An Electrical Analogue Model of Ice Ages

I got quite a strong response from the climate (sceptic) community for my Theory Of Ice Ages. Tallbloke reblogged my post on his blog.

But quite a few people were having trouble getting their heads round the idea of a system that oscillated between ice ages and interglacials. Like Peter Carter:

Are you telling me that if I half fill a polystyrene vessel with concrete, say, with a thermostatically controlled heating element embedded in it (the thermostat monitoring the element’s temperature to simulate the earth’s core being at a constant temperature), and then put a layer of water on top of it and stick it in a (thermostatically regulated?) freezer, I will see the ice periodically thawing out and then freezing? My gut expectation is that it would just reach an equilibrium, between ice thawed and frozen depending on the heating element temperature. What is the ‘magic’ that makes it oscillate?

Peter was trying to build a model, so that he could see how it might work. And I thought it was far too complicated. Something simpler and cheaper than that was needed.

Of course I’ve got my own model. It’s a computer simulation model in which I calculate heat flows through the Earth (and any ice on top of it) into the atmosphere. I wrote it myself a few weeks ago. I’m always constructing little dinky models of one thing or other that interests me. It’s almost a compulsion.

Maybe, when I’ve got it working a bit better, I’ll just publish the code, and allow people to run it themselves, and improve it or criticise it or refute it.

But it occurred to me late last night that there’s another way to build a heat flow model of ice ages, and it’s the way that people were doing it 40 years ago: build an electrical analogue model.

So I’m going to explain how this could be done with a few resistors and capacitors and a voltmeter.

First the basics. Heat flow is analogous to current flow. It also happens to be analogous to water flow (so I’ll try to explain how that works too). And if heat flow is analogous to current flow, then temperature is analogous to voltage, and temperature difference to potential difference, and thermal capacitance to electrical capacitance.

Right. That’s the theory. Now the practice. To build a simple heat flow model of the Earth you need a circuit board with a long chain of resistors with capacitors between the resistors.

One end of the chain of resistors represents the hot core of the Earth, and the other end represents outer space. Between the hot core of the Earth and outer space there will be, firstly, several resistors and large capacitors representing the solid Earth. And then secondly next to them there will be resistors and large capacitors represent a sheet of ice. And lastly there will be some big resistors and small capacitors representing the air in the atmosphere. In addition there’ll need to be a voltmeter that can read the voltages at any point along the chain of resistors. An oscilloscope would be better, and a storage oscilloscope better still.

Lastly, there will need to be a diode placed across the resistors that represent the ice. And the diode would need to be biased so that it only conducts when the voltage at it is whatever the voltage that represents 273ºK, the melting point of ice. So if the core of the Earth is at 10 V, and outer space is at ground, 273ºK would be represented by 2.73 V. And the idea behind this diode is that while the temperature of the ice is below 273ºK, current would flow through the resistor representing the ice, and when it was above 273ºK the current would flow through the diode, shorting out the resistors representing the ice. And this would simulate the presence of ice below 273ºK, and its absence above 273ºK.

When the model is run, and a 10V power supply or battery is connected, what should happen is that as the voltage at the ice rises slowly to 2.73V, the diode should short out the ice resistor, ‘melting’ the ice. And with one resistor in the chain now absent, the voltage at the surface of the ‘Earth’ should fall, and the current flow through it should increase. And when the voltage at the surface of the Earth falls back below 2.73V, the diode should cease conducting, and the ice resistor should become active again – at which point the current flow through the surface of the Earth should fall, and its voltage start to rise again. In this manner an oscillating system of ice ages alternating with interglacials could be simulated. It would probably take a bit of trial and error to arrange for the ice resistor to be near 2.73V, for if the Earth is too hot, the ice will never appear. And if it’s too cold, it will never melt.

There are probably other ways of simulating the arrival and departure of ice. The diode idea is mine, and maybe it’s unworkable. But I’m sure that any electronic engineer (I’m not one) would be able to arrange something that works.

After that, the model could be elaborated in all sorts of ways. Solar heating could be added at various points using current pumps (in my time I’ve made about 10 of them). The warming or cooling of the Earth could be simulated by applying a varying voltage to its core. It might be possible to simulate the deposition of ice by having a series of small resistors which can be added to simulate layers of ice deposition. The atmosphere could be made into a complex system that included clouds. And so on. The possibilities are endless.

All that’s needed to get going is a few resistors and capacitors and a circuit board to plug them into. It would cost next to nothing, apart from the voltmeter.

There are quite a few things online about such analogue models. Here’s one.

