Author Archives: Eann Patterson

Cow bladders led to modern strain measurement

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softball figureSir David Brewster was a prolific experimentalist who published seven papers in the Philosophical Transactions of the Royal Society during 1815 and 1816. In his report dated October 22nd, 1814 that was published by the Royal Society one hundred years ago in January 1815, he described his observations on the depolarisation in more than fifty materials as diverse as sulphur and the bladder of a cow. He followed this with a series of experiments on glass sheets subject to various loads and reported his observations in the of photographic plates that show photoelastic fringe patterns which would become instantly recognisable to generations of engineers. Two hundred year later, digital technology has revolutionised photoelasticity so that it is no longer necessary to generate fringes that can be ‘seen’, as in Brewster’s experiments. Instead, digital sensors allow us to measure changes in light intensity that are undetectable to the naked eye and digital computers permit the processing of arrays of tens of thousands of measurements in less than the blink of an eye to yield maps of strain magnitude and direction in complex components. However, the principles employed in digital photoelasticity are the same as those first elucidated by Brewster and involve collecting images at multiple rotational steps of one or more of the polarising elements in a polariscope and then using Fourier analysis or matrix algebra to solve the equations describing the stress-optic law, i.e. the relationship between the applied stress and the observed change in transmitted light intensity. A polariscope is the term given to the series of polarisers and quarter-waveplates used by almost every photoelastician since Brewster to observe photoelastic fringes. One of Brewster’s other great inventions was the kaleidoscope of which there is an early example in the Science Museum in London. Recently, the concept of the kaleidoscope has been combined with a polariscope to create the poleidoscope that allows the multiple images required for digital photoelasticity to be acquired simultaneously, which is useful for dynamic applications such as in the impact example shown in the picture. These advances allow digital photoelasticity to be used not only by laboratory-based stress analysts but also in quality assurance procedures, for instance to monitor in real-time the stresses induced in float glass during production, or to investigate the residual stress in silicon wafers using infra-red light.

The picture shows a sequence of maps of photoelastic fringe order (right) showing the stress induced in an epoxy resin block when impacted by a soft ball falling under gravity (left). The maps were obtained using a precursor to the poleidoscope and a high-speed digital camera recording 4000 frames per second for the 10x10mm area shown by the white box in the schematic.

For more a little more on photoelasticity see http://www.experimentalstress.com/basic_experimental_mechanics/photoelasticity.htm

Sources:

Brewster, D., Experiments on the depolarisation of light as exhibited by various mineral, animal , and vegetable bodies, with a reference of the phenomena to the general principles of polarisation, Phil. Trans. R. Soc. Lond. 105:29-53, 1815. http://rstl.royalsocietypublishing.org/content/105/29.full.pdf+html

Brewster, D., On the communication of the structure of doubly refracting crystals to glass, muriate of soda, fluor spar, and other substances by mechanical compression and dilatation, Phil. Trans. R. Soc. Lond. 106:156-178, 1816. http://rstl.royalsocietypublishing.org/content/106/156.full.pdf+html

Ramesh, K., Kasimayan, T., Neethi Simon, B., Digital photoelasticity – a comprehensive review, J. Strain Analysis, 46(4):245-266, 2011. http://sdj.sagepub.com/content/46/4/245.abstract

www.sciencemuseum.org.uk/online_science/explore_our_collections/objects/index/smxg-3823?agent=smxg-52657

Lesniak, J.R., Zhang, S.J., Patterson, E.A., The design and evaluation of the poleidoscope: a novel digital polariscope, Experimental Mechanics, 44(2):128-135, 2004.

Hobbs, J.W., Greene, R.J., Patterson, E.A., 2003, A novel instrument for transient photoelasticity, Experimental Mechanics, 43(4):403-409, 2003.

New Year Resolution

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I started 2014 with a post on January 1st about the ‘Knowledge Economy‘ in which I extolled the virtues of knowledge-based rather than energy-based agriculture and engineering.  At the end of the year, oil prices have dropped from $110 to about  $60 per barrel, making it likely that in most countries the energy-based economy will continue to dominate.  In the USA, sales are rising of huge gas-guzzling cars, such as the Escalade, which is 5.15m (17ft) long, weighs 2.59 tonnes and only manages an average of 17 miles per gallon!  Fossil fuels account for approximately 80% of world energy consumption and are responsible for most greenhouse gas production.  During 2014 it was reported that greenhouse gases were rising at the fastest rate for 30 years but still the countries of the UN meeting in Lima before Christmas only agreed that those countries who were ‘ready to do so’ should submit national pledges on cutting emissions in the first of quarter of 2015.

