Archive for the ‘Simple Science’ Category

Hydraulic jumps in the kitchen

September 1, 2018

It has been a difficult summer for me.

Putting on the Royal Society Summer Science Exhibition was utterly exhausting, and even two months on, I have not been able to catch up on all the extra days and hours I worked. And I fell behind on every other project on which I am working.

So every day as I enter work I have to catch my breath, staunch my sense of panic, and force myself to stay calm as I begin another day of struggling through tiredness to avoid failure on all the projects on which I am way behind.

But earlier this week my colleague caught me staring at the water flowing down the sink in the kitchenette where we prepare tea.

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I was staring at a phenomenon I have been fascinated by since childhood – the way water falling from the tap onto the bottom of the kitchen sink forms a smooth flat circle for a few centimetres around where the water lands – and then forms a ‘wavy wall’ around this circle.

My colleague said to me: “It’s great isn’t it. It’s called a hydraulic jump“. Learning that this phenomenon had a name lifted my spirits enormously and made me more curious about what was going on.

So today (Saturday) I have wantonly avoided catching up with my weekly tide of failure, stupidly neglected to pack for my week long conference in Belfast starting tomorrow, and spent the afternoon playing at the kitchen sink. I have experienced transitory happiness.

Hydraulic jump

Naming a phenomenon is stage#1 of the process of understanding it. Knowing this name allowed me to read a number of  – frankly confusing – articles on the web.

But after reading and playing for a while I think I am now beginning to understand what makes the circle form. There are two parts to my understanding:

The first insight arises from comparing:

  • the flow speed of the water with,
  • the speed at which waves travel on the surface of the water.

Inside the circle, the flow is faster than the speed at which waves can travel in the water.  So surface disturbances are swept outwards – the waves are not fast enough to travel ‘upstream’, back towards the centre.

As one moves further away from the centre, the flow speed falls and at the edge of the circle, the flow speed is just equal to the speed of water waves. So water waves travelling back towards the centre of the circle appear stationary – this what makes the circle appear to be ‘fixed’ even though it is a dynamically created structure.

Outside the circle, the flow slows sufficiently that water waves can travel upstream (towards the middle) but they can never travel into ‘the circle’. (There is actually a scientific paper in which this circle is used as an analogy to the ‘Event Horizon’ in a putative ‘White hole’!)

Hydraulic Jump Illustration

The second insight, arises from considering turbulence.

Once waves can travel in both directions in the water, turbulence builds up which slows the speed of the flowing water dramatically.

So in the steady state, the depth of the water builds up suddenly and the ratio of the depth of water inside the circle to the depth outside the circle is simply the ratio of the speeds of water flow just outside and just inside the circle.

So if the speed of flow is 10 times slower outside the circle, then the water will be be 10 times deeper outside the circle.

In the picture above and the video below, you can see the very strikingly different nature of the liquid surfaces. Shallow and perfectly smooth within the circle, and deeper and turbulent outside the circle.

Experiments

I began playing by finding a better surface than the bottom of a sink. I used an upside down baking tray and adjusted it to be as level as I could manage.

img_7695

Not knowing what to do, I began by measuring the diameter of the circle formed for different flow rates:

  • I measured the diameter roughly with a ruler
  • I measured the flow rate by timing how long it took to fill a measuring jug which I weighed before and after filling.

This produced a pleasing graph, but no real insight. An increased flow rate meant made the circle larger because it took more time (and distance) for the flowing water to slow down to the speed of water waves.

Graph

Looking at the algebra, I realised I really needed to know the speed of the water and depth of the water. But how could I measure these things?

I tried estimating the speed of the water by injecting food colouring into the flow and making a movie using the slow-motion mode of my iPhone camera.

Knowing the circle was about 8.8 cm in diameter, this allowed me to estimate the speed of flow as roughly 1.5 ± 0.5 metres per second in the centre zone. However I couldn’t think how to estimate the thickness (height) of the flowing layer.

By sticking a needle in I could see that it was much less than 1 mm and appeared to be less than a tenth of the thickness of the water outside the circle. But I couldn’t make any meaningful measurements.

Then I realised that I could I estimate the speed of the water in a different way. If I placed a needle in the moving water, it produced an angular ‘shock wave’.

This is similar to way an aeroplane travelling faster than the speed of sound in air produces a ‘sonic boom’.

  • For an aeroplane, the angle of the shock wave with respect to the direction of motion is related to the ratio of the speed of the plane to the speed of the sound.
  • For our flowing water, the angle of the shock wave with respect to the direction of motion is related to the ratio of the speed of the water to the speed of the water waves.

Unfortunately the angle changes very rapidly as the ratio of flow speed to wave speed approaches unity and I found this phenomenon difficult to capture photographically.

