Archive for the ‘Uncategorized’ Category

Christmas Bubbles

December 23, 2018
Champagne Time Lapse

A time-lapse photograph of a glass of fizzy wine.

Recently I encountered the fantastic:

Effervescence in champagne and sparkling wines:
From grape harvest to bubble rise

This is a 115-page review article by Gérard Liger-Belair about bubbles in Champagne, my most favourite type of carbon dioxide emission.

Until January 30th 2019 it is freely downloadable using this link

Since the bubbles in champagne arguably add £10 to the price of a bottle of wine, I guess it is worth understanding exactly how that value is added.

I found GLB’s paper fascinating with a delightful attention to detail. From amongst the arcane studies in the paper, here are three things I learned.

Thing 1: Amount of Gas

Champagne (and Prosecco and Cava) have about 9 grams of carbon dioxide in each 750 ml bottle [1].

Since the molar mass of carbon dioxide is 44 g, each bottle contains approximately 9/44 ~ 0.2 moles of carbon dioxide.

If released as gas at atmospheric pressure and 10 °C, it would have a volume of approximately 4.75 litres – more than six times the volume of the bottle!

This large volume of gas is said to be “dissolved” in the wine. The molecules can only leave when, by chance, they encounter the free surface of the wine.

Because the free-surface area of wine in a wine glass is usually larger than the combined surface area of bubbles, about 80% of the de-gassing happens through the liquid surface [2].

Thing 2: Bubble Size and Speed 

But fizzy wine is call “fizzy” because of the bubbles that seem to ceaselessly form on the inner surface of the glass.

Sadly, in a perfectly clean glass, such as one which has repeatedly been through a dishwasher, very few bubbles will form [3].

But if there are tiny cracks in the glass, or small specks of dust from, for example, a drying cloth, then these can trap tiny air bubbles and provide free-surfaces at which carbon dioxide can leave the liquid.

At first a bubble is just tens of nanometres in size, but it grows at a rate which depends upon the rate at which carbon dioxide enters the bubble.

As the bubble grows, its surface area increases allowing the rate at which carbon dioxide enters the bubble to increase.

Eventually the buoyancy of the bubble causes it to detach from its so-called ‘nucleation site’ (birthplace) and rise through the liquid.  This typically happens when bubbles are between 0.01 and 0.1 mm in diameter.

To such tiny bubbles, the wine is highly viscous, and at first the bubbles rise slowly. But as more carbon dioxide enters the bubble, the bubble grows [4] and its speed of rise increases. The rising speed is close to the so-called ‘Stokes’ terminal velocity. [5]

So when you look at a stream of bubbles you will see that at the bottom, the bubbles are small and close together and relatively slow-moving. As they rise through the glass, they grow, and their speed increases.

If you can bear to leave your glass undrunk for long enough, you should be able to see the rate of bubble formation slow as the carbon dioxide concentration falls.

This will be visible as an increase in the spacing of bubbles near the nucleation site of a rising ‘bubble train’.

Thing 3: Number of bubbles

Idle speculation often accompanies the consumption of fizzy wine.

And one common topic of speculation is the number of bubbles which can be formed in a gas of champagne [6]. We can now add to that speculation.

If a bubble has a typically diameter of approximately 1 mm as it reaches the surface, then each bubble will have a volume of approximately 0.5 cubic millimetres, or 0.000 5 millilitres.

So the 4.75 litres of carbon dioxide in a bottle could potentially form 4750/0.0005 = 9.5 million bubbles per bottle!

If a bottle is used for seven standard servings then there are potentially 1.3 million bubbles per glass.

In fact the number is generally smaller than this because as the concentration of carbon dioxide in the liquid falls, the rate of bubble formation falls also. And below approximately 4 grams of carbon dioxide per litre of wine, bubbles cease to form [7].

Thing 4: BONUS THING! Cork Speed

When the bottle is sealed there is a high pressure of carbon dioxide in the space above the wine. The pressure depends strongly on temperature [8], rising from approximately 5 atmospheres (500 kPa) if the bottle is opened at 10 °C to approximately 10 atmospheres (1 MPa) if the bottle is opened at 25 °C.

