Heat Transport: What I Wrote So Far.

Don’t worry, The Subversive Elkement will publish the usual silly summer posting soon! Now am just tying up loose ends.

In the next months I will keep writing about heat transport: Detailed simulations versus maverick’s rules of thumb, numerical solutions versus insights from the few things you can solve analytically, and applications to our heat pump system.

So I checked what I have already written – and I discovered a series which does not show up as such in various lists, tags, categories:

[2014-12-14] Cistern-Based Heat Pump – Research Done in 1993 in Iowa. Pioneering work, but the authors dismissed a solar collector for economic reasons. They used a steady-state estimate of the heat flow from ground to the tank, and did not test the setup in winter.

Cistern-Based Water-Source Heat Pump System Design, 1993[2015-01-28] More Ice? Exploring Spacetime of Climate and Weather. A simplified simulation based on historical weather data – only using daily averages. Focus: Estimate of the maximum volume of ice per season, demonstration of yearly variations. As explained later (2017) in more detail I had to use information from detailed simulations though – to calculate the energy harvested by the collector correctly in such a simple model.

Simple simulations of volume of ice[2015-04-01] Ice Storage Challenge: High Score! Our heat pump created an ice cube of about 15m3 because we had turned the collector off. About 10m3 of water remained unfrozen, most likely when / because the ice cube touched ground. Some qualitative discussions of heat transport phenomena involved and of relevant thermal parameters.

Ice formation during the 'ice storage challenge'[2016-01-07] How Does It Work? (The Heat Pump System, That Is) Our system, in a slide-show of operating statuses throughput a typical year. For each period typical temperatures are given and the ‘typical’ direction of heat flow.

System in September - typical operations conditions[2016-01-22] Temperature Waves and Geothermal Energy. ‘Geothermal’ energy used by heat pumps is mainly stored solar energy. A simple model: The temperature at the surface of the earth varies sinusoidally throughout the year – this the boundary condition for the heat equation. This differential equation links the temporal change of temperature to its spatial variation. I solve the equation, show some figures, and check how results compare to the thermal diffusivity of ground obtained from measurements.

Measured 'wave' and propagation time[2016-03-01] Rowboats, Laser Pulses, and Heat Energy (Boring Title: Dimensional Analysis). Re-visiting heat transport and heat diffusion length, this time only analyzing dimensional relationships. By looking at the heat equation (without the need to solve it) a characteristic length can be calculated: ‘How far does heat get in a certain time?’

Temperature waves in ground - attenuation length of about 10 meters[2017-02-05] Earth, Air, Water, and Ice. Data analysis of the heating season 2014/15 (when we turned off the solar/air collector to simulate a harsher winter) – and an attempt to show energy storages, heat exchangers, and heat flows in one schematic. From the net energy ‘in the tank’ the contribution of ground can be calculated.

Energy storage, heat exchangers, heat flow[2017-02-22] Ice Storage Hierarchy of Needs. Continued from the previous post – bird’s eye view: How much energy comes from which sources, and which input parameters are critical? I try to answer when and if simple energy accounting makes sense in comparison to detailed simulations.

Hierarchy of needs - ambient energy in ice months[2017-05-02] Simulating Peak Ice. I compare measurements of the level in the tank with simulations of the evolution of the volume of ice. Simulations (1-minute intervals) comprise a model of the control logic, the varying performance factor of the heat pump, heat transport in ground, energy balances for the hot and cold tanks, and the heat exchangers connected in series.

Simulations of brine and tank temperature and volume of ice, based on system state in 1-minute intervals.(Adding the following after having published this post. However, there is no guarantee I will update this post forever ;-))

[2017-08-17] Simulations: Levels of Consciousness. Bird’s Eye View: How does simulating heat transport fit into my big picture of simulating the heat pump system or buildings or heating systems in general? I consider it part of the ‘physics’ layer of a hierarchy of levels.

Simulation - levels of consciousnessPlanned episodes? Later this year (2017) or next year I might write about the error made when considering simplified geometry – like modeling a linear 1D flow when the actualy symmetry is e.g. spherical.

Grim Reaper Does a Back-of-the-Envelope Calculation

I have a secondary super-villain identity. People on Google+ called me:
Elke the Ripper or Master of the Scythe.

elkement-reaper[FAQ] No, I don’t lost a bet. We don’t have a lawn-mower by choice. Yes, we tried the alternatives including a reel lawn-mower. Yes, I really enjoy doing this.