Graph 2

But as the photographs below show, I could convince myself qualitatively that the angle was opening out as I placed the obstacle nearer the edge of the circle.

Hydraulic Jump Pictures

Observations of the shock wave formed when an obstruction is placed in the water flow. The top row of photographs shows the effect of moving the obstruction from near the centre to near the edge of the circle. The bottom row of photographs are the same as the top row but I have added dotted lines to show how the shock angle opens up nearer the edge of the circle.

Summary

  • My work remains undone.
  • I still have to pack in order to leave for the conference at 8:30 a.m. on Sunday morning: less than 8 hours away as I finish this. (Perhaps I will have a chance to complete some tasks at the airport or on Sunday evening?)
  • I have understood a little something about one more little thing in this beautiful world, and that has lifted my spirits. For now at least.

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Hot dry summers

August 10, 2018

Apparently its been hot all around the northern hemisphere this summer.

And that got me thinking about the long hot summer of 1976 when I was 16.

I have the general impression that summers now are warmer than they used to be. But I am aware that such impressions can be misleading.

Being the age I am (58), I fear my own mis-remembering of times past.

So was 1976 really exceptional? And will this year (2018) also prove to be really exceptional?

I decided to download some data and take a look.

Heathrow Data.

I popped over to the Met Office’s Climate pages and downloaded the historical data from the nearby Heathrow weather station.

I had downloaded this data before when looking at long-term climate trends, but this time I was looking for individual hot months rather than annual or decadal trends.

When I plotted the monthly average of the daily maximum temperature, I was surprised that 1976 didn’t stand out at all as an exceptional year.

Heathrow Monthly Climate Data July Maxima Analysis

The monthly average of the daily temperature maxima are plotted as black dots connected by grey lines. I have highlighted the data from July each year using red squares. Notice that since 1976 there have been many comparable July months.

In the graph above I have highlighted July average maximum temperatures. I tried similar analyses for June and August and the results were similar. 1976 stood out as a hot year, but not exceptionally so.

Ask an Expert

Puzzled, I turned to an expert. I sent an e-mail to John Kennedy at the UK’s Met Office  and to my astonishment he responded within a few hours.

His suggestion was to try plotting seasonal data.

His insight was based on the fact that it is not so unusual to have a single warm month. But it is unusual to have three warm months in a row.

So I re-plotted the data and this time I highlighted the average of daily maximum temperatures for June, July and August.

Heathrow Monthly Climate Data June July August Maxima Analysis

The monthly average of the daily temperature maxima are plotted as black dots connected by grey lines as in the previous figure. Here I have highlighted the seasonal average data (from June July and August) using red squares. Notice that 1976 now stands out as an exceptionally warm summer.

Delightfully, 1976 pops out as being an exceptional summer – in line with my adolescent recollection.

More than just being hot

But John suggested more. He suggested looking at the seasonal average of the minimum daily temperature.

Recall that in hot weather it is often the overnight warmth which is particularly oppressive.

In this graph (below) 1976 does not stand out as exceptional, but it is noticeable that warming trend is easily visible to the naked eye. On average summer, summer nights are about 2 °C warmer now than they were at the start of my lifetime.

Heathrow Monthly Climate Data JJA Minimum Analysis

The monthly average of the daily temperature minima are plotted as black dots connected by grey lines. Here I have highlighted the seasonal average data (from June July and August) using red squares. Notice that 1976 does not stand out exceptionally.

John also suggested that I look at other available data such as the averages of

  • daily hours of sunshine
  • daily rainfall

Once again seasonal averages of these quantities show 1976 to have been an exceptional year. Below I have plotted the Rainfall totals on two graphs, one showing the overall rainfall, and the other detail of the low rainfall summers.

Heathrow Monthly Monthly Rainfall

The monthly average of the daily rainfall total are plotted as black dots connected by grey lines. Here I have highlighted the seasonal average data (from June July and August) using red squares. Notice that 1976 was a dry summer. The data below 50 mm of rainfall are re-plotted in the next graph.

Heathrow Monthly Monthly Rainfall detail

Detail from the previous figure showing the low rainfall data. The monthly average of the daily rainfall total are plotted as black dots connected by grey lines. Here I have highlighted the seasonal average data (from June July and August) using red squares. Notice that 1976 was a dry summer.

de Podesta ‘Hot Summer’ Index

Following on from John’s suggestion, I devised the ‘de Podesta Long Hot Summer Index‘. I defined this to be:

  • the sum of the seasonal averages of the minimum and maximum temperatures (for June July and August),
  • divided by the seasonal average of rainfall (for June July and August).

Plotting this I was surprised to see 1976 pop out of the data as a truly exceptional hot dry summer – my memory had not deceived me.

