Trajectory of arrow vs golf ball

In My Humble Opinion
1

We were having a discussion on arrow trajectory today and one of the guys brought up golf balls that seem to go the furthest when hit with a driver that uses a trajectory of about 10 to 12 degrees. He supplied a link that explained this was because the driver put back spin on the ball which created lift. That might be true but I don’t buy that the driver hits the furthest because of that. My argument is that when striking something the most force can be delivered by hitting it square at 90 degrees. I compared it to jumping off of a roof and landing on sloped ground instead of flat ground.

Does anyone of an answer as to why a golf ball trajectory for best distance is 12 degrees instead of the usual 45 degrees? I think if you could hit the ball at 45 degrees with a 0 degree face it would go further but that’s not practical.

2

Dimples?

3

It’s a lot easier to learn Physics when you get rid of pesky details like drag and friction. You really can learn a lot about forces and motion by studying them in isolation; and an object fired through the air forms a nice, elegant parabola.

When you start accounting for drag and friction, it gets complicated. Even with a non-spinning ball I would expect the longest flight would not come from an exact 45 degree launch angle.

When you start adding in factors like spin and lift, all bets are off. It’s probably easier to go somewhere with a measuring tape and hit the damn ball than to grind through all the math involved.

But knowing this place, someone will be along shortly to try it, anyway.

4

I think that at less than 45 degrees, the path is shorter to where you are going, so you will be spending less time in the air getting dragged.

Imagine being underwater in a pool and throwing a pool cue, to mix metaphors. If you throw it at a 45 degree angle the ball will go up a bit but stop pretty quickly and then sink down. Whereas if you throw it straight, it will go the same distance and then stop, but it’s gone further forward due to the angle. Note that I haven’t done this experiment and indeed have just made it up on the fly.

Backspin also has something to do with it golf ball wise. The ideal angle for distance for regular artillery in air is more like 40 degrees than 15. (That is, until you shoot it fast enough that it enters the stratosphere. Then the ideal angle is more like 50 degrees because you reach the stratosphere – with little drag – quicker.)

5

Drag and lift will both cause the optimal angle to be less than 45 degrees. The amount of initial speed you can give the ball will also vary with angle, and that’ll probably also cause the optimal angle to be less than 45 degrees. Which effect is most relevant for a golf ball, I don’t know, and I don’t think it could be easily determined without experiments. You could, for instance, make a golf-ball launcher that could launch at any angle with the same speed, and find the optimal angle for that, and take high-speed film or some other way of measuring initial speed for an experienced golfer shooting at various angles.

6

https://goo.gl/images/pXVbYp
Check out the link for a visualization. The golf ball isn’t following a strict ballistic path: the spin on the ball and its interaction with the air means that the ball descends at a sharper angle than it went up. Plus, the spin on the ball is desirable for several reasons, among them that it helps the ball fliy straighter, and not like a knuckleball with no spin. Not to mention that spin is extremely important on other golf shots (like wedges to get it to stop quickly on the green) and you can’t change your ball between shots, so a ball that has low spin would be generally better for driver shots and terrible for most everything else.

But your point isn’t entirely wrong. Some very long hitters, like Bubba Watson, combine extreme swing speeds with a high launch angle and low spin. But his swing speed is basically 30% faster than your average duffer, so there is that.

7

I don’t think my question was actually addressed here. Could a major part of the reason for low launch angles simply be that a club striking the ball on angles instead of a square face looses a lot of impact force? So low angles drivers are used simply for better impact imparted to the ball?

8

Gotcha. I wonder if an even better distance could be had by teeing from a higher tee (even passing the point of legality) so that you can hit the ball flatly but on an upswing and so still impart a high angle.

9

I’ve repeatedly been confused about many aspects of golf physics - including this one, so I have little expertise to offer on that. But my experience is different from your premise. When I bought my last driver (maybe 5 years ago) on the demonstrators I clearly and consistently hit my 9.5 degree further than a more lofted driver.

I have no idea what the loft is on pros’ drivers. I guess I had ignorantly assumed that they were lower than amateurs used. But with those guys, it is a complete package as you suggest, between attack angle, loft, swing speed, and various aspects of the ball.

