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  • How Far Can Level and Flat Be the Same?

    I drive 35 miles one way most days in the flat MS Delta. It is obvious in some stretches that level goes for about 2 miles and suddenly it is like going over small a hill as the road tilts down almost imperceptibly, and again and again.

    I meet weekly in a mentoring session with a soybean and rice farmer. Recently we had a discussion on the curvature of the earth that is so noticeable in flat lands. He said "Of course it's noticeable. Our laser levels for leveling land for rice farming (filled with water to a depth only a few inches) - the laser levels are only good for 1000 feet either side of the level's stand. Beyond that, land will start going uphill if held to laser lights which is straight. And the rice fields won't flood on the edges at that point."

    I never thought that "level" was that limited.

    Comments?
    Hank Lee

    Experience is what you get when you don't get what you wanted!

  • #2
    Very interesting story you related. At a latitude of 30 degrees north (not far from extreme southern Mississippi), an online calculator told me that the circumference of that circle of latitude is 21,583.3662 miles. The radius of a circle of that circumference is 18137340.2538 ft. The drop for a tangent (level) line at that radius 1,000 feet away (using straight line to make this simple and approximate, not the curved line of the earth) may be calculated by:
    SQRT ( radius^2 + 1000ft^2) - radius, which is SQRT( 18137340.2538^2 + 1000^2 ) - 18137340.2538 = 0..02756 ft, or 0.33 inches (approximately 5/16").
    So it appears plausible that the laser level could detect the earth's curvature at 1,000 feet on the Mississippi delta, ignoring any surface irregularities. It would have to be a very precise and consistent level laser, however. More precise than a laser level used for carpentry.
    But I would expect that the "land will start going downhill if held to laser lights which is straight." In other words, if I have a laser shining out at a level plane, the earth would curve downward, away from the level line, not upward. It makes sense that "the rice fields won't flood on the edges at that (level) point."

    If I was mistaken to use the circle of latitude, and should have used the earth's radius instead, the result changes to about 0.29 inches (still approximately 5/16", just slightly under 5/16")
    Last edited by Slik Geek; 10-25-2019, 04:00 AM.

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    • #3
      But I would expect that the "land will start going downhill if held to laser lights which is straight."
      Your are right in what you say, but I guess I left out the context from which farmers work, which was an assumption on my part. This was a discussion based on what farmers do to get "flat" land. How do you measure "FLAT"? In buildings flat is flat, but in fields covered with water is flat relative to the curvature of the earth. SO how does one determine "flat" on a large scale with limited resources: Laser levels - which are accurate for leveling only within a prescribed distance.

      1. The MS delta it FLAT overall, but has minute' undulations. Until the last 20 years rice fields had what looked like terraces in relatively flat fields - 50ft to 300 or 500 ft between terrace rows undulating depending on where 2 to 3 inch drops were - here, there and yonder.
      2. Making the 100 to 500 acre fields perfectly flat - cut out a LOT of yearly tractor/labor hours, which before, had to be done in the making of terraces.
      3. This brings up the process of making the whole field FLAT, to eliminate terraces except around the perimeter of the whole field. What do you use?
      Laser levels are the best, within reason. Tractors pulling leveler machines follow GPS readings in conjunction the laser readings - and that works good up to a point.
      4. But we all know that laser levels do not conform to the curvature of the earth. So when the tractors following GPS readings - move dirt in conjunction with the LASER LEVEL, then the fields do not follow the curvature, but build UP dirt on the edges beyond 1000 ft, because the leveler/farmer is following the laser line, not the earths curvature, which in effect makes it HIGHER on the edges, ergo going uphill.

      The land DOES go downhill for curvature, but when leveling a field with laser levels for "flat" - that only works for a prescribed distance - relative to one place - where the laser level machine is located. Therefore on the edges of the laser level 1000 ft out, the laser light is fractions of an inch above (in altitude) than at the place where the laser originates. If the land is leveled according to a laser line, it (the land) is HIGHER beyond 1000 feet out.

      Leveling whole fields cuts out lots of machinery and labor time each year when rice farming, which requires 3 to 4 inches of water level for 2 to 3 months on end.