But I also noticed 1995 ‘popped out’ too and I had no recollection of that being an exceptional summer. However this data (and Wikipedia) confirms that it was.

Now I just have to wait until the end of August to see if this year was exceptional too – it most surely felt exceptional, but we need to look at the data to see if our perceptions are genuinely grounded in reality.

Heathrow Hot Dry Summer Index

The de Podesta Hot Dry Summer (HDS) index as described in the text.  Construct an ‘index’ in this way really flags up the exceptional nature of 1976, and also 1995.

John Kennedy’s blog

In typical self-deprecating manner, John calls himself a ‘diagram monkey’ and blogs under that pseudonym. 

His is one of just two blogs to which I subscribe and I recommend it to you highly.

Talking about the SI

June 24, 2018

In just a few days, we will be setting up our stand about the International System of Units, the SI, at the Royal Society Summer Science Exhibition (RSSSE).

In May 2019 the world plans to redefine four of the base units of the SI. The re-definition represents a profound change in our concept of measurement.

And it involves quantities with which most people are familiar, such as ‘a kilogram’, or ‘a degree Celsius’.

So we have thought long and hard about how to communicate this at RSSSE.

Where to start?

The geographical theory of knowledge  suggests that ‘explanations of concepts’ are like ‘directions from one place to another’.

And thus, when people visit our stand, we are obliged to start giving ‘directions’ from where they actually ‘are’.

Although we want to talk about the re-definition of the SI, we have to acknowledge that most people don’t actually know much about the SI.

So if we want to ‘start from where people are’, we first need to explain what the SI is now, and why it matters. And that is what we have done.

It’s about Measurement.

In the ‘orientation’ for colleagues who will be helping at the RSSSE, we have stressed three starting points to help orient visitors to the stand.

  • At the heart of science and engineering, there is measurement.
  • Measurement is the comparison of an unknown thing against a standard.
  • In the International System of Units there are seven standard things against which all physical quantities are compared.

We then have seven hands-on demonstrations – one for each of the seven standard quantities (called ‘base units’)- which will hopefully serve as starting points for conversations.

Keep it simple!

In developing the ‘hands-on demonstrations we worked with the magical people at Science Projects to build apparatus that was robust and simple.

They have years of experience developing hands-on kit for museums and interactive science centres.

As we honed our initial ideas, Science Projects staff constantly challenged us to ‘keep it simple’. And in (almost) every case, their instincts were sound.

A demonstration which is engaging and which can be immediately grasped is a dramatically better starting point for a conversation than one which is beautifully sophisticated, but only elicits the Ah-yes,-I-see-now-moment after 5 minutes.

NPL Stands for the RSSSE exhibition

Stands for the RSSSE exhibition

NPL tweaks!

We developed the demonstrations and tried them out on NPL’s Open Day in May. The stands all survived and people seemed happy with the demonstrations.

But because we are NPL, and because at RSSSE we also need to interact with Fellows of the Royal Society, we had to add some truly complex and amazing features that are right at the forefront of science.

  • The ‘time team’ decided to develop an app that would allow people to compare the time on their own phones with the time from NPL’s Caesium atomic clock.
  • The ‘length team’ decided they wanted to develop a laser interferometer that would measure the height of SI-bots in terms of the wavelength of light.
  • The ‘mass team’ wanted to put an actual working Kibble balance on the stand at the Royal Society.

As I write this on Sunday 24th June, – none of these demonstrations are ready! But my colleagues are working hard and I am cautiously confident they will succeed.

If you get a chance to visit, the RSSSE is FREE and runs from Monday 2nd July 2018 until Sunday 9th July 2018.

 

 

 

Summer Science

May 26, 2018

Video Capture 2

For some months now I have been preparing for the Royal Society Summer Science Exhibition.

We have been working with the fabulous team at Science Projects on developing seven demonstration experiments – one for each of the seven SI base units.

Being so distracted, the deadline for submitting a video almost passed me by. In fact my colleague Andrew Hanson and I remembered with just one day to go!

So after a necessarily short planning phase, Andrew and I shot the video below on Andrew’s iPhone.

The background noise on some of the sections was problematic and Andrew had to do a great deal of filtering to get anything close to intelligible.

But given that everything was shot in’one take’, we were pretty happy with it, even if it came out a bit long (5’20”)

The end of the film was forced on us because my colleagues from the ‘length team’ were both absent when the end of the film was shot at about 7:30 p.m.!

After feedback from the team at the Royal Society we were asked to shorten the video and we took that opportunity to re-shoot the start and end of the movie with a proper microphone.

And here is the final shortened version (2’34”) which should be on the Royal Society site next week.

I hope you enjoy it.

