# Is the surface of water ever "perfectly" flat?

#### strantor

Joined Oct 3, 2010
5,543
Before anybody goes off on a bent about "perfectly," let me explain; No, I'm not an Indian graduate student. When I say "perfectly" I mean by a machinist's standards; does it pass the test of a surface plate's flatness spec (like accurate to .0001").

I know there's either a concave or convex meniscus at the edge, and I know that the surface of the water will follow the curvature of the surface of the earth. But what I don't know, is if I were able to "freeze" (not as in freeze by cold temperature turning it into ice, which would change the size & shape, but "freeze" as in magically make it turn instantly solid without morphing) a bathtub full of water, would I have a "perfectly" flat surface in the middle, say 1" in from the edges? Or would it still have some radius (a tigher radius than the earth's radius) to it, like it's just the surface of one giant water droplet that just happens to be in a bathtub?

#### Glenn Holland

Joined Dec 26, 2014
705
Except for surface tension at the edges and with no motion, the surface should be almost flat.

Other liquids such as molten tin exhibit near flatness and the surface can be used as a reference and also a mold for casting other flat shapes. s an example, plate glass is made by applying molten glass over the surface of molten tin.

#### BR-549

Joined Sep 22, 2013
4,938
In your bathtub example, in theory, the inside surface area would have a curvature to it. It would be slight. The curvature would have a radius R, to the center of gravity of the earth.

You can get damn close with a machined surface to true flatness.

Probably the closest we can get to flatness is.........a stretched sheet of graphene.

#### MikeML

Joined Oct 2, 2009
5,444
Dont forget about the Moon's gravitational attraction.

#### BR-549

Joined Sep 22, 2013
4,938
Absolutely. The first bathtub curve will be modulation by a second and inverse curve with radius r.....to the center of gravity of the moon.

#### studiot

Joined Nov 9, 2007
4,998
The most obvious questions are

How big a flat surface do you want?
What do you want to do with it?
How long do you want it to last?

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#### strantor

Joined Oct 3, 2010
5,543
How big a flat surface do you wnat?
What do you want to do with it?
Use it as a surface to cast "perfectly" flat concrete slabs against.
How long do you want it to last?
long enough to cast at least one concrete slab.

I was thinking maybe it would be possible to pour a fraction of an inch of epoxy (one with a s.g. <1, and that cures in water) onto the surface of the water and "lock in" that flat shape. It would be fragile, easily disturbed, if it worked at all. From there i might be able to back it up with a couple of layers of something more substantial. Some process like blown-in fiberglass or sprayed-on stucco. Then back that up with a layer of concrete. Then drain the water and flip it over, and there's my casting surface.

I tried a small experiment with fastcap 2P-10 glue (2 part super-super glue; gel base with aerosol activator) in a glass of water last night. Strange results. The glue floats on water. The activator also floats on water. But when you have the glue on the surface and you spray it with activator, it turns instantly hard and sinks. It apparently does not cure under water; at least not completely. I dumped it out and grabbed the hard chunk like a dumbass, and the underside was still liquid super-super glue. Fingers made a gravelly noise when they rubbed together, for about 18 hours. Also ruined the glass.

#### sirch2

Joined Jan 21, 2013
1,029
The chemical reaction that causes concrete to set is exothermic and so the concrete heats and then cools, this process is not going to be even across the slab (the centre will cool more slowly) and so the end result may not come out "perfectly" flat however good the mold is.

I would level a layer of sand on a hard surface, and then place a ply (or sealed MDF) former on that and cast. Test the result and grind down any high spots.

#### studiot

Joined Nov 9, 2007
4,998
Good post, sirch2.

Except that steel 'pans' are more common for multiple uses. You can only get a few out of ply.
Steam curing and vacuum dewatering are used to counteract the deformation effects you describe.

I believe steel former pans are also used to cast the 'concrete board' as we call the 'cement bound particle board' that is becoming popular.
I remember wondering what use the 'guaranteed flat to 0.1mm' was when I bought some a few years ago.

Borden Chemical used to make an underwater epoxy called Epophen.

#### #12

Joined Nov 30, 2010
18,219
I once had a conversation with a structural engineer about using a water level vs a laser level on a large building. Something like 1000 feet and you're out of spec for, "flat" with the water level.

He never answered me. Probably because his daddy was an engineer and "forced" him to get a 4 year degree. It worked. He's financially secure and can't figure out how structures were built before lasers were available.

Anyway, I did the math to get the 1000 foot number, and you can too...if you care enough.
X^2 Y^2 Radius = 4000 miles etc.
Do the math and find out how flat bath tub water is!

#### strantor

Joined Oct 3, 2010
5,543
Don't think cement based concrete is what you want, if this is for your "machine". Have a look at this, it is used in precision machines. https://www.google.com/search?q=polymer concrete machine bas&ie=utf-8&oe=utf-8#q=polymer concrete machine base&spell=1
I've looked into polymer concrete before, and it isn't cheap. The epoxy itself is a killer; in order to minimize the amount of high dollar epoxy, you need to minimize the voids between the aggregate, which means you need specific ratios of specific grades/sizes of aggregate, from peanut size down to dust size, and some of the aggregates only ship from the type of places where you have to have commercial credit references and set up an account before they will even talk to you. By using the correct ratios of the correct aggregates, they can get the epoxy content down below 10%. With what I have access to, I would probably be over 25%. Even if someone donated me a perfect batch of aggregate, I would probably still spend more on the epoxy than what I've budgeted for the whole project. I see it as a more than viable alternative to cast iron, but not the alternative to spending money. More for the guy with too much time and money, and less for the guy with no money. Definitely NOT for the 3rd world bushman, who (hopefully) should be able to build this. I am hopeful that using a gross excess of common concrete will work in lieu of "just enough" epoxy granite.