GLB uses high-speed photography to measure the velocity of exiting cork, and gets results which vary from around 10 metres second for a bottle at 4 °C to 14 metres per second for a bottle at 18 °C. [9]

I made my own measurements using my iPhone (see below) and the cork seems to move roughly 5 ± 2 cm in the 1/240th of a second between frames. So my estimate of the speed is about 12 ± 5 metres second, roughly in line GLB’s estimates

Why this matters

When we look at absolutely any phenomenon, there is a perspective from which that phenomenon – no matter how mundane or familiar – can appear profound and fascinating.

This paper has opened my eyes, and I will never look at a glass of Champagne again in quite the same way.

Wishing you happy experimentation over the Christmas break.

Santé!

References

[1] Page 8 Paragraph 2

[2] Page 85 Section 6.3

[3] Page 42 Section 5.2

[4] Page 78 Figure 59

[5] Page 77 Figure 58

[6] Page 84 Section 6.3 & Figure 66

[7] Page 64

[8] Page 10 Figure 3

[9] Page 24 Figure 16

What can we learn from The American President?

December 12, 2018

The American President

I love the American President. It’s a weakness of mine of which I am not proud. No. Not that one: the film.

The American President was an Oscar-nominated film made in 1995 starring Michael Douglas as the eponymous hero and Annette Bening as a lobbyist who comes to Washington to campaign for a 20% cut in US greenhouse gas emissions.

The film is unremarkable in many ways. But the fact that cutting greenhouse gas emissions was a mainstream idea 25 years ago (albeit in a light-hearted romantic comedy-drama) puts into perspective just how slowly political reality has changed.

Constant

During the period from the fictional 1995 American President to the present 2018 incumbent, one thing has remain constant: the science.

Since 1981, when James Hansen and colleagues wrote a landmark paper in Science, the complexity of our models of the Earth’s climate has increased dramatically.

And our understanding of the way our Climate System works has improved, increasing our confidence in future projections.

But the core science has barely changed. Indeed, it hasn’t changed that much since Svante Arrhenius’ insight back in 1896.

Climate Change: My part in its downfall

I have been speaking and writing about Climate Change since 2004 or so. I think I have spoken to a few thousand people directly, and I guess each web article has been read a few hundred times. So perhaps I have helped a little to ‘raise consciousness’.

But regular readers will have noticed that recently I haven’t written about Climate Change as often as I used to. The reason is that I am lost for words.

Back in 2004, (9 years the American President) I thought there was a genuine public education requirement. But now, I don’t believe any rational human on Earth seriously doubts the reality of Climate Change or its causes.

[But just in case: if there is a rational human out there who doubts the reality of Climate Change, please drop me a line: I am happy to discuss any questions you have.]

Political Science

I still believe that despite The American President (yes that one, not the film) and his supporters, humanity will act collectively and decisively on Climate Change. Eventually.

I expect this because ultimately I think we will collectively understand that the alternative is in nobody’s best interest.

The ‘Natural Sciences’ have identified the existence of Climate Change, worked out its causes, laid out clear paths for how to combat it, and estimated the consequences of inaction.

But the path to action involves what Charles Lane writing the Washington Post has called ‘Political Science’. He identified the impasse as arising from the fact that we are asking the rich world (us) to pay now to solve a problem which will (mainly) occur in the future.

  • If the spending is effective, then the worst aspects of Climate Change will be abated and that expenditure may then appear to be a waste – the disaster was averted!
  • But if it the spending is ineffective, then the worst aspects of Climate Change will be experienced anyway!

This (and many other difficulties) are real and they are readily exploited by people who are acting – frankly – in bad faith.

So I expect we will act, but too late to avoid bad consequences for communities world-wide. And the political path we will take to action is not at all clear to me.

Reasons to be hopeful

But there are plenty of reasons to be hopeful. Renewable energy alternatives to fossil fuels are now feasible in a large and growing number of sectors. And once the transition begins, I think it will move quickly.

The speed with which coal has been (and is is continuing to be) phased out in the UK has shocked and surprised me. You can check current grid generating mix at Gridwatch.

The chart below shows the last 12 months of generation on top and the previous 12 months below that. You can see that coal use has almost disappeared in summer and is now only used on the coldest darkest days.

