Thanks for the calculation. We will provide the raw data to YOU in first hand to match our findings.
We are making it in AutoCad and showing you the results as well.
"1 foot/mile laser slope"
By this you mean that the laser should RISE about 1 foot / mile on the distance? roughly?
Can you make an expected laser beam height above water surface calculation at 5, 10 and 15 miles distance?
I am happy that we agree on the subject of leveling the laser! VERY important.
No, the point is you CAN'T level the laser to the degree of accuracy needed. Hence you need to factor that into the calculations (as I did above).
The laser might rise or fall, depending on its slope, which would give a positive or negative value for L. If you did manage to get the laser horizontal, then L would be zero.
But you are looking for r (or E, with the simpler equation), the math I did above allows you to eliminate the laser alignment error.
YES! I am planning to make measurements like this:
at 500 meters I calibrate the laser beam to the same height as the unit on the shore. waves may cause +-5cms difference in reading.
at 1000 meters I calibrate the laser the same way and record the value before and after the setting.
at 1500 meters again, and at 2000 meters away I do the FINAL calibration of the beam to the exact height as the unit on the shore.
NO! Don't do that. You are just progressively messing up the position of the laser. Once you've set the laser, it is very important that you do not touch it at all until the experiment is over. If you are calibrating it at 2000m, then you are tilting the laser down a bit.
Calibrate it at 2KM if you like, but then come back to the start, and take your reading from there. It's very important to have a constant value of L (the tilt of the laser) over the entire journey.
Then take as many readings as possible. You know how inaccurate holding a tape measure to the water surface is. Take lots of readings, record them with GPS, put them on a graph, get a weighted average to get the value at two wide points, then you can find r and L.
If the earth is flat then you'll get a very large value for r.