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What Happens at Impact
I'd like to thank Bernie
Baymiller for the
strobe pictures of impact. Bernie's father was the director of
R&D for Spalding Golf in the 1940s, which is where and when the
pictures were taken.
It's probably appropriate to begin
the discussion of impact with a highspeed strobe photo of
impact. So
here's one  perhaps the earliest ever taken. It was
taken by Harold E "Doc" Edgerton of MIT, the inventor of the strobe
flash.
Here are some facts about the impact shown here:
 The ball is a Spalding Dot 100compression balata
covered wound ball. The club is a wooden driver with a 12degree loft.
 The total duration of this impact is 0.0004 seconds;
that's 4/10,000 of a second, or 0.4 millisecond.
 According to the caption supplied by Bernie, the
clubhead moves 0.35" during impact, about a third of
an inch. (My calculations suggest it is longer  probably about an
inch.)
 The ball leaves the clubhead at 238 feet per second
(162
mph). It is consistent with a clubhead speed of 120 mph, with the
1940s clubhead and ball in the picture. That's quite a high swing speed
for that era, but achievable.
 The 1.68" ball diameter compressed to 1.56" on the
clubface,
and elongated to 1.78" as it left the face.

My usual rules of thumb for impact are pretty similar to the collision
described in the Spalding pictures:
 Impact lasts no more than a half millisecond.
 The clubhead moves less than an inch during this time.
 The
force between clubhead and ball can peak between 2000 and 3000 pounds.
(It can average about 1900 pounds over the 0.4 millisec of impact. The
peak is between 1.4 and 2 times the average force.)
So what is actually going on during that halfmillisecond or so of
impact? Here's the story, as described by Cochran & Stobbs
 and in somewhat more detail by Gobush:
 In the first microsecond of impact, we have the
irresistable
force meeting the immovable object. The ball has to react somehow to
the momentum of the clubhead, and the leastenergy way it can react is
by moving up the lofted clubface. Initially it slides
up the
clubface, because there isn't enough friction yet between clubface and
ball. But all that is about to change very quickly.
 The ball cannot acclerate to an upwards velocity in no time
at
all; that would require infinite acceleration, which requires infinite
force. So it can't get completely out of the way of the clubhead just
by sliding upwards. It begins to compress on the
clubface,
which creates a force between the clubface and the ball. If you don't
think this is a large force, just try to compress a golf ball by 30% of
its diameter using your fingers. Not even close! OK, use a vise; it's
still very hard to apply that much compression force. Remember, this is
a force that averages almost 2000 pounds during impact, and can easily
peak around 3000 pounds. This force of compression does two important
things:
 It begins to accelerate the ball with a horizontal
component, not just the vertical motion up the clubface.
 It creates a lot of friction between
ball and clubface. So, instead of sliding up the clubface, the ball
begins to roll instead.
 The
ball continues accelerating upwards (due to the loft) and
horizontally (due to the compressive force). The sliding has turned
completely into roll, so the upwards acceleration increases the
speed of roll. At some point, the momentum absorbed from the
clubhead through acceleration has the ball moving faster than the
clubhead. In other words, the elastic rebound of the ball's
acceleration allows the ball to release from the clubhead. At this
instant, its launch conditions are determined.
Launch Conditions
The term "launch
conditions" refers to the ball speed, the ball direction, and the ball
spin  all taken the instant the ball releases from the clubface. Here
is how impact conditions (things like clubhead speed, clubhead mass,
loft, and other less important parameters) affect the launch conditions.
Ball speed
In a perfect collision, the ball speed would be given by the simple
equation:
V_{ball}
= V_{clubhead}

