- #1
Wes Tausend
Gold Member
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- 46
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I was thinking of a thought experiment concerning different systems of gravity-like acceleration.
I've noticed that using a stringline in construction is close, but not very accurate because the string always sags to some degree. I have sometimes fabricated a water level by attaching short clear extensions on the ends of a garden hose and assuming the water self-levels to natural flatness in the clear tubes. This is a much better method if long distance accuracy is important for subtle lot drainage.
So a water level is good. But how good is this, really? I live in the higher US latitudes, so, for me, it is probably more accurate east-west, than north-south, because of the equatorial bulge. The south end of my water level should always be too high by the tiniest fraction, and even worse in a tidal condition.
In another scenario, if I had a bucket of water sitting on the floor of my home, I might suppose that the surface is perfectly flat. This is likely the principle of manufacturing "float glass". Making float glass allows molten glass to float very level, and cool to hardness, on a bed of heavier molten metal.
I think the truth, though, is that my bucket of water and the floating glass both must have a very slight convex curvature to their top surface. The bucket water surface should be shaped in a slight convex curvature exactly like the ocean and so should the float glass. Now, admittedly, this is pretty flat for most purposes. On the same token, some mirrors are specifically spun, in a molten state, to produce a precision parabolic concave surface that may be used in Newtonian Reflector telescopes. I imagine this "reverse type" curvature effect must be taken into rpm selection for the very finest mirrors, and yet may not be entirely possible to perfect.
Another gravity-like acceleration is that of rotating space stations. In this case, I imagine the bucket, sitting against the inside circumference of the outer rim, to possibly have a concave surface, just the opposite of earth. As an example, if I were to not like the constantly curved floor for walking in artificial gravity, I could build a polygonal series of short flat floors entirely around the inner circumference so that I may walk on "flat" floors. Here though, I think that the series of floor "flats" would feel like they had a high spot in the middle of each flat polygonal side, and a dip as one walked into the joint angles. If I spilled water, it should run "downhill" into these dips. The dips are further from the hub center, and I imagine, the further out, the more acceleration. My bucket, sitting on such a floor, should do the same and develop some sort of natural concave curvature to it's surface.
The arbitrary "level seeking", of the spilled water, seems like it might, or might not, also cause flow to the sides of the floor "flats", since the outer edges are also further from hub dead center. Then, on the other hand, the floor edges are all perpendicularly equidistant to the hub axis which may only cause water curvature in the direction of rotation, not side-to-side. Which is correct? The latter seems like it may rule.
Considering the accuracy, or inaccuracy, of the above, can I theoretically slowly swing a water bucket around on earth, with a rope, in such a simple fashion as to carefully balance the "opposing(?) curve" acceleration forces into a perfectly flat surface? The idea of the original thought experiment was to achieve perfect natural flatness right here on mother earth, a process that can not apparently be easily done any other way. As an example, one might use a laser light to measure a float surface, but of course, gravity very slightly bends light too, so even that would not be good enough for perfection on Earth (unless the process was done by machining, and measured by light vertically).
The final attempt at flatness might be to simply slowly spin the bucket on a turntable, by calculated rpm, until the centrifugal force just barely flattens the natural curvature of earth. But this may not work either, if the spin opposing force is unevenly distributed in such a fashion as to tend to a parabolic curve, rather than equal-radius curve such as the shape of earth. This slight force difference may technically make any earthmade-spun parabolic mirror also just a shade imperfect.
It might just be, that the only way to get a perfectly flat bucket of water, or a perfect mirror, is to accelerate in linear fashion in a gravity-free environment. Then I would need a smooth rocket... and persnickety natural earthbound surface flatness is out.
Is there any other natural way to achieve real world flatness?
Thanks for your thoughts,
Wes
...
I was thinking of a thought experiment concerning different systems of gravity-like acceleration.
I've noticed that using a stringline in construction is close, but not very accurate because the string always sags to some degree. I have sometimes fabricated a water level by attaching short clear extensions on the ends of a garden hose and assuming the water self-levels to natural flatness in the clear tubes. This is a much better method if long distance accuracy is important for subtle lot drainage.
So a water level is good. But how good is this, really? I live in the higher US latitudes, so, for me, it is probably more accurate east-west, than north-south, because of the equatorial bulge. The south end of my water level should always be too high by the tiniest fraction, and even worse in a tidal condition.
In another scenario, if I had a bucket of water sitting on the floor of my home, I might suppose that the surface is perfectly flat. This is likely the principle of manufacturing "float glass". Making float glass allows molten glass to float very level, and cool to hardness, on a bed of heavier molten metal.
I think the truth, though, is that my bucket of water and the floating glass both must have a very slight convex curvature to their top surface. The bucket water surface should be shaped in a slight convex curvature exactly like the ocean and so should the float glass. Now, admittedly, this is pretty flat for most purposes. On the same token, some mirrors are specifically spun, in a molten state, to produce a precision parabolic concave surface that may be used in Newtonian Reflector telescopes. I imagine this "reverse type" curvature effect must be taken into rpm selection for the very finest mirrors, and yet may not be entirely possible to perfect.
Another gravity-like acceleration is that of rotating space stations. In this case, I imagine the bucket, sitting against the inside circumference of the outer rim, to possibly have a concave surface, just the opposite of earth. As an example, if I were to not like the constantly curved floor for walking in artificial gravity, I could build a polygonal series of short flat floors entirely around the inner circumference so that I may walk on "flat" floors. Here though, I think that the series of floor "flats" would feel like they had a high spot in the middle of each flat polygonal side, and a dip as one walked into the joint angles. If I spilled water, it should run "downhill" into these dips. The dips are further from the hub center, and I imagine, the further out, the more acceleration. My bucket, sitting on such a floor, should do the same and develop some sort of natural concave curvature to it's surface.
The arbitrary "level seeking", of the spilled water, seems like it might, or might not, also cause flow to the sides of the floor "flats", since the outer edges are also further from hub dead center. Then, on the other hand, the floor edges are all perpendicularly equidistant to the hub axis which may only cause water curvature in the direction of rotation, not side-to-side. Which is correct? The latter seems like it may rule.
Considering the accuracy, or inaccuracy, of the above, can I theoretically slowly swing a water bucket around on earth, with a rope, in such a simple fashion as to carefully balance the "opposing(?) curve" acceleration forces into a perfectly flat surface? The idea of the original thought experiment was to achieve perfect natural flatness right here on mother earth, a process that can not apparently be easily done any other way. As an example, one might use a laser light to measure a float surface, but of course, gravity very slightly bends light too, so even that would not be good enough for perfection on Earth (unless the process was done by machining, and measured by light vertically).
The final attempt at flatness might be to simply slowly spin the bucket on a turntable, by calculated rpm, until the centrifugal force just barely flattens the natural curvature of earth. But this may not work either, if the spin opposing force is unevenly distributed in such a fashion as to tend to a parabolic curve, rather than equal-radius curve such as the shape of earth. This slight force difference may technically make any earthmade-spun parabolic mirror also just a shade imperfect.
It might just be, that the only way to get a perfectly flat bucket of water, or a perfect mirror, is to accelerate in linear fashion in a gravity-free environment. Then I would need a smooth rocket... and persnickety natural earthbound surface flatness is out.
Is there any other natural way to achieve real world flatness?
Thanks for your thoughts,
Wes
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