I was asked about how to figure the horizontal distance from where the shooter is to where his target is when shooting up or down a hill.
The first things you have to know are the slope distance and the angle from horizontal. Of course the accuracy you have in determining these two things controls the final results of your calculations. Yes, I said the “C” word. Don't be scared off by the word calculations. Doing math is like finding a gold watch that has been dropped in a dirty horse stall. You just throw out the crap until you find the gold.
The distance is easy to get. There are a whole bunch of laser range finders on the market. Depending on how much you want to spend, they will give you the slope distance (the distance form you to the target going up or down the hill) to within one yard all the way out to two or three thousand yards. Most of the ones we are concerned with range from up to 400 to 1,000 yards.
The vertical angle or zenith angle is a little harder to get. The most feasible way to obtain this information is with an ambi-level or clineometer. These are small devises that give you an angle off of the horizontal. They usually do this only to the closest degree. The last time I bought one, it cost me about $100.00. You can buy these things at surveyor supply stores. They measure either in vertical angles or zenith angles. All this means is that a vertical angle is measured with the horizontal angle being 0 degrees and a zenith angle has the horizontal angle being 90 degrees. A slope up or down hill of 5 degrees will read 5 degrees on a devise that measures in vertical angles. It reads 85 or 95 degrees on a device that uses a zenith angle.
Assuming you have the range finder and the ambi-level, the only other thing you need is to either steal your kid's scientific calculator or buy one for about $15.00 If you have an ambi-level that reads in vertical angles, use the cosine function on the calculator. If it reads in zenith angles, use the sine function.
All you have to do is read the distance on the range finder and the angle on the ambi-level. Lets say we have a 15 degree vertical angle or a 75 degree zenith angle with a distance of 500 yards. You take your calculator, hit 15 and the button that says COS if you are using a vertical angle or 75 or 105 and the button that says SIN if you are using zenith angles; then hit the times button and 500; then hit equal and read your horizontal distance of about 483 yards.
I have included a chart of angles and distances. But it is going to be a lot easier to just use the calculator than carry the chart. Also, the chart is only in 100 yard increments.
If you are like me, none of this matters because the target has to be hanging off the gun barrel before I can hit it.