Not many people seem to be aware that the clubhead is deflected
downward at impact. The physics is pretty easy, but the fact is
obscure. It is a partial explanation of why your clubs have to take
a divot. Beyond that, it may or may not be useful, but is certainly
interesting.
Let's start this discussion in the same context I first became aware of
the effect.
How many times have I listened to Peter Kostis narrate CBS TV's
KonicaMinolta SwingVision slowmotion videos like the one at the left?
(Kostis narrating a Tiger Woods shot, a short clip from a video
on YouTube.) Almost every time, the commentator will say
something about "hitting down through the ball" and "taking a good
divot". It is an article of faith that a divot taken after the ball is
necessarily an indicator of a downward strike.
At first glance, this would seem to be not just an article of faith,
but an article of geometry as well. How can you take a divot at all if
the clubhead
is not traveling notably downward coming into impact? You can't, right?
Look again at the video. Yes, the clubhead is descending as it
approaches impact. But at a rather shallow angle. Notice the difference
between coming into impact and as the ball is leaving the clubface. In
particular, notice that the clubhead is not only traveling slower (a
wellknown effect), but also on a more downward angle!
The more you
study videos of impact, the more you realize that this is the norm, not
a peculiarity of the KostisWoods example. For instance,
check out the video on
the right of Luke Donald's iron shot. (This is NBC, not CBS, and
the
trademark name of their slowmotion is "NBC HyperMo".) Here the ball is
teed
up, and the angle of attack is so shallow coming into impact that it is
easy to believe there will be no divot. But the clubhead is plainly
deflected downward at impact, and a shallow divot is the result.
It didn't take me too much thought to understand why this should be,
once
I realized that it is a very usual observation. In fact, the principle
is easily understood from high school physics, and the
calculations are no more difficult than most homework for Freshman
Physics 101. Let's take a look.
Why it happens
(The illustrations in this section are
created from frame snapshots of an
excellent video of slowmotion impacts made by the
Biomechanics Department at Manchester Metropolitan University.)
The key to this puzzle
comes from two very basic principles of physics, both directly from
good ol' Isaac Newton.
F = ma
Every action has an equal and opposite reaction.
The picture to the right shows a golf ball at maximum compression on a
clubface. The ball is about to take off in the direction of the green
vector. It is doing so under the influence of a force. The net force
during impact has to be in the direction of the launch angle, because
of F=ma.
The netting out of acclerations during impact gives us a velocity in
the same
direction as the netting out of forces. So the green vector F is the net
force
the clubhead exerts on the ball during impact, as well as an indicator
of the launch angle.
But ol' Isaac also told us that every
action has an equal and opposite reaction. The fact that the
clubhead exerts force F on the ball,
means that the ball exerts an exactly equal and opposite force on the
clubhead. That is the red vector R.
It is common
practice in physics to break down vectors into their vertical and
horizontal components. We have done that in the next picture. F and R have been
"resolved" (broken down) into:
A horizontal force accelerating the ball downrange, F_{hor}
A vertical force accelerating the ball upward, F_{vert}
A horizontal force slowing the clubhead, R_{hor}
A horizontal force deflecting the clubhead downward, R_{vert}
The last one, R_{vert},
is the reason the clubhead turns downward at impact. Any upward
acceleration of the ball  any launch angle greater than zero 
causes a downward acceleration of the clubhead!
How much happens
OK, we can see there must be a force
deflecting the clubhead downward. But the clubhead is heavy, and there
is a golfer on the other end of the shaft. So how big could the
deflection be? We could calculate these effects  and we will later.
But first...
Let's do some measurement of the highspeed videos to see if this
phenomenon is large enough to matter. In particular, let's see if it
would cause a divot to be taken when there would otherwise be none.
