What wind does to a drive
Dave Tutelman - December
Wind has an obvious effect on a drive. Into the wind makes the drive
shorter, and with the wind makes it longer. The stronger the wind, the
shorter or longer it makes the drive. That's all obvious. But there are
some less obvious effects as well:
We can see all of these effects when we look at data posted by Erik
Henrikson. Let's look at why
this happens, the physics involved. Then we will test our assertions by
trying them out on a computer model.
- Into the wind hurts more than with the wind helps. (Most
golfers have at least heard this.)
the wind makes a shot go more offline for a particular clubface angle
error. Also, with the wind actually reduces that dispersion.
pull and/or hook goes further than a straight shot into the wind, and a
push and/or slice loses distance. The converse happens downwind.
|On Dec 18, 2019, Erik Henrikson tweeted this graph,
along with the text:
- Dec 18
Erik is Ping's Director of Innovation and
Testing, so what he posts carries some weight. The next day, the graph
was shared to Facebook by Andrew
Rice, where I saw it. He added the thought:
Played in some very high winds a few weeks ago (a treat for a phx boy).
Hit some really crooked (and short) drives into the wind. Modeled my
typical delivery and variation up/downwind. Easy to see 'against' is
more hurtful than 'with' is helpful, and the effect on offline angle.
Andrew Rice Golf
I contacted Erik to find out what he means by "modeled my typical
delivery". He has computer records of a substantial number of his own
drives as recorded by TrackMan. (I haven't bothered to count the dots,
but it looks like about 80-100 drives in the data base.) In particular,
the data base contains full launch conditions for each recorded drive:
initial ball speed, ball direction (both vertical and horizontal) and
spin magnitude and axis. The differences from drive to drive reflect
the variability in Erik's ability to repeat the same contact from swing
to swing. He then plugs all those drives, one by one, into a trajectory
program. That computer program is a proprietary Ping R&D tool,
and is based on today's golf equipment. The program has the ability to
model wind as well as still air. The ball modeled is a 2019 Titleist
19 at 11:43 AM
Interesting data from @e_henrikson of @pingtour regarding driving with
a headwind and a tailwind! Not only shorter, but less accurate too. Get
better y’all! #andrewricegolf
The graph shows
carry distance (yards) and the yards offline for seven wind speeds from
-30mph to +30mph. (Negative wind speeds are into the wind, positive are
downwind.) There are not just the two effects mentioned, but three, all
clearly visible from the
scatter plots. Specifically:
start by looking closely at the chart, the data, in case you don't see
points #1, #2, and #3 right away. We'll see how the physics and
geometry makes this happen. Then we'll compare the
with my own trajectory program -- based on that physics -- to see how
well the results agree.
the wind hurts more than with the wind helps. The scatter
plots for negative wind speeds are farther apart than for positive wind
makes a shot go more offline, and down wind actually reduces dispersion.
The more upwind the drive, the wider the oval showing dispersion.
or hook goes farther if upwind, and push or slice goes farther if
downwind. The tilt of the oval tells you this. The upwind
ovals are tilted up to the left and downwind ovals up to the right.
the discussion of physics by making sure we understand the aerodynamic
forces on the ball and what they do to ball flight. In the diagram, the
black arrows are force vectors, and the red lines show the motion
of the ball relative to the air. Here are the forces -- all the forces --
on the ball. They are what control the flight of the ball.
It is worth noting that both lift and drag are proportional to the square of the speed
of the ball through the air. This square law relationship is important
in explaining our observations about how wind speed affects ball flight.
is the aerodynamic force along the path of the ball through the air.
(Those words "through
the air" are literally important and a bit subtle. It is the path of
the ball relative to
the air. If the air is moving -- think wind here -- that
affects the magnitude and often the direction of the red 'path' arrow.)
Drag slows the ball down. It stands to reason that the more the drag,
the less the
carry distance. That is a very simple relationship, other things being
is the aerodynamic force created by a combination of speed through the
air and spin.
The lift force is perpendicular to the path of the ball through the
air. It is also perpendicular to the spin axis.
