parabola? catenary? or what?

All of the mass experiences an acceleration of g downward. Each radial mass element experiences a radial acceleration dependent on the RPM. If the RPM were very high and the sides steep - ie. none sloshed out then the cement form would approach the straight up sides of the container and the general shape of the central void in the slab would approach a parabola. Since the sides are low and there is sloshing over there is no asymptote and the general shape of the void in the slab would be a hyperbola.

I'm not offering a proof on this because integral sums of radial accelerations are difficult mathematically. But, this is a pretty well studied problem. There are telescope designs that use this exact mechanism with mercury to achieve a highly accurate condensing mirror. Researching that topic may provide you with further information if you wish.

Sincerely,

Mr. Gee

I'm still pondering this... you're saying the type of curve would be dependent on the height of the container (see sketch superimposing high and low walls).

And the high walls give a parabolic shape, the low ones a hyperbolic shape. Is this correct?

Robert asks: "And the high walls give a parabolic shape, the low ones a hyperbolic shape. Is this correct?"

Hello Robert,

No, the shape of the surface is always a paraboloid regardless of the height of the tank.

-e

Hi Europium,

So (if you're not sick to death of this one yet) the formula for the focal length:

f = g/2ω²

is independent of the mass of the fluid and height of the walls.

However, intuitively, it seems that the shape of the parabola would alter with the height of the walls - a bit like in the sketch above.

If that's correct, does that mean the different height walls at the same RPM would produce a family of parabolas with more or less steep sides, but the same focal length?

Robert asks: "does that mean the different height walls at the same RPM would produce a family of parabolas with more or less steep sides, but the same focal length?"

Hi Robert,

No. Not a family of paraboloids; just a single paraboloid.

Let's consider for a moment a generalized tank having radius R and height H. Let's call the top edge of the paraboloid h. That is to say, h is the height at which the paraboloid meets the tank wall. The wall itself can be arbitrarily higher than h, but not shorter.

Equation 2 in Post #2 relates the height of the concrete to the tank radius and RPM. Re-writing Eqn 2 using our variable definitions above, we get

2.1) h = (ω²/2g) r²

The first thing you notice about Eqn 2.1 is that it does not include the quantity H. What this means is that the height of the concrete has nothing to do with the height of the walls.

On the other hand, Eqn 2.1 is valid only so long as h ≤ H. Were h > H, the liquid concrete would be flung out of the tank making you the hit of the neighborhood. What Eqn 2.1 does say is that the height of the paraboloid depends only on the force of gravity, the tank RPM and the tank's radius. All you have to do is to ensure that your tank's walls are high enough to contain the entire paraboloid, i.e., H ≥ h.

The dimensions of the paraboloid do not depend on the mass of the liquid.

To calculate the amount of liquid you need, subtract the volume of the paraboloid from the volume of the container at height h. (Keep in mind that the container may not be a simple cylinder as discussed elsewhere in this thread.) The volume of a paraboloid having a radius R at height h is defined as

2.2) V_par = ½πR²h (h, not H)

In keeping with your original post, the volume of a cylindrical tank of radius R at height h is defined as

2.3) V_cyl = πR²h (h, not H)

(Btw, notice the interesting similarity of these two equations. They say that for a given radius and height, the volume of a paraboloid is exactly half that of the cylinder that would neatly enclose it.)

The foregoing assumes the vertex of the paraboloid touches the bottom of the tank.

Hope this is helpful.

-e

...and that's why I love CR4.

Thanks for the illuminating, well written and beautifully illustrated response.

(fools! - armed with this knowledge I can now focus my giant death ray ... Mwoah ah hah hah hah!)

Btw Robert, for the concrete mix to reach the top edge of your 6 m dia., 1 m high tank, the tank must be spinning at 14.092 RPM. The focus of the paraboloid will then be 2.25 m above the bottom of the tank.

-e

And you'll need 4.713 m³ of concrete. That's about 444 ea, 50-pound bags of Quikrete Fast-Setting Concrete Mix #1004-50, or about six and a quarter yards of Ready-Mix.

I should know better than to post when I'm tired.