      Some machines and computers today take the curvature into account (laser levels do not). However, there are vastly different levels of costs. Early GPS farm equipment was accurate to within2 to 3 inches or so; a more accurate subscription GPS services guided farm equipment within fractions of an inch in location. And an even more accurate GPS system than that can be used in conjunction with "altitude" of an inch. Each upgrade "in accuracy" comes with a much higher cost. At some point, some things become cheaper to do yourself. My farmer friend does the leveling himself. Corporate farms of 10,000+ acres can pay the price for self leveling systems which take the earths curvature into account as it levels. 1000 - 2000 acre farm owners do more work themselves and use their own laser levels.

      Another subject indirectly related: Driverless cars: we read about them, but how accurate are they? My farmer friend has GPS Tractors and Combines (a harvesting machine). When he sets up a field, he turns on the GPS and a map of the field; the GPS takes over and plants the field. The stored information guides all future operations, and even weed or insect spraying that needs to be done, including turning the sprayers outboard spraying arms on and off or decreasing the flow when it is spraying near the edge of the field to prevent spray "drift". The stored GPS of the field - controls the harvesting combines (and cotton pickers). To cut down on having to stop every 20 minutes or so to unload the grain, the harvesting combine's GPS sends coordinates to a driverless tractor pulling a large grain trailer. At specific intervals, the driverless tractor pulling the trailer, automatically pulls up beside the combine while it is still cutting; the tractor is controlled within a inch or so and follows any directional changes the combine does within an inch, while the combine unloads the grain onto the grain trailer as harvesting continues without stopping. Only one person is needed to be on board the combine or harvester for emergencies.

      My friend only farms soybeans and rice. Cotton farmers also have the same capabilities. Today's mechanized cotton picker machines can cost $500,000. Half a million dollars or more.
      Last edited by leehljp; 10-25-2019, 09:43 AM.
      Hank Lee

      Experience is what you get when you don't get what you wanted!

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      • #4
        Ha! I'm going to use th hr curvature of the earth to explain my 200 yd grouping.
        Last edited by durango dude; 10-26-2019, 04:38 PM.

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        • Black walnut

          Black walnut
          commented
          Editing a comment
          That is mirage.

      • #5
        Originally posted by durango dude View Post
        Ha! I'm going to use th hr curvature of the earth to explain my 200 yd grouping.
        Well, looks like your rifle is shooting correctly, and the curvature of the earth is just falling away!
        Hank Lee

        Experience is what you get when you don't get what you wanted!

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        • #6
          Originally posted by leehljp View Post
          Driverless cars: we read about them, but how accurate are they?
          GPS is one reference for navigation, but is not consistent enough or accurate enough to navigate an autonomous vehicle. Autonomous vehicles use a combination of GPS, INS, video to watch the lane markings, LIDAR, and RADAR to sense the road and surroundings. Primary navigation is based on stored maps, and gathering that high resolution map data is one big obstacle to development of autonomous vehicles.

          --------------------------------------------------
          Electrical Engineer by day, Woodworker by night

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          • #7
            If you go here http://earthcurvature.com, you can calclulate the curvature of the earth over a given distance. Hank, over your 35 mile drive, the curvature would account for a drop of 816.92 feet on your "level" drive.

            College was too long ago to put out the effort understand the math without additional motivation.
            Chr's
            __________
            An ethical man knows the right thing to do.
            A moral man does it.

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            • #8
              Originally posted by twistsol View Post
              If you go here http://earthcurvature.com, you can calclulate the curvature of the earth over a given distance. Hank, over your 35 mile drive, the curvature would account for a drop of 816.92 feet on your "level" drive.

              College was too long ago to put out the effort understand the math without additional motivation.
              Thanks! That curvature calculator basically states what they farmer said: 1000 feet for each side of the laser stand equals about 2 inches difference from one side to the other (2000ft distance) when making it by a laser level instead of allowing curvature.
              Hank Lee

              Experience is what you get when you don't get what you wanted!