I had thought (in my ignorance) that folk generally went with a higher lofted driver because they have generally been considered easier to hit. Tho driver is pretty much my favorite club, and I CANNOT consistently hit a 3-wood - even off the tee, many/most people will say that a 3-wood is easier to hit than driver. And very few golfers can consistently strike a 1-iron.

I was unaware that there was a max height of tees. And you do strike the ball with driver on the upswing - as opposed to the irons which you hit on the downswing.

You want to complicate things, start talking about shaft flex and kick point! :wink:

10

Oh, I see. I couldn’t tell what you meant by hitting it at 90 degrees – golfers would say that you would be using a club with 0 loft.

I think maybe 10 years ago or more, there were a few pros who would use a driver with a loft as low as 7 degrees. Now, most are in the 9-10 degree range. There’s long drive competitions where golfers use lofts as low as 4 degrees.

This is one of those questions where the physics of how a club hits a ball, the coefficient of restitution, and so forth are not my forte. However, I can speak from experience and reality as to how a golfer maximizes driving distance.

One starts from the assumption that a golfer is not going to radically change his swing for a driver. There are a few tweaks like width of stance and ball position, but no fundamental changes. Then, a golfer can use a launch monitor to examine in very precise detail how the ball leaves the face of the club. These machines use either radar or optical sensors to precisely measure things like swing speed, ball speed, launch angle, backspin, side spin, and angle of attack.

Based on this data, club fitters can change several variables: the loft on the club, the ball itself, length of the club, and literally a hundred different things with the shaft of the club. After an hour or two worth of tinkering, even the average golfer can end up with a club that optimizes all those various factors that the launch monitor measures. The benefits can be very substantial: it is not totally unreasonable for a golfer who hit a drive 235 yards with an old driver to now be hitting close to 260 with a perfectly fit driver. Such a big increase in distance isn’t guaranteed, but I would say that adding 5, 10, even 15 yards with a well-fit driver is a pretty reasonable expectation.

So I’m not answering your question about the physics of it, but this does address the practicality. In none of these scenarios does a clubfitter recommend a club with no loft. It does not happen, for duffers, pros, or long drive champions. It is a fact that longer drivers swing extremely fast, tend to hit more on the upswing, have lower-lofted drivers, and have lower spin rates. But that does’t mean that hitting even MORE on the upswing, even LESS lofted drivers, and even LOWER spin rates will result in longer drives. Based on real-world experiments, which anyone can do at a driving range, at some point a golfer starts losing distance with those changes.

Ok, so let’s go back to the starting assumption. Could a golfer adopt some kind of different swing to maximize distance using a driver with zero loft, teeing the ball higher, and hitting more on the upswing? Beyond a certain point, I’m just not sure that’s physically possible. Let’s examine the golf swing.

As the club approaches the ball for a right-handed golfer, in the last few inches or so before impact, the club is slightly open (pointing off to the right), reaches the lowest point of the swing. Within centimeters, the club squares up to the swing path, and starts a very small upswing. After contact, the club face starts to close (point off to the left slightly), and continues the upswing. All the while, the path of the club is generally travelling at first from the inside of the swing toward the outside, squaring up to hit the ball, and after contact starting to travel back to the inside of the path of the ball flight. See the solid yellow line to visualize this better.

If the ball position is moved forward by several inches, and a longer tee is used, in order to use a zero-lofted club, a lot of things start to happen. First, you’d have to use a longer driver, which increases swing speed and seriously degrades accuracy. Second, somehow the golfer still has to square up the face of the driver, but at a location that is probably about 8 inches beyond his front foot. Look at a picture of a swing arc – here. So if the ball is moved forward about 2 feet from this pic, at the point that there’s a substantial upswing, the club would be naturally closing its face. I’m not even sure how one could compensate for that. Also note that unlike this picture, the swing arc isn’t a perfect oval. In reality, the arc on the downswing is considerably sharper than the arc on the follow-through, which is necessary to generate clubhead speed.

So, in sum, to generate substantial positive angle of attack (which there are a few freak golfers who do), we are likely talking about extremely difficult swing changes that involve substantial tradeoffs in accuracy and swing speed. I just can’t see how it would be worth it.

11

Just to clarify, you are talking about not assuming an exaggerated swing like the long drivers, right? Because the sweeping swing for woods is certainly different than the downswing used for short irons.

