However, when it comes to practical planning, water acts like it's level. It's an explanatory fiction - in that it isn't exactly precise but from the practical point of view using this works. From our point of view as humans digging swales, water acts level so we say it's level.
What if someone asked us to design for a continent or the whole world? Do we use our observations, techniques and common senses or do we go with theoretical math?
Gravity pulls towards the centre of the globe. If you keep the trench the same distance from the centre - altitude - then that's what we mean by level.
I was told years ago about a reflecting pool, was to have edge a few feet above the ground, and they wanted the water to sheet gently and evenly over the edge all the way around, to be caught at an outer trough moat and pumped back into the pool. It wouldn't sheet except in the middle of the long sides... at five hundred feet long. They had to take into account of the curvature of the Earth, and lower the edges very slightly towards the shorter ends to get it to sheet over the way they wished to.
There was a Flat Earth Society chapter that a few members went to a beach and tried to measure the curvature of the Earth and their lack of accurate measuring devices up to the task plus the span they tried to measure, seemed to prove to them, in the accumulated errors, they couldn't detect that curvature.
Spirit levels work because of the linear horizontal spanned distance is so small the surface curvature from gravitation influence isn't measureable practically. Who cares if it's a few micros difference? Not us trying to level a foundation, set piers or dig a pond. (200 microns is the average thickness of a sheet of plain 20# copy or printer paper)
Edit, note too, in the time of the ancient Greeks, using the the measurement of shadows, they figured the diameter of the Earth to within 5%.
s wesley wrote:Thanks for the replys! I am genuinely confused. So there is no such thing as level? Isn't this so basic and simple since we use water to level things? I know, speaking for myself, I have never seen a still body of water with a surface any sort of shape other than level. It is a fair question is it not? If we design for a continent for example...north america....or just the usa....would we have to calculate 2,680 ish miles (horizontal width) worth of curvature.....so 820 or so miles of curvature. Or do we consider it a plane with hills, valleys, mountains and other topography. Has anyone ever considered curvature in their design?
You do IF you're building a continuous construct (such as the pool mentioned) that will highlight that issue. If I was digging a 500' long lined pond in the ground, and I used a spirit level (say 520' of clear poly tubing with food colored water in it) and was going to drop a custom liner in there and put nice rockwork around the edge, an inch or two isn't going to show from end to end. It's all the scale AND the precision you must hold.
For general sake, if I am going to landscape a fairly flat piece of land, one acre is 208' on a side. So it doesn't make a big difference, I can for all intents and purposes treat that as a flat surface.
When the railroad laid rail, they want things as flat as possible relatively speaking, so the engines didn't have to pull or brake to deal. Rolling on the level was best. They could approximate this without it really showing, for many mile stretches. It relates to how far from the center of gravity the surface is... and the curvature isn't noticeable on the scale being used and the precision needed to make it all work.
Where I live now the land is relatively flat, but. There is an illusion. To the east about an hour drive is another city, and it is about 1000 feet lower in elevation. You won't notice it while driving. But to drive west to here, you go up. Some gentlemen had a computer tuned and controlled pickup they were messing with, trying to get it to do optimal gas milage and they stopped by our courthouse circle and one stopped me as I walked past to sort out the map. It's confusing to drive through here sometimes, on the way to elsewhere. I heard the other one complaining as he was checking equipment and connections about their mileage per gallon had taken a hit. I enlightened them about the elevation rise and they were totally surprised about the information, but it also explained the mileage difference. It wouldn't have come up with a normal vehicle.
So. Unless you are planning to dig tunnels through mountains or divert great rivers, treating smaller chunks as flat or for general purposes even treating a somewhat larger chunk as flat, won't make a difference.
Take a circle. Figure the circumference. Put a triangle inside it, and add up those sides. It falls short? yep. Draw a square and add those sides up. A little bit closer? Now a pentagram... keep going. The more sides you add, the closer the sum of the sides will equal the circle's circumference.
It all has to do with the scale of what you are working on, and the precision needed. It comes back to that.
What are you trying to work on? What are you designing? What is the scale? What is the precision you need?
If you squeeze out some water in space (like aboard the ISS, where the gravity of the Earth is somewhat negated for those inside because it is falling around the Earth, it's in freefall), it will take surface tension and the inherent microscopic amount of gravity of it's own mass and stick together and form into a sphere. Gravity likes to form spheres. Hence the Earth is roughly spherical... so. I will ask again, what are you working on? What are you trying to design? And what is the scale of the project and what is the precision needed.