I made an animated GIF from several frames of the video from Manchester
Metropolitan University. It traces a point on the clubhead from
before impact to after the ball is on its way. The yellow trace shows
the movement of the clubhead. It is decidedly deflected downward during
impact. The angles of attack during various intervals are:
Clubhead approaching ball
0.4º
Average angle during impact
6.3º
Average angle from first
contact to maximum compression
4.3º
Average angle from maximum
compression to separation
8.4º
Immediately after
separation
12.5º
Points to note:
The angle of attack approaching impact is 0.4º. That is
hardly "hitting down on the ball"; it is a nearly horizontal "pick".
By the time the clubhead leaves the ball, the downward
angle is more than 12º. That is pretty steep for an angle of attack,
and would definitely leave a prominent divot. Given that the original
angle of attack is nearly zero, this
can truly be called a "Newton's Divot".
At
maximum compression, the downward angle has changed by almost exactly
half the entire change during impact. So half the change occurs before
maximum compression, and the other half after.^{[1]}
(This doesn't seem important now, but we will use it later when we
examine the significance of TrackMan measurements of PGA Tour data.)
Even the driver?
Most physics analyses of driver impact assume everything happens in a
horizontal direction. With the lower loft of drivers, this is not a bad
assumption  if you are looking to find only ball speed. But even a
drive has a nonzero launch angle, so there is some downward
deflection, at least in theory.
Is there enough to see in a video?
Here is a video that shows it. Taking frame snapshots and measuring the
angles, we get:
Clubhead approaching ball
1.8º
Immediately after
separation
5.0º
Launch angle of ball
10.3º
To get a feel for the angles, we should "normalize" them to the angle
at which the clubhead approaches the ball. When we do that, we get:
Clubhead approaching ball
1.8  (1.8) =
0.0º
Immediately after
separation
5.0  (1.8) =
3.2º
Launch angle of ball
10.3  (1.8) =
12.1º
This has a much better "feel of reality" to it. We will compute values
like this later.
Unlike videos of irons, which almost always show a downward
deflection, driver videos sometimes do and sometimes don't. Why should
this be? Here are a few possibilities:
The best drives are struck with an upward angle of attack,
so the deflection may merely level out the head motion from its
original upward direction.
If the ball is hit above or below center, the clubhead
rotates face up or face down. If the strike is above center  which
gives the best drives, so pros try for this  then the face is moving
upward after impact, with respect to the center of the clubhead. So the
center may be deflected down, but the face may be moving up relative to
the CG and making it appear that the clubhead is not deflected. The
irons do not have nearly as much offset between center of gravity and
face, so clubhead rotation
does not provide much vertical clubface motion.
TrackMan Tour averages
The
original posting of this article (1/22/2014) was based on the
definition of Attack Angle published on the TrackMan web site. It turns
out that the definition is not an accurate description of how TrackMan
measures Attack Angle. We now have a more accurate definition, and
I have recomputed the tables based on it.
On January 11, 2014 Adam
Kolloff
pointed out to me that in 2013 the average
driver angle of attack on the PGA Tour was negative. That struck me as
odd. Physics says the drive will be longer (higher launch for a given
spin) with a positive angle of attack. Therefore, I would expect the
best golfers in the world to be trying for an upward angle of attack.
PGA
TOUR AVERAGES (from WWW.TRACKMANGOLF.COM)
Club
Speed
(mph)
Attack
Angle
(deg)
Ball
Speed
(mph)
Launch
Ang.
(deg)
Driver
113
1.3°
167
10.9°
3wood
107
2.9°
158
9.2°
5wood
103
3.3°
152
9.4°
Hybrid
1518°
100
3.5°
146
10.2°
3
Iron
98
3.1°
142
10.4°
4
Iron
96
3.4°
137
11.0°
5
Iron
94
3.7°
132
12.1°
6
Iron
92
4.1°
127
14.1°
7
Iron
90
4.3°
120
16.3°
8
Iron
87
4.5°
115
18.1°
9
Iron
85
4.7°
109
20.4°
PW
83
5.0°
102
24.2°
Adam sent me a copy of his
source information: a table from the TrackMan web site. Selected
columns are
reproduced here as a web table.