That means lift is not necessarily vertical. In fact, it is seldom
perfectly vertical. Here are two important cases that will help you
understand ball flight:
- Lift is perpendicular to the path of the ball
through the air. That means, while
the ball is rising
has a component pointing backward. So an excess of lift force can limit
the distance you can hit the ball directly, with a backwards force. Now
you understand "ballooning";
it's not just jargon, but a real physical effect. It is the backward
component of the lift force pulling the ball back if the spin is
excessive for the upward tilt of the path.
- If the spin axis is tilted sideways, then there is
sideways component of the lift force. That component moves the ball to
the right or left along its path. Now you know why a tilted spin axis
produces a slice
is not an aerodynamic force. Its magnitude (which is proportional to
the mass of
the ball) and direction (straight down) do not change with wind speed,
so it is not interesting in our discussion.
Now let's look at how this causes the three effects wind has on ball
hurting hurts more than helping helps
won't surprise anybody that a golf shot into the wind doesn't carry as
far as a golf shot with the wind. That's perfectly intuitive. In a few
moments, we'll see the physics that says it should be so. But for now,
let's just observe that intuition serves us well for this one -- which
it too seldom does in understanding the science behind golf.
But this chart says more! In the comment thread on Andrew Rice's
Facebook post, Leon M Marks wrote, "Against
the wind is clearly hurting more than downwind
helping." And indeed, Erik Henrikson's own caption in his
tweet says the same thing.
case you don't see it right off the bat, I have indicated the average
carry distance for no wind (the green cluster), with a 30mph wind (the
lavendar cluster), and against a 30mph wind (the blue cluster). The
differences in distance are labeled "Hurting" and "Helping".
So we see that a hurting wind hurts
about twice as much as a helping wind helps, if both winds
are 30mph. (Don't take "twice as much" as universal gospel. For
instance, it is less than twice at lower wind speeds.)
- A 30mph helping wind increases carry distance about
- A 30mph hurting wind decreases carry distance about
Effect of drag
look at the physics of what is going on. The key here is aerodynamic
drag. As discussed earlier, drag is the aerodynamic force in exactly
the opposite direction
that the ball is moving. If you increase the drag (with no other
changes), you will decrease the carry distance. And vice versa.
So let's start with the naive assumption that the drag force is
proportional to the wind speed felt
by the ball. Another way of saying that is, it is the air
motion relative to the ball. The technical term for this is the apparent wind (a term used mostly
Let's try to get a feel for this. (If you understand apparent wind, you
can skip this paragraph.)
Relative wind works the same as relative current. Look at the graph. I
have noted three different relative wind speeds:
- Imagine walking at 3mph along a stream flowing at
3mph. If you walk downstream, anything in the stream floating on the
current will be going at your speed. Looking at something the water, it
will be going zero speed relative to you; the speed of the current is subtracted from
- Now imagine walking upstream. Everything in the
stream looks like it's moving faster than if you were standing still.
Think about the previous example -- walking downstream. This time,
instead of being subtracted, the speed of the current is added to your
So it is pretty clear that going into the wind generates more drag than
going with the wind. So upwind drives should not carry as far as
downwind drives. And they don't.
- The ball speed in still air is 165mph. Since there is
no wind, that is also the relative wind speed or apparent wind speed.
- The ball speed downwind in a 30mph wind is 135mph.
That's because, going downwind, the wind speed is subtracted from the
ball speed to get the air motion that the ball feels.
- The ball speed upwind in a 30mph wind is 195mph.
That's because, going upwind, the wind speed is added to the ball speed
to get the
air motion that the ball feels.
But how much should upwind take off a drive's distance, and how much
should downwind add? In the graph above, it would appear that the drag
added upwind is the same as the drag subtracted downwind. But that is
because we assumed drag is proportional to airspeed. It isn't! We said
earlier that aerodynamic
forces are proportional to the square of airspeed. Let's
see what this square law does.
In this new graph, we kept the blue proportional line and added a red
square-law curve. I chose the coefficients so that the two drag curves
(red and blue) would have the same value at 165mph, the case with no
wind at all. Let's see what has changed in the range between 135mph and
The second point, the one about curvature, assures that a hurting wind
hurts more than a helping with helps.