When I was in mechanical engineering, they sent the students through hands on labs, materials labs. We learned how metals and other things could be worked, how they were handled and various things like surface finishes. And how to not overdesign something that wasted resources, time, and money, to produce. The idea was when we got done, we understood what could be made, how it could be made, and how to be more efficient. Why specify 20 microinches surface when 40 would do it and be percentages faster to produce....
s wesley wrote: Sorry if I missed something. Differences in elevation I understand. Maybe subtle changes sometimes can’t be detected. But larger changes or the difference between the start and finish can be. Things like your ears popping (pressure changes) let you know and depending on the topography your view may change. Without floating off into metaphysics and space... let’s consider scale. At what scale would the curvature of earth come into one’s design? If I have a few properties say… 4 all connected and all separately designed but incorporated together for things like water. They are 5,000 acres each and connected lengthwise. They are say 5 miles at each length….so total 20 miles length. And I want to put a swale across them and it happens to work out. If I am at water level at the beginning of the swale and looking toward the other end of the swale according to curvature math it would need to be 260+ feet under that level at the beginning. How can it be level and curving 260+ feet down at the same time? Doesn’t common sense and observation take over at some point? At what scale does water start to curve? I am missing the curve...
It is relative to the surface that you are standing on, stuck to, by gravity. Think of the Earth not being there but somehow the gravity is, and the thinnest of layer that will hold you up, the former surface of said Earth. At the very center of this theoretical model, is a point that has a chain firmly anchored to it. And it extends all the way up to you. And is attached to your waist. Now walk the 20 miles. The surface may rise and fall a bit beneath your feet but your chain will stay roughly the same length. So the curve works itself out.
If I run my spirit level across your 20 miles, if say it appears to be 'level ground' and the elevation doesn't rise or fall unduly, I will be able to strike a level between A and B. Then I walk five miles towards the other end. Once more, I can strike a level. It's relative to the surface I'm on.
You are not going to build a 20 mile continuous swale. You might build twenty miles of swales, but it won't be one single one.
Apples and oranges. I stick some tape to the skin of the orange, a thin strip. It will add that thickness, lumps and bumps and all, to the surface of the orange. You are building your swales on the surface of the ground. So it's the tape on the orange. Design in general your layout of your swales, then start building. Install each one, level, arc, and true each one to itself and where it's installed. Then go to the next one. Fit them to your surface. It'll work.
Water flows down from higher elevation to lower, fueled by gravity. Period. No matter where you are, it does this. So just fit each swale to control the desire of the water to go down powered by gravity, to go where you want it to. The Grand Canyon is just a huge reminder of Lots of Water, Lots of Time and Lots of Elevation Difference. The water went from higher to lower, gravity powered, and along the way eroded away and cut the canyon. So, work your project in sections. And like making and fitting clothes to be comfortable and functional, fit your construction to your site. Work uphill to downhill. The curve issue will sort itself out as you fit each one into place.
To me the problem with that question is how that could be done. It seems to me that there is only way to implement such a "design". There would have to be an absolute dictator, who could by political and "military" force cause every single person living on that continent or world to comply with such a plan. In the absence of such authority and force, there would be at least some people who would not comply. And the plan would fail.
For the last 120 years on our planet, a series of total control dictators had held sway for various lengths of time. As much as they tried, it never went well. For all their complete planning, it never went well.
s wesley wrote:At what scale would the curvature of earth come into one’s design?
The Earth is not a sphere — it's actually an oblate spheroid — but since oblate spheroid math requires a university degree to understand, we can simplify things by treating the Earth as a sphere. That makes the calculations understandable by anyone who has passed, say, Grade 10 or 11 high school math.
The mean radius, r, of this simplified Earth sphere is 6,371,008m.
Let d be a straight-line distance that you project at a tangent from any point on the Earth's surface:
Application of Pythagoras' Theorem gives the following:
c² = a² + b²
(r+h)² = r² + d²
r+h = √(r² + d²)
h = √(r² + d²) - r
...where h is the height of the end point of that line above the surface of the Earth.
A distance of 1,000m is something that most people on this forum can relate to, and is probably near the upper limit of what you would use for large-scale projects, so I'll use that distance to calculate the magnitude of curvature of the Earth.
Solving with d = 1,000m we get:
h = √(6371008² + 1000²) - 6371008
h = 6371008.078480516 - 6371008
h = 0.078480516m
h ≈ 78mm
So, to put this in a way that I hope everyone can understand: The surface of the Earth is not now, nor has it ever been, flat — it falls away from a perfectly straight line at the rate of 78mm every 1,000m.