As lots of folk have observed, “distance” balls are generally low spin. I long ago decided I did not need a couple of extra yards off the tee, but would benefit far more by making my shots into the green stop. So I use a higher spin ball (among whatever I’ve managed to find in the weed/water.) Also, I hit a pretty straight ball, so I don’t have to worry about the spin magnifying a tendency to hook/slice.

12

But a lot of this is due to the different setup (ball position, forward press, slight difference in shoulder and spine angles, etc) as opposed to having a different swing path, eliminating lag, etc. which I would say are major changes.

13

Here’s a good article on exactly the question asked by the OP in, of all places, Forbes:

14

Don’t neglect roll into the equation. In general.the longer the rollout, the longer the drive. Maximizing flight is not the ideal for a golf swing, especially if the hole is flat or downhill. There was a tournament a few weeks ago in Hawaii where the 18th hole was a long downhill shot and the roll for a well-placed tee shot was well over 100 yards, maybe closer to 200 yards.

15 
I am going to change my question to just one factor maybe it will be clearer. Does the impact force on the ball increase as the angle of the club face decreases. In other words ignore distance and trajectory. Would a ball hit with a 0 degree face have more energy in it than a ball hit with a 20 degree face.
16

This doesn’t exactly address your question, but it may be helpful to know that the bodies governing golf put an upper limit on the coefficient of restitution of drivers. COR measures how much energy is transferred from the face of the driver to the ball, and the limit is 0.83. (IOW, a maximum of 83% of energy may be transferred to the ball.) So to the extent that someone designs a club that transfers more energy to the ball, if it exceeds that limit, it is a non-conforming piece of equipment that can’t be used in competitions (which sounds like it wouldn’t be such a big thing, but in effect it means that nobody wants to buy it). I’m also glossing over that COR has been partially replaced by a similar measurement, but I think I’m already in the weeds here.

The discussion of COR has primarily revolved around the materials used in the face of the club, but I don’t see why it wouldn’t have anything to do with the loft if the physics showed that loft impacts COR, which I really don’t know for sure… but there are iron sets that claim that every club (each of which has increasing loft) has consistently high COR. I’m not totally sure on this, but if a 16 degree 4 iron doesn’t have a ton more COR than a 52 degree pitching wedge, I’m guessing it might not make a huge difference.

Cite – “Each iron 4 through PW is designed with a COR of at least 0.805”

ETA: in addition, it doesn’t seem clear to me that tinkering with COR matters all that much. I’ve been told that adding 0.01 COR to a driver may add a yard to the drive. I can’t verify that.

17

All things being equal, probably not. It would be different, with energy going to speed decreasing with loft, but energy going to rotation increasing. I don’t know the math behind it, and there are no real world applications I can cite - there are just too many variables in golf that affect striking force, ranging from club length to angle of attack. This page has interesting charts, but doesn’t really answer your question.

18

My first eagle was a 525 par 5, dogleg left about 200 yards from the tee box…cart path on the right side of the fairway, trees lining the left…I hit my typical pretty straight shot, it went about 225 yards in the air, land on the cart path beyond the dog leg, bounced about 40 feet in the air, turned left, landing FURTHER down the cart path, bouncing and bouncing until it popped a final left and rolled onto the fairway less than 150 yards from the pin…it was during league play, so with guys I know well, we all watched silently until one of them blurted, “OH, YOU HAVE GOT TO BE F$CKING KIDDING ME!”…so I can honestly say I drove a ball greater than 375 yards…and ‘drove’ is a pretty subjective term here…still had to make the second shot and the putt, I was actually happier with that than my freak of nature drive…

19

There’s a famous story about ‘Titanic’ Thompson, a legendary golfer (and golf hustler) of the 1930s through the 60s. He made a bet that he could drive a ball 500 yards. The conditions were that he could select the site, but it had to be level, and he could hit the ball downwind, but no more than a gentle wind was allowed.

His chosen site was a frozen lake near Chicago; his drive measured nearly a mile.

20

Ages ago I read of a stunt where a foursome started at the tee of one golf course, went down the fairway and off of the course, across the city to another course where they finished up in the cup of one of the holes there. There was a team ahead to spot where the balls landed and another behind to pay for damages. It was noted that the farthest distance achieved on a stroke was a 500-yard, downhill putt.