## Slope Measuring

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.

active| newest | oldestRegards,

Tiger

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 areductioncompared 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.NASA page on pretty much the same thing:

http://www.grc.nasa.gov/WWW/K-12/airplane/flteqs.html

L