It is utterly exhausting – there is no other outdoor activity in summer that leaves me with the feeling of really having achieved something!

So I was curious if Grim Reaper the Physicist can express this level of exhaustion in numbers.

Just holding a scythe with arms stretched out would not count as ‘work’. Yet I believe that in this case it is the acceleration required to bring the scythe to proper speed that matters; so I will focus on work in terms of physics.

In order to keep this simple, I assume that the weight of the scythe is a few kilos (say: 5kg) concentrated at the end of a weightless pole of 1,5m length. All the kinetic energy is concentrated in this ‘point mass’.

But how fast does a blade need to move in order to cut grass? Or from experience: How fast do I move the scythe?

One sweep with the scythe takes a fraction of second – probably 0,5s. The blade traverses an arc of about 2m.

Thus the average speed is: 2m / 0,5s = 4m/s

However, using this speed in further calculations does not make much sense: The scythe has two handles that allow for exerting a torque – the energy goes into acceleration of the scythe.

If an object with mass m is accelerated from a velocity of zero to a peak velocity vmax the kinetic energy acquired is calculated from the maximum velocity: m vmax2 / 2. How exactly the velocity has changed with time does not matter – this is just conservation of energy.

But what is the peak velocity?

For comparison: How fast do lawn-mower blades spin?

This page says: at 3600 revolutions per minute when not under load, dropping to about 3000 when under load. How fast would I have to move the scythe to achieve the same?

Velocity of a rotating body is angular velocity times radius. Angular velocity is 2Pi – a full circle – times the frequency, that is revolutions per time. The radius is the length of the pole that I use as a simplified model.

So the scythe on par with a lawn-mower would need to move at:
2Pi * (3000 rev./minute) / (60 seconds/minute) * 1,5m = 471m/s

This would result in the following energy per arc swept. I use only SI units, so the resulting energy is in Joule:

Energy needed to accelerate to 314m/s: 5kg * (471m/s)2 / 2 = 555.000J = 555kJ

I am assuming that this energy is just consumed (dissipated) to cut the grass; the grass brings the scythe to halt, and it is decelerated to 0m/s again.

Using your typIcal food-related units:
1 kilocalorie is 4,18kJ, so this amounts to about 133kcal (!!)

That sounds way too much already: Googling typical energy consumptions for various activities I learn that easy work in the garden needs about 100-150kcal kilocalories per half an hour!

If scything were that ‘efficient’ I would put into practice what we always joke about: Offer outdoor management trainings to stressed out IT managers who want to connect with their true selves again through hard work and/or work-out most efficiently. So they would pay us for the option to scythe our grass.

But before I crank down the hypothetical velocity again, I calculate the energy demand per half an hour:

I feel exhausted after half an hour of scything. I pause a few seconds before the next – say 10s – on average. In reality it is probably more like:

scythe…1s…scythe…1s…scythe…1s….scythe…1s….scythe…longer break, gasping for air, sharpen the scythe.

I assume a break of 9,5s on average to make the calculation simpler. So this is 1 arc swept per 10 seconds, 6 arcs per minute, and 180 per half an hour. After half on hour I need to take longer break.

So using that lawn-mower-style speed this would result in:

Energy per half an hour if I were a lawn-mower: 133kJcal * 180 = 23.940kcal

… about five times the daily energy demands of a human being!

Velocity enters the equation quadratically. Assuming now that my peak scything speed is really only a tenth of the speed of a lawn-mower, 47m/2, which is still about 10 times my average speed calculated the beginning, this would result in one hundredth the energy.

A bit more realistic energy per half an hour of scything is then: 239kcal

Just for comparison – to get a feeling for those numbers: Average acceleration is maximum velocity over time. Thus 47m/s would result in:

Average acceleration: (47m/s) / (0,5s)  =  94m/s2

A fast car accelerates to 100km/h within 3 seconds, at (100/3,6)m/s / 3s = 9m/s2

So my assumed scythe’s acceleration is about 10 times a Ferrari’s!

Now I would need a high-speed camera, determine speed exactly and find a way to calculate actual energy needed for cutting.

Is there some conclusion?

This was just playful guesswork but the general line of reasoning and cross-checking orders of magnitude outlined here is not much different from when I try to get my simulations of our heat pump system right – based on unknown parameters, such as the effect of radiation, the heat conduction of ground, and the impact of convection in the water tank. The art is not so much in gettting numbers exactly right but in determining which parameters matter at all and how sensitive the solution is to a variation of those. In this case it would be crucial to determine peak speed more exactly.

