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Article
Contents
Intro
Data
Physics
—Distance
—Dispersion
—Asymmetry
Model
—Details
Conclusion
Footnotes

What wind does to a drive

Dave Tutelman  -  December 29, 2019

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 more shorter or longer it makes the drive. That's all obvious. But there are some less obvious effects as well:
  1. Into the wind hurts more than with the wind helps. (Most golfers have at least heard this.)
  2. Into the wind makes a shot go more offline for a particular clubface angle error. Also, with the wind actually reduces that dispersion.
  3. A 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.
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.

The data

On Dec 18, 2019, Erik Henrikson tweeted this graph, along with the text:
Erik Henrikson  @Ehenrik - Dec 18
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.
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:
Andrew Rice Golf
December 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
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 Pro-V1x.

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:
  1. Into the wind hurts more than with the wind helps. The scatter plots for negative wind speeds are farther apart than for positive wind speeds.
  2. Upwind makes a shot go more offline, and down wind actually reduces dispersion. The more upwind the drive, the wider the oval showing dispersion.
  3. Pull 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.
Let's 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 data with my own trajectory program -- based on that physics -- to see how well the results agree.

Physics

Let's start 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.
  • Drag 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 equal.
  • Lift 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 lift 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 a 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 or hook.
  • Weight 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.
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.

Now let's look at how this causes the three effects wind has on ball flight.
 

Distance - hurting hurts more than helping helps

It 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.

In 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".
  • A 30mph helping wind increases carry distance about 25 yards.
  • A 30mph hurting wind decreases carry distance about 55 yards.
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.)

Effect of drag

Let's 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 in sailing).[1]

Let's try to get a feel for this. (If you understand apparent wind, you can skip this paragraph.)
  • 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 your speed.
  • 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 walking speed.
Relative wind works the same as relative current. Look at the graph. I have noted three different relative wind speeds:
  1. The ball speed in still air is 165mph. Since there is no wind, that is also the relative wind speed or apparent wind speed.
  2. 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.
  3. 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.
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.

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 195mph.
  1. 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!
  2. 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.
The second point, the one about curvature, assures that a hurting wind hurts more than a helping with helps.
 

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:
  • 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.
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.


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.[2])

Let's 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 drive.

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 -- ballooning.


Now 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.

This 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.

Dispersion - more offline into the wind

In the comment thread on Andrew Rice's post, David Arrignon wrote, "Very interesting 😉. 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?
This figure shows the just the variable part of the wind, not the total wind. The total wind includes ball speed, which is the same for all the ovals.[3] 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 speed and direction, not forces.

There 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 primary wind 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.

The parallel component 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 hook. Therefore:
  • 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.
This is the effect David Arrignon refers to as the amplification of sidespin.

The perpendicular component 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 ball toward the target line. The stronger the wind, the bigger this force, and the narrower the dispersion.

If 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.
 

Asymmetry of 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.
  • 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 these extremes.
What would cause this effect?

To 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.

If 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.

For 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.

Mathematical model

What I have said so far is just words and pictures, what I sometimes call "hand waving". But according to Kelvin, a noted 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 conjecture by working the physics quantitatively -- with numbers, not just words and diagrams.

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: distance, dispersion, and asymmetry. Even the numbers are quite similar, if you know how to interpret them.

Look 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 data.

  • Distance - 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.
  • Dispersion - 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.
  • Asymmetry - 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.
I consider this a pretty good confirmation that we now understand the physics behind the distance, dispersion, and asymmetry in the Henrikson data.

Details of the model

(Feel 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:
  1. Provide a result that matched the data.
  2. Be 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.

Impact parameters

I 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.

Deviation

The 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 gave deviations 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 golfer's 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 than nominal 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.

Tuning

The 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 up the agreement with the downwind data. Not a keeper.

How about 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:
  • 9.0° loft, with 2.0° angle of attack (this kept the launch angle OK, but allowed much reduced spin).
  • 114mph 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).
Those are the parameters used in the final computer model graphed above. 

Errors

While 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.
  1. Our 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.
  2. TrajectoWare 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).

Conclusion

The Henrikson data tells us some interesting things about what wind does to ball flight. We know enough of the physics to explain those things.
  • Distance - Into 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.
  • Dispersion - Upwind makes a shot go more off line, and downwind actually reduces dispersion. 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.
  • Asymmetry - Pull 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.
Our mathematical model of the related physics confirms all three.

Footnotes

  1. I 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.
  2. 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.

    Here's 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..
  3. As long as we are just talking about wind speed, this is perfectly OK. But it is not 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 the square 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.

Last modified -- Jan 10, 2020
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