- The slope
of the red curve is greater than that of the blue curve, at all points
in the interval. That means
that the aerodynamic forces have more of an effect on distance than we
would have guessed from the blue curve. Wind is a more serious problem!
- The curvature
of the red curve means that the 30mph added wind speed gives more extra
drag (65 extra units of force) than 30mph subtracted wind speed saves
(only 54 units saved). So we should expect upwind
drives to encounter 65 more units of drag, but downwind drives to see
only 54 fewer units of drag.
Effect of lift
So far, the effect of aerodynamic drag on the ball seems to be enough
to explain what we see in the data. But wait; there's more! In order to
get as strong a difference as we see between upwind and downwind, we
also need to include the effect of aerodynamic lift. Let's emphasize a
couple of points about lift:
Let's start with drives into the wind. I used a computer program called
TrajectoWare Drive (we'll hear more about it later) to draw profiles of
the trajectory of the drive we are using, for various headwind speeds.
- It is going to be proportional to the square of
velocity through the air, and also proportional to the spin of the
ball. (We should know that by now, but it bears repeating.)
- It is essential for distance. Spin is what keeps the
ball in the air -- seeming to float or fly when experience says it
should drop. As experienced golfers, we no longer expect the ball to
drop. But I still remember seeing a good drive for the first time (age
about 12), and marveling eyes-wide how the ball stays in the air "on a
rope". That is a large part of our distance. Without lift, well-struck
drives would go less than half as far. So we need lift for distance,
but lift can also rob us of distance. Let's see how.
Note how, as the hurting wind increases (we took it to 40mph in this
graph, not just 30mph), there are more changes than just the distance.
Sure, all the trajectories start out at the same launch angle. But the
more the headwind, (a) the higher the peak and (b) the more the
upward portion of the ball path has to curve even more
upward. (Don't let anybody tell you a shot can't curve
upward; it certainly can.)
relate this to lift. If the flight of the ball is level, then lift is
an upward force. But don't let the word "lift" fool you; it isn't
inherently upward, just perpendicular to the path of the ball. If the
ball is rising, as it is early in each of these drive trajectories,
then the lift has two components: one up and the other backward. Lift
is retarding the ball's distance! Not only that; if the lift becomes
too great, the path curves upwards. That means that the angle of the
path is increasing, and the backward component of lift increases. This
is the picture and the cause of ballooning, which costs distance on a
So why do we see more ballooning as the wind increases?
Remember what causes lift: spin and ball speed relative to the air. The
higher the hurting wind, the higher the air speed felt by the ball --
hence the higher the lift. And, as before, the effect is square law, so
increasing headwind has a big effect on the lift. So some of those
distance losses upwind are not due to drag, they are due to lift --
let's look at what happens to lift when we go downwind. As it was with
upwind, all the trajectories start out at the same launch angle. But
the more the wind "helps", the more the trajectory loses lift.
That's because there is more subtracted from the wind speed that the
ball sees -- the ball speed minus the helping wind speed. If there is
less apparent wind then there is less lift, and it's a square law
relationship as well.
So the "lack of help" downwind is even
more serious than just a lack of help; it is sucking the distance out
of the drive even faster than the drag is going away. We originally
stopped at 30mph because that is where Henrikson's data stopped. But
look at this picture. Actually, a 30mph helping wind is as good as it's
ever going to get. Increasing it to 40mph would have been very
instructive; it would pick up less
than a yard of additional distance. And after that, it's all downhill;
drives actually lose distance when the helping wind is increased above
40mph. Deprived of a strong lift, the ball wants to "fall out of the
air", and does so before it reaches maximum possible distance.
is a rather remarkable result! You would think that a helping wind
would keep increasing the distance, albeit slowly, forever. After all,
a stronger helping wind does indeed reduce drag. So any limit on the
maximum amount the wind can help can't be due to drag effects; the
answer is loss of lift.