This year UK Yearly generating mix

UK Yearly generating mix

UK Electricity Generating Mix for the last 12 months. Notice that coal generation – in black – is only significant for a few months of the year, and has declined this year (top) compared with last year (bottom)

Science is our greatest cause for hope.

Imagine if we were observing changes in climate and had no idea what was happening? We would be doomed to confusion and inaction. This has been the situation in which humanity has existed since the dawn of time.

But now, our collective scientific understanding  has allowed us quantify Climate Change, to discover its root cause, and to identify the practical steps we can take minimise the harm.

Humanity has never been in this position before. We have never previously known in advance the hand which nature will deal us.

So I see our inability to act collectively – as exemplified by the slowness of progress in the 23 years since the debut of the celluloid American President – as a temporary state.

I take hope from the fact that we when the political reality permits, science will guide us to the best available solution in the circumstances.

I just wish I could figure out what I can do to make that happen faster.

Links

On this site:

On Variable Variability

On IPCC web site

Refrigerators: Part#1

December 2, 2018

A month ago our refrigerator stopped working. A repair didn’t seem possible, so we headed to the shops to search for something as similar as possible to what we had just lost.

Thankfully, the snappily-named Bosch KGN33NW3AG fridge-freezer has proved to be entirely adequate.

Of course a new refrigerator requires testing (obviously) and an assessment of how close to specification it is performing. So…

How much energy should a fridge use?

Fridge Freezer Pictures

I made a ‘guess-timate’ by estimating the rate at which heat which would flow into the fridge. My thought was that this should be similar to rate at which the fridge would use energy.

[Aside: the actual calculation is tricky, but I’ll come back to it in a later post]

To estimate the heat flow into the fridge I measured the size of fridge and freezer compartments and the thickness of the insulation.

Then I calculated the area of each compartment that faced the room which I assumed to be at a nominal 20 °C.

Heat will constantly flow from the room, through the insulation, into the cold compartments and a simple rule (called Fourier’s Law) allows me to calculate the rate at which energy flows (watts).

I assumed that a perfect ‘heat pump’ – the scientific name for a refrigerator – would pump all this heat back out again, but would (unrealistically) not require any energy to operate.

By multiplying the rate of energy flowing into the refrigerator (in watts) by an amount of time (in seconds) I could work out how much energy (in joules) even a perfect refrigerator of this size must use.

I could then convert the energy used (in joules) into kilowatt-hours – the charging unit used by electricity companies – by dividing by 3.6 million (the product of 3600 seconds in an hour and 1000 watts in a kilowatt).

My calculations indicated that heat flows would be:

  • About 16.4 W into the refrigerator, amounting to around 144 kW-h over a year.
  • About 14.8 W into the freezer, amount to around 130 kW-h over a year.

So if the device were perfect, I calculated it would use 274 kW-h per year.

EU Label

The specification for the fridge says that it will use 290 kW-h per year, just 6% more energy than I estimated a perfect fridge would use. This indicates a fridge performing surprisingly well.

I assume that Bosch’s estimated consumption is realistic. So how wrong could my estimate be?

Well I assumed that the thermal insulation around the fridge had a thermal conductivity of 0.03 W/K/m – just three time greater than that of still air. This is exceptionally good insulation. But my estimate could easily be wrong by 10% or so if improved insulation had been used.

Opening the door.

Many people think that opening the door of the fridge will affect its energy consumption, but my calculations indicate that it is not really a very big problem.

I assumed that at worst, opening the door could replaces all the air in the fridge with room temperature air. If this were the case then:

  • opening the fridge door 10 times a day every day would use an additional 3.7 kW-h of energy per year which is just over 1% of the annual expected usage.
  • opening the freezer door once a day would use an additional 0.4 kW-h of energy per year which is much less than 1% of the annual consumption.

So my calculations indicate that as long as door is not left open for many minutes at time, perhaps by careless children tired of their parents nagging, then it will have relatively little effect on the energy consumption of the fridge.

Data

I logged data at four locations in the fridge/freezer over a day or so last weekend.

