Calculus at WHS

Calculus for Dummies - with thanks to Trevor Prior

Chris Snuggs - Berners/Halls 58/65: Calculus? I could work out the area of a circle or the volume of a sphere and if I knew two interior angles of a triangle I could work out the third. I could even work out averages and just about managed simultaneous equations - though I never really understood what use they were - but calculus? In my defence, as far as I was concerned NOBODY at WHS ever explained what it was FOR - What USEFUL problem you could solve with it. Michael Girling - who in 4A in 1962 had the thankless task of trying to teach me maths - plunged straight into integration and differentiation and the space below curves (What on EARTH is the point of knowing THAT?), but it was for me all meaningless. I had never before at school felt such a total failure. In 5A four of us dunces sat at the back of the class doing old "O" Level papers for a year while the rest prepared for "S" Level maths. That helped me get a 2 in Maths 'O' Level, one of my most proud (and astonishing) achievements.

SIXTY YEARS LATER Trevor Prior has come to the rescue!

Trevor Prior - Halls 73-80: My subject at Woolverstone was maths, but having obtained an unconditional offer, my enthusiasm for studying hard somewhat waned, hence an E (maths) and two Os (physics and Chemistry). However, we were well taught so, even if the exam grades were poor, the knowledge was there and has helped me consistently through my career. It even allowed me to help my son during his maths degree!!

: Let's try to help with a real world use. The picture shows a pair of insoles with force sensors. The green curve is the force under the foot (y axis) over the time (x axis) for one step. The blue line is the pressure time curve (now physics as force per unit area). The area under the curve is the force time or pressure time integral. This value can increase if the force and / or the time increases.

We use this to assess people walking and running, sports injuries, designing shoe inserts and footwear.

However, larger values are also linked to ulceration under the foot. The two main complications of diabetes in the foot are a lack of sensation (neuropathy) and / or circulation. When you cannot feel your feet, you are not aware of increased pressure and the skin can ulcerate which can then become infected.

The single largest cause of lower limb amputation in the world is diabetes (someone loses a leg every 30-60 seconds worldwide) and 85% of those are preceded by a foot ulcer. Therefore, knowing the force and pressure time integrals is an important part of the process although thankfully, it is all calculated for us.

This is a force/time curve for a runner with a heel strike (blue dotted line - red is forefoot).

This is for a runner with a forefoot strike - see how the blue line starts later and there is a different shape to the curve. The force under the foot is directly proportional to the number of steps you take per minute (cadence) because the longer the step, the more time you spend in the air and therefore the greater force when you hit the ground.

I am involved with a running shoe that changes the denisty of the material beneath the forefoot and heel in each model so you can select the right model for the speed at which you run.

As I tell my daughter, life is all about maths and physics.