Here is a graph that captures both the
upwind and downwind effects. You can see the help from the wind level
off at a wind speed of around 38mph. That is less than a quarter of the
ball speed at launch (166mph initial ball speed). That can't be due to
anything but loss of lift.
- more offline into the wind
In the comment thread on Andrew Rice's post, David
Arrignon wrote, "Very
I knew that the effect of a headwind was more important than the one of
a downwind, but nothing about the dispersion. Seems logical due to the
possible amplification of a 'sidespin'."
As with distance, let's start by looking at
Henrikson's chart. This time we'll look at the width of each oval,
because that is the prime measure of offline dispersion. Let's pay
particular attention to the extremes: 30mph downwind (the lavendar
oval) and 30mph upwind (the blue oval)
It is easy to see that the into-the-wind (blue) oval is the widest and
the with-the-wind (lavendar) oval is the narrowest. We can also see a
steady widening of the oval as we go from downwind to upwind.
What is the physics? Why should this be?
figure shows the just the variable part of the wind, not the total
The total wind includes ball speed, which is the same for all
But for now, we'll just look at the 30mph into and against.
Please note that the vectors in this diagram are velocities, the wind's
and direction, not forces.
are two reasons to expect the dispersion to be greater into the wind
and lesser with the wind,
and both reasons arise from wind speed vectors in this figure. The
speed vectors are the black
arrows. They depict the wind from the target (into the wind) or toward
the target (with
the wind). They are vector-added to the 165mph wind speed (not
shown explicitly) in
exactly the opposite direction of the green
ball path. The figure shows the black vector resolved into two
components: parallel to the ball path (blue)
and perpendicular to the ball path (red).
The two reasons for wind to affect dispersion are related to the blue
component and the red
component of wind speed, respectively.
of the 30mph wind increases the "apparent wind" seen by the ball when
hitting into the wind. It decreases it with the
wind. We know that aerodynamic
forces increase with the square of the apparent wind, and lift
is one of those aerodynamic forces. Remember that lift isn't only
vertical; if the spin axis is tilted, then lift is creating a slice or
This is the effect David Arrignon refers to as the amplification of
- Into the wind, with the increased wind
speed relative to the ball, the hook or slice will increase, and it
increases as the square of the apparent wind.
- With the wind, with the decreased wind speed
relative to the ball, the hook or slice
will decrease, and it decreases as the square of the apparent wind.
of the 30mph wind acts across the path, and thus curves the path of the
ball -- completely apart from hook or slice, which are caused by spin.
As we can see from the diagram:
- Into the wind, the
perpendicular component pushes the ball away from the target line. The
stronger the wind, the bigger this force, and the wider the dispersion.
- With the wind, the perpendicular component pushes the
the target line. The stronger the wind, the bigger this force, and the
narrower the dispersion.
the ball's direction is due solely to the clubface angle at impact
(which is often the case), both effects reinforce one another and the
change in dispersion with wind speed is signficant. The
mathematical modeling at the end of this article suggests that the
variation in Henrikson's data was due largely to face angle changes.
loss of distance
In the comment thread on Andrew Rice's
post, Brent June wrote, "Also
interesting that pulls or draws go longer into the
wind, but cuts or fades are longer downwind."
To see this final effect, let's look at the tilt of the ovals.
What would cause this effect?
- With the wind (the lavendar oval) there is more carry
on the misses right and less carry on the misses left.
- Into the wind (the blue oval) there is more carry on
the misses left and less carry on the misses right.
- There is a pretty even variation in tilt between
answer that, we should first ask what is causing the off-center shots.
We don't really know, but I'm going to make the assumption that the
clubhead path has much lower variation than the club face angle. That
does match reality for most golfers, so the assumption, while perhaps
rash, is likely to be true.