The figure below shows a composite view of the data from the top of the fridge and the freezer over a period from 7 p.m. on Saturday to 4:30 p.m. on Sunday.

Composite Data

I’ll analyse this data more in the next article, but here I will just note that the data show:

  • The basic cycle of the heat pump which switches on around once every 45 minutes.
  • The more rapid cycling of the air within the fridge – every 10 minutes or so.
  • The effect of leaving the door open.

It is pretty clear that when my son and his friend arrived home at approximately 5 a.m. on Sunday morning (!) they contrived to leave the door open for the best part of an hour!

Composite Data Close up

I thought this was impressive detective work on my part and it could well be the start of a new mode of behaviour analysis: Forensic Thermometry.

Perhaps I should propose °CSI Teddington. 😉

Anyway. More on the temperature and humidity data in the next article.

Mug Cooling: Visualising complexity with peanut butter

November 20, 2018

I hope you’ve enjoyed the last couple of articles (1, 2)  about mug cooling. I have enjoyed writing them, but I am having trouble stopping.

My problem in trying to finish this investigation is the sheer complexity of the physics involved in the cooling of beverages.

Complexity? Yes, mind-boggling complexity. In the liquid, the air, and the profoundly mysterious ‘boundary layer’ between them.

First there is the liquid.

When one looks at a cup of tea or coffee, its opacity hides the complexity of the flow patterns in the liquid.

But with different fluids, such as the mixture of Marmite™, Peanut Butter, and hot water shown in the movie at the top, the turgid flows become visible.

[ASIDE: Some might ask: “Michael, what made you think of mixing Marmite™, Peanut Butter, and hot water?”.  Sadly, the answer is confidential, but I urge readers: please: do try this at home, but please don’t blame me!]

These flows are driven by the convective instability of the liquid.

  • The hot liquid near the surface cools as its fast-moving molecules either evaporate or lose energy by colliding with the slower-moving air molecules.
  • As the liquid cools, its density increases until it begins to sink beneath the liquid layer below.
  • This lower layer is now lifted to the surface, cools, and then sinks in turn.
  • And so a circulating flow pattern can be established and sustained by a liquid cooling at a surface.

In the case of the  Marmite™  and Peanut Butter concoction in the movie above, matters are further complicated by oil from the peanut butter which appears to have formed a stable surface layer below which the convective flow takes place.

This roiling turmoil can also be measured quantitatively.

I repeated the cooling measurements from the previous articles, but this time I placed all four thermocouples close to the surface.

Thermocouples near the surface

Four thermocouples measuring the temperature close to the surface of hot water in an insulated mug.

Looking in detail at the data from just two of the thermocouples one can see apparently random heating and cooling events.

These temperature fluctuations are caused by rising and falling convecting liquid .

Slide 11

Then there is the air.

Analogous processes also occur in the air above the liquid. 

These are harder to visualise, but I have created a simulation of the process in the amazing (and free!) Energy2D application – more details at the end of this article.

Large Gif
Animated GIF made from selected frames of an Energy2D simulation of the  air cooling of a liquid in insulated mugs with a lid (left) and without (right).

In the simulationthe flow patterns in the air quickly develop a breathtaking fractal complexity that is completely familiar.

The simulation is not entirely realistic. It is only in two-dimensions, does not include the effects of evaporation, does not include convection in the ‘liquid’ (so it is more like a solid), and yet some how, when the data is exported, it looks qualitatively similar to that which I observed experimentally in a real 3-D mug!

Slide 10

Graph of data exported from the Energy 2D simulation showing the cooling of an insulated beverage cup with and without a lid.

 

Underlying the ‘simple’ beverage cooling curves are processes in both the liquid and the air which are at the limit of what can be realistically modelled.

And as we approach the interface between the liquid and the air and look in ever more detail, matters only get more complex.

At this apparently ‘static’ interface there are multiple dynamic processes:

  • The liquid is evaporating, cooling and convecting away from the surface.
  • Air molecules and liquid molecules are interacting strongly.
    • The air is dissolving in the liquid
    • The liquid is evaporating and re-condensing both as droplets in the air (steam) and back into the liquid.
  • The air is warming and convecting away from the surface.