In physics you can say the same thing in different ways – choosing one way over the other can make the problem less complex. As in this case, using total energy is often easier than trying to figure out the evolution of forces or torques with time.

results-achieved-by-scythe-masterThe two images above were taken in early spring – when the ‘lawn’ / meadow was actually still growing significantly. Since we do not water it relentless Pannonian sun already started to turn it into a mixture of green and brown patches.

This is how the lawn looks now, one week after latest scything. This is not intended to be beautiful – I wanted to add a realistic picture as I had been asked about the ‘quality’ compared to a lawn-mower. Result: Good enough for me!

Scything: One week after


Theory and Practice of Trying to Combine Physics with Anything

You have told me, you miss my physics posts. I have missed them, too, and I give it a try. But I cannot help turning this into a cross-over again, smashing together half-digested psychology, physics, IT networking, and badly hidden autobiographical anecdotes.

In 2005 I did research on the incorporation of physics-style thinking and mathematical models into non-science disciplines. Actually, it was a small contribution to an interdisciplinary research project, and I have / should have covered science-y ideas related to how revolutionary new ideas percolate society.

In retrospect, my resulting (German) paper was something in between science writing, thorough research including differential equations in detail – and some bold assumptions, partly inspired by popular science, cliché and science fiction. Probably like my posts, but more long-winded and minus the very obvious rants.

I built on my work in laser-materials processing, superconductivity, phase transitions, and I tried to relate chaos in thermodynamic systems and instabilities in fluids with related non-predictable diffusion of ideas.


Simulation of Rayleigh-Taylor instabilities at the interface of fluids with different densities. You could probably test this with Caffe Latte.

I learned that there is a discipline called Networking Theory:

Many networked structures obey very similar rules. Networks of WWW hyperlinks, citations scientific papers, food chains, and airline networks are called scale-free networks, because the distribution function for the number of links follows a power law.

A small number of nodes has a high number of connections and the structure the networks appears the same on every scale applied – it is self-similar. The power law is only valid for ever growing networks.

Barabasi Albert 1000nodes

Network following a power-law distribution of connections. The backbone of the network is established by a few strong, well-connected nodes, and the vast majority of nodes has only a few connections.

The dynamics of such networks could be modeled using the same math as esoteric Bose-Einstein condensation, which allowed me to combine anything and relate networks and the quantum phenomena in superconductors.

But the basic idea is really simply: The more popular nodes attract more links. This is a winner-take-all model.

Companies have started monetizing network research by analyzing and modelling hidden structures and unveiling the the fabric underlying politics and economy.

Re-visiting that old article of mine I spot an application of physics in something-else-dynamics I have missed: One of the classical non-academic jobs for a (theoretical) physicist is Wall Street quantitative analyst or quant. Quants apply models taken from thermodynamics, such as diffusion in supernovas, to the finance world.

I would put The Physics of Wall Street – A Brief History of Predicting the Unpredictable on my Books-to-Read List if it would be available on Kindle, as I enjoyed this review:

The author, James Owen Weatherall is

an assistant professor of logic and philosophy of science at the University of California, Irvine, has two Ph.D.’s — one in physics and mathematics, and one in philosophy.

The book gives an overview of different models that resemble physics or are borrowed from physics – such as the Black-Scholes model that uses Brownian motion to model the dynamic development of prices of derivative financial products. Don’t ask me for details – I am just dropping keywords here.

The book seems to be based on optimistic assumptions:

Weatherall wants a new Manhattan Project to determine what’s wrong with economics, and he thinks it should be based in no small part on the contributions of physics-oriented economists, some of whom he believes have been treated unfairly by the establishment.

Here it is getting very interesting:

He has little use for Nassim Taleb, whose best-­selling book “The Black Swan” argues that the models used by traders disastrously underestimated the possibility of very negative outcomes — the black swans. To say that a model failed, Weatherall contends, is not to say that no models can work. “We use mathematical models cut from the same cloth to build bridges and to design airplane engines, to plan the electric grid and to launch spacecraft,” 

… as I am currently reading Nassim Taleb’s The Black Swan

In my outdated review article I finally came to the conclusion that some aspects of seemingly complicated systems – including those based on human beings – can be modeled using models of a baffling simplicity in relation to the alleged complexity of human nature. I am not ashamed of pointing out this glaring contradiction with my recent posts on gamification.

I would hailed Weatherall’s book and thanked him for contributing to my confirmation bias.

But Taleb speaks to me – in particular his chapter about Ludic Fallacy.