Thanks to similar triangles and the metric system, you can interpolate easily from that number:
78mm @ 1,000m == 7.8mm @ 100m == 0.78mm @ 10m == 0.078mm @ 1m
So, if you built a house that was 10m long on top of a perfectly flat concrete raft, and placed it on the surface of a perfectly spherical Earth, the curvature of the Earth would result in a 0.78mm gap under one edge of the raft. It would take 8 sheets of 75gsm photocopy paper or 1 grain of coarse sand to fill that gap.
If a 0.78mm fall over 10m (or any of its equivalents) does not compromise the integrity of your construction, then you can safely ignore the curvature of the Earth — pretend that the Earth is flat — and just build it. No-one will suffer.
I hope that answers your question.
PS: Water, similarly, is not now, nor has it ever been, flat — its curvature is simply difficult to detect at small scales with the human eye, and difficult to measure with the sort of measuring devices ordinary folks can buy at a hardware store. The statement "we all know the surface of water at rest is always level" is not true because it suggests 'the surface' of an entire body of water is a singular entity. The original and correct quote is "water seeks its own level", which has an entirely different meaning. Water seeking its own level does not make the surface of any body of water a singular entity, or flat — never has, never will. Individual molecules of water seeking a level make no statement or assertion whatsoever about the final shape of the water body as a whole. The former is governed primarily by air pressure; the latter is governed primarily by gravity. The surface of every body of water on Earth is curved — at the planetary scale, at the kilometre scale, at the metre scale, even at the millimetre scale. The challenge folks have in measuring that curvature at small scales is due simply to a) the lack of precision and accuracy of their instruments, and/or b) their lack of mathematical skill. To be fair, very few of us construct things on a scale where we need to factor in curvature of the Earth, so we can happily go through life ignoring its existence. That doesn't mean curvature doesn't exist — it just means ordinary folk don't need to calculate it, compensate for it, or even worry about it, in their day-to-day lives. Rest assured, however, that every modern engineer that signs off on a bridge, stadium, dam, airport runway or terminal, canal, supertanker, cruise liner, cargo ship, hospital, aircraft carrier, freeway intersection, railway station, shopping mall, or tunnel has obtained super-accurate measurements and crunched the numbers to compensate for curvature of the Earth — to ensure that their constructions don't fail and that people don't die.
Nope it IS a 20 mile swale I am talking large scale remember.
If I took that chain and walked along my 20 mile swale it would dip 260+ feet from the start… or would it sit right on top of the water level…you know… level? How can it be curving while the surface of the water is level? Tolerance isn’t going to explain that much curve is it? It seems, to me, you guys aren’t quite understanding. Correct me if I’m wrong… If you take tiny sections of something and level them…..then put them back together in the same orientation…wouldn’t they be level. Now enlarge and enlarge and enlarge….at what point does it go from level to curved? Let’s talk in terms of real life everyday examples if we can. If I can consider the surface of water level up to and past a mile or 500’ or whatever distance, when does that change? According to all the earth curvature calculators there is a point where the curve starts to significantly change that level line in relation to the beginning point. How can we consider water being level and curved at the same time? It’s a mind bender based on math and assumptions correct? If all we have to go on is functional practical everyday experiences observations and patterns aren’t we to assume that water is level and therefore long distances and large areas are more or less level too? I understand topography and elevation changes…but significant curvature that is required if we are on a globe is simply lacking…for me at least. If you had to build your view of the world from the ground up and you saw water in a pond seek it’s level then applied that to a small swale then bigger then bigger then bigger…. at what point does the original observation get thrown out the window and curvature applied to a level contour line? If we can’t say the surface of water at rest is level… how can we claim anything in reality behaves like anything. Isn’t it a basic permaculture technique to use everyday observations and our common senses to recognize patterns and apply them to our designs? Maybe I’m living in a different world? Can someone please explain from the ground up with everyday functional practical observations? I could bring up other things but for the sake of permaculture I think we need to figure out when are we to throw out our common senses and include, in my opinion, fantasy of a ball/sphere/globe that curves about 8 “ per mile squared. So a swale 1 mile long would start level and curve 8” down from that level and yet still be level at the end? Does that make any sense in reality? Thanks for the responses. I understand what your saying and that the math works out when solving for x. I just think we aren’t quite on the same page yet. I think permaculture needs to not drift off into theoretical constraints.
