Hi all,
I think I have found the right forum to post my math for calculating distances. Are you ready?
The math looks like a lot. I used to do the calculations on a handheld calculator. I finally wised up and built an
excel spreadsheet where I just type in the data and get the answer. This is the distance formula as explained below:
distance to hit = d + w*(d/210)*sin(A) + 0.4 * e + {d/(bs+ 0.14*e)}/{1+(w/20)*BB}
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Explanation
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There are four "terms" involved:
1. "d" is the distance shown to the hole.
2. "w*(d/210)*sin(A)" is the amount of yardage to compensate for the wind against or with you. A negative angle,
tailwind, subtracts yardage and a positive angle adds. More explained below.
3. "0.4 * e" adds or subtracts yardage from the strike due to elevation. A negative elevation subtracts yardage and a
postive one adds.
4. "{d/(bs+ 0.14*e)}/{1+(w/20)*BB}" When using backspin yardage needs to be added. This term is explained in detail
below.
In its most basic form it does not calculate for backspin:
distance to hit = d + w*(d/210)*sin(A) + 0.4 * e
where:
d = The distance to target in yards.
w = windspeed.
e = elevation in feet
210. This means that at 210 yards the wind strength against you knocks off 1 yard for every 1 mph. So if you are at
105 yards it only knocks off about 1/2 yard per mph. Wgt varies this a bit but I use 210 right now, it seems to vary
between 190 and 270. Also, changing this values has little affect on overall outcome, but its necassary to get within
a few yards on your strike.
e = elevation. I use 0.4. This adds or subtracts yardage to the hit according to elevation change. 0.4 seems to be
perfect and constant.
A = the angle of the wind. If it is against you use 90 degrees, and for pure tailwind use -90 degrees. Pure crosswind
is 0 degrees, etc. The wind vector that affects the balls travel distance is the sine of the angle. For the wind
vector that affects the lateral movement of the ball, how much the ball gets pushed sideways, I use the cosine of the
angle.
Using full backspin requires adding yardage to your strike. To do this I have found that each club (and ball!) has a
characteristic number to divide the distance, d, by. It varies from club to club. For wedges I typically use between 6
to 8 yards, and for irons it varies from 13 to 68 from small yardage to large yardage irons. For example, if the
distance to the hole is 100 yards, then divide 100 by 6.75 or 100/6.75 = 14.8 yards. The new equation looks like this:
distance to hit = d + w*(d/210)*sin(A) + 0.4 * e + d/bs
where:
bs = the backspin divisor for the club in use.You will have to experiment with this number. To start, for high degree
wedges (like 52, 60, 64 Clevelands) I use about 8.
*On a side note my Cleveland 60 deg 80 yard wedge has so much backspin I don not use it at all and hence dont use the
d/bs part, so the formula is simpler.
This does get the distance closer and allows for using the full backspin confidently. However, elevation effects the
balls ability. This can be compensated for. The new part of that formula becomes:
d/(bs+0.14*e)
This has the affect of decreasing the added yardage for higher elevations and increasing the added yardage for lower
elevations. 0.14 seems to be the right value to use. The new formula becomes:
distance to hit = d + w*(d/210)*sin(A) + 0.4 * e + d/(bs+ 0.14*e)
Added backspin distance is also, unfortunately, effected by the direction of the wind. Into the wind and the ball
bites best, while with a strong tailwind it bites the least. To compensate for this effect the whole term d/(bs+
0.14*e) can be divided another number that is dependent upon the wind angle. If pure headwind, dividing the term by 1
has no affect, and with pure tailwind dividing by 2 seems to have the best result. The new formula becomes:
distance to hit = d + w*(d/210)*sin(A) + 0.4 * e + {d/(bs+ 0.14*e)}/AA
where AA is a number dependant on wind angle. The numbers I use for AA for 90 degrees is:
1 (pure headwind). For other angles use:
80 deg = 1.06
70 = 1.12
60 = 1.17
50 = 1.23
40 = 1.31
30 = 1.33
20 = 1.37
10 = 1.385
0 = 1.4 (pure crosswind)
-10 = 1.576
-20 = 1.752
-30 = 1.928
-40 = 1.104
-50 = 1.28
-60 = 1.456
-70 = 1.632
-80 = 1.81
-90 = 2.0 (pure tailwind)
This gets it even closer. However, wind speed affects these numbers. It seems most accurate for 20 mph. A stronger or
lighter wind makes it act different. To compensate for this modify the backspin distance formula divisor AA to be
equal to AA = 1 + (1 - AA)*(w/20). For a wind stronger than 20 mph this has the affect of decreasing the yards added
for backspin, with the largest effect for pure tailwind all the way to no effect for pure headwind, which is how the
ball acts when played. For a lighter wind than 20 mph it has the effect of adding more yards, even with a tailwind.
For no wind the term d/(bs+0.14*e) is simply divided by 1, having no effect, which models the scenario well. If we
call AA AAA andsomething like BB and consider the (1-AA) term, a new and simpler formula can be divised. Here are the
new values for BB:
BB for 90 deg = 0, or for:
80 = 0.06
70 = 0.12
60 = 0.17
50 = 0.23
40 = 0.31
30 = 0.33
20 = 0.37
10 = 0.385
0 = 0.4
-10 = 0.576
-20 = 0.752
-30 = 0.928
-40 = 0.104
-50 = 0.28
-60 = 0.456
-70 = 0.632
-80 = 0.81
-90 = 1.0
The new formula becomes:
distance to hit = d + w*(d/210)*sin(A) + 0.4 * e + {d/(bs+ 0.14*e)}/{1+(w/20)*BB}
Best of luck!