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Encap

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Even a laser with a 1mRad divergence and a 1mm beam at the aperture will produce a dot that grows bigger 1mm per meter --- so at 4 miles 6470 meters it you make a dot that is 6470mm/254 inches/21.2 feet wide if the output has not been clipped/reduce in size in any way --so.... getting any accurate reading is probably out of the question and you would have been able to guess had you looked into the reality of lasers before jumping of the high dive into a pool with no water.

A laser that produces perfect uniform diameter beam over any distance chosen, and produces a dot of same diameter at any distance, exists only in your imagination.
A laser is a poor choice for the type of measurement you want to make---there are several problems with even if an idealized imaginary laser existed

From the thread Alaskan provided see:https://laserpointerforums.com/f53/friend-i-want-measure-curvature-earth-using-laser-lake-98000.html
"Originally Posted by LSRFAQ View Post
If your just doing this for fun, skip reading this post.

If you need a real measurement or this is a science fair project, read on...
Save your money and hire a surveyor.
Here is why:

You will have atmospheric scintillation and refraction that does not quit.
Coherent light is subject to interference at the detector for each photon's beam path.

You get horrid low and high frequency noise. This is why light bulbs or Leds are used as sources for long distance light communications.

Next Question. How will you accurately find the centroid of the LARGE blob down range? Helps if your Blob is Guassian with a brighter center, but you would still have to find the center some how. This is going to need some serious robotics.
Or at least a photodiode/photomultipler sliding on a calibrated arm and a piece of graph paper.

The traditional way, used for surveying the Pacific Missile Range Islands by a team that included my Father...
Dad was helping with the planting of early Loran "A" NAVAIDs
1. Build a Bilby Tower at each end of the transit plus one offset a known distance on shore. This gets you above the small part of the refraction from ground convection.

2. Place a taped down Jeep Headlight on a leveled platform at the top of the first tower. The light is taped down to the central portion of the collimated beam.

2. Place a Theodolite or Transit on the other two towers. Measure carefully the spot of light, then swing the instrument to the other tower. Then swing upwards, catch a few stars at a precisely known time. Then Star site reductions at night to establish a Geodetic control point. These days differential GPS provided by WAAS or similar commercial services might get you closer. Then you still have to correct for the Ellipsoid.

Farmers and Road Builders hit milestones within inches with specially assisted GPS signals broadcast from temporary "control" stations and satellites. Often a local FM radio broadcast has the corrections on a Subcarrier.
You can lease/borrow the specialized receiver.
Refs:
NOAA 200th Feature Stories: Bilby Towers

Scroll to Bottom to see what/why NOT lasers.

MODULATED LIGHT DX

"And the US Coast Guard used a 5 mW Hene with an Upcollimator as a NAV AID at 1500 yards with an eye as a detector."

http://www.dtic.mil/dtic/tr/fulltext/u2/a170823.pdf

Theodolites are all over the place. They eliminate the "guess the blob center" problem.
(insert safety warning about optically aided viewing of high power lasers here)
This is a fun project, but you need to level the source laser some how, relative to local gravity. I'd suggest starting with bubble levels.

I just did a proposal for a specialized laser Navaid of sorts. :)

Steve"

PS Welcome and enjoy the forum--you can search the LPF database using the Search function at the bottom of the page.

PPS Nobody who has tried such a thing ever reported back to LPF any successful results---may or may not be significant--maybe they didn't actually attempt to do their plan---who knows.

PPPS here is a good link on earth's curvature soundly proven. https://www.metabunk.org/soundly-proving-the-curvature-of-the-earth-at-lake-pontchartrain.t8939/
 
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hakzaw1

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What we ask is that you complete your profile and edit/combine your triple post.. even double posting w/o A good reason is frowned upon at LPF..

got questions>>--search first PLEASE
 




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