 grams is good enough for what we need to know.
If the USGA is setting a limit, I have to believe there is a
performance advantage to exceeding the limit. So we would expect
manufacturers to want to build balls right up to that limit without
exceeding it.
I grabbed a bag full of golf balls and took them to
my basement workshop, where I weighed them. I used an inexpensive
digital scale with a resolution of a tenth of a gram. Here is the
distribution I observed.
 It's pretty close to a bell curve, considering the
size of my sample (28 balls).
 Only one ball was over 46 grams in weight, and that
one only by a tenth of a gram.
 All but two of the balls were in the halfgram range
from 45.5g to 46.0g.
 The two outliers were out by 0.1g, one at each end of
the distribution.
The balls were everything from inexpensive distance rocks to premium
balls like the ProV1, ChromeSoft, and B330. There did not seem to be a
bias in the distribution by make or model, but that was just by
eyeball; I didn't run any statistical tests, and I doubt there were
enough balls of any one model to draw a valid conclusion. All in all,
that suggests
that the ball makers work to keep ball weight as close to 46 grams as
they can without exceeding it.
Here's
another fun fact for you. One pound is 454 grams. That
means 10 golf balls weigh almost exactly one pound. If you have a
bag of balls and want to know how many are there, just weigh the bag in
pounds and move the decimal point one place to the right.
At this point, we have answered both questions in the title. The rest
of this article is an analysis and "lab experiment" that looks
more closely at "why?" Specifically, it asks what advantage there is to
a ball that exceeds the limit. It doesn't come up with information that is particularly
useful for a golfer or a consumer; I just want to record it here in case the question
arises again.

Why the rules limit?
What is the advantage that the rules try to take away by limiting balls
to 46 grams? Usually, when the USGA limits what you can do with
equipment, the first suspect is driving distance. So let's investigate
how driving distance varies with the weight of the golf ball.
Computer simulation

The TrajectoWare Drive
computer program accurately simulates carry distance of a drive (as
long as spin does not exceed 4000rpm), and permits varying lots of
conditions  including the weight of the golf ball. So I tried varying
the ball weight and seeing how the distance varied. I expected that the
distance would go up markedly as weight increased. Much to my surprise,
it didn't. At the 95mph clubhead speed and 10.5° loft I used, the peak
distance occurred at just about 46 grams of ball weight. That isn't the
sort of performance that usually motivates the USGA to set rules
limits. Let's look further.
I tried varying the clubhead speed. I set up the
driver loft at 12° to give maximum distance at about 100mph, used
"neutral" numbers like 200 grams for clubhead weight and zero angle of
attack, and varied the ball weight.
This gave a much more interesting result. For clubhead speeds at 100mph
or more, there is a distance advantage to a heavier golf ball.
How much variation are we talking about? The curves on the graph are
pretty flat, and it's not that easy to see. So I tried displaying them
a different way. 
I
normalized all the curves so each would show the distance relative to its
distance with a 46gram ball. This shows very clearly the value of
departing from the limit set by the rule.
And there is very real value there. A ball weight of 52g, 6 grams over
the limit, can get another 13 yards of carry (the orange curve). And
notice that the curve is still going up sharply, suggesting that a
ball closer to 60g would do even better. That is certainly
reason for the USGA to limit the ball weight.
But you have to be a very big hitter for that much gain; you would need
120mph of clubhead speed. At a PGA Tour average clubhead speed of
113mph, you would see about 8 extra yards for the same 52g
ball. And the potential gain at 100mph is less than a yard for any ball
weight.
But wait! It also works the other way. For clubhead speeds of 90mph or
less, you lose
distance with a heavier golf ball. No rule needed for them. But that
raises an interesting question: can
a slow swinger get extra yardage from a lighter ball? And
if so, why didn't the USGA put both upper and lower limits on the
weight of the golf ball?
Yes, there certainly is distance to be gained from a lighter ball. At
70mph (probably typical for a women's golf league, or at a seniorsonly
course), a 40g ball will get 8 extra yards  and the curve says there
is more to be had from still lighter balls.
Before we get to the question of USGA intent, let's see if we can
explain the surprising result  heavy balls give more distance for big hitters but less distance
for slow swingers  in terms of physics.