If most of the dispersion with a
color group is the face angle at impact, what would cause that
variation of face angle? The most likely cause by far is the degree to
which the shaft has rotated at the moment of impact. Let's see where
this assumption leads us.
the club was designed with a vertical shaft like (a) in the figure,
then rotating the shaft about its axis only changes the face angle,
nothing else. But a perfectly upright lie like that is nowhere near the
truth. A real club has a lie angle that is nowhere near 90°, usually
between 55° and 65°. And an
angled shaft like (b) has a more complex description of the clubface
motion due to a rotation around the shaft axis. It not only changes the
face angle, it changes the loft as well. If you attach a laser pointer
to the face of a club, you will see what a shaft rotation does to where
the face is pointing. You will see that it points higher (more loft) as
the clubface opens, and lower (less loft) as the clubface closes.
modern drivers, the lie angle is somewhere around 58°. That means you
will get a change of 1° of loft for every 1.6° of face angle change.
(1.6 is the tangent of 58°).
So hitting a drive with an open
clubface means you are also hitting the ball higher in the air. As we
all know, that will make the ball go farther downwind and shorter
upwind. Conversely, if the clubface is closed, there is less loft and
the ball will fly lower. That goes farther into the wind than a higher
shot, but loses distance downwind because of not enough loft. And that
explains the tilt of the ovals, and why they tilt in opposite
directions upwind and downwind.
|What I have said so far is just words and pictures,
what I sometimes call "hand waving". But according to Kelvin,
British scientist of the 1800s, "When you can measure what you are
speaking about, and express it in numbers, you know something about it.
But when you cannot measure it, when you cannot express it in numbers,
your knowledge is of a meager and unsatisfactory kind."
Let's see what we can do about numbers. We have some numbers from Erik
Henrikson that constitute our source data. We have my conjecture about
the physics purporting to to explain the data. Now we need to test the
working the physics quantitatively -- with numbers, not just words and
The calculations to obtain the trajectory, or even just the distance,
of a drive are complicated.
There isn't a closed-form equation that you can plug numbers into. Even
the limited rules of thumb that exist don't have enough physics built
in to deal
with wind differences, which is exactly what we are trying to test. You
have to solve several simultaneous differential equations by numerical
methods, usually done iteratively. Here is a link to a brief description of
how that needs to work. You are not going to do this by hand or even on
a calculator. You need to program a computer to do it.
But we are in luck. In 2007, Frank Schmidberger and I put
together a computer program, TrajectoWare Drive, that does this
computation. It is based on exactly the physics described above. So we
can try to emulate, with this program, the conditions that Henrikson
used to get his data. I reverse-engineered the same conditions as the
data (having to
make a few guesses -- see below), and here are the results shown
overlaid on Henrikson's graph.
The heavy curves of the same color as the data are the points I
calculated with TrajectoWare Drive. They clearly show the effects of
wind, both hurting and helping, that we observed in the raw data:
and asymmetry. Even the numbers are quite similar, if you know how to
at the dots that make up the "constellation" for each wind speed. The
upper edge of the constellation's envelope is more defined than the
lower edge, which is ragged to the point of not being able to draw an
edge. That is because the upper edge is composed of strikes on the
sweet spot; any other dots represent a less-than-ideal impact. The
computer model assumes a smash factor of 1.47, the maximum possible
given the loft of the driver. But not every drive is hit on the sweet
spot. So, if the calculations match the data exactly, each heavy line
should be along the upper edge of the cluster for that wind speed --
the dots that represent impact on the sweet spot.
With that understanding, let's look at how well the model matches the
I consider this a pretty good confirmation that we now understand the
physics behind the distance, dispersion, and asymmetry in the Henrikson
- The model and the data match quite well, except into a 30mph wind,
where the model allows the wind to affect distance even more than the
data shows. The discrepancy isn't much -- perhaps 5 yards out of over
200 yards. I'd say this is a rather good match, but still a discrepancy
worth looking at.
- The length of the heavy line is the model's measure of dispersion. It
represents the landing point of the ball over a face angle from -1.4°
to +1.4°. It tracks the long diameter of each oval, at 85-95% of the
oval's width. This is quite a good match.
- The slope of the heavy line matches the slope of the oval for
into-the-wind drives. The model ascribes more slope than the data shows
for downwind drives. Although there is some discrepancy in the numbers,
the trend is certainly consistent with the data. So the physics
conjecture can indeed explain the trend, there is probably some error
in the details.