Thanks 

Thanks to everyone who helped: Andrew Hanson, Brian Madzima, Rachel Godun, Stuart Davidson, Robin Underwood, Teresa Goodman, Lucy Culleton, Masaya Kataoka and Jonathan Fletcher

 

The James Webb Space Telescope

May 10, 2018

Last week I was on holiday in Southern California. Lucky me.

Lucky me indeed. During my visit I had – by extreme good fortune – the opportunity to meet with Jon Arenberg – former engineering director of the James Webb Space Telescope (JWST).

And by even more extreme good fortune I had the opportunity to speak with him while overlooking the JWST itself – held upright in a clean room at the Northrop Grumman campus in Redondo Beach, California.

[Sadly, photography was not allowed, so I will have to paint you a picture in words and use some stock images.]

The JWST

In case you don’t know, the JWST will be the successor to the Hubble Space Telescope (HST), and has been designed to exceed the operational performance of the HST in two key areas.

  • Firstly, it is designed to gather more light than the HST. This will allow the JWST to see very faint objects.
  • Secondly, it is designed to work better with infrared light than the HST. This will allow the JWST to see objects whose light has been extremely red-shifted from the visible.

A full-size model of the JWST is shown below and it is clear that the design is extraordinary, and at first sight, rather odd-looking. But the structure – and much else besides – is driven by these two requirements.

JWST and people

Requirement#1: Gather more light.

To gather more light, the main light-gathering mirror in the JWST is 6.5 metres across rather than just 2.5 metres in the HST. That means it gathers around 7 times more light than the HST and so can see fainter objects and produce sharper images.

1280px-JWST-HST-primary-mirrors.svg

Image courtesy of Wikipedia

But in order to launch a mirror this size from Earth on a rocket, it is necessary to use a  mirror which can be folded for launch. This is why the mirror is made in hexagonal segments.

To cope with the alignment requirements of a folding mirror, the mirror segments have actuators to enable fine-tuning of the shape of the mirror.

To reduce the weight of such a large mirror it had to be made of beryllium – a highly toxic metal which is difficult to machine. It is however 30% less dense than aluminium and also has a much lower coefficient of thermal expansion.

The ‘deployment’ or ‘unfolding’ sequence of the JWST is shown below.

Requirement#2: Improved imaging of infrared light.

The wavelength of visible light varies from roughly 0.000 4 mm for light which elicits the sensation we call violet, to 0.000 7 mm for light which elicits the sensation we call red.

Light with a wavelength longer than 0.000 7 mm does not elicit any visible sensation in humans and is called ‘infrared’ light.

Imaging so-called ‘near’ infrared light (with wavelengths from 0.000 7 mm to 0.005 mm) is relatively easy.

Hubble can ‘see’ at wavelengths as long as 0.002 5 mm. To achieve this, the detector in HST was cooled. But to work at longer wavelengths the entire telescope needs to be cold.

This is because every object emits infrared light and the amount of infrared light it emits is related to its temperature. So a warm telescope ‘glows’ and offers no chance to image dim infrared light from the edge of the universe!

The JWST is designed to ‘see’ at wavelengths as long as 0.029 mm – 10 times longer wavelengths than the HST – and that means that typically the telescope needs to be on the order of 10 times colder.

To cool the entire telescope requires a breathtaking – but logical – design. There were two parts to the solution.

  • The first part involved the design of the satellite itself.
  • The second part involved the positioning the satellite.

Cooling the telescope part#1: design

The telescope and detectors were separated from the rest of the satellite that contains elements such as the thrusters, cryo-coolers, data transmission equipment and solar cells. These parts need to be warm to operate correctly.

The telescope is separated from the ‘operational’ part of the satellite with a sun-shield roughly the size of tennis court. When shielded from the Sun, the telescope is exposed to the chilly universe, and cooled gas from the cryo-coolers cools some of the detectors to just a few degrees above absolute zero.

Cooling the telescope part#2: location

The HST is only 300 miles or so from Earth, and orbits every 97 minutes. It travels in-to and out-of full sunshine on each orbit. This type of orbit is not compatible with keeping a gigantic telescope cold.

So the second part of the cooling strategy is to position the JWST approximately 1 million miles from Earth at a location known as the second Lagrange point L2.

At L2 the gravitational attraction of the Sun is approximately 30 times greater than the gravitational attraction of the Earth and Moon.

At L2 the satellite orbits the Sun in a period of one year – and so stays in the same position relative to the Earth.

  • The advantage of orbiting at L2 is that the satellite can maintain the same orientation with respect to the Sun for long periods. And so the sun-shade can shield the telescope very effectively, allowing it to stay cool.
  • The disadvantage of orbiting at L2 is that it is beyond the orbit of the moon and no manned space-craft has ever travelled so far from Earth. So once launched, there is absolutely no possibility of a rescue mission.

The most expensive object on Earth?

