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Slope Measuring Answered

     I'm interested in making a yardage book for one of the golf courses i play at. The only problem is that i don't know an accurate way to measure the change in distance through elevation. For instance if a shot to a green with no change in elevation requires a 7-iron, then a shot of the same distance that is downhill should require a club that will hit the ball a shorter distance.
      My question is, is there a formula of some type that i can enter the rate of change in slope and the distance, and get the actual distance needed for the shot.


I'm a physicist, not a golfer, so bear with me if this analysis is overly naive.

Unless you're hitting into a strong headwind, you should be able to assume that the ball follows an approximately ideal ballistic trajectory. That means, among other things, that the angle of the ball going up will be the same angle coming back down. So, when you hit a ball, do you know (approximately) how steep the trajectory is? 30 degrees? 45 degrees? 60-70 degrees?

If you can't easily estimate the angle, what about the maximum height vs. distance? If you can estimate that, then you can use height vs. half-distance (since the peak of a ballistic parabola occurs at the midpoint) to estimate the angle [tan Y = height/(dist/2), so Y = atan(2*height/dist)].

Now, assume you've got the angle from one of the methods above. Then, the extra drop in elevation, E, corresponds to an extra distance of travel D according to tan Y = E/D, or D = E / tanY. If you're shooting to a higher elevation, then D is a reduction compared to the level-ground distance.

By the way, if you were able to answer the second question (maximum height of the ball), but not the first, then you can skip the tangent function entirely! Since tanY = 2H/dist = E/D, you can directly solve for D = E*dist/2H, where "dist" is the level-ground distance.

Since each club travels on a different angle, it would just get way too complicated. Also when you hit a golf ball, the grooves on the clubface and the angle, (which varies between clubs), apply a lot of backward spin on the ball (in order to make the ball stop quickly on the green). This backward spin also keeps the shape of the trajectory from being a parabola. So, the height vs. half-distance method would not work. Below is a rough picture of the shape of the trajectory a golf ball takes.


Thank you! The backspin certain is an issue, along with the variations due to club, swing, etc. Basically, the only really quantitative way to solve your problem is to know the angle of the trajectory where the ball is descending. If you approximate that angle as constant, then the tangent formula I gave you gives the exact relationship between vertical drop and range (horizontal distance).