The global average temperature is within one degree of the maximum temperature in the last million years, and a 2 degree rise would be equal to the temperature three million years ago when the sea level was 15 to 23m (80 to 130 feet) higher.  A 1 metre rise in sea level would displace 145 million people, and there is evidence that it has been  rising at 3.5mm per year during the last 20 years which is twice as fast as during the previous 80 years.

How bad does the condition of the planet need to get before effective action is taken?  How many more islands, like the Carteret Islands, will have to disappear?  How many more people than the 7 million in 2012 will have to die prematurely as a consequence of air pollution? Cities such as Beijing are beginning to be described as ‘almost uninhabitable’.  Kofi Annan has suggested that grass roots action is needed because our leaders will not take action in time. So tonight make it your New Year Resolution to reduce your carbon footprint in 2015 by 15%.

Estimate your current carbon footprint using an on-line calculator and starting working out how to reduce it.  If you want to find out the carbon footprint of your organization then the Carbon Trust has useful information and services.

Sources:

‘Inside Beijing’s airpocalypse – a city made “almost uninhabitable” by pollution‘ by Oliver Wainwright in The Guardian on Tuesday 16th December, 2014.

Blockstein DE, Wiegman L, The Climate Solutions Consensus. Island Press, Washington, 2010.

Links to previous posts:

‘Year of Air:2013‘ on November 20th, 2013 or ‘Mass-produced nuclear power plants?‘ on November 12th, 2014.

Stimulating students with caffeine

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milk in coffeeFood and drink seems to have been a recurring theme in my undergraduate lectures recently which as we are approaching a festive season is perhaps not inappropriate. At the moment, I am teaching thermodynamics to three hundred first year undergraduate students.  Zeroth and first laws of thermodynamics before the Christmas break and then the second and third laws in the New Year. Toast, pizza, barbecued steaks, hot coffee, bottled water, and cold milk shakes have all featured as Everyday Engineering Examples of thermodynamic systems in recent lectures. We can define a thermodynamic system as a quantity of matter capable of exchanging energy with its environment. And, most food preparation processes involve heating, chilling and, or doing work on the food by stirring, beating etc. which are all forms of energy exchange, so the opportunities for Everyday Engineering Examples are many and varied.

In one recent lecture, I asked the class to consider the quickest way to cool your coffee with milk. It was a multiple choice question to which students could respond in real-time using their phones and a website called polleverywhere.com. There was more than one correct answer depending on the assumptions you made about the quantity and temperature of the milk as well as the temperature of the coffee and environment. The core issue is that the rate of cooling is proportional to the temperature difference. While discussing the possible answers, I made a throw-away remark about stirring the coffee involving doing work on the coffee and thus increasing its internal energy and temperature, which would be a step in the wrong direction. I was delighted when one of my students picked me up on this and sent me this link about stirring tea.

It is great to know that at least one student is listening and sufficiently engaged to do a little research. Only 299 left to inspire!

Footnote:

The hot coffee will transfer heat to its cooler surroundings by natural convection and radiation at its free surface and by conduction through the ‘walls’ of the cup. Similarly, the cup will transfer heat to its surroundings by natural convection and radiation from its outer surfaces. This process will establish a temperature gradient in the coffee that will induce a very slow convection flow that would be accelerated by stirring, i.e. introducing forced convection. This is likely to increase heat transfer slightly by carrying hotter coffee to the surfaces. The additional heat transfer (loss) might be more or less than the work done to stir the coffee. Who would have thought something as simply as stirring coffee or tea could be so complicated!

Previous posts on Zeroth Law:  ‘All Things Being Equal ‘ on December 4th, 2014, ‘Arbitrary Zero‘ on February 13th, 2013 and ‘Lincoln on Equality‘ on February 6th, 2013.

Previous posts on First Law: ‘Thunderous Applause‘ on July 16th, 2014,  ‘Sizzling Sausages‘ on July 3rd, 2013, ‘Closed system on BBQ‘ on June 19th, 2013 and ‘Renewable energy‘ on January 7th, 2013

Sources:

‘The Thermodynamics of Pizza‘ by Harold J. Morowitz, Rutger University Press, 1992.

http://what-if.xkcd.com/71/