I love the concept of the JWST. At an estimated cost of $8 billion, if this is not the most expensive single object on Earth, then I would be interested to know what is.

But it has not been created to make money or as an act of aggression.

Instead, it has been created to answer the simple question

I wonder what we would see if we looked into deep space at infrared wavelengths.”. 

Ultimately, we just don’t know until we look.

In a year or two, engineers will place the JWST on top of an Ariane rocket and fire it into space. And the most expensive object on Earth will then – hopefully – become the most expensive object in space.

Personally I find the mere existence of such an enterprise a bastion of hope in a world full of worry.

Thanks

Many thanks to Jon Arenberg  and Stephanie Sandor-Leahy for the opportunity to see this apogee of science and engineering.

Resources

Breathtaking photographs are available in galleries linked to from this page

 

Air Temperature

April 1, 2018

Recently, two disparate strands of my work produced publications within a week of each other.

Curiously they both concerned one of the commonest measurements made on Earth today – the measurement of air temperature.

  • One of the papers was the result of a humbling discovery I made last year concerning a common source of error in air temperature measurements. (Link to open access paper)
  • On the other  paper I was just one amongst 17 authors calling for the establishment of global reference network to monitor the climate. My guess is that most people imagine such a network already exists – but it doesn’t! (Link to open access paper)

I am writing this article because I was struck by the contrasting styles of these papers: one describing an arcane experimental detail; and the other proposing a global inter-governmental initiative.

And yet the aim of both papers was identical: to improve measurement so that we can more clearly see what is happening in the world.

Paper 1

In the middle of 2018 I was experimenting with a new device for measuring air temperature by measuring the speed of sound in air.

It’s an ingenious device, but it obviously needed to be checked. We had previously carried out tests inside environmental chambers, but the temperature stability and uniformity inside the chambers was not as good as we had hoped for.

So we decided to test the device in one of NPL’s dimensional laboratories. In these laboratories, there is a gentle, uniform flow of air from ceiling to floor, and the temperature is stable to within a hundredth of a degree Celsius (0.01 °C) indefinitely.

However, when I tried to measure the temperature of the air using conventional temperature sensors I got widely differing answers – varying by a quarter of a degree depending on where I placed the thermometer. I felt utterly depressed and humiliated.

Eventually I realised what the problem was. This involved stopping. Thinking carefully. And talking with colleagues. It was a classic case of eliminating the impossible leaving only the improbable.

After believing I understood the effect, I devised a simple experiment to test my understanding – a photograph of the apparatus is shown below.

tubes-in-a-lab-photo.png

The apparatus consisted of a set of stainless steel tubes held in a clamp stand. It was almost certainly the cheapest experiment I have ever conducted.

I placed the tubes in the laboratory, exposed to the downward air flow, and  left them for several hours to equilibrate with air.

Prior to this experience, I would have bet serious amounts of money on the ‘fact’ that all these tubes would be at the same temperature. My insight had led me to question this assumption.

And my insight was correct. Every one of the tubes was at a different temperature and none of them were at the temperature of the air! The temperature of the tubes depended on:

  • the brightness of the lights in the room – which was understandable but a larger effect than I expected, and
  • the diameter of the tubes – which was the truly surprising result.

Results 1

I was shocked. But although the reason for this is not obvious, it is also not complicated to understand.

When air flows air around a cylindrical (or spherical) sensor only a very small amount of air actually makes contact with the sensor.

Air reaching the sensor first is stopped (it ‘stagnates’ to use the jargon). At this point heat exchange is very effective. But this same air is then forced to flow around the sensor in a ‘boundary layer’ which effectively insulates the sensor from the rest of the air.

Air flow

For small sensors, the sensor acquires a temperature close to that of the air. But the air is surprisingly ineffective at changing the temperature of larger sensors.

The effect matters in two quite distinct realms.

Metrology

In metrology – the science of measurement – it transpires that knowledge of the temperature of the air is important for the most accurate length measurements.

This is because we measure the dimensions of objects in terms of the wavelength of light, and this wavelength is slightly affected by the temperature of the air through which the light passes.

In a dimensional laboratory such as the one illustrated below, the thermometer will indicate a temperature which is:

  • different from the temperature of artefacts placed in the room, and
  • different from the temperature of the air.

Laboratory

Unless the effect is accounted for – which it generally isn’t – then length measurements will be slightly incorrect.

Climatology

The effect is also important in climatology. If a sensor is changed in a meteorological station people check that the sensor is calibrated, but they rarely record its diameter.

If a calibrated sensor is replaced by another calibrated sensor with a different diameter, then there will be a systematic effect on the temperatures recorded by the station. Such effects won’t matter for weather forecasting, but they will matter for people using the stations for a climate record.