Details of the model
free to skip this part if you're not interested in how I chose the
parameters for the model. You will also find here a discussion of the
factors that may be causing error, especially distance errors. This
chapter exists for people who want to understand the
methodology, but also -- admittedly mostly -- for my own records so I
can recall how I did it.)
In order to use TrajectoWare Drive as a mathematical model to test the
explanation of the data, I had to choose a number of parameters for the
computer runs. Here is how I did it, and the reasoning behind it.
The parameters choice had two goals:
- Provide a result that matched the data.
plausible! That is, the parameters should reflect real (and preferably
fairly common) driver specs and the swing characteristics of real
golfers, not supermen nor contortionists.
needed to choose a set of impact parameters (clubhead speed, loft, and
angle of attack) that worked. Most important was to match the distance
of 275 yards for a straight drive (zero face angle and clubhead path)
in zero wind. This is the "pivot" for the whole study, since we are
looking at deviations due to wind.
Without knowing anything about Erik Henrikson's swing or
driver, I started with something as plain vanilla as I could. I set the
loft at a the most common, 10.5°, and the angle of attack at zero. With
those given, it is easy to use TrajectoWare Drive to determine the
clubhead speed that gives 275 yards of carry; that was 114mph, and gave
a ball speed of 167mph if impact was perfect.
side-to-side deviation should be a result of variation in clubhead path
and face angle. By eye, the green oval (representing zero wind) has
foci not far outisde ±25 yards. So I decided to find conditions that
of 25 yards left and right at zero wind, and test those conditions at
all the wind speeds.
I'd love to remember where I heard this and
reference it, but I have read that the large-muscle mechanics of a
swing are more repeatable than the small-muscle mechanics. For
instance, the clubhead speed and clubhead path are considerably more
repeatable than the clubface angle. This strongly suggests getting the
left-right variation by varying just the clubface angle, and that is
what I did. With a 0° path, it takes a clubface angle difference of
1.5° to give a
push-slice or pull-hook a final carry deviation of 25 yards. With a lie
angle of 58°, that means the push-slice is struck with 0.9° more loft
and the pull-hook with 0.9° less loft than nominal.
I plotted the seven curves (from -30mph to +30mph in 10mph steps), each
drawn as a spline connecting three calculated points:
- 1.5° left face angle with nominal-0.9° loft.
- Zero face angle and nominal loft.
- 1.5° right face angle with nominal+0.9° loft.
curves were not a bad fit to the data, but there was a substantial
bias. The into-the-wind drives were being affected more by the wind
(carry distance being reduced more) than the data showed. (The curves
for zero wind and with-the-wind were close to the data; no problems
there.) I decided to tweak things to try to remove or at least minimize
the into-the-wind error.
My first try was to decrease the loft.
If the wind was having more effect than it should, the let's try to
keep the ball out of the wind on a lower trajectory. A 9.5° loft went a
good part of the way to fixing the upwind problem but messed
the agreement with the downwind data. Not a keeper.
reducing the spin? Think about ballooning; it comes from too much lift
while the drive is rising. It gives a higher ball flight and shorter
carry. Lift, we should recall from the physics discussion above, comes
from spin and the square of ball speed relative to the air. Into the
wind would exaggerate the wind speed, and increase lift and thus
ballooning. It also puts the ball higher into the wind, which further
reduces carry. So reducing spin and thus ballooning might have a much
bigger effect on upwind performance than downwind -- exactly what we
need in order to remove the upwind bias.
After some trial and error, I settled on impact parameters of:
Those are the parameters used in the final computer model graphed
- 9.0° loft, with 2.0° angle of attack (this kept the
launch angle OK, but allowed much reduced spin).
clubead speed, giving 168mph ball speed. (Slightly more ball speed than
initially, because of the reduced loft. Less obliqueness of impact
gives more speed and less spin.)
- ±1.4° face angle (open and closed), along with 0° for
a straight drive, and the consequent ±0.9° change in loft to 8.1° (when
closed) and 9.9° (when open).
we got a remarkably good match between the computer model and
Henrikson's data, There are a few discrepancies where it might be
better. The most glaring is the distance error for 30mph into the wind.
