NATHAN COPPEDGE--Perpetual Motion Concepts
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Perpetual Motion Machine Concept Utilizing Rising and
Free-Falling Buoys, Second Iteration.
EQUATIONS
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
tank
f = estimated frictional loss at any given time including wheel
resistance
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
Free-Falling Buoys, Second Iteration.
EQUATIONS
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
tank
f = estimated frictional loss at any given time including wheel
resistance
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
