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Can we make a machine that takes a mass of sand from the top of a sand dune keeps it in a box. Then moves it horizontally until it is hovering above the lowest point near the slipface of the dune. Then lets the box containing that sand fall under gravitation while it's kinetic energy is used to run an electric generator. Next step once it reaches the ground the box opens from below and the let go of the sand in it. Now raise the empty box up and start again, is such a machine going to turn the gravitational potential energy into electrical current?

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  • $\begingroup$ Yes, until you run out of sand dunes, because this machine uses up the sand dunes and makes them flat. $\endgroup$ – user253751 Mar 6 '19 at 1:07
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It's a cute concept, but rather impractical. Yes, you could convert the sand's potential energy to electricity, but there are numerous technical difficulties and inefficiencies. Due to friction, it takes energy to scoop the sand into your box, and it takes some energy to move the box horizontally to the release point, and even the very best generators have losses so they cannot convert all of the potential energy to electrical energy.

This system is only renewable if you do it in a region of active sand dunes, that is, where the wind is rebuilding the dunes at least as fast as your dune machine is demolishing them. And that means there's a lot of wind blowing around a lot of sand. That's not a pleasant environment to work in, and the wind-blown sand will abrade your machinery, and have a tendency to bury it. And your machinery has to deal with the fact that when it wants to move this way, the wind may try to blow it that way. I wouldn't even try to build a standard design wind farm in such an area because there'd be so much wear and tear on the equipment.


But how much energy are we talking about here? Here are some very rough calculations that ignore friction and all the other practical difficulties. Assume each dune is an isoceles triangular prism of uniform density, so the the cross section through a series of dunes looks like this: /\/\/\. Seif dunes are approximately of this form.

Let the width of the base of each isoceles triangle equal $2b$, the height equal $H$, and the length of a dune equal $L$. For most of this analysis we can ignore $L$. Let the base angle of the triangle equal $\theta$, so $H = b \tan \theta$. The maximum value of $\theta$ that a given substance can be piled up is known as the angle of repose. For dry sand that's about 34°, real dunes will generally be much less steep than that, but let's be generous and use $\theta = 34$°.

If we completely flatten the dunes, our triangle of height $H$ and base $2b$ becomes a rectangle of height $h$ and base $2b$. The area is preserved (assuming we don't change the packing density of the sand), so $h = H / 2$. The change in potential energy is equal to the weight of the sand times $y$, the change in the height of the centre of mass. For the triangle the centre of mass is $H / 3$, for the rectangle it's $h / 2$, so $y = H/3 - H/4 = H/12$.

The volume of a dune is $bHL$, so its weight is $bHL\rho g$, where $\rho$ is the density, and $g$ the acceleration due to gravity. Hence the energy available from flattening a dune is

$$\begin{align}E & = LybH\rho g\\ & = LbH^2\rho g/12\\ E & = Lb^3\tan^2\theta \rho g/12\end{align}$$

According to the Coastal Engineering Manual dry dune sand density ranges from $\rho = 1610 kg/m^3$ for loose sand through to $\rho = 1760 kg/m^3$ for packed sand.

Letting $L=b=1$ metre and plugging these numbers, along with $g=9.81m/s^2$ and $\theta = 34$° into Google Calculator we get

Loose: 598.809267 joules
Packed: 654.59895 joules

So if our dunes have a base of $2b = 20$ metres, and hence a height of $\approx 6.75$ metres, if we can flatten $L=1$ metre of dune per second, then we get around 600 kilowatts of power. But of course, then we have to take all of the losses due to friction etc into account. The real available power would be far less. By way of comparison, a typical modern wind turbine has a generating capacity of 1.5 megawatts.

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To be renewable you need to keep renewing the source of the sand at the top.

That is, the sand has to somehow return to the top. That won't work (as it requires at least as much energy as the fall generated). If you don't do that you need to fetch sand from further and further away and sooner or later that will cost more energy than it generates.

Note that if you compare this to a water wheel you see that the water wheel relies on the environment to circulate water by evaporation and rainfall which is the "free renewable" part of how a water wheel works.

Your system has the additional problem that the sand will pile up. If you never move it (which costs energy) it will reduce the amount of energy gained by the fall until such time as the fall is zero height.

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    $\begingroup$ I'd say the environment also creates the dune in the first place and will do it again if the conditions remain. A bid disadvantage of the setup is the time scale involved in the dune buildup. $\endgroup$ – stafusa Aug 6 '18 at 8:39
  • $\begingroup$ @stafusa The problem with that is the environment may move the sand, but it won't naturally move sand to the place you want (or need). It's relatively easy to control the flow of water from a river or stream (e.g. you can divert it for a low one-off cost) but you can't do anything like this with a dune. It's where it is and where the sand is ultimately deposited is more random - you may get a "replacement" dune, but it could be anywhere. $\endgroup$ – StephenG Aug 6 '18 at 14:38
  • $\begingroup$ Yes, at least in general you're right, but I wonder if there are some dunes that would be rebuilt in the same place if excavated due to the local geographical configuration. $\endgroup$ – stafusa Aug 6 '18 at 14:42
  • $\begingroup$ @stafusa From an engineering point of view if there was enough energy (=wind) to move enough sand around consistently, we could just build a wind-driven power generator in the first place. The kind of dune engineering you're describing implies we could create a very reliable wind system I think. $\endgroup$ – StephenG Aug 6 '18 at 14:49
  • $\begingroup$ Certainly. I have no hope OP's idea could be a good solution, I was just trying to find situations where it might be less unfeasible. $\endgroup$ – stafusa Aug 6 '18 at 14:51

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