(scribbles really.... I'll attempt to make some sense out of it)

https://docs.google.com/spreadsheets/d/1YzocJ_dc7pXwHq1Vr9mzXBdS5-nP51xNjlSPsEVPN_M(some figures below are rounded or just close to what the actual are)

First... let's take a system with an arbitrary 32 'buckets' (these are the things that hold the air and cause bouyancy), we'll discount 4 on the top and bottom in transition from upright to downright (inverted to non-inverted?) leaving 28, 14 with air rising and 14 empty and falling. The mechanism tying them together and material of the buckets themselves essentially irrelavent because it's balanced on rise and falling side. It will play a role as inertia, it will take a bit of time to accelerate/decelerate the mass of the mechanism.

Buckets can be constructed of PVC tube, with holes drilled out with a holesaw of any appropriate size... I started looking at largest in-stock and nearby materials, which are 8" tubes. Tubing is measured by Inner Diameter... so we can compute from a diameter of pipe and a length cubic space (ft^3)... and can translate that to gallons which is 8 pounds per gallon... (I know all this non metric stuff, whatever)... anyway, a certain separation between buckets is also required to get air into them in-between...so I chose and arbitrary 4 inches to make 1 foot per bucket, which means I'd need a tank at least 14 feet in depth, which is 4.2m... let's round up to 5m. Every 10m of water is +1 atmosphere.... so 1.5 atmospheres of pressure at the bottom.

It is also considered that the buckets at the bottom will be under more pressure, making the volume of air in them less... and the displacment also less.. if the were filled to 100% capacity, air would leak out as they rose uselessly... so if we fill them to 66% capacity ( 1.5 atmosheres is 3/2 atmospheres and 1 is 2/2 atmospheres ... anyway the three in there makes it be 1/3 something) so as they rise, at the top they will be 100% full and no bouyant force is every lost.... but... this means that each bucket going down has slightly less displacement... and therefore slightly less bouyant force. (top+bottom * one_side_bucket_count / 2 ) ends up being the calculation for total displacment of all buckets rising... (1+0.66 * 7 ) or 11.62 buckets... which is only 83% capacity. But this is 'optimal' and one could overfill the bottom so there is 14 buckets of force always ... with air spilling out as they rise and get slightly more work out of them. (sterling allan'snews suggested there is possiblility of load-following, which reminded me of this).

Force of a bouyant object is strictly the mass of the displacement of liquid times gravity. (please do correct me if I'm wrong, because actually I neglected that 32.1 ft/sec^2 in my later calculations... which means the output is always G times the input... and actually would work)

(this was later refined, and this is an erroroneous calculation) adding up the total I found the rising side would have some 1080 gallons of displacment causing them to rise... to get force have to multiply by 'g' ..

32.174 ft/s^2 .. which gives some 32000 ft-pounds/sec or 58HP... or

44683 Watts! 44KW ! well... that will certainly power MY house... this looks promising.

[size=78%]--------------

So.. let's scale this back a little, and see if maybe I can make a table-top version.

so if we have a 3 inch pipe, 1 foot in length, it will have 0.05 cubic feet or hold 0.367 gallons... which will be a displacment of 2.93 pounds per tube.

if I use a 1 inch separation, there's 3 tubes per foot of vertical space... if I use the same 32 sections (14 effective floats), it will be about 5 feet in height... which is only 0.14 addtional atmospheres of pressure...

This well have an optimal displacement of 40.7 pounds.

That's all well and good, but, how much work is it to compress normal air from 1x to 0.86x of it's volume? (increasing pressure the of air from 1 to 1.14 )

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Well turns out this is all over ... and it's

nRT * ln(V2/V1)...

where n is moles of air (1.19804 per cubic foot)

R is 'gas constant' (6.13244 ft-lb/ k-mol) (multiplying this by n and K remove the divid and you get ft-lb)

K is the tempurature of the gas (I used 65 farenheight ... 291.3333 Kelvin)

0.1472578125 cubic feet (v1)

0.1289202028 cubic feet (v2) .. (v1 * 0.86) (the 0.86 is from the computed atmosphere pressure difference above.... assume tempurature remains the same, P1V1T1 = P2V2T2 ... or V2 = P1(1)/P2(1.14) * V1 )

which yields

41.91757564 ft-lb.

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So now I'm discouraged... because 40.7(pounds lift) is slightly less than 41.9(ft-lb to compress)... but I guess my units are not matched there... I figured the feet came from the distance the thing traveled... (3 buckets fit in 1 foot, so the volume was computed as the bottom 3 buckets) ... BUT I forgot to mulitply by G.

so no matter what I did with the sizes... unless I had negative distance separating the buckets (overlap) I could not exceed the force to compress the air.... So the conclusion yesterday was 'this is barely break even'... but ... I forgot to multiply the displacment weight times gravity force... so maybe this IS possible.

Some things to consider... increasing the operating bucket count (extending the height) did not increase pounds above ft-lb ... because the taller column of water increased the required pressure...

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So now... to source some parts... this thing turns very slowly, so it will have to be geared up, it will lose HP output what it gains in speed... so if I was at 36RPM to start, and wented to get to 3600RPM to power a gas-powered generator instead of the motor, I am at 100x less power I can apply to the generator... so a wind turbine that works 360RPM would be better... being only a 10x loss.

Was considering what I might be able to use instead; a continuous pump would be better than a piston pump if I were to directly drive the pump from the output shaft... Might be able to use an archemides screw sort of thing with a light oil seal (only dealing with 0.15 an addtional 2psi ).. but not sure what to make the screw out of... what other sort of continuous pumps? (displacment pumps, but they do higher pressure at lower volume, and really I want high volume)

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3 sections per section of the 3 inch/1 foot PVC buckets is 0.147 cubic feet/sec) or 8 CFM.... that's a lot more than an aquarium pump will output (can get 12V aquarium pumps, which reduces the voltage requirements of output generator)...

can get a 3.5CFM at 90psi 2.5HP pump for $80... but then that's 120V AC... (though this was when I was looking at 8inch diameter by 2feet tubes, which is

55.84CFM ... and a 25+CFM pump is $2500!

but maybe I can manufacture a cheap pump with concentric PVC... a 1 foot stroke pump for 8CFM is only 5.16 inch diameter tube...

the problem with that is it's only 50% duty cycle so it would pump for 3 tubes and be drawing in air for 3 tubes... so really could make it a 2 inch stroke and do 2 strokes per bucket (1 draw, 1 pump)... or maybe some sort of sterling engine... saw a very large solar heat engine using a very large rubber membrane (rubber sheets?)...

And; again if I forget the conversion to electric to drive a pump and recover from a generator it should simplify the system, and at least demonstrate closed-loop self running... can attach a fan or something to drive a generator (tinman's venturi thing... also dyson has a air accelerator that's a ring making a very thin drive force around a very large venturi (

http://www.dyson.com/fans-and-heaters/cooling-fans/am06/am06-desk-fan-10-inch-iron-blue.aspx (small fan in base, feeds air out through the outer edge of the ring)

)

then hook up some other load to it...

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fewer buckets generates less lift... but requires less work to pressurize the air.

But then there's also that G is ft-per-second-squared ... and maybe that squared is more signifcant giving more tubes more travel time?