And that brings me to Paper 2

Paper 2

Hadcrut4 Global Temperature

When we see graphs of ‘global temperatures’ over time, many people assume that the data is derived from satellites or some ‘high-tech’ network of sensors. Not so.

The ‘surface’ temperature of the Earth is generally estimated in two quite distinct parts – sea surface temperature and land surface temperature. But both these terms are slight misnomers.

Considering just the land measurements, the actual temperature measured is the air temperature above the land surface. In the jargon, the measurement is called LSAT – the Land Surface Air Temperature.

LSAT is the temperature which human beings experience and satellites can’t measure it.

LSAT data is extracted from temperature measurements made in thousands of meteorological stations around the world. We have data records from some stations extending back for 150 years.

However, it is well known that data is less than ideal: it is biased and unrepresentative in many ways.

The effect described in Paper 1 is just one of many such biases which have been extensively studied. And scientists have devised many ways to check that the overall trend they have extracted – what we now call global warming – is real.

Nonetheless. It is slightly shocking that a global network of stations designed specifically with the aim of climate monitoring does not exist.

And that is what we were calling for in Paper 2. Such a climate network would consist of less than 200 stations world-wide and cost less than a modest satellite launch. But it would add confidence to the measurements extracted from meteorological stations.

Perhaps the most important reason for creating such a network is that we don’t know how meteorological technology will evolve over the coming century.

Over the last century, the technology has remained reasonably stable. But it is quite possible that the nature of data acquisition for meteorological applications will change  in ways we cannot anticipate.

It seems prudent to me that we establish a global climate reference network as soon as possible.

References

Paper 1

Air temperature sensors: dependence of radiative errors on sensor diameter in precision metrology and meteorology
Michael de Podesta, Stephanie Bell and Robin Underwood

Published 28 February 2018
Metrologia, Volume 55, Number 2 https://doi.org/10.1088/1681-7575/aaaa52

Paper 2

Towards a global land surface climate fiducial reference measurements network
P. W. Thorne, H. J. Diamond, B. Goodison , S. Harrigan , Z. Hausfather , N. B. Ingleby , P. D. Jones ,J. H. Lawrimore , D. H. Lister , A. Merlone , T. Oakley , M. Palecki , T. C. Peterson , M. de Podesta , C. Tassone ,  V. Venema, K. M. Willett

Published: 1 March 2018
Int. J. Climatol 2018;1–15. https://doi.org/10.1002/joc.5458

Mugging

February 18, 2018

IMG_6849

After writing about ‘singing glasses’ previously, I was discussing the effect with my friend and colleague Andrew Hanson.

Have you done the mug thing?” he asked. And proceeded to hit the rim of a mug with a spoon.

As he moved the location at which he struck the mug, the pitch of the note changed.

And then he explained. Looking from the top, if the handle of the mug is at 12 O’clock, then:

  • Striking the mug at 3, 6, 9, or 12 produces one note – a lower note.
  • Striking the mug between 1 & 2, between 4 & 5, between 7 & 8 and between 10 & 11 produced a second note – a higher note.

Mug Vibrations 01

Andrew said the explanation was that in a mug, there are two types of flexural oscillations, and the frequency of the oscillations depends on whether the handle moves or not.

I was fascinated. How had I never noticed that before? And why was the note that sounded when the mug was struck ‘on the quarter hours’ lower?

This is a very long article, and I apologise. But the physics of this phenomenon is complex and it took me a long time to get to the bottom of it.

Investigations

I picked 5 mugs from our domestic collection which were as straight-sided as possible, and which had walls which were as thin as possible. I thought these choices would make the vibrational spectrum simple.

First I measured the mugs: their diameter and the wall thickness, and then I picked a wooden striker and started hitting the mugs. (Speadsheet)

The place where one strikes the mug produces an oscillation with the striking location as a local maximum of the oscillation.

For a glass, it wouldn’t matter where one struck – any location on the rim is equivalent to any other. But for mugs, the striking position matters because of the handle.

Mug Vibrations 02

To see if I could understand what was going on I arranged the mugs in size order, from the smallest radius to the largest and struck each one three times at each location.

You can hear the sound here.

I also recorded the ‘spectrogram’ using the wonderful Spectrum View app for the iPhone. A screenshot from the app is shown below together with the mugs which made the noise.Mug Vibrations 03.png

A spectrogram shows:

  • time along the horizontal axis
  • frequency along the vertical axis
  • and the loudness of a sound at a particular frequency and time is shown by the colour: blue is quiet and yellow and red are loud.

On the spectrogram above one can see vertical lines which result from the ‘impulse’ sound of me hitting the mugs. This dies away quickly and one is just left with the ‘ringing’ of the mugs which I have outlined with dotted lines.

One can see that each mug rings at two closely-spaced frequencies. The two notes differ in frequency by between 5% and 15%.