You'll need 14.137 m³ of concrete, not 4.713 m³. That's about 1332 50# bags of Quikrete, or about 18.5 yards of Ready-Mix (not to mention the bottom of the paraboloid assuming a thickness of zero in these calculations ).

-e

To reduce the liquid concrete to be rotated, you make a backup structure about 50 mm inside the mathematical curve you will be getting finally. Now start rotating the drum and start pouring the liquid concrete.

With less material, you will achive the results.

The shape of the surface does not depend in any way on the shape of the tank, ie, the tank need not be cylindrical so long as the walls of the tank do not intersect the paraboloid (except where the paraboloid is supposed to intersect the edge; presumably near the rim). Look at my derivation, above, and you'll see that the test particle, m, has no knowledge of the tank's shape but only of the forces that act on m. The tank could be conical, for example, or a series of connected conical sections that roughly follow the shape of the paraboloid and give it thickness for strength. You're right; that is a lot of concrete, but the good news is that it's not actually necessary to use all of that concrete in practice.

Btw, rather than building a Death Ray, how's about using this technique for making solar cookstoves for third-world countries where fuel is scarce? Just a thought...

Cheers!

-e

Unless I missed it in another post, the apparatus will act like a centrifuge and will separate out , by density, all the components of the cement. You will wind up with a stratified mess of aggregate, damp cement powder, and a surface of dirty water that probably won't set up very well. It would be better to use a quick setting plaster that won't stratify in the short time it takes to set up. Use that to make a "plug" (reinforced shape) and cast the concrete over the plug.

See Post #25

Looked at post 25, but why wouldn't it act as a centrifuge and stratify the components of the slurry?

Centrifuges function after they are up to speed (it is not just the startup acceleration), too. That is why they are spun at a specified speed for a specific duration. The various densities stratify over time.

Of course this is outside the original design of the question.

Hmmm - your idea has merit. Perhaps a switch on the back - Death Ray / Solar Cooker. That way we don't discriminate against people who really want a death ray.

"inside the mathematical curve" outside would be bettre ?

Inside/outside - doesn't really matter. Looking at a cross-section (through the focus & vertex of the paraboloid), there's a parabola, which cuts a plane into 2 regions. There is no inside/outside.

It matters since an internal support will not support anything. I would suggest you read more carefully what is written. Sorry if it dsturbs you but engineering is a precise matter and words have a precise meaning.

Yes, you are correct dimetrically. What I mean was physically.

Yep - in context I understood that you meant build the frame inside the vat rather than inside the void. And your good idea has cut my cement costs so the Plasma Laser Death Ray 3000.. er... I mean ... the solar Belgian off-grid chocolate cooker (whew - that was close) ... is back under budget. Let me know where to send you some chocolate.

Wen I was a boy me and some friend one day began circling inside a 5m x 1.2m round cement reservoir (why? a boy of 12 don't need a reason). We eventually had the body of water spinning.

We did not intend any experiment but I can remember at least 3 facts that tickled my curiosity.

1) Most floating objects accumulated at the centre.

2) A lot of suspended matter also gathered on the floor at the centre.

3) There was a slight downward movement at the centre.

I think a vortex could have formed if we could increase the speed.

You may have to add more shapes or limit the rotational speed.

I think this experiment can be done with some clay in a front loader washing machine with a solid drum and turned on its back. (I am out- my wife will kill me dead)

I forgot - no friction.

Hi Hendrik.

There are at least 2 reflecting telescopes in existence that are constucted of a large circular chamber that is half filled with mercury, when it is spun at a constant speed the mercury forms a perfect parabolic mrror.

Spencer.

Hi Scapolie,

Roger Angel at the University of Arizona pioneered the technique of spin-casting very large (8+ meter) single-piece glass* telescope mirrors. His technique makes possible mirrors which require far less bulk than mirrors made using older techniques. Consequently, Angel's mirrors cool much faster after casting than, say, the 200" Hale Telescope mirror which took two full years of controlled cooling before it could be figured. They are a lot easier to transport, as well. (Btw, the Keck telescopes' 72 mirror segments were delivered to the top of Mauna Kea by FedEx.)

Angel spin-casts his mirrors in a rotating kiln whose rotation rate is very precisely controlled. This makes it possible to cast a mirror having a nearly ideal paraboloid shape requiring minimal grinding.