2
1
+ m/M

Where m is the ball mass and M
is the clubhead mass.
But in real life, the collision is not so perfect. There is some loss
of speed for a variety of reasons. Here are the major reasons, and for
each a factor to correct for it.
 Energy loss due to compression of the ball
 As the ball
compresses on the clubface, and as it rolls in that compressed state,
it loses energy to internal friction. (In fact, it's a USGA rule that
it must lose a certain amount of energy, or the
ball will not
be approved as conforming.) In a collision, energy lost to internal
friction is accounted for by a factor called the "coefficient of
restitution", the fraction of velocity left after the loss of energy.
Golf literature refers to this as COR, and
physicists and engineers call it e in equations. In
order to correct for this, replace the "2" in the ball speed
equation by (1+e).
Some interesting values of the coefficient of restitution are:
 0.78 for the typical club today.
 0.83 for drivers today, which get a little more
restitution from flexible, springy faces. For more information on this,
see my article
on hard clubfaces.
 0.67 in some of the older literature. When
Cochran &
Stobbs wrote their book, clubs and especially golf balls were not as
"live" as today.
 Glancing blow due to loft
 The "perfect" collision of the equation above assumes that the impact
is at right angles to the clubface. This implies not only a
"squaredup" clubface, but also a zeroloft club. I don't know anybody
who plays with zeroloft clubs, so we better have some way of
accounting for oblique hits. Apparently different engineers estimate
this loss differently. The diagram at the right shows four different
estimates of ball speed loss due to loft:
 Cochran
& Stobbs,
in Figure 23:5 of their book, present the effects of loft on launch
conditions for lofts of 0°, 10° (a driver), 30° (a 5iron),
and 45° (a 9iron). They measured the launch conditions  ball speed,
launch angle, and spin  using a multipleflash strobe photo on a
marked ball.
 The two trajectory
programs
I use, one from Tom Wishon and the other from Max Dupilka, compute
launch conditions from collision conditions. I used those programs to
compute the launch conditions for the four lofts in Cochran &
Stobbs. The programs did not agree with each other, nor with the book's
data.
 I also computed the launch conditions using a
simple formula. Just multiply the original ball speed by the cosine
of the loft angle. That tracks the Dupilka program's output
rather well, and lies between Wishon's and C&S' estimates.
 Offcenter impact  If you don't
hit the sweet spot of the
clubface, you will lose distance (ball speed). How much? I have seen a
roughandready estimator that says you lose 7% of your
distance for each halfinch from the sweet spot. This is
suitable for a first guesstimate, but isn't really correct. Two reasons
it can't be correct we can deduce from an article by Howard Butler
in Clubmaker magazine, dealing with clubhead moment of inertia:
 The loss depends on the moment of inertia of the
clubhead. Butler reports that highMOI heads have 50% better resistance
to loss of ball speed than nonperipherallyweighted heads. But the 7%
rule includes nothing to account for MOI.
 The loss is not linear  that is, a constant
percentage
per halfinch. It is "square law"; if you double the amount you miss
the
sweet spot, you quadruple the loss of ball speed.

So, after accounting for all these losses, the initial ball speed is
more like:
V_{ball}
= V_{clubhead }

1
+ e
1
+ m/M

cos(loft)
* (1  0.14*miss)

where miss is the amount (in
inches) by which the sweet
spot is missed. That last factor is the most suspect in the formula,
but is halfway decent for a first estimate if you need to account for
offcenter hits.
Direction of the
ball
Let's
take another look at the release of the ball from the clubface. The
picture shows the direction and the spin of the ball (the red arrows), along with two
other important directions: the direction the clubface is pointing (blue arrow) and the direction
the club is moving (green arrow).
The direction of the ball  called the launch angle
 is
always between the arrows, and is almost always closer to the clubface
direction. If there were no friction involved, then the ball would
slide up the face and release in exactly the direction the clubface is
pointing. But friction causes the ball to roll on the clubface instead
of slide. The upwards motion of the ball is used to get the ball
spinning. Since the ball has a moment of inertia, it takes some torque
(force at the edge of the ball) to make it spin. That force comes out
of the upwards acceleration of the ball, so it takes off a little lower
than the clubface is pointing.