Hitting the rim at either location produces mainly one mode of oscillation, but also a little of the other.

Let’s get numerical!

I used the app to locate the frequency of each note and plotted it on a graph of the frequency versus the mug diameter. I plotted each ringing note as a red dot, and their average as a black dot.

mug-vibrations-04.png

There was a general trend to lower frequency for the larger mugs, but the Toronto mug didn’t fit that trend.

I noticed that the walls of the Toronto mug were much thicker than the other mugs. So I wondered whether I could compensate for this by dividing the frequency by the thickness of the wall.

I did this based on the idea that the speed of the wave would be proportional to the  rigidity of the mug wall against bending. And that rigidity might be roughly proportional to the wall thickness. This seemed to be confirmed because the formerly ‘anomalous’ mug frequency now sat quite sweetly on a smooth trend.

Mug Vibrations 05

Now that the data seemed to fit a trend, I felt I was getting a handle on this problem. Could I understand the dependence of the resonance frequency on diameter?

Frequency

All waves obey the wave formula v = f λ. That is, the speed of the wave, v, is the product of the frequency of the wave, f, and its wavelength  λ.

For the waves on these mugs, the wavelength of the wave which runs around the rim of the cup is just half the perimeter i.e.  λ = π D/ 2 where D is the diameter of the mug.

  • So if all the waves travel with the same speed, then the resonance frequency should vary with diameter as f = 2 v / (π D) i.e. inversely proportional to the diameter.
  • However, for flexural waves, the material supporting the wave becomes floppier at longer wavelengths, and the speed of a flexural wave should fall with increasing wavelength. If this were the case we would expect the resonance frequency to vary inversely as the diameter squared.

Which of the above cases described the data best? I have plotted the two predictions on the graph below.

Mug Vibrations 06

I adjusted the speeds of the waves to match the data for large mugs and then calculated how it should vary for smaller diameter mugs.

Overall I think it is the theory in which the  speed of the flexural wave changes with wavelength that matches the data best.

Test

So now I had a theory that the speed of a flexural wave that runs around the rim of a mug is:

  • Proportional to the wall thickness
  • Inversely proportional to the diameter
    • So the resonance frequencies are inversely proportional to the diameter squared.

After I had finished all these measurements I came across another mug that I could have included in the study – my wife’s ‘Do more of what makes you happy‘ mug.

I decided to see if I could predict its resonant frequency from measurements of its wall thickness and diameter.

I have plotted data on this mug as crosses (×) on the graphs above and I think that overall it fits the trends rather well.

The two notes

If you belong to the minority who have read this far, then well done. It is only you who get to understand the final point about why the ‘quarter hour’ notes are lower.

What is the role of the handle? There are two possibilities.

  • Does it act as an extra mass which slows down the wave?
  • Or does it provide extra stiffness, which would speed up the wave?

Since the quarter hour notes are lower, it seems that it is the extra mass which appears to dominate in the mugs I have examined.

mug-vibrations-07.png

Wonder and Science

January 31, 2018

Recipes for Wonder

My good friend Alom Shaha has a new book out!

And discussing it over dinner the other evening I was struck by an analogy.

Talking and listening and reading and writing 

Children have no problem learning to understand and speak their mother tongue.

All they require is to be exposed to people speaking and they will learn to speak

But this ability does not make them ‘good at languages’.

In contrast with the ease with which children learn to speak, is the great difficulty they have in learning to read and write.

A web search tells me that 15% of the UK population are ‘functionally illiterate’ – a figure which I think has not changed much in recent years.

Reading and writing are hard: they take practice:

  • learning letter shapes.
  • learning the relationship between shapes and sounds.

And it can be a long time before all this becomes automatic and there is a payback on the effort expended.

Nonetheless, widespread literacy is considered essential for a functioning democracy.

And most people who have been taught to read and write are happy with the extra possibilities their new skills enable.

Wonder and Science

Similarly, I think children have an intrinsic sense of wonder.

Or at least they can acquire the sense with ease if they are exposed to adults who express interest in the world around them.

But going beyond the simple pleasure of “Wow!” is hard work.

However, it is that step – from ‘Wow!” to “How?” that is the step from wonder into science.

Why is it hard?

Firstly, imagine how well parents would teach their children to read and write if they were themselves illiterate.

Similarly, scientifically illiterate parents – or more commonly parents lacking confidence in their own abilities – can find teaching science hard.

And secondly, everything is complicated. So it is easy to spread confusion rather than enlightenment.

Consider a ‘simple’ experiment – the kind of activity that people recommend for kids – such as making a wine glass ‘sing’.

Just managing to make this happen is pleasurable – it is intriguing and surprising to hear. It is, literally, wonder-ful.