I may try to construct one myself. I don’t need it because I’ve got my own digital simulation model. And if I did construct one, I’d have to choose some appropriate scale factors. Back when I was working on this stuff 40 years ago, I seem to remember that we used a scale factor of 0.1 volts/degree, and a time scale factor of 1 second/day. But we were modelling buildings. For an ice age model, you’d probably need a scale factor of 1 second/century, and a scale factor of 0.01 volts/degree.

And the hydraulic model of heat flow? I did actually see one working once. It was a contraption with lots of glass tubes filled with coloured water, something like this:

Heat flow rate was water flow rate. Water height represented temperature. And I seem to remember the pipe diameters represented thermal capacitance. When it was in operation, and water was flowing out of it, the level of the water in the pipes would change to show a gradient along the chain of pipes. I think water probably had to be added to maintain the level in the water tank.

But I only saw it working once. And I also remember that the floor of the laboratory ended up covered in water.

About Frank Davis

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7 Responses to An Electrical Analogue Model of Ice Ages

  1. Peter Carter says:

    I’m still slightly dubious about how such a system could oscillate. I’m really going to have to think hard on this one! I have made a (simulated) circuit that oscillates using a single transistor, but that seems to be cheating…

  2. Mick Walker says:

    Too early in the morning for a serious comment from me, yet!

    But the essence of an oscillator is negative feedback and a delay, and probably some gain (transistor or op-amp needed?)

    But yes, there’s nothing unusual about oscillating systems.
    In fact it can be quite hard to achieve a desired equilibrium rather than oscillation. (I repair industrial control systems)

  3. sackersonwp says:

    When the ice has recently melted there will be (I suppose) much more water vapour in the atmosphere so more of a greenhouse effect storing heat from solar radiation and from the hot rock; it will take a while for the heat to be dissipated, then more snow formation?

    You’re doing interesting work here. I wondered about listing all possible heating/cooling factors a long while ago but I haven’t the science.

  4. Peter Carter says:

    What is the difference between ‘delay’, and a ‘phase shifter’ circuit such as might be built from R and C?

    A true delay line allows an ‘impulse’ to be set off through it such that *nothing* emerges at the output until after the allotted time, and sending out another impulse but this time negative while the original is still in the delay line would have no effect on the original impulse.

    The output of an RC circuit on the other hand begins to change *immediately* when an impulse is fed into it. In this sense it is not really a genuine delay line..?

    Is heat travelling through rock an example of a delay line, or more akin to the RC circuit? I can see that oscillation might be achieved with a genuine delay, but not so easy without some gain in the circuit in the case of the phase shifter.

  5. Smoking Lamp says:

    O/T Looks like they are getting ready to move on imposing an outdoor smoking ban for outdoor areas of bars and pubs in Ireland. Check out “Poll: Should smoking be banned in outdoor areas where people are eating?”

    • Rose says:

      Amongst the usual wall of antismoking noise, there are a couple of interesting comments.

      “I smoked for 30 odd years, never around my children though, and always tried to be considerate to non smokers, I was fit, healthy enough, no cough and lungs were clear on X-rays etc. However as time went on I became more worried about my future health, (I never got flu or colds) I stopped with aid of vaping, 4 years on I have put on over weight, I have diabetes, osteoparenia , and just after getting over my second flu this year, I am on 12 tablets a day just to keep going. I wish I had never given up smoking somedays. A doctor recently told me that what happened was my immune system basically collapsed ( I pick up everything ) after stopping smoking, and that while going back on them now would do more harm than good , stopping so abruptly sent my immune system into shutdown, and my energy just drained. Moral of story? If you a long term smoking seek medical advice before stopping and on best ways to stop without putting your health at risk”

      @dec dunne:
      “I have some sympathy with your experience. I am a reformed smoker for the last 3 years. Since giving them up I have been hopitalised 3 times, once with viral pneumonia. I have put on 15 Kgs, damaged both hips requiring an urgent replacement of one, recently diagnosed as a type 2 diabetic etc. However I feel so much better, no smelly clothes or awful unpleasant car etc. Be warned however, I gave up smoking in October 1981 and after 22 years went back on them again. Unfortunately you are an addict for the rest of your life and it is important never to forget that.”

      I wonder which of the missing bits caused their health to collapse after quitting smoking. I have read about the systemic inflammation that sets in but there are several possible candidates, not least the tiny amount of inhaled carbon monoxide that comes with every cigarette.

      Harvard and U. Pittsburgh researchers explain carbon monoxide’s anti-inflammatory effects
      “Specifically, mitochondria react to low levels of carbon monoxide by releasing chemical signals that reduce or shut down the body’s inflammatory response, raising the possibility for the development of new anti-inflammatory therapies, one of which may be low levels of inhaled carbon monoxide.”

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