|Perpetual Motion Machine Concept Utilizing Rising and
Free-Falling Buoys, Second Iteration.
Rising and Free-Falling Buoys Continuous Motion Concept.
For the purposes of calculating the relative merit of various heights of the upper
tank, sizes of buoys, and widths of the lower tank, I used the following equation:
Over-unity if (w + b) > (r + f)
where w = effective weight of buoys on the falling line
b = effective buoyancy of buoys in upper and lower tanks
r = entry resistance for the single buoy entering the lower
f = estimated frictional loss at any given time including wheel
w isn't the full weight of the falling buoys, but rather the proportion of their weight
that is vertical. Thus where u is the upper angle, I had to use the equation
(90 - u) / 90 = proportion vertical
I could then multiply the proportion that is vertical by the weight of the falling
buoys (requiring a calculation of the length of the falling line times the number of
buoys per meter). Then I would have the effective gravity i.e. the pull force in
kilograms exerted by the falling line.
So we have w.
The buoyancy within the upper tank is simply the buoyancy per buoy times the
number of buoys in the upper tank, since they are rising vertically.
I estimated the buoys in the lower tank exerted half their force, since they are rising
at a 45 degree angle, assuming the wheels are well attached to the support structure.
0.5 * number of buoys in lower tank * buoyancy per buoy
Adding the upper and lower buoyancy, we get b.
The entry resistance r is equal to the proportion of the water in cubic meters
supported per square meter of the bottom, times the cross-sectional area of the
buoy at its widest point, in square meters.
The proportion of the water in cubic meters supported per square meter of the
bottom is found by taking the water weight of the volume of the upper cylindrical
tank, adding it to the weight of water contained by a cylinder with the average
circumference of the lower tank, and dividing by the area in square meters of the
bottom of the lower tank.
Thus there is a strong reduction in entry resistance using a broad lower tank and
elongated upper tank, since much of the upper water weight is distributed over the
surface of the bottom of the lower drum.
Factoring in the size of the buoy, smaller buoys require much less resistance, but
are capable of much less buoyancy and gravity. Beyond a certain size the minimum
entry resistance may be prohibitive. But less so than would be the case in a simple
cylindrical tank along the lines of Frank Tatay's design of 1929.
I have had difficulty estimating friction, in part because I believe that a minimum of
constant force would render friction irrelevant for all purposes but determining
percentage over unity.
We know that when things fall, they keep falling until they meet the ground, and
when things float they float until they reach the surface. It seems doubtful that
either of those forces would be stopped by friction. Slowed yes, stopped no.
Thus what remains is wheel resistance, something that is largely a matter of
technology, and which I estimate is proportionally less significant the larger the
scale of the device, much like a wider barrel of a gun generates much greater
force. Only I don't intend to use explosives.
Rising and Free-Falling Buoys Data nathancoppedge.com