How much lower? The equation is
complicated, but not nearly as
ambiguous as ball speed was. The three references (C&S, Wishon,
and
Dupilka) agree on the numbers for launch angle. For
very small lofts, the direction of the ball is nearly the same as the
direction of the clubface. Put another way, the launch angle is the
same as the loft.
As the figure shows, the launch angle becomes a smaller fraction of the
loft as the loft increases.
 For typical driver lofts, the launch angle is about
88% of
the loft. For a 10° driver, the launch angle is just under 9°.
 At about 20° of loft (the beginning of the irons) the
launch angle is down to about 80% of the loft (the yellow dotted line).
For lofts in this range, you can think about an 80:20 rule; the ball is
80% to the clubface direction and 20% to the clubhead path.
 In the area of the wedges, the launch angle is still
more
than 60% of the loft. So, for all reasonable golf clubs, the ball's
initial direction is closer to the clubface direction than to the
clubhead path.
While
the equations to come up with launch angle are complex, there is a
simple formula that fits the curve very well. ("Fits the curve" means
that the equation has nothing to do with the physics of the situation,
but it happens to give the same result for all practical purposes.)
This formula is:
LaunchAngle
= Loft * (0.96  0.0071*Loft) 
It gives results within a tenth of a degree up to 40° of loft, and
stays within about a degree up to 60° of loft. These results are rather
accurate for a full swing making clean, dry contact with the ball. At
lower speeds or less friction, the launch angle can be much higher.^{[2]}
I'd like to reiterate that this formula is based only on fitting a
simple equation to the raw data from my three sources. See footnote [1] to better understand
its limitations. 
The
same physics works in the horizontal direction. If the clubface isn't
square to the path, the ball takes off between the two directions, and
much closer to the clubface direction.
Since the loft is probably a
bigger angular difference than the horizontal lack of square, you can
use the loft to set the percentage difference of direction. For
instance, the graph above shows that a 12° driver has about 85%
conversion of loft to launch angle. So the sidspin due to a few degrees
of nonsquareness is also probably 85% in the clubface direction and
only 15% in the clubhead path direction.

Spin
We've already seen the basics for
creating spin. The ball compresses on the clubface, creating a lot of
friction between the ball and the clubface. So the ball can't slide up
the clubface any more; it has to roll. By the time it releases from the
clubface, the roll has produced some number or RPM, which continues as
the initial spin.
How much RPM? It is proportional to:
 A decreasing function of the moment of inertia of the ball
itself. Remember, MOI resists rotation, so the higher the MOI the lower
the spin.
 An increasing function of loft. Higher loft means more
spin, all other things being equal.
 An increasing function of clubhead speed. Harder impact
means more spin.
 A decreasing function of the internal friction of the ball,
specifically its resistance to rolling while compressed.
When you factor all these things in, and remember that golf balls these
days are rather similar in their gross physical properties, you get a
formula:
Spin = 160 *
V_{clubhead} * sin(loft)

Where the spin is in RPM, the velocity in MPH,
and the loft in degrees.
Again, we can look at our three references for launch conditions. Their
estimates of loft follow fairly similar  though not identical 
paths. Our estimator based on the sine function tracks them well. (I'm
not sure the Cochran and Stobbs numbers for spin were very carefully
measured or calculated. They were rather casually listed as 60, 120,
and 180 revolutions per second, as if the lofts were evenly spaced 
but they were not.)

