Archive for Vector Algebra

What’s the Vector, Victor?

Posted in Film, mathematics, The Universe and Stuff with tags , , , on February 18, 2020 by telescoper

Following on from Sunday’s post about the trials and tribulations caused by Storm Dennis, here is a clip of a plane (an Airbus 380)  landing at Heathrow airport on Saturday.

There are other clips of this same event on Youtube and some of them describe this landing as `dangerous’. Although it undoubtedly involved skill and concentration by the pilot it’s not actually dangerous. Aircrew are trained to land in windy weather like this, and it’s fairly routine. My plane to Dublin (an Airbus 320) landed like this on Saturday evening and, although the pilot got a well-deserved round of applause on landing, nobody was ever really at risk.

As it happens, this week I start teaching vector algebra to my first-year Engineering students, so the weekend’s weather events have  given me a good illustration of vector addition. The plane has to have a velocity vector relative to the air such that the sum of it and the wind vector adds to a resultant vector directed along the runway. Lots of people seem to think this is just guesswork but it isn’t. It’s applied mathematics.

This is in principle simple as long as the crosswind is steady, but obviously the pilot needs to be alert to gusting and make adjustments along the way. When the plane has slowed down enough to land in normal conditions, the wind over the wings is still causing a bit of extra lift. You can see that in the last moments before touchdown this aircraft is gliding because of this effect. I’m told that because of this, in windy conditions planes usually descend at a steeper angle than usual.

The interesting bit for me is that the plane touches down in such a way that its body is at an angle to the runway. As soon as it has landed it has to correct this and point along the runway. I think this is done with the rudder rather than the undercarriage, but I don’t know. Perhaps any experienced pilots that happen to be reading this could give more details through the comments box?

P.S. The title of this post is a reference to the film Airplane!

 

Lecture Demonstration

Posted in Education, The Universe and Stuff with tags , , , , on February 18, 2019 by telescoper

I am very proud to be at the forefront of teaching innovation, frequently deploying sophisticated new technology in the classroom for the benefit of the student learning experience.

I thought I’d share one of the latest devices I have developed for the Linear Algebra part of my module on Engineering Mathematics as I am all too aware that not all lecturers have such a firm grasp of the range pf possibilities offered by novel educational appliances.

This sophisticated yet lightweight tool utilizes a pressure-sensitive adhesive (`blu tack’) to attach shapes cut from a flexible sheet of a substance derived from cellulose pulp (`paper’) to a rigid plastic geometric measuring device (`ruler’) in order to represent the magnitude and direction of a vector. Illustrated here is the version designed for use with a chalkboard; an alternative version in black is available for use with a whiteboard. The head can be detached in order to separate the concept of magnitude from that of direction.

Made from lightweight materials this device is easily carried to and from the lecture theatre and can be deployed in all weather conditions (apart from rain, wind, snow, etc).

This simple yet effective hi-tech teaching tool is available for purchase throughout the European Union for just €19.99 and in the United Kingdom for £599.50.