And yet all we just notice is that our coffee is getting cold!

Energy 2D

Energy2D is a wonderful FREE application that carries out complex two-dimensional calculations based on real physics.

I have found it difficult to get exact numerical matches between simulations and real world situations, but the physics which the software simulates is deeply insightful.

I strongly recommend that you waste several hours playing with its example demonstrations.

 

Where have I been all this time?

October 26, 2018

It’s been almost two months since I last wrote an article for this blog. In the 10 years since I began writing here, that is the longest gap ever.

What’s up?

Broadly speaking, I have been very busy and very unhappy at work.

My unhappiness at work is nothing new. Regular readers may remember my article on ‘Coping by Counting‘ back in February 2017 where I extolled the virtue of counting down the time to retirement month-by-month.

Colleagues will know that I have been able to immediately tell them how many months, weeks  and days (and occasionally hours!) until my planned retirement date.

This technique really helped me through the last 20 months, but recently it became apparent that I would not last another 86 months and two weeks.

The only possibility seemed to be to resign, and a couple of weeks ago that is what I decided to do. But after talking with friends, family and colleagues, I was ‘talked down’ from this precipitous step and urged to look for alternatives.

So I have been negotiating to work part-time, and happily this seems to be achievable. This is due in no small part to my exceptionally kind line manager. So from January 2019 I will begin working three days a week. Hopefully this will be sustainable.

Perspective & Reflections

At the moment, this step feels like a humiliating defeat. Being unable to cope in a 21st Century working environment feels like a very personal failure. But I hope these feelings will fade.

Firstly, when I have told colleagues of my decision, they have reacted with a mixture of empathy and envy. They too are feeling the strain. So I have sense that it is not ‘just me’.

Secondly, looking at my career more broadly, in my 18 years at NPL I have managed to achieve a thing or two.

  • I was part of the team that made the second most accurate measurement of the Boltzmann constant ever.
  • I was part of the team that made the most accurate temperature measurements ever.
  • I have affected the lives of many people with my outreach work.
  • In 2009 I met the Queen and she gave me a medal!

And importantly I have managed to earn money, stay married, and bring up two children.

So from this wider perspective, reducing the amount of work I do and focusing more on writing and general pottering seems reasonable and not really a sign of defeat and failure.

So…

Over the next few months I will hand over (or drop) the responsibilities that  fitted into the previously normal 6/7 working days, and find a package of work projects that I can achieve in 3.00 working days.

  • Did you notice the decimal point?

This will require a change in perspective on my part. I will need to let  go of some projects which I have been holding onto in the hope that I would be able to find some time to move them forwards. This won’t be easy.

But on the other hand, the prospect of several days a week on which I have no agenda items whatsoever already feels exhilarating.

 

 

 

Error Bar: Update

April 17, 2018

Error Bar

Friends – I have found the author of the above image that I mentioned in my previous post

And I knew them all along! What are the chances of that!

The author is John Kennedy from the Meteorological Office who blogs under the pseudonym ‘diagram monkey’.

The story of the image’s creation can be found here.

It is based on a real similarly-named barthe Aero Bar in San Diego.

The Aero Club Bar

The Aero Club Bar, San Diego

The World of Diagram Monkey

John’s blog contains some wonderful resources.

Do check out his post to find out how he came close to a humiliating early death at the hands of an orange.

 

 

Factfullness

April 7, 2018

Factfullness

Back in December 2010 I wrote about Hans Rosling with a post titled:

Hans Rosling: You’re my hero

Sadly, Hans Rosling died in February 2017.

But aware of his imminent death, he worked with his son and daughter-in-law to write a book which captures some key elements of his world view, which he summarises as…

…Factfulness

The book has two strands that run through all the chapters.

  • The first strand is that we are tremendously ignorant about the world. Repeatedly he expresses his surprise at our levels of ignorance. And given our access to facts, he asks why we are not just randomly ignorant, but have views which are  systematically wrong. He suggests it is a kind of cognitive bias.
  • The second strand is that we can stop being ignorant if we want to. And with this aim, he and his son invented delightful ways to view developmental data.

I won’t try to precis the book, but as someone who experiences intense anxiety in everyday situations, I found the section “Statistics as Therapy” particularly affecting.