But when one begins to ‘step beyond’ wonder, it all becomes difficult. I have just spent a happy thirty minutes with my wife investigating. And even with two PhDs, an iPhone equipped with a slow motion camera, and spectrogram software we found it difficult!

For example:

  • Is it the glass or the air in the glass which is vibrating?
  • Why can one see very fine waves running on the surface of water in the glass?

If you search for clues as to what is happening you will find a dearth of answers on the web.

Alom’s book?

As I understand it,  Alom’s aim in writing his ‘recipes for wonder’ is to hold hands with parents and children so that their first steps beyond wonder into science are beguiling and delightful rather than bewildering and demoralising.

Such a book is sorely needed. I hope it does well.

By the way, if you would like to hear Alom talk, he will be appearing at the Royal Institution on March 8th .

P.S. What is happening with the ‘singing’ glass?

I am afraid, the physics is too complicated to explain in full, so here is a summary.

Firstly, the fundamental mode of vibration being excited is a ‘flexural’ oscillation of the glass rim and bowl.

Wineglass

Normally if one calculated the resonant frequency of a sound wave in a glass object of similar dimensions to a wine glass, one might expect a resonance at a very high frequency – perhaps 10 kHz or higher.

This is because the speed of sound in glass is over 4000 metres per second‚ more than 10 times higher than the speed of sound in air.

However, when a material is formed into a ring, it has a ‘soft’ mode of flexing illustrated in the animation above. (The bowl of the glass is not quite a ring, but the upper part of the bowl is ‘almost’ a ring.)

Even if the speed of sound in the material is very high, as the material of the ring becomes thinner, then it becomes easier to flex, and the restoring force pulling the ring back into shape becomes weaker.

This causes the speed a flexural wave in a glass ring to be much lower than the speed of a sound wave in glass. Thus the resonant frequency falls as well.

Once the vibration is established, it vibrates the air around the glass which is what we hear.

But note that this is not a resonance of the air in the glass. If it were, then adding water to the glass would reduce the size of the resonant cavity and cause an increase in the resonant frequency. In fact adding water lowers the resonant frequency.

A spectrogram showing how the frequency of a singing glass is lowered by adding water. Note, the application was paused at 3.8 seconds and then re-started with water in the glass.

A spectrogram showing how the frequency of a singing glass is lowered by adding water. Note, the application was paused at 3.8 seconds and then re-started with water in the glass.

Note also that the gravity capillary waves that can be observed on the surface of the water are also a red herring.

IMG_6825

These waves have a very low speed – about 30 centimetres a second, and so at few hundred hertz, they have a wavelength of much less than 1 millimetre.

Finally, there is also a connection between the noise made by a glass and that made by a xylophone. Xylophone

The vibrations excited by hitting the xylophone keys are not sound waves in the metal but flexural waves.

The speed of flexural waves falls in long thin (floppy) bars – getting less and less for longer bars. So for thin materials, the flexural wave can have a low speed leading to a low resonance frequency.

The fact that a xylophone uses flexural waves explains the relative sizes of the keys.

To make a key for a note one octave lower (i.e. half the frequency) of the top key, one does not have to double the length of the key. In fact one only needs to lengthen the bar by a factor of the square root of two (i.e. make about 41% longer).

Like I said: everything is complicated!

 

 

 

 

Candles at Christmas Revisited

December 21, 2017

Last week I gave a presentation at NPL on the physics of candles.

Above is a video of the slightly chaotic 32 minute presentation and if you are so inclined, you can download the PowerPoint file here.

I have spoken before about the wonderful physics of candles. But in revisiting the subject I learned that wax is basically not flammable and I felt obliged to mention this inconvenient truth!

The highlight of the talk is using a candle to power a thermo-electric generator, which in turn powers a USB port, which in turn powers a torch, which is brighter than the candle.

nikita-pic.jpg

Sadly, in the rush at the end of the talk I forgot to actually measure the brightness of the torch!

Next time!

And by the way, here is the slow-motion candle-relighting movie that is embedded in the PowerPoint but which doesn’t show up well in the lecture theatre view.

Thanks to Brian Madzima for the videography and editing, and Nikita Mezhnyakov for the photograph.

How do we know anything?

November 18, 2017

How do we know Anything MdeP-NPL

This is an edited video of a talk I gave recently to the NPL Postgraduate Institute about the forthcoming changes to the International System of Units, the SI.

It’s 36 minutes long and you can download the PowerPoint slides here.

It features the first ever public display of the Standard Michael – the artefact defining length in the SM, le systeme de moi, or My System of Units. (It’s shown at about 6 minutes 40 seconds into the video).

The central thesis of the talk is summarised in the slide below:

Measurement

In the talk I explain how the forthcoming changes to the SI will improve future measurements.

I hope you enjoy it.

 


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