Sure enough, the average Angle of Attack (AoA) for the driver was 1.3º
in 2013. For a while, I considered downward deflection as an
explanation. This speculation was reinforced by
another bit of information Adam sent, TrackMan's definition of Angle of
Attack:
Attack
Angle  The vertical direction of the club head’s center of gravity
movement at maximum compression of the golf ball
It
turns out that this is not quite the operative definition that TrackMan
measures. It is more like an extension of the clubhead path into the
middle of impact, without the clubhead deflection. The exact method is
given on the next page.
Given the data in the four
columns of the Trackman chart, it is not a difficult physics problem to
calculate the downward deflection angle of the clubhead.
Accounting
for Downward Deflection
TrackMan
Attack
Angle
(deg)
PreImpact
Attack
Angle
(deg)
Impact
Deflection
(deg)
Divot
Potential
(deg)
Driver
1.3°
1.6
6.6
7.9
3wood
2.9°
3.2
6.1
9.0
5wood
3.3°
3.6
6.0
9.3
Hybrid
1518°
3.5°
3.8
5.8
9.3
3
Iron
3.1°
3.4
5.4
8.5
4
Iron
3.4°
3.7
5.4
8.8
5
Iron
3.7°
4.0
5.6
9.3
6
Iron
4.1°
4.4
6.0
10.1
7
Iron
4.3°
4.6
6.2
10.5
8
Iron
4.5°
4.8
6.4
10.9
9
Iron
4.7°
5.0
6.6
11.3
PW
5.0°
5.3
6.9
11.9
The results are in the next table. (The math itself is done in a later chapter; you
don't have to follow the math
to understand the results.) Here is an explanation of
each of the columns, and how to interpret them.
Trackman
Attack Angle  The AoA as defined and recorded by TrackMan. This
column is just transcribed from the previous table.
PreImpact
Attack Angle

The calculated AoA as we normally
think of it, the angle just before contact with the ball. (Working
backwards from the TrackMan definition, it is the TrackMan Attack Angle
minus a slight path curvature of about 0.3° ^{[2]})
Impact
Deflection  The calculated downward deflection of the clubhead
due to impact, as an angle in degrees.
Divot
potential  I thought it would be amusing to include the
vertical angle of the clubhead after
impact. This, not the AoA, is the number that really determines
the potential for cutting a divot from the sod.
Discussion
I still find it odd that the AoA for the driver remains
negative. But that is what the data says! Perhaps the average Tour
player (remember, these are average numbers, not just the big hitters)
are going for solid contact at the expense of distance. The debate
continues between the "bomb and gouge" strategy and the "fairways and
greens" strategy. This suggests the latter is adopted by the average
Tour player.
Suppose we look at competitions where the players need more distance. Here are a
couple.
The LPGA Tour players do not have the clubhead speed that
the men do. If they are going to get distance from their driver, they
need distance mechanics in their swing. TrackMan has published their
averages as well, and the driver AoA is +3.0º. That's a very upward
swing path. And the upward AoA is only for the driver; they treat the
rest of the clubs as control clubs and have a negative AoA.
Distance is everything in the long drive! You get six
tries. Only one has to hit a very wide "fairway", but that one better
be looooong! Fredrik Tuxen tells me that TrackMan measured
everything at the recent ReMax World Championship. Those guys have
around a +5º AoA, and at least one close to +10º. Now that is high launch angle with low
spin!
The downward deflection of the clubhead is within a degree
of 6º
for every club. I suppose it makes some sense. As loft increases, the
launch angle increases, so the downwards component of the reaction
force increases  at least as a fraction of the total reaction force.
That
would make one expect the deflection to increase with loft. However,
while the downward component's share is increasing, there are at least
two things happening that are limiting the downward deflection:
The ball speed is decreasing. So, while the vertical
share of momentum may be greater, it is a piece of a smaller total
momentum.
The clubhead mass is increasing. The 200g driver head
becomes 291g by the time it gets to the PW. Since F=ma, an
increase in mass requires a decrease in acceleration. And less downward
acceleration means less deflection.
