Running the maths

GCSE Plus student Shanique Wilson runs every day, so she decided to use her OCN maths project to investigate how running affects her, and how the choices she makes affect her running.

For several weeks, she kept records of distances, routes, times of day, days of the week, locations, biological indicators and other measures.

She investigated several interesting links between variables, including the differential between base heart rate and the raised rate after a run. Particularly surprising, though, was the discovery of a strong association between the length of time a run lasts and the end pulse rate, regardless of the start rate. The relationship was not a straight line, but a definite and easily sketched curve.

Having discovered this association, Shanique entered the data into a spreadsheet. Exploring different lines of best fit produced one which gave a very close prediction for end of run pulse rate from the run time in seconds.

The equation of the curve is shows that heart rate increases roughly in proportion to the fourth root of run time. The overall correlation coefficient of the prediction is R=0·94, and improves still further as the run time increases. (Click the graph image for a larger view.)

Elissa investigates social attitudes to hair

GCSE Plus student Elissa Hunter writes:

“Tyra Banks, a well known American model, hosts a chat show on which a special series discussed the issues around African-American women’s hair. This show seemed to demonstrate that this is a very important thing among African-American communities.

Many different points were raised, with one in particular that was most prominent. This was the tendency for many black women to adapt or cover up their hair in ways that gave them the effect of having long, straight, and silky hair, instead of their natural locks. The thoughts were raised that a lot of black women do this, do it because they essentially want 'white' [people’s] hair. There are also women who are deliberately going against this, and deliberately having their hair as 'natural' as possible.

All this interested me, and I wondered if this is such a big issue here as in America. How do women in this area feel about their hair? Are black women that much lacking in self esteem when it comes to their hair? How do black and white women’s thoughts and feelings differ on this? And finally, who is more happy with their natural hair, white or black women? To find this out, I conducted a study involving 30 white and 30 black women in Bristol.

Taking the questionnaire answers overall, it seems that, in my area of Bristol at least, black women are not less happy with their hair than white women, in fact it may be the other way round.

The difference seems to be in how women see the place of treatments and additions in their lives. Neither seems to see them as a way to hide or to 'be what they are not'. White women tend, on the whole, to see them as one way to make a temporary change of look, of dressing for an occasion, while back women see them instead as a longer term part of fashion.”

Strong relationships

Among the first numerical data analysis fruits of James Burns' archive research (see "Gunning for data", 22 February) are a set of surprisingly strong correlations between crewing levels, tonnage and gunnery on British naval ships during the Revolutionary and Napoleonic Wars period.

James comments on the correlations below, and his plots to illustrate them are reproduced here (click them for an enlarged view in a separate browser window or tab).

“The pairwise relationships between all three variables can be represented as linear, as shown in my scatter and trendline.

The plots also show that a third order polynomial (or cubic) model fits the relationship between tonnage and crew level even better. I explored other models, but found that a second order (quadratic) fit brought very little improvement, third order was the big step, and that there was no benefit from going beyond that to fourth, fifth or sixth order.

This is interesting because it means that crewing was a greater relative overhead cost of expansion in mid range vessels than in first rate ships of the line or in the smaller sloops and brigs.

Although the regression fit for gunnery power against tonnage can be slightly improved by moving to a quadratic model, the difference is not great enough (on this data set, at least) to justify the change.

The correlation of gunnery to crew is firmly linear, and shows no improvement at all if the polynomial order of the model is increased. This probably reflects the composition of fighting vessel crews of the period. There were no separate gunnery personnel, and watch rotation was suspended during military engagement, so total ship's the crew reflected the numbers required to man guns at action stations.”

Gunning for data

Sixteen year old GCSE+ student James Burns has been fascinated for years by the British navy in the late eighteenth and early nineteenth centuries CE. He has his sights set on an academic career built around his interest, and so it seemed the obvious basis for his Higher Project Qualification this year.

His chosen project title is An investigation into the relationship of equipage and materiel to ship size in British naval vessels of the Napoleonic era, with some modern comparisons, but like any enthusiast he has not limited himself strictly to it: his project submission will summarise a much larger paper (currently 5500 words and counting, with an estimated final length of 15000) to be published separately.

The work has also spawned two websites which support and document his research, of which he comments:

“I have made two trips down to Portsmouth, the home port of the royal Navy and where I’m most likely to find the sources I needed. The first, late last year, was to the Royal Armouries in Fort Nelson, on Portsdown Hill. I was looking primarily at guns; their weight, calibre etc.

My second visit, during last week's February half term, was far more interesting. I was fortunate enough to view some of the documents in the archive of the Royal Naval Museum located at the Historic Dockyards in Portsmouth (also the home of HMS Victory). There were some interesting moments when attempting to get through security, but once past that it all went incredibly smoothly. I was taken to the reading room and presented with the documents I had requested (mostly ship drafts and sail plans). Looking at the sources was fascinating and, to be honest, I feel very privileged to have been allowed to view them.

With my research complete (for now, at any rate...), all I have to do is write it up!”

New York City 2009

The United Nations

Brooklyn Bridge

Statues of Liberty!

Times Square

The flight (8 hours to go...)

James Nicholls completes HPQ design phase

James Nicholls, Sixth Form Academy student, has been working throughout this term on a Higher Project qualification based around his passion for architectural design.

Taking an assignment from his maths course as his starting point, James gathered the dimensions, textures and notes necessary to construct a detailed model of Millennium Square.

James describes the square as “a large out-door public space in the city centre. It was constructed around 1999-2000, as part of the @Bristol development of tourist attractions. The Square sits above an underground car park and includes public seating areas, water features and sculptures. One of the most striking features of the Square is the large, stainless-steel mirror sphere which houses the Planetarium.”

He also researched the software tools available to him. As he says in his working notes, “There is a wide range of CAD programs available, all with slightly different features and varying levels of functionality”. He examined the features available in a selection of these programs, finally settling on Google's SketchUp. “I have chosen to use SketchUp due to its ease of use and being available as freeware”, James comments. “Even though it's a free program, it does seem to be quite capable of producing professional-looking models, just as good as the high-end programs which can cost several thousands to purchase in full version. It runs on both MacOS and Windows, giving it a wide field of potential use.”

Starting from the basic measurements of the square and its major features, James began by constructing a skeleton representation of the space. Making repeated return visits to acquire more detailed dimensional and positional information, he then progressively refined this first model. Smaller and smaller features were added, and the representation of each aspect developed.

On each visit to the square James also used the camera in his phone to gather photographs from which he could derive visual aspects of the model – surface textures and the exact curvature of a roof line, for instance. Components within the model (such as the car park, the water features, the @Bristol building and planetarium shown here, and so on) were initially developed as separate, free standing entities, finally being brought together for integration into the whole.

As the term ends, James has unveiled his complete model complete with vegetation and a population of visitors. The image here gives a general overview from one angle, but users with access to the model itself (more than 25 megabytes of it!) and a copy of SketchUp can fly through it, look at it from any viewpoint (including a bird's eye or pedestrian's eye view, for example), zoom in to closely examine each part of it, and so on.

Click on any image to enlarge it. For more information on the Higher Project and Extended Project qualifications, contact the Sixth Form Academy.

A-level art trip to the New Gallery, Walsall

pictures supplied by Alex Everitt
(click on any image for a larger view)