Large telescope mirrors flex as the telescope's elevation angle changes. Even the thick, heavy Hale telescope mirror sags a bit, but the effect is far more pronounced in the large thin mirrors of Angel's design. This isn't necessarily a disadvantage, however. In the latest generation of large telescopes the mirror is backed by a stiff framework sporting a network of "whiffle trees" - mechanical actuators that dynamically deform the mirror under computer control. Thus, the mirrors are not only corrected for sag as the telescope changes position, but are deformed in real time to correct for atmospheric aberration (the same effect that makes stars twinkle - nice for romantics and poets, but hell on astronomers trying to snap a clear picture of a distant supernova).

* More specifically, Zerodur. Zerodur has a very low thermal expansion coefficient - it is relatively insensitive to temperature changes - and belongs to the glass-ceramic composite class of materials. As such, Zerodur has both an amorphous (vitreous) component and a crystalline component.

Congratulations, you just (re-)invented the cyclonic filter!

Robert:

When I tried this (forty-some years ago), with a pan of epoxy on a record turntable, the nominal paraboloid of revolution was spoiled by vibration induced ripples on its surface. Concrete may not be so sensitive. Good luck with your death ray.

DickL

I believe that the university of Arizona has made several reflecting type telescopes using this exact method only using glass instead of cement. they put the glass in in chunks and started the table revolving and then added heat to melt the glass.

some grinding of the glass was nessasry to bring it to its final parabolic shape but by using this method they eliminated a lot of grinding.

oilcan13

Frist if you fill the container to the max spin it till it sets you would have the top and the bottom parallel. Spinning it at any speed would force the concrete over the sides of the container. That is un less you spin the container very slow.

Hello Hobo,

If you fill the container exactly half-full of liquid (okay, concrete), then spin the container at 14.092 RPM, the vertex of the paraboloid will just kiss the bottom of the container whilst the top edge of the paraboloid will just reach the rim (decreasing to zero thickness at that point).

The total concrete weight will be approx 55,470 pounds, or about 25,161 kg (assuming 3000 pounds per cubic yard according to the local Ready Mix plant).

-e

this is how they make concrete street light poles ... construct the mold for the pole (anywhere from 9ft finished to 70 ft finished,w/knockouts for hand holes etc) pull rebar wire under stress against the ends and then pump it full of concrete and spin until the concrete set leaving a raceway through the middle. then put the poles in a curing oven until complete American Concrete, div of Union Metals have been making them that way for 60+ yrs or more My father and I worked for them when i was still in high school (just before dirt was invented) only problem was sometimes they would spin too fast and run off the rollers and THEN the fun would start... it is an amazing amount of energy that kind of gets a mind of its own when you spin a 70ft long concrete pole that weighs 15K lbs finished in a very large mold just a little to fast ... its also when you learn that some nouns and verbs can be combined into some very useful action words while running for your life:(

There is a difference the poles are spun in a horizontal position !

The problem mentioned concerns a rotation around a VERTICAL axis.

Conditions are not the same. If you remember that the concrete is cast with a guide which is moved axially and the mold turns already during casting.

i realize that the problem is for a vertical axis application, my post was meant for information.......the molds are meant to turn axially until they get "away". it is a very strange thing when you see a 74ft mold which weighs about 27k LBS w/concrete start wandering randomly around the bay by itself.....thats when the random axis of rotation in space/combination of action words/run for your life thing starts.....it's rather fascinating how fast fat little irish guys can actually run when being chased by flying concrete and metal.....also there is actually no center piece to the mold, the final raceway in the pole is acheived by centrifugal force when the concrete sets

Out of interest, what's the cross-sectional shape (circle, hexagon etc.) - or do they make a variety?

I have a close kinship with lamp-posts, having demolished one as a kid (while swatting a fly in the car) and having had to pay for a replacement. It was only an octagonal Al alloy version.

American Concrete made mostly hex shaped.... found them to be the most stable and they had been making them that way sincethe 20's but would make squares in the lower heights (under 16 ft) ...we shipped for them all over the world. another company we did work for was Centrecon from Japan and they made mostly round poles as did Great lakes Concrete from WI and several other companies

What is it about one of these things escaping that is so attractive? No one would want to be there in the room but let's be honest - is there anyone (except maybe the owner) who wouldn't love to watch a concrete lamppost imbued with all that energy roaming freely about a workshop?