Physical explanation
Why
should a heavier ball go farther than a lighter one? This is surprising
on the face of it. After all, the heavier ball will have lower initial ball speed,
all other things being equal. Perhaps even more surprising is that the
lighter ball goes farther with a low clubhead speed.
The answer is aerodynamic forces. Here are the forces  the only
forces  on a ball in flight.
 Drag
is an aerodynamic force exerted exactly opposite to the direction the
ball is traveling.
 Lift
is an aerodynamic force exerted exactly perpendicular to the direction
the ball is traveling. It is usually upwards, hence the name "lift".
 Weight
is a gravitational force always directed straight down.
Let's look more closely at each of these forces. 
Force 
Direction 
Proportional to: 
Helps or hurts
distance 
Drag 
Opposite ball's
path 
 Square
of ball speed
 ... other things ...

Hurts 
Lift 
Perpendicular to
path, generally upwards 
 Square
of ball speed
 Spin
 ... other things ...

Usually helps 
Weight 
Straight down 

Hurts 
The reason I emphasized "square" is that squarelaw variation makes these forces substantially
different for the different clubhead speeds. When we compare 120mph
with 70mph, the ratio is 1.7.When we compare their squares,
the ratio is 2.9, almost 3. That's very substantial. If lift and drag
on the big hitter's ball is three times that on the slow swinger's
ball, we should expect big differences in the trajectory.
Don't believe it? Let's look at what happens in the absence of lift and
drag.
Here are the trajectories of two balls hit identically, except one
travels in a vacuum and the other at sea level air density. You might have expected
drag to cause the ball not to go as far in full atmosphere. But in
fact, lift plays an even bigger role than drag. Lift keeps the ball in
the air, working against the weight force which pulls the ball to the
ground. So lift will make the ball go farther, because it keeps the ball moving
forward through the air longer. The ball may slow
down because of drag, but it is still going forward at a significant
pace, so keeping it in the air will increase the carry distance.
So lift helps. But drag hurts; it slows the ball. How much? Back to
basics: Newton's F=ma can be solved for acceleration: a=F/m.
Any slowing down of the ball is deceleration, or negative acceleration.
Why negative? The drag force (see the diagram above) is exactly opposed
to the direction the ball is traveling. So it is a negative force in
that it is opposite the direction of motion. If the force is
negative, then the acceleration will also be negative  slowing the
ball. For a given amount of drag, you can reduce the deceleration
by increasing the mass of the ball. So we can count on mass to
work against drag and limit how much the ball slows down.
Let's get back to those big differences between the big hitter and the
slow swinger, and how that factor of 3 difference in lift and drag will
affect their ball flight and hence their distance.

Big
hitter:
clubhead speed = 120mph 
Slow swinger:
clubhead speed = 70mph 
Drag 
The big hitter
is helped a lot by the extra mass of a heavier golf ball. 
Since the drag
is only 1/3 that of the big hitter, the advantage of extra mass is not
nearly as great. 
Lift 
The big hitter
has three times the lift, due to the extra ball speed. But it's even
more than that; the lift advantage is probably over 4 when you factor
in the extra spin due to higher clubhead speed. With all that lift, a
heavy ball isn't much of a problem. 
The slow
swinger, with only a quarter of the lift, has trouble keeping the ball
in the air. Remember, lift is working against gravity. Too little lift
and gravity wins earlier; the ball tumbles from the sky and stops its
forward progress. Any extra weight on the ball is going to be a problem
here. 
Excessive
Lift 
If the lift
force is so large as to actually be greater than the weight,
the ball is going to curve upwards. This is called "ballooning", and it
hurts distance. Remember, lift is mostly
upwards, not completely upwards. It is perpendicular to the path of the
ball. If the path of the ball slopes upward more, then the
perpendicular lift slopes backwards more. That backwards component is
another force decelerating the ball from getting downrange. Ballooning hurts distance, and extra
weight helps the big hitter by reducing ballooning. 
Excessive lift?
What "excessive"? Give me more of it! I don't have enough lift. If you
can't give me more lift, then at least give me less weight in the ball. 
So ball weight counters drag, and the big hitter has a much bigger drag
problem. Ball weight also counters lift. But lift is good for the slow
swing and probably bad for the big hitter. Bottom line: it is no longer
surprising that a big hitter wants more ball weight and a slow swinger
wants less.
Let's take another look at that graph of relative distance. We made a
mistake there, and now we're in a position to understand how and why.
The mistake was to use the
same loft for all the clubhead speeds. The graph assumes
the same driver loft for all clubhead speeds. But the
ideal loft will be greater for lower clubhead speeds.
Here is a table of the best loft for each clubhead speed.
Clubhead speed 
70 
80 
90 
100 
110 
120 
Optimum loft 
18° 
15.5° 
13.5° 
12° 
11° 
9.5° 
So let's assume that each of the golfers at each of
the speeds was properly fitted for their driver, and plot relative carry
distance vs ball weight again.
The general shape is still the same; big hitters get more distance from
a heavier ball, and slow swingers more distance from a lighter ball.
But the gains and losses from ball weight are much smaller.
 A 52g ball now only gets 4 extra yards for a big
hitter, compared with the previous 13 yards. At least as important, the
curve looks like 5 yards is the maximum it can ever improve.
 A 40g ball only gets 2 extra yards for a slow
swinger, compared with the previous 8 extra yards. And it looks like 2
yards is the biggest the improvement is ever going to get.
The physics should tell us why. The slow swinger's fitted driver will
have 18° of loft to the big hitter's 9.5°  almost twice the
loft. Loft does two things  increases launch angle and increases spin 
that the slow swinger needs. If they didn't get it from added driver loft, they'd have to make up for it with a lighter
ball. So the difference in loft makes up for most of the difference in
ball weight. The shape of the curve for the fitted driver is similar to
that for the fixedloft driver, but the amplitude of the curve is less
than a third the size.