There are a few more topics to consider about spin: friction, grooves,
and gear
effect.
Grooves
do nothing for spin if there is clean, dry contact
between the clubhead and the ball. Yes, I know this is
counterintuitive; but it's true. So what about all the buzz you hear
about the spin produced by square grooves?
For a little more insight into how and why square grooves help, let's
think about automobile tires for a moment. Why do tires have tread
patterns? To grip the road? Nope! If that were the case, then why would
racing cars on a dry track wear "racing slicks", tires without any
tread at all? The purpose of slicks is to have as much surface as
possible in contact with the road. That, not a fancy tread pattern,
will maximize traction. In fact, a tread pattern reduces
the area of rubber in contact with the road.
So why do we have deep tread patterns on our nonracing tires? Because
we don't always drive on a dry road. For allweather
use, you need a tread pattern to prevent hydroplaning, which is a
complete loss of traction when the space between the tire and
the road is filled with lubricating water. The grooves in the tread
give a place for water to be channeled away, so rubber remains in
contact with the road. If you look in a racing tire
catalog, you'll see the different categories racing slicks
and racing wets;
even racers don't use slicks when the track is wet.
So how does this apply to golf clubs? It's a fact that grooves 
square or otherwise  have little
effect on spin for a fairway hit or a tee hit. Spin comes from the
conversion of sliding to rolling as the compressed
ball moves up the clubface. A ball compressed on the clubface by
hundreds or even thousands of pounds of force can hardly get more
friction than it already has, even if there are no grooves at all. (A
study reported in Cochran
& Stobbs gives more detail on this.)
But suppose there's some nice juicy grass between the clubface and the
ball. It may provide enough lubrication to allow the ball to
"hydroplane" on a smooth clubface. Like the tread on a tire, the
grooves provide somewhere for the lubricant to be channeled away and
allow steel to be in intimate contact with the ball.
So why are square grooves more effective than Vgrooves in channeling
away slime? The square grooves have a bigger volume, as you can see
from the figure above. Remember, the USGA and R&A have
rules setting the
maximum width and depth of grooves. For the same width and depth, the
square grooves have twice the volume; it's
simple geometry. So you can channel away more lubricant
with square grooves than with Vgrooves. You may still lose some spin,
but you lose less with square grooves.
I'm sure you've heard TV announcers talk about pros "hitting a flyer"
from the rough. Now you can understand what's going on. The grass
between clubface and ball
lubricates the contact, allowing more sliding to take place. The
results are:
 Less spin, of course.
 Higher launch angle! Because of the reduced friction on the
face,
the ball accelerates upwards more  so it takes off much closer to the
direction the clubface is pointing.
The combination of higher launch and lower spin allows the ball to fly
farther  a flyer.
As a "bonus" (but one the player usually doesn't want) the lower spin
means it will roll farther after it has already flown the green.
Andrew Rice has an impressive video demonstration
of how friction affects spin  and launch angle as well.
Gear effect
is sidespin which is the result of an offcenter hit
with a club whose center of gravity
is well back from the clubface. Without both these
conditions, gear
effect does not happen. Here is a very short description of gear
effect. If you are interested in more, I have written a very detailed article
on it.
Let's
see what causes gear effect. In the picture at the right, we have two
offcenter impacts, one on an iron and the other on a driver. Both are
toe impacts, which means it is to the toe side of the center of gravity
of the clubhead. (The CG is denoted by the fourquadrant
blackandwhite circle; it's a pretty common notation for CG.) What
does Newton say about such an impact? The CG wants to continue moving
forward in a straight line, but there is a force on the clubhead that
is off that line. That creates a torque that wants to twist the club.
The result is that the CG keeps moving forward, but the club rotates
around the CG in a clockwise direction (red
arrows).
The CG of the iron is close to the clubface. So, where the clubface and
ball meet, this rotation (the red
arrow)
consists of the clubface "falling away" from the ball. This results in
loss of distance (the momentum transfer is not as complete as it should
have been), and perhaps the ball flying somwhat to the right as the
face opens. But there isn't any special effect on spin.
The driver is a completely different story. Its CG is well behind the
clubface. When the driver head rotates around its CG, the whole face of
the club moves sideways. Look at the direction of the red arrow where the clubface
and ball meet; it is mostly parallel to the clubface, with only a bit
of "falling away".
So the club's face is moving to the right while the
ball is compressed on it. The
result is that the ball starts to rotate so its surface doesn't slide
along the clubface; remember it's compressed so sliding is difficult.
This rotation is the blue arrow
in the
picture. If the clubhead is rotating clockwise (as in the picture),
then the ball rotates counterclockwise. It's as if the clubhead and
ball were a pair of gears, with their teeth meshing where they meet.
That's why a toe hit with a driver tends to hook. For all the same
reasons, a heel hit with a driver tends to slice. You don't have this
effect with an iron. Well, you do, but not nearly as much. The CG of an
iron head isn't in
the face; it is slightly behind the face. And since this was first
written, iron heads are being designed with the CG further and further
back, to make them more forgiving and higher launching. So today's
irons have more gear effect than 20 years ago, but not nearly as much
as drivers.