There is also an asymmetry error downwind. Let's look at two possible
sources of those errors, especially the distance error.
computer program, TrajectoWare Drive, does not compute gear effect,
either vertical or horizontal. A ball struck higher on the clubface may
carry farther, because of reduced spin. For that reason, it is entirely
possible that gear effect might further reduce ballooning into the wind.
Drive was written in 2007, and the golf ball aerodynamics it uses comes
from data taken in 2003-2006. Golf ball development has come a long
way since then. The industry has made many changes in the ball since
the 2003 version
of the Titleist Pro-V1 (the primary data that TrajectoWare Drive was
developed to emulate). It is reasonable to think that a prime design
goal for golf ball developers would be to "inoculate" the ball against
a headwind. If the golf
ball manufacturers had any success at that, it would explain the
difference between my calculations (based on the 2003 Pro-V1) and
Henrikson's data (based on a 2019 Pro-V1x).
The Henrikson data tells us some interesting things about what wind
does to ball flight. We know enough of the physics to explain those
Our mathematical model of the related physics confirms all three.
the wind hurts more than with the wind helps. The main reason is the
square law relationship between wind speed and aerodynamic drag; into
the wind increases the drag more than with the wind decreases it.
makes a shot go more off line, and downwind actually reduces
Two reasons: (1) into the wind increases the lift force component
causing hook or slice, while with the wind decreases it; (2)
into the wind provides a drag force component away from the target
line, while with the wind provides a component toward the target line.
or hook goes farther if upwind, and push or slice goes farther if
downwind. The reason is that an open clubface also increases loft and
makes the ball fly higher, while a closed clubface decreases loft and
makes the ball fly lower.
linked to this particular video to explain apparent wind not because it
is most relevant to golf, but because I feel a personal connection to
it. The sailboats shown racing in the introduction to the video are
Albacores. If you go back far enough (1969-'75), I was a very active
competitor in the Albacore class. In fact, in 1975 I was the US
Northeast District Albacore champion. When I went looking for a concise
explanation of apparent wind, I was pleasantly surprised to find
one featuring Albacores.
- Let's take the discussion of upward curve of the ball out
of the main line of the lesson. But it is worth discussing. An upward
curve of the ball implies that the lift force is pulling up more than
gravity is pulling down on the ball. There is no physical reason why
this can't happen. Perhaps there may be practical reasons a golfer can't
generate enough spin to curve the path upward, but it isn't fundamental
physics. And in fact that "practical reason" does not exist; a golf ball can and often does curve upward.
a test you can apply to prove it to yourself. Watch some pro tour golf
on TV. (Turn the sound off if you can't stand the science errors the
commentators keep spouting.) Wait for a shot taken with a camera
pointing back down the fairway toward the golfer; the shot is coming
toward the camera. It should be a lengthy shot, preferably a fairway
wood. If the camera is mounted on a tower of the right height (they
often are), you should see the ball first moving down the TV screen then moving up.
Record it on your DVR and play it back slowly or frame by frame. When
the ball is struck it moves to successively lower scan lines on the
screen; then it changed gross direction and moves to successively
higher lines. There is no way this can happen
unless the path is curved upward. No optical illusion can create that
effect unless the camera itself is moving. And you can tell if the
camera is moving by watching the background. If the background doesn't
move, grow, or shrink, the camera is not creating an illusion of path
curvature; the curvature is real..
- As long as
we are just talking about wind speed, this is perfectly OK. But it is
mathematically correct if we also apply the same conclusion to force.
It would be all right if the aerodynamic forces were
proportional to airspeed. But by now we know they are proportional to
of airspeed. So we can't just add the components due to separate
components of the airspeed. Why is this not correct? Because:
a2 + b2
≠ (a + b)2
At this point, we are just trying to understand intuitively why
dispersion depends on wind speed. Let's try to understand using a naive
proportionality assumption to begin with. The effects will be even
larger when we take the square law into account. And we will take it
into account later when we model it mathematically.
modified -- Jan 10, 2020