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Hmm, give me some time to consider all of this. If you are correct then I'm happy someone has given me their time to contribute to my understanding.

One last question before I go to study...

Why do you say that the force is of no use but displacement is? This makes little sense to me since we are discussing the forces acting on a golf ball in flight. How could the magnus effect (which everyone knows is what keeps the ball in the air) be completely useless when we're discussing exactly what makes the ball move through the air?

You are quite correct that the force applies, the problem is that, in isolation, it does not tell you anything terribly useful.

If a force of a trillion newtons is applied, one might assume that it would have a large effect. But if applied for only an attosecond, the result of the force will be miniscule. So you have to consider how the force is applied, not simply what the force is. In this case, in effect, the velocity terms in the force become 'cancelled out' when one includes the mathematical description for application of force.

I guess what I am saying is that whilst the force is a cause, it is the effect which matters in this example.

WHAT? A trillion newtons applied for an attosecond would result in miniscule effect?

Well then how does swinging a club and being in contact for .0005 seconds make the ball fly for hundreds of yards?

Something else that doesn't make sense is, if I'm wrong, how come when you hit into the wind any errant shot will curve more? When you hit down wind, errant shots curve less. But you're telling me the speed of the wind accross the surface of the ball has nothing to do with how much the ball curves.

Are we still talking to the issue of the ball slicing/hooking more as the vector velocity decreases?

Your problem is arising because you are not thinking about the numbers in context with each other. A trillion newtons on a golf ball is an acceleration of 2exp(13) m/s^2. But an attosecond is 10^-18 of a second. Displacement = half acceleration x time squared. You then find that the displacement is of the order of 10^-23 m orders of magnitude smaller than a proton!

The solution to ball carry requires a slightly different analysis. You assertion was that more velocity means more off line movement. This must be time independent else it will also be distance dependent and it becomes daft. That would be like saying if I hit the balls with the same spin, one I hit hard enough to go a mile, the other only 200 yards, which will move further off line? The mile shot of course, but that is not what you have asserted. In saying it to be velocity dependent, you need to keep the distance constant. So for a given spin and given distance (say 100 yards) which one will have moved further off line - the answer is now different and is the answer pertinent to this discussion.

You cannot apply the same arguement to the ball at impact, it is not a force which is constantly applied as in our magnus force approximation. You give it an initial velocity and then a set of undefined forces (e.g. air resistance) combine to reduce that velocity over a relatively long time. In the magnus example, the force is effectively constant over the relatively short time we consider.

If you do not believe me then I have no problems with that. But, unless you can show a flaw in the mathematics, then you cannot reasonably argue that what I have said is wrong.

Yup, if you scan back, I derived a relationship for the off axis displacement (for a given linear displacement) as a function of initial velocity. The mathematics suggest an inverse relationship.

I suspect the problem here is a matter of definiton. 'More' velocity means 'more' off axis displacement. From my viewpoint, 'that means that all other variables need to be kept constant. After all, there is no point is saying more velocity means more off axis displacement if one ball travels a mile and the other only 100 yards. I suspect that this is being overlooked.

Now that I've gone back and read your work, I feel like I need to go back to school. I can follow most of it, but not quite the entirety.

To me, it's just common sense that the ball has vector and angular velocity. The angular velocity takes greater effect the further the ball gets downrange. It's common sense because you can see it quite visibly. If you hit a wicked slice, the ball starts out fairly straight and by the time it's 50 yards from the end of it's flight, you can see it's tailing further and further to the right.

The same is true with ballistics. If you shoot a bench rest rifle at 1000 yards with a 10 MPH crosswind, the bullet will be less effected by the crosswind from muzzle to 100 yards than it will be from 900 to 1000 yards because the bullet has lost velocity (even though it's still a 100 yard area of examination).

With that in mind, have you considered time in your equations? We make the statement that the ball curves more as it slows down. Think of it this way... In the initial 50 yards of the golf ball's flight, it isn't affected by spin as much as the last 50 yards of flight.

Let's say the ball travels at an average velocity of 100 MPH for the first 50 yards of a drive. At 100 MPH, the ball leaves the tee and arrives at 50 yards from the tee in 1.023 seconds. If in the last 50 yards of a drive, the ball travels an average of 30 MPH, then it would take 3.409 seconds for the ball to travel those last 50 yards.

I guess the velocity figures would have time factored into them...

Martini78: The mathmatical description is entirely in agreement with your observations. Time has been included in what I derived and is effectively the reason why the velocity terms in the force become cancelled out.

Again, why does the ball curve more INTO the wind than DOWN wind? Airspeed is increased around the ball and causes the magnus effect to be more dramatic. THAT is simple to understand and very repeatable. But then again I must be a moron cause I don't speak in equations.

Doesn't that just prove Buns' point? The ball curves more into the wind because it loses vector velocity a lot quicker so the angular velocity becomes dominate at an earlier point. It curves less downwind for the exact opposite reason.

Since you understand airplane, think of it this way. If you roll your airplane sideways for a turn, does the radius of the turn become bigger or smaller when you travel at a higher airspeed? The answer, the higher the speed, the bigger the radius. So you can't turn as sharply going at higher speeds than lower speeds. This is true with cars or any other vehicles. This is just basic physics.

That depends on how you measure the amount of curve. The Magnus force is indeed higher at higher velocities.
The Magnus force is approximately equal to
Velocity * spin frequency * diameter of the ball ^3 * mass density of the air

But even though the sideways acceleration is greater in the beginning of the ball's flight, it's less noticeable because the forward velocity is so much higher. In other words, what someone said about the spin needing more time to take affect and move a ball noticeably is true.

The other thing you have to think about is that once the ball has changed direction, the magnus effect continues to be at a right angle to the direction of flight. So even though the ball appears to be moving farther and farther to the right in the last half of it's flight, that doesn't mean the magnus effect is increasing. It just means that the ball is traveling to the right. In other words, the curve is not getting sharper, it's just that the ball is now moving sideways relative to your position.

Think about it. If you hit a high fade, do you really think the ball "curves" more in the last 50 yds of it's flight? The answer is NO. It moves the farthest to the right of the fairway in that last 50 yds, but only because that's the direction it's travelling.

So...
The ball doesn't curve much in the first 100 yds because it's travelling so fast that the sideways motion isn't very noticeable compared to the huge distance it's traveled forward.
The ball doesn't curve much in the last 50 yds because it's not travelling fast enough for the Magnus force to move it very much.
There's a point in the middle where the ball is travelling fast enough to generate a strong Magnus force, but slow enough that the sideways movement is significant compared to the forward movement.

That is partially correct. However, it also curves more into the wind because it's travelling at a higher speed relative to the air around it, which does in fact, cause a larger Magnus force. The fact that it loses velocity more quickly relative to the ground means that the effects of that Magnus force are more noticeable.

Thank you! The lightbulb just went off.

That was the exact conclusion I finally came to after his comments and it makes much more sense as opposed to just saying the magnus effect does nothing like was originally stated.