Notes:
[1] Limitations
of the launch formulas: I am sometimes involved in
discussions that my simple launch condition equations do not answer. It
is important to understand where those equations came from, and what
limitations that implies. As an example, here is the gist of my
response to a question about what launch angle looks like above 60º of
loft...
The answer is, "I don't know."
If you read and understood where I got the formula, you would know why
I say this. But let me be more explicit here.
I had three sources of "data" for my relatively simple formula:
 Measured data from Cochran
& Stobbs, only 0º to 45º.
 Computed data from Wishon's
trajectory program.
 Computed data from
Dupilka's trajectory program.
I'm not sure where Wishon or Dupilka got their information from. I
don't know if they measured spin or computed it from basic principles
of physics. I don't even know if their source was independent of
Cochran & Stobbs. I don't know  period. All I know is the
numbers they give; and those numbers are in rather good agreement.
The C&S data only goes to 45º. I know it was measured. They did
it with highspeed strobe photos, a technique originally developed by
Harold E. "Doc" Edgerton. (I knew him when I was at MIT.) It is still
the basis of some launch monitors today.
I was able to plug in lofts to 60º with the Wishon and Dupilka
programs.
But, as I said, I don't know where their source info comes from.
All I did  the only
thing I did  was to try to curvefit a simple
formula to the data from my three sources. A straightline fit was not
very good; so I tried a quadratic fit and got a really good agreement
with the existing data. Note that there
is no physical basis for thinking
the actual mathematical model should give a quadratic equation. But the
physical data, as much as I have seen, gives the same numbers as this
simple quadratic over the range from 0º to 60º.
And, as I said, I'm not sure where the Wishon and Dupilka data came
from.
If you have TrackMan data, you are still
in the same boat I am. That is
because TrackMan reports loft, but not by measuring it. Loft
is computed from a
mathematical model of impact, based on clubhead movement before [and
perhaps after] impact and ball movement after impact. Their model is
not public, so you are no better off using it than taking numbers from
Wishon's or Dupilka's programs and accepting them  which is what I
did. You may trust the TrackMan engineers to come up with a valid
model. You may trust them more than you trust Wishon or Dupilka. (I'd
say the latter may well be a valid position to take.) But it's still
based on trusting a group of engineers to have come up with a
mathematical model that they won't reveal to you. "Trust me!"
So now you know where my formula comes from. It is only matched by
knowntobe measured data through 45º, and that measurement is almost
50 years old. Wishon and Dupilka
may not be basing their programs on actual measured data, but rather a
model  perhaps a model as naive as mine. So take it with a grain of
salt.
[2] Role
of friction in the launch formulas: The formulas for both
spin and launch angle depend heavily on a full swing and clean, dry
contact with the ball. At slower speeds and especially with lower
friction between the ball and the clubface:
 The spin will be lower.
 The launch angle will be closer to where the clubface is
pointing.
This is where "flyers" come from. They are highlaunching, lowspinning
shots from the rough that fly farther than intended. They happen from
the rough, where grass between the ball and the clubface produces much
more slippery contact, much lower friction.
Andrew Rice has done an excellent demonstration of how
friction affects both launch angle and spin; his video is well worth watching.
If you are using less than a full swing  for instance, short pitches
or putts  the ball will also leave the club closer to where the face
is pointing and further from the path the clubhead is traveling. This
affects both launch angle and directional dispersion. For instance,
there is a generally accepted 8515 relationship to describe what direction
a ball leaves the driver: 85% determined by clubface and 15% by
clubhead path. But that is closer to 955 for a putt. Slower speed and
less friction.
Last modified Nov 28,
2017


