At 6 miles out, only 10 feet of the target would be hidden by curvature.  They claim that 24 feet were hidden.  So why?

Another independent study found that the largest lake in Europe is flat.  The team is compiling a video but a slide show is presently available.  

https://fecore.org/lake-balaton-results-success-at-12-km/


Of the many problems docuмented in this kind of testing is the spreading of the laser over distances. Perhaps a factor in the test in the OP.  The source of the information is questionable since Discovery Channel is basically main stream media.  Also, the lax way the test was performed left a lot to be desired.  One tiny movement of the laser would change the trajectory of the beam to include the discrepancy.  They need to show how that wasn't a factor or it can be assumed.  Otherwise, level just isn't level and that is ridiculous. As far as the helicopter going behind the water before it landed, that is an old theory debunked many times since the water between the two sites appears higher at the farthest end than it really is.  This is proven with a telescope or camera which will bring the copter back into view, a test shown repeatedly to be easily done.  The copter only appeared to go behind the water which visually grows taller over a long distance according to the eye of the viewer.  This is because the waves appear as a single layer yet represent many layers and heights over a long distance that come together as one. Distance over the surface of turbulent water is not as easily resolvable to the naked eye.  To not include this reality and give the impression that the helicopter went behind the curve is somewhat dishonest.    

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You're spinning your wheels!
You can play around with curvature calculators but it's not conclusive because of inadequate data.
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Insufficient information is provided by the video. This is not scientific. But it could easily be accurate, that is, not fake.
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The location of the lake is not provided.
What are the longitude and latitude coordinates?
Is this in Canada, perhaps near Quebec or Toronto?
Is it in Maine?
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These would be highly problematic locations for example.
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The fact that they show a "level laser" (they do not explain how they knew it was "level") only a few feet above the water surface (they measured it with a tape measure and they MUMBLED the tape measure read "TWO FEET SEVEN INCHES" or 33"), then the same laser beam marked "their first reading at 500 feet from the shore" only about the same height above the water (they never measured how high above the water the marked place on the boat was!). They should have had their board down the CENTER of the boat so their physical movement on board would not change the measured height of the beam. You can see as the guy leans out around the side of the boat to mark the board, the boat rolls sideways, making the laser appear to be higher on the board. VERY SLOPPY MEASUREMENT!! Even dangling over the side to shoot the video makes the beam appear to be higher.
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Then at 3 miles out on the lake the beam was 6 feet higher (something like a total of 9 feet above the water, or what? They don't say!).
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Are they aware of how CONTRIVED it appears when they say "We're going to have to measure it on -- something else" and she reaches between the seats on a small boat to pull out a convenient corrogated panel of white fiberglass. DOESN'T EVERYONE WITH A SMALL BOAT CARRY A CORROGATED PANEL OF FIBERGLASS ON BOARD, "just in case?" (In case of WHAT? Quicksand? Portuguese man-o'war? a tsunami??) Not to mention the fact that having junk on deck you can trip on is a safety hazard. Unbelievable. But in any case, putting that panel on the side of the boat makes it roll to that side even MORE, and marking it requires even MORE weight on the side of the boat causing further inaccuracy. All BAD news here. Sloppy, amateurish and inconclusive.
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So they're describing a laser beam that begins parallel with the water's surface then rises rather quickly at 3 miles out to 6 feet higher. It's really unfortunate that they didn't go further out to see if perhaps the laser beam would come BACK DOWN when measured at 6 miles, for example. I suspect it very well might have come back down, before it rises back up again further from shore! This means that the surface of the water could have highs and lows. IOW just because it's water doesn't mean it's reliably a straight line, even without the waves.
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The fact that they're doing this over water introduces several problems that are not helpful. And the additional facts that they do not record the time of day, the date of the year, the temperature, the humidity, the temperature of the water, and a meteorological description of atmospheric conditions that day are very problematic. How can we rule out any inversion layer or refraction? The laser beam could be bending over the water, and it would LOOK STRAIGHT in a refraction condition because ALL the light going over the water would be bending the same way, so it would ALL appear to be straight just like the laser does!
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When you measure points along a supposedly straight line of sight down to a presumably level surface of the earth over an extended distance, what you are actually measuring is the distance from a perhaps questionable reference line (the laser beam) down to the geoid.
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What is the geoid?
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The geoid is essentially the surface of an open, at rest body of water. (Not a flowing river or aqueduct or channel.)
So that MUST be a reliable surface, no?
NO.
It's not reliable as a measure of the "straightness" of the surface (or the curvature for that matter!) because the precise direction to the pull of gravitational force (or which way your "weight" pulls you PRECISELY) is a variable entity. There are places on earth where what would seem to be level is exactly the SAME as what seems to be level 3 miles away, but then checked in the opposite direction, what seems to be level is suddenly far different than both the previous two cases.
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This is because the geoid is not consistent. It undulates up and down all over the earth.
The surface of a lake could have a low area AND a high area both of which are not discernible by the unaided eye.
Large expanses of water always have some disturbances going on so these highs and lows don't appear obvious.
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Measured over very small distances you don't notice any difference or inaccuracy, but over three or 6 miles, you can notice quite a bit, if you have sensitive instruments.
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If they were doing this over solid land, for example, they could set up a tripod at each station and check vertical angles to monuments like tops of tall mountains or artificial points elevated such as a flashing red beacon on a high antenna, a favorite reliable elevation marker.
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They could use readings of star locations but then you have to employ accurate time stamps and spherical trigonometry, which is a lot more complicated.
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In the final analysis, they could have set up the laser at a local high point, taken their first measurement @ 500' still in the local high point, then at 3 miles in a local low point causing the beam to appear much higher, then further out around 5 miles where they didn't bother to go the laser could have been back down to 33 inches above the water because it's a local high point in the geoid.
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Do you see the problem?
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Laser set up at a local HIGH point
First measurements @ local HIGH
Second meas. @ local LOW point (looks like beam is 9' above water)
Third meas (not taken) @ local HIGH point (beam could be back at 33")
Fourth (where helicopter went) another local LOW point, beam appears 20' above the water
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This is quite feasible since they say the laser appears to be on the water's surface in the far distance, so they took a helicopter over there only to be surprised to find the chopper disappeared behind the water's apparent horizon. This could be explained by a dip in the geoid at the other shore line so that an apparent hump in the water surface hid the chopper, but it might have been a geoid hump and not a curvature hump.
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Notice the theatrics to appeal to a vain sense of entertainment. They have two attractive ladies running around, they have a man who tries real hard to ACT SURPRISED when the laser beam appears 6 feet higher than they thought it would be at 3 miles out, they just HAPPEN to find a 9-foot panel of white fiberglass lying on the deck of their tiny boat (where every square inch is valuable space!), then a helicopter just HAPPENS to show up right on time to give the pretty girls a free ride (but they didn't bother to check for pilot license or maintenance records!), and finally the chopper DISAPPEARS over the water to the man's amazement, Yeah, Sure, Like He Didn't Know That Would Happen, Riiiight.
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