Balls for slow swingers
Still, if
you don't have much clubhead speed, there is some small advantage to a
lighter ball than 46 grams. Do the ball manufacturers take
advantage of it and make, say, a 40g ball for seniors and women? Well,
most of the ball companies do make one or more women's model golf
balls. They didn't show up in my first set of measurements because I
didn't have any around my "lab". (My wife gave up golf more than 10
years ago
because she wasn't physically up to it.) But if there is an advantage
in practice and not just on a graph, you would expect that women's golf
balls would be the place it would show up.
So how do I get a variety of them to weigh?
Colonial Terrace GC, my town's municipal course, has a women's league
that plays on Tuesday mornings. So the next Tuesday, I showed up at 7am
and got permission to hang out at the registration desk and ask to
weigh women's golf balls. (Get that snide grin off your face.
I got enough of that on Tuesday.) Here are things I learned from that
effort.
 Only
half the women in the league use (or even have in their bag) a women's
model ball.
 Of those that didn't, only half were even aware that
women's golf balls exist.
 The balls were lighter than the men's golf balls. But
hardly at all; there was only a 0.3g difference in the average weight.
Here are the statistics for the weights that I found.

Men's
model 
Women's
model 
Average 
45.71 gram 
45.41 gram 
Std.
Dev. 
0.16 gram 
0.22
gram 
Median 
45.7 gram 
45.5 gram 
The display on the graph is an oldschool way to visualize the
relationships of empirical probability distributions. The horizontal
bar is the mean (average) and the rectangle behind it extends one
standard deviation each side of the mean. Note that the rectangles have
a bit of overlap between them (not much at all), and the standard
deviation of neither distribution extends all the way to the mean of
the other. That suggests a small but probably significant difference in
the underlying distribution.
A curious result, which leaves us a
dilemma. The women's balls are lighter (probably with statistical
significance), but not nearly enough lighter to give a physical
advantage. So the golf ball manufacturers seem to be doing it
deliberately, but not for the purpose of greater distance. How can we
explain this? There are a few possibilities:
 There is no
performance need to make them lighter. Golf ball manufacturers can
increase lift by playing with the dimple pattern and thereby affect the
aerodynamic lift force. This is probably easier and even more effective
for performance than making a whole line of lighter golf balls.
 The
only performance aspect we've mentioned so far is distance. How about
wind resistance? It is a good thing for a ball's flight to be less
affected by a crosswind or headwind. And a heavier ball is more windresistant. So
let's keep that aspect of performance.
 But the women's model
balls are indeed lighter, if not enough to affect performance. Why?
Notice that the standard deviation is larger. Perhaps each manufacturer
decided to reduce costs by widening the limits of quality control (larger
standard deviation), but still stay under 46 grams by designing to a
lighter center of the distribution (lower mean weight). That's a strong
statement considering what a small sample size I have, so it is
speculative at best.
In any event, there is some small
distance advantage to be had by making lighter balls for lower clubhead
speeds. I haven't seen any indication that ball manufacturers are
taking advantage of it.

ConclusionGolf balls are manufactured to be just under 46
grams in weight. Men's or genderneutral golf balls tend to be within a
half gram of that, women's balls maybe a third of a gram lower than
men's.
The
rules set an upper limit of 46 grams, and there is a
distance advantage that big hitter gain with heavier balls. But there
is a small distance advantage for slow swingers to use lighter balls.
So the rule seems less interested in keeping things equal than
"protecting" golf courses from big hitters.
Last modified  June
29,2017