The result: The downward deflection increases for each
club in the irons by a very small amount (from 5.4º in the 3iron to
6.9º in the PW). It
is a steady, monotonic increase averaging about 1/5 of a degree per
club.
The Divot Potential column also makes sense  mostly. As
the loft increases, the downward angle of the clubhead after impact
also increases. That comes from an increasing attack angle and a
substantial downward deflection. And that downward deflection, at least
in the irons, increases slightly as the loft increases.
The one anomaly I see in the Divot Potential column is that
the driver is moving downward after impact at an angle of almost 8º.
How can it do this and not take a divot? I can't cite a real study,
neither experimental nor analytical, but let me venture some fairly
good guesses.
The ball sits up on a tee, not on the ground. So the
clubhead has some room to move downward without hitting the ground, as
long
as the downward motion does not continue too long.
The pros can control where they hit the ball on the
clubface, and the best place to hit a driver is high on the face. This
gives a higher launch angle and lower spin than nominal for the driver,
resulting in more distance. That means that the clubhead is turning
faceup after impact; moreover, because the CG is so far behind the
face, the face is moving up
as well as turning
up. If the clubhead is going to strike the ground at all, it will be
the tail of the clubhead  which is not going to dig but just bounce.
For a rather graphic example, see Figure 47 in my article on Gear Effect.
The other side of the Divot Potential coin is how far
downward the clubhead continues. Looking at high speed video, the
downward deflection is fairly short term, then the downward motion
becomes limited by shaft rigidity and bounce from the ground. Consider:
The shaft is almost a string during impact; I have
explained that in several places in my writings. However, as
milliseconds build up after impact, the influence of the shaft  and a
large mass of golfer at the other end of the shaft  will limit the
downward motion of the clubhead.
If the ball is sitting on the ground, then resistance
from the ground may limit downward motion even before the shaft does. A
backoftheenvelope calculation shows the clubhead moving downward at
about a quarter inch per millisecond. It reaches the ground pretty
quickly at that rate, and ground resistance will lessen
the downward motion.
So the clubhead motion in the 20 milliseconds after
impact is pretty complex, and I'm not going to try to analyze it more
than I just have  at least not for now. But I will note...
Bobby Clampett, in his book "The Impact Zone"
(St. Martin's Press, 2007), hammers at the point that the swing bottom
(the lowest point of the clubhead's travel) should occur well after
striking the ball. He maintains that scratch and tour players have a
swing bottom four inches in front of the ball. In fact, he cites an
informal study showing that each inch in front of the ball is worth
about four strokes in the handicap. The downward deflection probably
contributes in some way. Think about it. With that much down angle just
caused by ballonface impact, you need a diet of very thin or somewhat
fat hits to avoid a forward swing bottom. If you catch the clubface solidly, the
reaction force will guarantee the clubhead is traveling downward when
it leaves the ball  even if you don't have an aggressively downward
AoA.
The bottom line
The clubhead is definitely deflected downward at impact. The divot
taken by an iron is at least as much due to the downward deflection as
it is to the angle of attack before the clubface contacts the ball.
In fact, PGA Tour players have rather shallow angles of attack, but
their clubheads are traveling much more downward after the ball is
gone. There are other things that are explained by downward
deflection, such as the negative angle of attack reported by Trackman
for driver strikes; that seems to be an artifact of Trackman's
definition of AoA and the fact of downward deflection of the clubhead.
Calculating the downward deflection
We can calculate the downward deflection if we are given the clubhead
speed and angle of attack before impact, and
the ball speed and launch angle after impact.
If
you are a mathophobe, you don't have to read this section. The results
can be
understood without wading through the math. But if you want to
investigate this sort of thing yourself, you should really understand
it thoroughly. From a math and physics standpoint, it is quite
easy. The physics is freshman physics 101, and the math is high school
algebra and trigonometry.
Velocities
and angles:
Here are all the velocities before and after impact.