Water flows down from higher elevations to lower elevations. That is gravity at work, the flow is gravity powered.
Water seeks the lowest level it can't run out of to a lower place, closer to the center of the gravitational pull making it flow.
The Earth does curve, yes. Fairly inperceptable on the scale of things that we normally deal with.
Water can be solid (ice), liquid, or gas. When it is liquid, it will flow if it gets the chance because gravity is relentless, the water molecules are not being held in any sort of lattice structure, with rigidity (see: ice)
The ocean surface appears flat to us when we are at or near that surface, (if the wind or a tide is not stirring it up) yet it curves to cover the surface of the Earth.
Building the swale doesn't matter if you shoot a laser from end to end, the center of the swale built that way with a laser perfect level top, will let water go over it before the ends will. The ends will be too high, from the Earth curving away from the middle.
Fit the swale to the topography at the level needed at that point to catch or prevent the water from flowing over the top and escaping. If you have a strong enough laser and fire it from one end to the other, yes the center will seem to be higher. What matters is it holds the water.
Build as you go somewhat, fit it to the place as you go, and your swale will curve naturally yet still do the job. Use a spirit level to do a periodic check, like trying to get a hem straight when you've cut a ragged bottom on that pantsleg, and that will give you the small segment check that will conform to your curve. Or if you are good with survey equipment, then use say, every 1000 feet, to strike a height measurement. The error on that far for a 3' tall swale will be acceptable for most purposes. (using the figures below, I guess just over inch 'drop' on 1000 feet of curve versus laser flat line.)
Your surface you go over won't be perfectly even and flat either. So finding the high or highest spots and working towards the lowest spots will be your work. Break it down into smaller sections and fit them to the topography. It'll work. That would give you six check points for first mile roughly and five for each one thereafter. True each one within each thousand foot section...
r ranson wrote:If you keep the trench the same distance from the centre - altitude - then that's what we mean by level.
Precisely. Water engineering isn't about "level", or "flat", it's all about how far something is from the center of the Earth. In my two acre field, the difference in elevation from one side of the field to the other is around ten feet. The difference in "water level" due to the curvature of the earth is a half inch over that distance. Much smaller than the height of any swales that I might build, so it can be ignored.
On the 20 acre field, the difference due to curvature of the Earth is about 2.4 inches. Again, small enough to be ignored. Especially considering that the changes in elevation on that field are hundreds of feet.
The techniques for compensating for the curvature of the Earth are so completely incorporated into modern society, that there is rarely a need to say anything about it. For example: My brother that builds footings for buildings "levels" them with a "water level" because that automatically compensates for the curvature of the earth. My father that builds houses, and schools, "plumbs" the walls, so that they are perpendicular to the surface of the Earth where they stand. But the walls are not parallel to each other... They are ever so slightly wider at the top than at the bottom. When I plan a water project it is grounded in the idea of "elevation" not in the idea of level or flat.
Functionally, the people who have built the planes, communication satellites and other peices if technology all subscribe to the model of a round earth.
And their tech works. Your using it right now.
So if you want to build this theoretical swale, use conventional methods and you can achieve your goal.
If you believe the earth is flat,hollow, or some other shape and don't trust the conventional science and engineering, build your swale accordingly.
You objections to the idea of a round earth conflate level with strait.
A strait line is geometrical,level is a function of gravity.
But honestly, I fail to understand what difference it makes.
Our understanding of how electricity works has continued to evolve,even as most of our basic circuitry has remained the same.
More bluntly, how should a flat earth change the goals or techniques of permaculture?
Let's assume the earth is flat. Cover crops? Oil based agriculture? Rotational grazing? How should the practices be veiwed in light of this revelation?
If you substitute "perpendicular to the force of gravity" for the word "level" maybe it will make sense for you. "Level" is just a word that people use to indicate a surface is perpendicular to a line that goes to the center of the earth. It does not mean straight.
So I can have a 6 foot long amazingly accurate carpentry device that tells me it is situated perfectly level here in Wisconsin. A long way away in Texas, Tyler can have another carpentry device (often called a "level") that is also perfectly perpendicular to the force of gravity in Texas. They are both indicating "level" and if they were sitting on a pond they would perfectly touch the water's surface.
Now fill in the distance between the two of us with a million more levels. Each of them would be indicating that they are perpendicular to the force of gravity. As you stand there and look at the nearest 500 levels, you would swear that they are parallel to each other (forming what you perceive is a straight line). But they are slightly curving with the surface of the earth.