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              • #9
                Originally posted by woodturner View Post

                GPS is one reference for navigation, but is not consistent enough or accurate enough to navigate an autonomous vehicle. Autonomous vehicles use a combination of GPS, INS, video to watch the lane markings, LIDAR, and RADAR to sense the road and surroundings. Primary navigation is based on stored maps, and gathering that high resolution map data is one big obstacle to development of autonomous vehicles.
                Yes, automobiles do use "something" (several things) in addition to GPS because of the human factor all around. GPS guidance has several degrees/levels or options available but there is a cost factor as it gets more precise.

                1. Tractors with "general" GPS follow rows to within 2 or 3 inches for over a mile. NO video looking at the row plants or lidar or INS. Purely GPS.

                2. With a more precision GPS which is a subscription service will take it into millimeters. These GPS systems are on board the tractors that are guided by the previous layout of the field. The "millimeter" guidance system uses two items: GPS and stored memory of the previous GPS. If a tractor goes straight for 1/2 mile and makes a 2ft detour around a tree stump, the plows which follow in a month will do that driverless.

                I'm not sure how much you know about farming but when row crops are planed, plows have about 6 inches max between them, meaning that the driver must go the whole length of the row/field without deviating more than 3 inches or the row crop will be plowed up. The GPS does this driverless, not with video or other but simply by GPS and comparing it to the planting GPS chart that was generated when it was planted.

                Actually the subscription GPS is more accurate than human driving, as mentioned - down to millimeters.

                ON Cars, GPS, video, Lidar, INS alone don't work at this stage of development because there are "human" factors all around, unlike in GPS farming!
                Hank Lee

                Experience is what you get when you don't get what you wanted!

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                • #10
                  Originally posted by leehljp View Post

                  I'm not sure how much you know about farming but when row crops are planed, plows have about 6 inches max between them, meaning that the driver must go the whole length of the row/field without deviating more than 3 inches or the row crop will be plowed up. The GPS does this driverless, not with video or other but simply by GPS and comparing it to the planting GPS chart that was generated when it was planted.
                  I don't know much about contemporary farming practices, so thanks for the explanation.

                  Actually the subscription GPS is more accurate than human driving, as mentioned - down to millimeters.

                  ON Cars, GPS, video, Lidar, INS alone don't work at this stage of development because there are "human" factors all around, unlike in GPS farming!
                  The human factor is definitely an issue, but one main issue with GPS for ADS is the relatively slow update rate and the weak signal, which is why phones and navigation systems periodically will report "GPS signal lost". A car or truck driving at 70 MPH is travelling around 100 feet per second and that second or two to recover the GPS signal is enough to depart the lane.

                  Autonomous driving is rather a difficult problem and the experts say it will be 20 years before we have L5 autonomy.

                  --------------------------------------------------
                  Electrical Engineer by day, Woodworker by night

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                  • #11
                    Here, I wrote a excel spreadsheet that calculates the deviation from flat of the earths curve from a laser-flat line.
                    There's three plots, for distances of 0-1000, 0-5000 and 0-10,000 feet. Notice the vertical deviation is in inches and the horizontal displacement is in feet.
                    Click image for larger version  Name:	earthcurve1.JPG Views:	0 Size:	50.1 KB ID:	837433Click image for larger version  Name:	earthcurve2.JPG Views:	0 Size:	54.1 KB ID:	837434Click image for larger version  Name:	earthcurve3.JPG Views:	0 Size:	46.3 KB ID:	837435 I was going to include the spreadsheet but I can't upload .XLSX files. Seems like that would be a handy thing to do... Admins? Can we allow spreadsheets? Or is that a security issue.

                    Anyway, up to 1000 feet away the drop off is less than 1/3 of an inch. At roughly a mile it goes to 7 inches. At 2 miles you are off 30 inches or so.
                    Loring in Katy, TX USA
                    If your only tool is a hammer, you tend to treat all problems as if they were nails.
                    BT3 FAQ - https://www.sawdustzone.org/forum/di...sked-questions

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                    • twistsol
                      twistsol commented
                      Editing a comment
                      Let me see what it would take to upload different file types.

