genorb:
Well that's not necessarily a good idea to use the formula from another guy (many would not agree with mine, I am sure). The formula give you an idea of the effective distance to the pin. But then you can still play with the amount of spin you set. For example, if the pin is at an effective distance of 168 yds, I can use my 165yds iron with almost no spin, or use my 180yds with full back spin and reduced power. In addition, all irons do not react the same way. My 165yds iron is a bit short for me while my 150yds iron is a bit long for example.
You should construct the formula yourself (see below). An important point is that the distance to add or subtract due to the wind is always a % of the distance between you and the target (this is not a constant distance to add). Indeed, let's take the following example. You have a given headwind and you set 100yds of power. The ball travels only 90yds due to the wind. Now you have the same headwind and you set 200yds of power. What would be the distance travelled? Not 190yds but 180yds. indeed, when the ball travels the first 100yds it loses 10yds, but the ball will again lose 10 yds during the remaining 100yds.
I hope I am clear enough...
That's not complicated to contruct the formula but it takes some time.
Collecting the data
Pick up a course like Kiawah or Bethpage (not STA because the fairway are rolling too much) and tee off with your irons with full power (take for example your 195yds iron (I see you are using the R11 irons)) and the spin you like or use the more (once on the fairway, you can still play another shot). Do it until you get perfect headwind. You need also to ding the shot if you play full back spin. So with full power the ball goes normally to 195yds, but that with that headwind (X1 mph) the ball goes to 180yds. So the factor in the case is
F(X1) = 195/180 =1.08
(so you know that with that wind you need to multiply the distance by that factor. So to reach 195 yds you need actually to set 195*1.08 = 211 yds of power)
Now later on you get another perfect headwind (X2 mph). Again with full power the ball goes normally to 195yds, but that with that headwind (X2 mph) the ball goes to 185yds. The factor in this case is
F(X2)= 195/185 =1.05
Ideally, you need to get several data for each value of the wind and you do an average.
Constructing the formula
Now you know two things
- If there is no wind, the factor is 1. This mean that F(0) = 1
- the larger the wind the larger the factor F
So when you have enough data you can search for the simplest formula (a linear relationship between the factor F and the wind velocity X) which fit your data and is in agreement with the two points above. Such a relation reads
F(X) = 1 + X * A
(indeed F(0) = 1 and F increases linearly when X increases if A is a positive quantity)
The data you have accumulated will help you to determine what should be the value of the constant A.
Now of course you still need to figure out how to modify your formula when you have 8 o'clock wind for example (wind between cross wind and full headwind)... That's a bit more tricky.
I hope I was clear enough.
Titus, Genorb, et al,
I commend you both on finding the system that has improved your games. I must confess that I'm among the group that doesn't entirely understand your calculations, but that doesn't mean I don't appreciate them.
With all due respect, (and I may have overlooked its mention), but I think there are a couple criteria you may not have factored in.
1. Ball flight. Specifically the parabolic changes from one club to another. For example, a 1 iron (yes, I know), that goes a potential 200 yds, and a PW rated for 100 yds are not necessarily affected by wind (and other factors) to the same ratio.
While the distance traveled is 2:1, I think you'll find the PW is more affected my wind than the 1 iron (yes, yes. I know already. sheesh.) because the arc of the higher lofted club needs more flight time/route to travel a given distance.
To put it another way, If I have a 100 yard approach and choose to hit a 60 degree wedge, the ball will actually travel 166 yards on its way to the hole when you factor in the rise and fall of the golf ball. (If that math is wrong, and it might be, it irrelevant to the point).
If you were very very stupid and decided to hit a 1 iron in this hypothetical situation, the ball flight might only travel a total of 120 yards to reach the 100 yards-away pin because of the change in loft.
You see where I'm going with this...
The wedge has 30% (ish) more time just floating around in the air letting itself get pushed around by the wind.
My second point is the force of ball in flight. Most people know you can power through the break on a fast green if you need/want to. The effect of the wind on a ball in flight is essentially the same thing, i.e. the harder you hit it, the less the wind will have an effect on it.
Because a golf ball flies at a faster speed when hit by a driver than when it's hit by a wedge, it has more initial inertia to mute the effect of the wind than a wedge does.
As any golfer knows, the wind affects the end of the ball flight much more than the beginning of the ball flight. Since different clubs have different trajectories, some clubs will be affected much later in the parabolic return to Earth than others.
Now, I'm not a mathematician, but I am logically minded. I understand that these are factors when hitting a golf shot and I take them into account, but only insofar as I can still play it by feel.
I don't have a calculator in front of me when playing (maybe I should), but that's not to say I discount the relevant factors that can affect a shot. I try to factor it all, and I usually know why I missed when I do.
If these points are too much minutiae, I apologize, but if you're going to develop a formula, they are definitely factors to take into account.
(I'm drinking rum right now, so if this isn't as clear on paper as it is in my head, it's entirely my fault. Well, it's the rum's fault, but I'm an accomplice)
I admire both Genorb and Titus for delving into the mathematics of it all.