On Over-balanced Wheels and their Ilk



Tom Napier



The search for a over-unity device never ends but it 
continually moves on into new fields. Presumably, as the public 
becomes more scientifically literate it becomes increasingly 
difficult to convince them, or yourself, that some simple device 
is going to generate energy from nothing.

Mechanical devices have been abandoned; the fringe has moved 
on to unusual thermal engines, odd magnetic motors and 
electrolytic cells. As the negative results mount up and these 
devices too become commonly understood, no doubt they will also 
fall by the wayside. The search for some loophole in the 
conservation of energy will then move into new territory.

However even the hoary old over-balanced wheel and its cousin 
the self-pumping waterwheel still catch out the unwary. There is 
something so fundamentally obvious about a wheel which has 
weights further from its pivot on one side than on the other. 
Simple lever action shows that it should turn.

To say that any machine using this principle must always have 
more weights on the short-lever side than it does on the long-
lever side and that it is therefore in balance may be true but it 
doesn't sound very convincing. It leaves one wondering whether 
there could be some ingenious arrangement of levers and ramps 
which will make it turn. Could there be something which centuries 
of hopeful inventors have missed?

The answer is to ignore the left and right axis altogether and 
instead, to concentrate on just one weight moving up and down. 
For the wheel to rotate, each part of it must be making a 
complete cycle round the axis before returning to its starting 
point. For the wheel to keep rotating at least one part of the 
wheel, in making a complete circuit, must be gaining energy.

Now any circular motion, no matter how convoluted, can be 
examined as the sum of an up-down motion and a side-to-side 
motion. Motion from side to side requires energy to get started 
but in principle one gets that energy back as one stops unless 
any of it is lost in friction. However there's nothing there 
which allows one to gain energy, that's why I said that the 
differing lever arms didn't matter. 

Motion up and down is different, moving up requires an input 
of energy since a weight is being moved against the Earth's 
gravity. When it is at its lowest point, a weight on the rim of 
the wheel has minimum potential energy and has zero kinetic 
energy in a vertical direction. It has maximum potential energy, 
but still zero kinetic energy, when it is at its highest point. 
(At other points in its travel it has some kinetic energy and an 
intermediate potential energy.)

So, as the weight went once round the wheel, it gained 
potential energy. The wheel did work on it while it was going 
from its lowest point to its highest point. Coming back down it 
gave up that same potential energy and made its contribution to 
keeping the wheel turning.

However the weight always comes back to its starting point 
once per cycle. The energy gained from gravity on the way down is 
always exactly equal to the energy lost to gravity on the way up, 
less, of course, any losses. This argument applies to every point 
on the wheel whatever path it follows.

Since there is no gain in energy, and friction turns the 
wheel's initial kinetic energy into heat, the wheel eventually 
stops moving. Given a push it ends up making the environment a 
little bit warmer.

The technical way of saying that the energy you get out as you 
lower something is exactly equal to the energy which you put in 
as you raise it, is that gravity is a conservative field. No 
matter how convoluted a path something takes through a static 
gravitational field, if you end up at your starting point your 
net energy gain or loss is always zero. Thus no machine of the 
over-balanced wheel variety can generate energy.

The same argument applies to the everlasting waterwheel. The 
energy gained as water falls through the wheel is needed to pump 
the water back uphill again, you never come out ahead.

Although it is less obvious, the energy of motion which one 
gains when two magnets attract or repel is exactly equal to the 
energy needed to restore the starting position, no matter how you 
arrange the magnets. Of course, unlike gravitational fields, 
magnetic fields can be turned on and off. However, it takes an 
input of electrical energy to do so.

Unfortunately, it can be quite tricky to compute the true 
input and output powers when playing games with electromagnets so 
there is still scope there for chicanery. An electric motor is a 
device which generates motion from a changing magnetic field but 
it takes a power input to get a power output, a point which even 
the aficionados of Joe Newman must be willing to concede by this 
time.