I do enjoy the clichéd characters of Fat Tony, the intuitive deal maker who hacks the real world, versus Dr. John, the nerdy engineering PhD who is fond of building mathematical models.

Taleb says:

Have you ever wondered why so many of these straight-A students end up going nowhere in life while someone who lagged behind is now getting the shekels, buying the diamonds, and getting his phone calls returned? Or even getting the Nobel Prize in a real discipline (say, medicine)

I took all my self-irony pills in order to recover. How could I not remember my indulgence in this diagram proving the braininess / nerdiness of physicists (and philosophers) – and my straight As of course. Did I mention that I am not a high-powered executive today or an accomplished professor? So it is Dr. Jane speaking here.

How could I not remember those enlightening anecdotes in David Goleman’s pop-psychology bestseller on EQ – emotional intelligence, first published in 1996. I enjoyed the story of two equally gifted students of mathematics, one becoming a rock star scientist, the other one becoming a mere computer consultant. I have read this book in German, so I will not give you a verbatim quote translated back to English. Actually, Goleman said something like: He pretended / claimed to be happy as a computer consultant. It says a more about me than about Goleman that I can quote this from memory without touching the book. I could say a lot of things about the notion of pretense here, but I will not repeat my most recent loosely related rant.

Goleman and Taleb both agree on the overarching role of intuition, thinking outside-the-box, gut feeling or whatever you call this. Luckily, Taleb is not concerned so much with proving which part of the brain is responsible for what because this is the part of pop-psy books I find incredibly boring. Nobody in his right mind would disagree (with the fact that interpersonal skills are important, not with my judgement of pop-psy books).

Even I tend so say, my modest successes in Mediocristan are largely due to my social skills whereas technical skills are needed to meet the minimum bar. Mediocristan is Taleb’s world of achievements limited by natural boundaries, such as: You will not get rich by being paid on time and material. You might get rich in Extremistan, as a best selling author or musician, but you have to deal with the extremely low probability of such a Black Swan of a success.

I am trying my hands at Occam’s Razor now and attempt to sort out this contradictions.

I believe that mathematical models of society make sense, and I do so without having read more propaganda by econo-physicists. I do so even if I will go on ranting about physicists that went into finance and caused a global crisis, because they just wanted to play with nice physics (as we said at the university) – ignoring that there is more at stake than your next research grant or paper.

Models of society and networks make sense if and only if we try to determine a gross statistical property of an enormous system. This is perfect science based on numbers that are only defined in terms of statistics – such as temperature in thermodynamics.

Malcom Gladwell is a master story teller in providing some convincing examples that proves that sometimes it only context that matters and that turns us into automata. For example subjects – who were not informed about the experimental setup – were inquired about their ethical standards. Would you help the poor? Of course they would. Then the experimental (gamified!) setup urged the subjects to hurry to another location, under some pretext. On their way, they were confronted with (fake) poor persons in need. The majority of persons did not help the poor, not missing the next fake meeting was the top priority. Gladwell’s conclusion is that context very often matters more – and in a simple and predictable – than all our sophisticated ethical constructs.

This is probably similar to our predictability as social networking animals, that is: clicking, liking and sharing automata.

People in a stadium clapping their hands will synchronize, in a way similar to fireflies synchronizing their blinking. You can build very simple models and demonstrate them using electrically connected light bulbs equipped with trigger logics – and those bulbs will synchronize after a few cycles.

Enthusiasm ends here.

I believe that using and validating those reliable models we learn something about society that is not exactly ground-breaking.

We can model the winner-take-all behavior of successful blogs to whom all the readers gravitate by Bose-Einstein condensation. But so what? What exactly did science tell us that we did not know before and considered trivial everyday wisdom?

In particular, we learn nothing that would help us, as individual nodes in these networks, to cope with the randomness we are exposed to if we aimed at success in Extremistan.

Mr. Taleb, keep preaching on!

However, I still need to wrap my head around the synthesis of:

  • not falling for the narrative fallacy, denarrating, and ignoring TV and blogs.
  • but yet: focusing on the control of my decisions and trying to grasp the abstract concepts of probability in every moment.
Black Swan

Black Swan (Wikimedia). I wanted to embed an image of Nathalie Portman in Black Swan ballet dancer’s costume, but I did not find a public domain image quickly, and I am not bold enough to do so without cross-checking copyright issues.


Further reading – two related popular science books I had enjoyed in 2005:
Linked: The New Science Of Networks
The Tipping Point: How Little Things Can Make a Big Difference