Buoyancy Motor No. 4 comments by Donald Simanek.

A couple of critics object to the inclusion of this device in our collection because it forces us to push materials to the limit. We are accustomed to giving inventors viscous-free liquids, frictionless materials, and in this case we'd also have to do something about that pesky surface tension. With real liquids a buoyant object would have to have considerable velocity to break through the surface and go completely underwater long enough to make it around the bend in the tube. Then it would have some difficulty popping up above the surface. Picky! Picky!

The work done by and against gravitational force adds to zero around the loop, so we needn't be concerned about that. The system is "primed" by (1) raising the water level on the right, which requires work done by an external agent. It also requires work by an external agent to force the ball to the bottom of the liquid. Thus, the system begins with stored energy. It also begins with the system components (the liquid) located far from its equilibrium position.

Some extra work is required to push the ball floating at the surface down until it is entirely below the surface. The ball will recover this amount of energy as it breaks through the surface again on the way up. But then it will lose that amount as it crashes through the lower surface on the left. Still, after the first half cycle, these losses and gains add to zero.

So, allowing the idealization of zero viscosity, etc., the ball should execute more than one cycle around the loop. Does this continue forever? Can we extract a bit of energy from it during each cycle, forever?

I, with Dave Carvel's permission, have simplified the gates. Instead of using "flap" or hinged gates, I use these neat iris diaphragms which do not "push around" much water. Yet still, the gates present a problem more subtle and fundamental than mere inertia of water.

Niket Padwardhan was the first to email me [12 Sept 2002] the absurdly simple reason why a device with such gates, even perfect ones, will not work.

The system will eventually run out of energy by lowering the water level. This will happen even with perfectly rigid components [and perfect gate seals]. Consider what happens when the ball goes through a gate. The total volume in the two spaces connected by the gate must remain constant, so if the ball goes up, a volume of water equal to the volume of the ball must come down. In each iteration through the loop one ball's worth of liquid effectively moves from the top section to the bottom section. The upper level stays the same—until the ball pops up from the top surface, at which point the level drops by one ball volume worth.

It seems that nature always has a "gotcha" to thwart the cleverness of the perpetual motion machine inventor.

I was reluctant to include this device for reasons stated at the top of this page. So I was surprised to discover that the idea wasn't new, and is part of the long and sordid history of failed devices. So much ingenuity has been wasted on perpetual motion machines over the last few centuries that it's rare that anything really new comes along. This figure illustrates that this idea is at least as old as 1825. It appeared in the June 1825 issue of "The Mechanic's Magazine" and is discussed in Phin's book. But (why am I not surprised?) Phin didn't give, or didn't know, the basic, insurmountable flaw explained above. The person who submitted the machine writes:

I beg leave to offer the prefixed device. The point at which, like all the rest, it fails, I confess I did not (as I do now) plainly perceive at once, although it is certainly very obvious. The original was this—to enable a body which would float in a heavy medium to sink in a lighter one, to pass successively through the one to the other, the continuation of which would be the end in view. To say that valves cannot be made to act as proposed will not be to show the rationale (if I may so say) upon which the idea is fallacious.

The glass tubes contain water on the left, air on the right. A water reservoir is below, but isn't strictly needed. Balls less dense than water are used. The apparatus has valves at points 2, 3, 4, and 5. It is just like the version we have discussed above, except for the neat addition of the curved portion of the tube (4, 5, 6) on the right. This is adjusted for timing so that the balls take the same time to fall on the right as it takes them to rise on the left. The valves have springs and are opened by the balls themselves, then closed by the springs. The balls must be timed so that the two valves on the left aren't open at the same time. They therefore "sustain the whole column of water."

We've said a lot about this kind of device. What more can be said? Consider this:

Perpetual motion machine inventers often acknowledge flaws found in their devices. Typically their response is to try to "fix" the flaw by redesign. Suppose we fix the flaws noted above by eliminating one of the gates, and substituting a "black box" B at the bottom which not only sustains the water column on the right, but cleverly allows the ball to move from air to water without letting any water out. This gate mechanism prevents the water on the right from ever being depleted. This eliminates the flaw explained above.

Eliminating that flaw reveals another flaw, even more fundamental, which prevents any buoyant device of this type from working. The energy gain of the ball falling through air on the left is m_bgH where m_b is the mass of the ball. The energy required to push the ball from air into the bottom of the water column is equal to the potential energy of the water volume of height h and cross-sectional area Aat the top of the water column, i.e., m_wgH where m_w is the mass of that water. Forcing the ball into the liquid raises the liquid level a height h, equivalent to a volume Ah equal to the volume of the ball. Archimedes' principle has thwarted our hopes again.

An equivalent way to analyze this is to note that pushing the ball into the water requires work to overcome the pressure difference between air and water. The pressure at the bottom of the water is r_wgH. The work required is VD P = r _wVgH. The energy the ball has after falling distance H from rest is mgH = r _bVgh. This isn't enough to push the ball into the water.

But wouldn't the ball rising in water gain energy, an additional energy which might be enough to keep this system cycling? We are generously assuming perfect components, so we can disregard friction and viscous drag. Under these ideal conditions the ball in water experiences a force upward of size B - W, and accelerates upward, gaining kinetic energy. How much energy gain? It gains (B - W)H, where W is the weight of the ball and B is the buoyant force on it. This is just the amount of energy we put in when we pushed the ball to the bottom of the liquid (priming the device, so to speak)! It's also the additional amount of energy needed to actually push the ball to the bottom of the liquid by any means. So we conclude that if we prime the device, putting in energy by pushing the ball to the bottom of the liquid, then it can cycle continuously, going on forever, but producing no excess useful work. We have called this a device of type (1).

This is a nice example of a "primed" device of type (1) which turns continually. Whenever we eliminate dissipative processes like friction, we get, at best, a system which cycles continually, but produces no useful work.

We also saw in Dave Carvell's clever puzzle device how gates in liquid systems (even highly perfected gates) can allow liquid transfer which eventually destroys the priming, of the machine, bringing it to a stop.

We have indulged ourselves in this discussion and tried the reader's patience. First we swept aside irrelevant considerations such as friction and viscosity, then looked for more fundamental flaws. The first ones we found exposed others. Analyzing a perpetual motion machine proposal in this way is like peeling an onion—it makes you cry (when you realize that the fatal flaw is insurmountable). To "correct" such a flaw would require violation of very basic laws of physics.

This just in.
Yet another version arises.
Discredited ideas never die.

This inventor seemed to realize that the gate-valves are a problem, and spent considerable effort in their design (24, 25, 26). He also must have realized that some water would transfer across the gate (26) as it opened and closed so he provided a valve (41) which somehow takes the excess water and pushes it up a tube (42) to reservoir (43). It's unclear what provides the work to do that. He also has some kind of linkage (37) between gate (26) and the ball release at (32). It must prevent the balls from piling up somwhere, though it's not clear whether (32) triggers (26) or vice versa. This linkage (37) seems improperly drawn, for it seems to me that the dotted and solid lines should be swapped. But perhaps I just don't understand the subtle and mystical principles employed by the inventor.

With all that attention to these irrelevant details, the inventor has completely overlooked the real reason (discussed at length above) why this thing won't work. We often tell students to sweat the details. But this inventor was so focused on engineering details that he forgot to attend to the basic principles of physics.

Rube Goldberg would have loved this one. You have to admit it's a magnificent contraption.

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