U
a velocity before impact
V
a velocity after separation
c
a subscript designating
the clubhead
b
a subscript designating
the ball
x
a subscript designating
horizontal rightward motion
(leftward is negative)
y
a subscript designating
vertical upward motion
(downward is negative)
Other notation we will use:
P
Total system momentum.
Since momentum is a vector quantity, it has separate horizontal and
vertical components which take subscripts x and y.
M
Mass. Can take c subscript for
clubhead, or b
subscript for ball.
 Clubhead mass for a given club (say, a 5iron) does not vary
much among most manufacturers. For each club, I took a consensus number
from several catalogs. (E.g. 200g driver, 256g 5iron, 291g PW.)
 All competitive golf balls are right at 46 grams.
L
Launch angle.
D
Deflection angle.
A
Preimpact angle of attack
We know some of these  e.g., from launch monitor or Trackman readings
 and will calculate the rest of them from the
principle of conservation of momentum. Momentum
is the sum of the masstimesvelocity for every mass in the system.
Conservation of momentum says that the total momentum of the entire
system  all the masses involved  is
the same after impact as it was before impact.
Find
system momentum before impact:
Momentum is just mass times velocity. The only thing moving before
impact is the clubhead. So the momentum's horizontal and vertical
components are those of the clubhead:
(Equations
1)P_{x}
= M_{c} U_{cx} = M_{c} U_{c} cos A P_{y}
= M_{c} U_{cy} = M_{c} U_{c} sin A
Equate
the momentum to postimpact momentum:
Impact happens. We get impact and separation. Now we have to find the
postimpact velocities that
satisfy conservation of momentum. That means that the P_{x}
and P_{y}
we calculated above must be the same P_{x}
and P_{y}
after impact.
Since momentum is mass times velocity:
(Equations
2)P_{x}
= M_{c} V_{cx} + M_{b} V_{bx}
= M_{c} V_{cx} + M_{b} V_{b} cos L P_{y}
= M_{c} V_{cy} + M_{b} V_{by}
= M_{c} V_{cy} + M_{b} V_{b} sin L
We already know P_{x}
and P_{y};
conservation of momentum says they must be the same as the momentums we
calculated before. In fact, the only things we don't know here are the
head velocities V_{cx}
and V_{cy}.
For each of these unknown velocities, we have an equation that is
easily solvable for the head velocity. The solutions are:
(Equations
3)V_{cx}
= P_{x }/ M_{c}  (M_{b }/
M_{c}) V_{b} cos L V_{cy}
= P_{y }/ M_{c}  (M_{b }/
M_{c}) V_{b} sin L
The
velocities give us the clubhead path and deflection angle:
Now we have the clubhead velocity, both magnitude and direction,
after impact. The direction is simply arctan(V_{cy}/V_{cx}). If you don't see this immediately,
look at the the "Just after separation" picture above.
The deflection of the clubhead's path is, by definition, the difference
between the direction after impact and the direction before impact.
Expressed mathematically:
(Equation
4)D
= arctan
(V_{cy}/V_{cx})  A
Acknowledgements
I would like to thank Adam
Kolloff
for getting me off my butt to write about this. He showed enough
interest to come up with some data that requires knowing about downward
deflection in order to explain it.
Also, thanks are due to Fredrik Tuxen, founder and CTO of Trackman, for
spending time with me to explain how they measure Attack Angle.
Notes:
The measured numbers are 3.9º of
deflection occurring before max compression and 4.1º after. These are
amazingly
equal, given the measurement imprecision. Remember, these angles were
picked off a screenshot, where the unit of resolution is the pixel. For
the
resolution of our source frames and the short distances involved within
the impact times, one pixel is worth perhaps a third of a degree.
The 0.3º difference is not a constant, though
the calculations treat it that way. The actual amount is the midimpact
direction minus the preimpact direction. It is determined by a time,
225 microseconds, which is half the duration of impact. So the actual
number depends on club head speed, swing plane and swing radius, but
always comes out close to 0.3º0.4º.
Last modified  Feb 1, 2014
Copyright Dave Tutelman
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