We're sitting on a huge ball (or oblate spheroid). At any point on the surface when we look at a "level" it will show us the plane that is perpendicular to the force of gravity. The ball/earth is very very very big. And we are very small. So if your hypothetical 20 mile long swale holds water and you take a cross sectional look at it from the side, it would have a curve to it that matches the radius of the Earth. The surface of the water all along the swale would be the same distance from the core of the earth. Thus a curve. And also level. And if it helps, the Earth is round.
A lot of people here have made swales, some miles long, using the traditional, gravity based level. It worked. You want a practical demonstration on how to make a large swale, that's all one really needs.
If you think it works differently, then I suggest you make two, one mile long swales. One using the traditional method (level) and one using a laser (flat). Document it and tell us how it goes.
What do 'flat earthers' think is on the other side? I am very visual and all I can picture when this comes up is dangling roots and soil...and what about the 'edges'...is there a drop off?
s wesley wrote: Has anyone ever considered curvature in their design?
I wrote a program for the ground systems for spacecraft that take pictures of the earth. The spacecraft circles the earth every 93 minutes. Each time the spacecraft makes a pass, it is typically (on average) around 10:30 (am for the light side and pm for the dark side) Part of my app was to task the spacecraft to take new pictures. And, to directly answer your question: for people buying imagery, we sold it by the square kilometer. So my algorithm calculated the area with consideration for the curvature of the earth. After all, the points of the "are of interest" are given with latitude and longitude. And for a big enough rectangle in the northern hemisphere, where the left edge has the same longitude and the right edge has the same longitude, then the top of the rectangle is shorter than the bottom. Therefore, the rectangle is actually a bit of a trapezoid.
Judith Browning wrote:
What do 'flat earthers' think is on the other side?
My understanding is that the world rests on the back of four humongous elephants. The elephants are standing on the back or a tortious.
At least that's what they taught in History of Philosophy class. When I asked what the tortious is standing on, he replied, "it's tortoises all the way down".
The total field acreage here is 20% more than what the USDA says it is. The difference lies in they rely on satellite imagery, and I rely on real world acres. The difference is, this is Maine with very rolling, hillsides so there is some acreage to be gained when going over the contour of the ground. To illustrate what I mean, take a normal 11 x 8-1/2 inch piece of paper and trace around it on another legalized piece of paper. Then twist and bunch up the ends, and basically contour the piece of paper so it resembles a rolling hillside field, and match it up with the pattern drawn on the larger piece of paper. The ends of the paper will all have been withdrawn from the previously drawn edges. This represents the difference in how I look at my fields, and the USDA. Since the piece of paper is the same size, I would need a much bigger piece of paper to contour it AND have it meet the same edges as before.
Another explanation might be the treeline. With branches sticking out into the field...many long to gain sunlight that is out in the field, the USDA might be missing 20 feet of field under that canopy. It does not sound like much, but one of my fields is exactly 1 mile around it...5280 feet. The lose of that 25 feet equals 132,000 square feet. That is a lose of 3 acres in that one field alone!!
Granted the latter is not 20%, but between the two, it might be why there is such a discrepancy. It really sucks because my annual subsidies are based on those base acres...20% less than what I really have. Drat!
Their equipment will assume level is a straight line, but obviously that may not work with a rail tunnel 3 km long?
This thread is chewy, thankyou! I loved math guy's response, I'd like to work his numbers into something sacred. However, I think I get what the permie is trying to put down. And along the permiculture lines, here is my take:
I observe the patterns of water and see constant movement, even still water shivers. If I chose that element in nature to use as my inspiration for designing permiculture systems and buildings, I would note how water is effected by gravity. (Lets say I do not understand 'gravity') Then I would see how water always wants to flow to the lowest point. I would build around this point. Using the force of nature to dictate my design. I would spend the four seasons noting the behaviour of the land with the weather at this point. Then I would know all the ways I could utilise the power of this water pattern there; what work I could not do. This design would use the land at it's peak ability with no waste of energy.
How could I apply this design principle to a "bigger picture" environment? HRM! This thread really got me thinking! Perhaps there is a flaw, or at least, an improvement can be made in how we build our infrastructure, urbanly. (Is that a word? Just call me Shakespeare.)
There is a flaw in building large. If we followed nature, everyone would have clean water, and food to eat. Smaller communities that maintain their own utilities...what a dream. Personally, I'd love BC to get some bullet trains and the province to give away deforested plots of land so micro cities could grow like wildfire...instead of wildfire.
So basically, the flaw is: water is not level.