I'm realizing as Sirch2 pointed out that just about anything that turns from liquid to solid is going to change shape as it does so. So casting a perfect flat is pretty much out. That leaves me with grinding a perfect flat, which takes sophisticated machinery. ...or does it? I'm now researching the feasibility of lapping two large surfaces together in a rotary fashion like these guys use for making DIY telescope lenses. Conceptually right now I see two large concrete castings rotating just like in the video, lapping each other into "perfect" flatness. Then you have an extra one laying around in case you mess one up.

#### strantor

Joined Oct 3, 2010
5,543
I once had a conversation with a structural engineer about using a water level vs a laser level on a large building. Something like 1000 feet and you're out of spec for, "flat" with the water level.

He never answered me. Probably because his daddy was an engineer and "forced" him to get a 4 year degree. It worked. He's financially secure and can't figure out how structures were built before lasers were available.

Anyway, I did the math to get the 1000 foot number, and you can too...if you care enough.
X^2 Y^2 Radius = 4000 miles etc.
Do the math and find out how flat bath tub water is!
alright I'll take a stab at it, but first, ...
If you're looking for level, I say, a hose full of water is the only thing that's going to give you a true level.
If you use a bubble level or laser, you're shooting two tangent lines out from your position on the face of the earth, into space. if you were run your level or laser in either direction along that line, as soon as you leave dead center (where you took the measurement), you're going to be off by more and more cunthairs the further you go out.

So, having said that, I'll use the Distance to the Horizon formula in order to determine the difference between FLAT and LEVEL, at 1000ft.
distance to horizon formula:
d = 1.22h
d = distance in miles
h = height in ft

Rearrange to solve for h:
h=d/1.22
h=0.1894mi/1.22 = 0.15525ft = 1.863"

Now confirm with pythagorean theorem:

A^2+B^2=C^2
436,957,148,390,400ft2 + 1,000,000ft2 = c^2
C=20,903,520.02391941642909571014096ft

C-A = 0.02391941642909571014096ft = 0.287033"

Big difference there. I suspect the pythagorean theorem is the closer one to correct. What was your number?

anyway, same pythagorean method substituting in my 4ft instead of your 1000ft, yields .00000459253" over 4ft. Good enough for me

#12

#### strantor

Joined Oct 3, 2010
5,543
I think I've moved on from the water idea, but to clear things up, the question wasn't so much about the radius of the earth and all that; I know/knew that the effect would be negligible in the scale I'm talking. My question is/was more about water "piling up". That's the reason why I would go to the trouble of all this bathtub-full-of-water nonsense instead of just pouring a thin layer of epoxy onto an already almost-"perfectly"-flat surface and let it settle flat just like the water. I'm afraid the epoxy, being not 100% fluid, might never settle to a "perfect" flatness like water, even if it took a week to set up.

Look at a snot rocket or similar; when it hits the ground, it spreads outward like liquid but not all the way. The thicker the substance, the less it spreads out; the runnier, the more it spreads out. until you get down to true liquid like water. ...but even at that level, does it really spread all the way out? Or is still just a "pile" of molecules that looks flat enough to deceive the human eye? Looking at the silhouette of a water droplet and at the meniscus in an a plastic cut makes me wonder...

#### WBahn

Joined Mar 31, 2012
26,398
Why does some bushman need a "perfectly" flat slab of concrete?

How flat is truly needed for the intended purpose?

Is your bushman going to have the capability to lap two large slabs of concrete together?

What about the aggregate in the concrete? Won't some of that tend to abrade the surface cement in the other slab? Seems like lapping is only going to work at anything approaching the scale you are talking about when both slabs are homogeneous down to the scale you are talking about.

What about mechanical deformations when these slabs are moved around? Might not that dwarf the scale of the flatness you are trying to achieve?

#### #12

Joined Nov 30, 2010
18,219
I just thought it was a fun math problem. Kind of like, "How many angels can dance on the head of a pin" from Chemistry 101. (And I forgot the exact answer I calculated.) Still, I was reminded that a sailor knows about curvature effects to the horizon. Thanks for that.

Then there is the idea of, "frame of reference". A water level is a wonderful tool for finding level to the surface of the earth, but if you use a water level to lay the first row of blocks in the Sears Tower, you're going to have to do some compensating to keep it from being wider at the top.

ps, I don't know whether WBahn just insulted strantor by calling him a, "bushman". Is that slang for, "people that have to work with physical reality"?

#### WBahn

Joined Mar 31, 2012
26,398
From Post #12: "Definitely NOT for the 3rd world bushman, who (hopefully) should be able to build this."

#### BR-549

Joined Sep 22, 2013
4,938
distance to horizon formula?

Sure?

#### studiot

Joined Nov 9, 2007
4,998
Why would cement bound particle board?

Surveyors use the following formula for the divergence of a circular curve from a straight. (offset distance of the curve from the tangent)

R = radius, L = distance along tangent, D = divergence, all measured in the same units.

$$D = {\frac{(L)}{{2R}}^2}$$

The mean radius of the Earth is 3959 miles = 20903520 feet.

So the deviation between the laser straight line and a level line is 12*(1000)^2/(2*20903520) = 0.287 inches.

#### sirch2

Joined Jan 21, 2013
1,029
If this is for your machine I would separate the precision parts from those that provide rigidity. Look at a typical machine tool, it has massive cast parts that provide rigidity and only small areas of these are ground to provide accurate surfaces. So you could embed a steel track into a concrete bed and then just grind and lap the track.

That said I wonder if standard concrete will fall apart under the vibrations?