@GavinPalmer1984
Try this little quiz I made.
Put the following in order of least to most energy required.
1) Lifting 1000kg - 1 meter high - in one second
2) Lifting 1000kg - 1 meter high - in three seconds
3) Lifting 1000kg - 1/2 meter high - in one second
4) Lifting 1000kg - 1/2 meter high - in one half second
Hope this will get the point across.
Energy required for the partition to get up to max velocity:
W1 = (m * d1 * g) + (1/2 * m * v^2)
Energy required for the partition to move with acceleration = 0, aka constant velocity:
W2 = (m * d2 * g)
Energy required for the partition to slow down to v = 0 and reach destination:
W3 = 0
So the overall work will be:
W = (m * d * g) + (1/2 * m * v^2)
d1 + d2 = d ~= 2 * H/n
So:
Work(1) = 1000kg * 1m * 10 + 1/2 * 1000kg * 1
Work(1) = 10000J + 500J = 10500J
Work(2) = 10000J + 56J = 10056J
Work(3) = 5000J + 125J = 5125J
Work(4) = 5000J + 500J = 5500J
Realistic dimensions would mean that the height (y-dimension) of the output unit's holding container would be roughly equal to the depth(z-dimension). The width(x-dimension) would be larger than the output unit's width. The height and depth would be roughly twice the height of the output unit. So each partition would have a width and depth which is equal to the output unit's container's width and depth.
Let's use these dimensions:
Output Unit:
(y-coordinate)height = 22 meters
(x-coordinate)width = 3.7 meters
(z-coordinate)depth = 3.7 meters
Let us assume that the mass of the output unit itself is zero and only the falling mass (piston) is accounted for. We will also ignore resistive forces for now. There are efficient geometric shapes which should be used... I may not be using the most efficient shapes.
mass of piston < Volume of output unit * density of water
m(p) < V(ou) * p(h2o)
this is where you would account for a temperature window so that the output unit is always buoyant no matter the temperature... temperature affects density.
m(p) < 22 * 3.7^2 * 980kg/m^3
m(p) < 295,156.4 kg
The mass will be able to fall roughly 1/2 of the output unit's height.
Output Work = m * d * g
OW = 295,156.4 * 10 * 9.81
OW = 28954842.84 J - (f1 * 10)
f1 = friction on inner walls over 10 meters
Output Unit's Container:
height = 45 meters
width = 4 meters
depth = 45 meters
mass of water exchanged = m(h2o)
remember, water exchanged must be greater than the height of the output unit.
m(h2o) = Volume of h2o * density of h2o
m(h2o) = 4 * 45 * 22 * 980
m(h2o) = 3,880,800
Partition:
width = 4 meters
depth = 45 meters
ignore inner-operations for now (there is potential energy which can be harvested from other sources within the process)
Input Work = work needed to exchange the m(h2o) = IW
IW = (m * d * g) + (1/2 * m * v^2) + (f2 * d)
d = 2 * 22/n
n = number of partitions
m = m(h2o) = 3,880,800kg
f2 = friction encountered while lifting
We need:
OW > IW
OW = 28,954,842.84 J - (f1 * 10)
IW = (m * d * g) + (1/2 * m * v^2) + (f2 * d)
28,954,842.84 - (f1 * 10) > (3,880,800 * 2 * 22/n * 9.81) + (1/2 * 3,880,800 * v^2) + (f2 * 2 * 22/n)
Ignoring friction:
28,954,842.84 > (3,880,800 * 2 * 22/n * 9.81) + (1/2 * 3,880,800 * v^2)
n = 100;
v = 0.22 m/s;
height of a partition = 0.22 meters;
28,954,842.84 > (3,880,800 * 2 * 22/n * 9.81) + (1/2 * 3,880,800 * v^2)
28,954,842.84 > (16751085.12) + (93915.36)
28,954,842.84 > 16,845,000.48
Excess work = 12,109,842.36 J
with friction:
28,954,842.84 - (f1 * 10) - staticfriction1 > (3,880,800 * 2 * 22/n * 9.81) + (1/2 * 3,880,800 * v^2) + (f2 * 2 * 22/n) + staticfriction2
28,954,842.84 - (f1 * 10) - staticfriction1 > (1675108512 / n) + (1,940,400 * v^2) + (f2 * 44/n) + staticfriction2
n = 100;
v = 0.22 m/s;
height of a partition = 0.22 meters;
28,954,842.84 - (f1 * 10 meters) - staticfriction1 > (16751085.12) + (93,915.36) + (f2 * 0.44 meters) + staticfriction2
28,954,842.84 > 16,845,000.48 + (f2 * 0.44) + (f1 * 10) + staticfriction1 + staticfriction2
Relatively bad coefficients of kinetic and static friction are 1.0 and higher.
Force of friction = Normal force * coefficient of static friction + normal force * coefficient of kinetic friction.
Unrealistic worst-case friction:
normal force is related to the area of contact between materials and the pressure exerted.
width of seal = 0.05m
the piston is cube shaped = 4 sides that are 1m long
use 2 seals
normal pressure might be 75,000 N/m^2
for staticfriction = kinetic friction (I am using bad coefficients so this is safe)
f1 = Area * Pressure * coefficient of friction= (0.05m * 1m * 4 * 2) * (75,000) * 1.0 = 30,000 N = staticfriction1
28,954,842.84 > 16,845,000.48 + (f2 * 0.44) + (f1 * 10) + f1 + staticfriction2
28,954,842.84 > 16,845,000.48 + (30,000 * 10) + 30,000 + (f2 * 0.44) + staticfriction2
28,954,842.84 > 17,175,000.48 + (f2 * 0.44) + staticfriction2
28,954,842.84 - 17,175,000.48 > f2 * 0.44 + staticfriction2
11,779,842.36 > f2 * 0.44 + staticfriction2
if f2 + staticfriction2 / 0.44 < 26,772,369, then this device can definitely be perpetual.
check this out:
OW = m1 * d1 * g - f1 * d1
IW = m2 * d2 * g + f2 * d2
Doubling the dimension:
OW = 2*(m1 * d1 * g - f1 * d1)
IW = 2*(m2 * d2 * g + f2 * d2)
All of the masses double.
d1 will double.
d2 can stay the same... aka double the partitions.
If you ignore friction, doubling dimensions and partitions will quadruple OW but only double the IW.
The work done by friction for OW will quadruple because of the increased distance for f1 and the area of contact for f1.
I will not make the claim that the work done by friction for the OW will increase with doubling the dimensions... that just limits the innovation of the design.
Also, I know that there are better geometric shapes which should be used... I happened to use bad ones, and still brought forth great evidence that perpetual motion is possible.
I should add that any other losses within the system are a direct result of the design and implementation to achieve the desired (basic) operation. For example, creating electricity from kinetic energy has inherent losses. And storing / transferring that electricity has large inefficiencies. The designers should conclude, that the use of electricity to maintain a desired state of the device should be avoided... Unless the electrical conversion/storage/transfer processes are increased to an efficiency which is at least equivalent to the inherent resistant forces (friction) within a system which avoids the use of electricity (compare direct mechanical work through pulleys and levers to that of an electric motor) for the same purpose.