I can't say that I am entirely certain of what it is you're doing, but I think I have an idea of what's going on and decided to take a stab. To use spherical coordinates you need 3 pieces of information:
1. A radius (which it looks like for you is 50m)
2. An angle measured from the vertical axis
3. An angle measured in the horizontal plane
We write spherical coordinates using these three quantities in that order (radius, angle from vertical axis, angle measured in horizontal plane). For example, a data point from your first set of measurements in "spherical coordinates" might look something like
(50, 90, 22.5),
where 50 is the radius, the second coordinate is 90 degrees because your first measurements were taken in the horizontal plane which is at a 90 degree angle to the vertical axis, and 22.5 which is the angle measured in the horizontal plane that you provided in your data.
Again, I'm just trying to get in the ballpark of what you're getting at (I wouldn't put your reputation at work on the line for what I've said here). If I have misunderstood or made things more confusing let me know; maybe then we can nail down what you're looking to do. Otherwise, good luck!