As one specific example I went to the download page of Gapminder and downloaded a Powerpoint file with a graph showing how extreme poverty in the world has changed over time.

Extreme Poverty

It is clear that collectively humanity has made truly astonishing progress in reducing the awfulness of crushing poverty. [The Powerpoint file and the web site includes links so you can chase the data sources and check them.]

Why do we not celebrate this fantastic achievement?

This graph tells a good news story compared with which any news story we have experienced in the last 10 years is irrelevant.

This is a story of an epochal and positive change in the world of which most people – including myself – are largely ignorant.

The idea that the world – while acknowledging all its faults and injustices – is dramatically better than it is has ever been, feels like a balm against the ‘news-ification’ of reality that we experience.

Hans Rosling’s Death

I leave you with a video which I find intensely moving.

It shows Hans, his son,and his daughter-in-law explaining why they wrote the book.

Somehow knowing that he is no longer with us feels like a very intense – and despite the fact that I never knew him, personal – loss.

 

Videos

The fact that I feel Hans Rosling’s death personally is probably a cognitive bias caused by his many engaging video appearances.

This page on the Gapminder website contains links to many of his best videos. I cannot recommend them strongly enough.

SI at the RI

February 23, 2018

 

MdeP at the RI

On Monday 16th October 2017 I gave a talk at about the International System of Units (the SI) at the Royal Institution (the RI) in London.

It wasn’t a great talk, but it was at the RI. And I stood where Michael Faraday stood!

The RI have now processed the video and produced an edited version: enjoy 🙂

The RI have tended to retain the video of me talking rather than showing the animated PowerPoint slides. If you would like the full multimedia experience, you can download the presentation using the link below.

On the day

I was nervous and arrived ridiculously early with a couple of glass Dewars containing triple point of water cells.

I waited outside the lecture theatre for Martin Davies from the RI to arrive.

When he arrived, he noticed the Dewars and without hesitation he turned to the wall and pointed out the painting above where I was standing, and said:

“What a coincidence: your standing by a picture of Sir James Dewar lecturing in this theatre!”

Henry Dewar at the RI

It’s hard to convey the historical significance of Royal Institution without sounding trite. So I won’t try.

But it is a special place for chemists and physicists alike, and I feel honoured to have even had the chance to stand on that spot.

================

Thanks to Chris Brookes and Martin Davies for a memorable day.

Why is it so hard to lose weight?

February 21, 2018

After several years of looking, I think I have finally found the answer.

So if people follow a calorie-controlled diet based on government guidelines, almost everyone will put on weight.

Let me explain…

Mifflin St Jeor

The minimal basal metabolic requirements (BMR) of a human being have been the subject of scientific study for more than a century.

The best estimate of our requirements are the Mifflin St Jeor (MSJ) Equations which state that the calorific requirements for men and women are given by:

Men:     BMR = 10 × [Weight in kg] + 6.25 × [Height in cm] – 5 × [Age in years] – 5

Women:     BMR = 10 × [Weight in kg] + 6.25 × [Height in cm] – 5 × [Age in years] – 161

This is the amount of food (expressed as kiloCalories (kCal) per day) required to maintain a given weight and do nothing else: no exercise at all.

A sedentary male lifestyle

The MSJ equations are generally multiplied by a factor to reflect the amount of physical activity one undertakes during the day. And there is considerable uncertainty about which factor applies to any particular individual!

The factor 1.2 is commonly chosen to represent a “sedentary lifestyle”. In a moment I’ll come back to whether this factor is justified or not.

But based on this factor, the blue line on the graph below shows how the actual calorific requirements of a man of my weight and height vary with age. The equivalent graph for women is shown in the next section.

Calories versus Age

The most striking thing about this graph is that the actual amount of calories I need to maintain my weight (1860 kCal/day) is 25% less than the government recommend (2500 kCal/day).

The difference is not a rounding error – it amounts to 640 kCal/day which is a reasonably-sized meal!

A man of my age living a sedentary lifestyle and following government guidelines would put on weight at a rate of several kilograms per year.