Someone dropped a link on somewhere about a Russian UFO experiment that spun up a multi ton metal flywheel until it jumped its bearings and moved out through the wall of the building...

(just found it - http://www.rense.com/general41/grat.htm)

I have read all post to this date.

Seems dd that no one has consicered the mass/volume differential of the composit elements of the concrete...cement ( which is produced bt air classisication)...agreggate ,,,which varies from air swept sand/grave/ small rocks....all clasified by screening processes into experience or engineered dictated ratios.

In the suppose experiment the greater mass particle would accumalate with the greatest mass/volmue..mass controled...greater mass particles displacing the lesser mass particles vertically displaced upward by the centrifical verticle in gradiant to the individual particulate mass..subject to the water content (fluidity).

In other words (facitiously)

rocks on your bottom...powder in your lips........spit dry....rotationally speed dependant

Mr. Guy writes: "Seems dd that no one has consicered the mass/volume differential of the composit elements of the concrete...cement ( which is produced bt air classisication)...agreggate ,,,which varies from air swept sand/grave/ small rocks....all clasified by screening processes into experience or engineered dictated ratios."

Hello Mr. Guy,

As the system is in equilibrium, it doesn't matter whether the material is a homogeneous liquid or a mass of ball bearings. There is no movement of material with respect to the reference frame and therefore no mechanism to cause settling. Movement with respect to the reference frame occurs only when the system is coming up to speed. After that the forces on each particle cancel exactly.

Cheers!

-e

> As the system is in equilibrium, it doesn't matter whether the material is a homogeneous liquid or a mass of ball bearings.

Ok, as a system is in equilibrium, it doesn't matter whether the material is a homogeneous liquid (like water) or an heterogeneous one (like a mass of ball bearings, well-mixed concrete or "stratificated" concrete).

So I think your claim is not in contradiction to Mr. Guy one, since the classification could be done _before reaching equilibrium_. Obviously, once the equilibrium is reached, no further classification happen.

Your calculations are based on the steady-state hypotesis, and the Mr. Guy can be done in the warm-up phase, so I think there is no conflict.

Disclaimer: I'm a non-native english speaker and a telecommunication engineer, so my knowledge in English and mechanics are not high :( ... so excuse me in advance.

Parabola

If it were a Newtonian Fluid (i.e. has a single number for viscosity, the relationship between applied stress and rate of shear) then there are a range of votes on the correct answer to choose from above.

Cement is not a Newtonian Fluid, and therefore will behave differently. So it is very difficult to say, and the answer is best determined by experiment.

I think that there is a problem with fluids of the Bingham type: as long as the shear does not go over athreshold there is no layer sliding. May be you could have alook to this not so seldom aspect for instance the fluids in earth drilling have such a behaviour. I shall try to have a look too may be we combine the efforts.

Did you see this: apparently old back projection TVs had a Fresnel lens as part of the screen, and, you can pick them up for almost nothing.

http://www.instructables.com/id/Giant-Fresnel-Lens-Deathray-An-Experiment-in-Opti/

Interesting, I have one of those screens sitting around that I had salvaged from an old TV a few years ago. I pulled it out of my closet lastnight and was thinking of discarding it. My friend asked me if it was a Fresnel lens and I didn't know. I guess I will have to find something useful for it now.

I hope I am not "throwing a spanner into the works" here, and although I agree that for most of the length, the result would be a paraboloid, wouldn't surface tension in any fluid or fluid-based mixture (like wet cement) create a distortion of the shape as it approached the top edge? I would think there would be a bulge at the edge, causing a rounded end rather than a true taper, and causing a small back up which would further distort the parabolic shape for a short way away from the edge as well.

Just a thought.

Dear Mr.RobertOz,

The answer for your Question is - THE SHAPE IS PARABOLA. It is not CATENERY, not SPHERICAL INDENTATION.

If the spinning speed is LESS, the parabola will be shallow, and if the speed is HIGH, the Parabola will be steep.

Thanks,

DHAYANANDHAN.S