                  • #12
                    The way I calculated and plotted it, I showed and plotted the deviation as a positive value.
                    Would it have been better to have plotted it as a negative value and it would have shown the drop off vs horizontal displacement as we view it? I hope I didn't confuse anyone.
                    Loring in Katy, TX USA
                    If your only tool is a hammer, you tend to treat all problems as if they were nails.
                    BT3 FAQ - https://www.sawdustzone.org/forum/di...sked-questions

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                    • #13
                      Originally posted by leehljp View Post

                      Thanks! That curvature calculator basically states what they farmer said: 1000 feet for each side of the laser stand equals about 2 inches difference from one side to the other (2000ft distance) when making it by a laser level instead of allowing curvature.

                      Actually Hank, I tried the calculator using his formulas, and for 1000 feet it came up with (after all the units conversions done properly), 0.287 inches at 1000 feet. The same number I came up with. Not 2 inches.
                      I had to use his formulas because his display rounded off to .01 meters.

                      From EarthCurvature,com:
                      Angle = .009 Degrees x distance (km) = .009 x .3048 km
                      H = Radius x (1-cos(angle)) = 3959 miles x 1,146e-9 = -4.537 e-6 miles = -.02395 feet = -.2875 inches
                      Last edited by LCHIEN; 10-30-2019, 09:49 AM.
                      Loring in Katy, TX USA
                      If your only tool is a hammer, you tend to treat all problems as if they were nails.
                      BT3 FAQ - https://www.sawdustzone.org/forum/di...sked-questions

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                      • #14
                        Originally posted by LCHIEN View Post


                        Actually Hank, I tried the calculator using his formulas, and for 1000 feet it came up with (after all the units conversions done properly), 0.287 inches at 1000 feet. The same number I came up with. Not 2 inches.
                        I had to use his formulas because his display rounded off to .01 meters.

                        From EarthCurvature,com:
                        Angle = .009 Degrees x distance (km) = .009 x .3048 km
                        H = Radius x (1-cos(angle)) = 3959 miles x 1,146e-9 = -4.537 e-6 miles = -.02395 feet = -.2875 inches
                        Loring, I appreciate the research you put in. In one estimation I had about an inch and on another I had nearly 3 and that is with my guestimation, which is never precisely accurate.

                        Now to throw a kink into the discussion - how accurate is it for the earth at any given point? By that I mean that the earth is not exactly a pure sphere. Kinda like Mt Everest is the highest mountain in altitude from sea level but due to the bulge at the equator, the highest point above Earth’s center is the peak of Ecuador’s Mount Chimborazo, by about 2000+ meters.

                        https://oceanservice.noaa.gov/facts/highestpoint.html

                        I don't think that would change your calculations. I will keep these and show him what he needs to shoot for in leveling!

                        .287 is .574 (1/2 inch) at 2000 ft on a fairly good sphere. And how accurate is his leveling ability?


                        This was not a problem 15 years ago as rice fields in flat lands were still terraced. But with micrometer locating GPS leveling of the last 10 years, machines only have to level a field once for years to come, and have a single levy a foot high in a 1/2 mile by 1/2 mile square, or 1/4 of a square mile.

                        I'm just intrigued how farming has changed in the last 10 - 15 years and how scientific it has become.

                        • Half a million dollars for a single cotton picker!
                        • One person can drive/control two huge machines at the same time;
                        • machines don't deviate more than a millimeter on a path a mile long. Stopping on a "dime" is so old tech!

                        Thanks for everyone's input!
                        Hank Lee

                        Experience is what you get when you don't get what you wanted!

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                        • #15
                          Originally posted by leehljp View Post
                          Now to throw a kink into the discussion - how accurate is it for the earth at any given point? By that I mean that the earth is not exactly a pure sphere... the bulge at the equator...
                          I'm guessing that bulge is at least in part due to the earth's rotation. I worked on a project at the south pole a few years back. The altitude there is 9,300 feet, but because of the earth's rotation, the centrifugal force pulls the earth's atmosphere towards the equator, resulting in an effective altitude of about 11,000 feet. This was important because this causes workers there to be affected to some degree by hypoxia (low oxygen). We had to design systems to be extra idiot proof. Less oxygen in the brain = reduction in skills.

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