Category Archives: Learning & Teaching

Formula Ocean

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I have had intermittent interactions with motorsport during my engineering career, principally with Formula 1, Formula SAE and Formula Student teams.  The design, construction and competition involved in Formula Student generates tremendous enthusiasm amongst a section of the student community and enormously increases their employability.  As a Department Chair at Michigan State University, I was a proud and enthusiastic sponsor of the MSU Formula SAE team.  However, I find it increasingly difficult to support an activity that is associated with profligate expenditure of energy and resources – this is not the impression of engineering that should be portrayed to our current and future students.  Engineering is about so much more than making a vehicle go around a track as fast as possible.  See my posts on ‘Re-engineering Engineering‘ on August 30th, 2017, ‘Engineering is all about ingenuity‘ on September 14th, 2016 or ‘Life takes engineering‘ on April 22nd, 2015.

There are many other challenges that could taken up by student teams, in competition if that encourages participation, which would benefit human-kind and the planet.  A current hot topic in the UK media is the pollution of oceans by waste plastic [see for example BBC report]; so, engineering undergraduates could be challenged to design, construct and operate an autonomous marine vehicle that collects and processes plastic waste.  It could be powered from the embedded energy in the waste plastic collected in the ocean.  It would need to navigate to avoid collisions with other vessels, coastal features and wildlife, and to locate and identify the waste.  These represent technological changes in chemical, control, electronic, materials and mechanical engineering – and probably some other fields as well.  I have shared this concept with colleagues in Liverpool and there is some enthusiasm for it; maybe some competition from other universities is all that’s needed to get Formula Ocean started.  The machine with the largest positive net impact on the environment wins!

 

Season’s greeting

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zurich christmas tree

Christmas tree in Weinplatz, Zurich

Best wishes during the holiday season to all my readers.  I’m in digital detox over the Christmas and New Year holidays.  So no post today.  If you’re having withdrawal symptoms or want to know more about digital detox then read ‘Digital detox with a deep vacation‘ posted on August 10th, 2016. Otherwise ‘Slow down, breathe your own air‘ [see my post on December 23rd, 2015].

A reflection on existentialism

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Detail from stained glass window by Marc Chagall in Fraumunster Zurich from http://www.fraumuenster.ch

I was in Zürich last weekend.  We visited the Fraumünster with its magnificent stained glass windows by Marc Chagall [see my post entitled ‘I and the village‘ on August 14th, 2013] and by Augusto Giacometti (1877-1947).  The Kunsthaus Zürich has a large collection of sculptures by another Giacometti, Alberto (1901-1966), a Swiss sculptor, who is famous for his slender statues of people which portray individuals alone in the world.  He was part of the existentialist movement in modern art that examined ideas about self-consciousness and our relationship to other people.  For me, this echoed a lecture that I contributed last week to a module on Scientific Impact and Reputation as part of our CPD programme [see my post entitled ‘WOW projects, TED talks and indirect reciprocity‘ on August 31st, 2016.  In the lecture, I talked about our relationship with other professional people and the development of our technical reputation in their eyes as a result of altruistic sharing of knowledge. This involves communicating with others, building relationships and understanding our place in the community.  The post-course assignment is to write a reflective essay on leadership and technical quality; and we know, from past experience, that our delegates will find it difficult to reflect on their experiences and the impact of those experiences on their life and behaviour.  Maybe we should help them by including a viewing of existential art in one of the Liverpool art galleries as part of our CPD programme on Science and Technology Leadership?

How many repeats do we need?

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This is a question that both my undergraduate students and a group of taught post-graduates have struggled with this month.  In thermodynamics, my undergraduate students were estimating absolute zero in degrees Celsius using a simple manometer and a digital thermometer (this is an experiment from my MOOC: Energy – Thermodynamics in Everyday Life).  They needed to know how many times to repeat the experiment in order to determine whether their result was significantly different to the theoretical value: -273 degrees Celsius [see my post entitled ‘Arbitrary zero‘ on February 13th, 2013 and ‘Beyond  zero‘ the following week]. Meanwhile, the post-graduate students were measuring the strain distribution in a metal plate with a central hole that was loaded in tension. They needed to know how many times to repeat the experiment to obtain meaningful results that would allow a decision to be made about the validity of their computer simulation of the experiment [see my post entitled ‘Getting smarter‘ on June 21st, 2017].

The simple answer is six repeats are needed if you want 98% confidence in the conclusion and you are happy to accept that the margin of error and the standard deviation of your sample are equal.  The latter implies that error bars of the mean plus and minus one standard deviation are also 98% confidence limits, which is often convenient.  Not surprisingly, only a few undergraduate students figured that out and repeated their experiment six times; and the post-graduates pooled their data to give them a large enough sample size.

The justification for this answer lies in an equation that relates the number in a sample, n to the margin of error, MOE, the standard deviation of the sample, σ, and the shape of the normal distribution described by the z-score or z-statistic, z*: The margin of error, MOE, is the maximum expected difference between the true value of a parameter and the sample estimate of the parameter which is usually the mean of the sample.  While the standard deviation, σ,  describes the difference between the data values in the sample and the mean value of the sample, μ.  If we don’t know one of these quantities then we can simplify the equation by assuming that they are equal; and then n ≥ (z*)².

The z-statistic is the number of standard deviations from the mean that a data value lies, i.e, the distance from the mean in a Normal distribution, as shown in the graphic [for more on the Normal distribution, see my post entitled ‘Uncertainty about Bayesian methods‘ on June 7th, 2017].  We can specify its value so that the interval defined by its positive and negative value contains 98% of the distribution.  The values of z for 90%, 95%, 98% and 99% are shown in the table in the graphic with corresponding values of (z*)², which are equivalent to minimum values of the sample size, n (the number of repeats).

Confidence limits are defined as: but when n = z², this simplifies to μ ± σ.  So, with a sample size of six (6 = n ≥ z²  for 98% confidence) we can state with 98% confidence that there is no significant difference between our mean estimate and the theoretical value of absolute zero when that difference is less than the standard deviation of our six estimates.

BTW –  the apparatus for the thermodynamics experiments costs less than £10.  The instruction sheet is available here – it is not quite an Everyday Engineering Example but the experiment is designed to be performed in your kitchen rather than a laboratory.