The second striking feature of the graph is reduction in calorific requirements with age. The slope of the graphs is 50 kCal/day per decade.

This means that if I was maintaining my weight in my forties, then unless I changed either my eating habits or my exercise habits, I would slowly begin to put on weight.

Eating 50 kCal/day too much amounts to putting on weight at around 2 kg per year.

Is the sedentary lifestyle factor 1.2 appropriate?

One way to assess whether the factor 1.2 applied to the MSJ equations is appropriate is to consider the calorific equivalent of some exercise.

For a man of my weight and height, running 1 kilometre uses up about 74 kCal.

So if I were to run 25 km per week, then this would allow me to eat about another 260 kCal/day and still maintain my weight. This is shown as the red line on the graph above.

Most people would consider running 25 km per week to be quite serious exercise. Comparing this amount of exercise to the work done in a sedentary day makes me think that the factor 1.2 is probably about right.

Women

The equivalent graph for women is shown below

Calories versus Age Women

It shows a similar disparity between government recommendations and actual metabolic requirements, but not quite as dramatically wrong as for men.

Government Guidelines

The reason I searched out the MSJ equations was because I know from experience that if I eat anything close to 2500 kCal per day I put on weight.

Calorific intake is notoriously difficult to estimate with an uncertainty better than about 10%,  but the MSJ figure of about 1860 kCal/day for a man of my age weight and height seems about right.

The UK Government guidelines are – frankly – nonsense, and given that the UK has something of a problem with obesity – not least with people of my age – it would seem a sensible first step to just get this simple factual message about right.

One important step would be to emphasise the reducing calorie requirements with age.

Government guides in the US such as this one are closer to reality, but if you want real information I recommend this helpful calculator.

Gravity: one more thing

January 28, 2018

I am a great admirer of James Clerk Maxwell.

And amongst his greatest achievements was the prediction that waves in electric and magnetic fields should travel at the speed of light.

He arrived at his prediction by considering the observed strength of static electric magnetic fields.

  • For example, studies had established the strength of the force from a given amount of electric charge at a given distance.
  • This electrical force was characterised by a constant called (for historical reasons) the permittivity of free space. It was given the symbol ε0 – the greek letter ‘epsilon’ with a subscript of zero. It was considered to represent in some way how ‘disturbed’ the space was around an electric charge.
  • Similarly, studies had established the strength of the magnetic force from a given electric current at a given distance.
  • This magnetic force was characterised by a constant called (for historical reasons) the permeability of free space. It was given the symbol μ0 – the greek letter ‘mu’ with a subscript of zero. It was considered to represent in some way how ‘disturbed’ the space was around an electric current.

Maxwell analysed these static experiments and predicted that there should be coupled waves in the electric and magnetic fields and that they would travel with a speed of:

image002

And when Maxwell calculated this number he arrived at a number very close to the previously measured speed of light.

He observed that this was unlikely to be a coincidence and concluded that light was a wave in the electromagnetic field.

I can still remember how I felt when – aged 19 – I followed Maxwell’s footsteps and ‘discovered’ this connection: I was gob-struck!

Other waves

This type of formula is typical of expressions for the speed of waves. For example, the speed of a wave on a stretched wire or string is given by:

image002

where T is the tension in the string and m is the mass per unit length of the string.  So a wave will travel quickly when the string is taut and low mass.

And in general we expect the speed of waves to reflect how the medium in which the waves travel responds to a disturbance.

Gravity waves

And that is why last years’ announcement (LIGO, Popular Report) that gravity waves travel at the speed of light is so profoundly important.

This discovery implies that there is a connection between:

  • electricity and magnetism – responsible for just about all the phenomena we experience around us – and…
  • gravity – which is associated with space and time and mass.

Alternatively, it could indicate a connection between them both and something else we don’t know about.

But the experimental fact of this connection astounds me as much if not more than the connection that Maxwell made.

And it makes me wonder just what he would have to say about the discovery.

Now I know this connection is not ‘new’: I can remember being told that gravity waves would travel at the speed of light many years ago.

But the discovery of the experimental fact of the speeds of light and gravity being equal seems to me to be more profound than the mere expectation that it should be so.

You can see more about the discovery in the LIGO video below

 


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