Square Wheels and Catenary Roads

5 August 2007 | 2 comments

The other day Paul told me that square wheels (and, indeed, any regular polygon except a triangle) can ride on a road constructed of inverted catenaries. A catenary is the curve made by a telegraph wire when stretched between two poles — a cable hanging under its own weight.

The length of the curve and the height <span class="maths">h</span> are the important parameters in getting the right curve. A little bit of thinking about the road makes you realise that the length of the catenary s must be the same as the length of the side of the square, and the height h must be

h = s(√2 − 1) / 2.

This is because the centre of the square, the axle, must remain at a constant height from the ground for a smooth ride.

Anyway, armed with this information, I spent this afternoon making a real-life version of this. I used some string to mark out a catenary of the right size, and used it as a template on two bits of plywood. A fair bit of jigsawing and filing later, I had this:

The real thing. Check <a href="http://video.scholesmafia.co.uk/?id=22">the video</a> to see how smoothly it goes!

I was really surprised how well it worked! Check the video to see how smoothly the “wheel” runs along the “road”!

Feeling Guilty

24 May 2007 | 1 comment

This just goes to show how little time I spend in the department: After my meeting with Stefan today, we went to photocopy the work sheet, and I checked the pigeon holes for any mail. Shamus saw me looking and said, “you won’t find any mail in there; that’s for postgrads.”

Er…

Waiting to Exist

3 October 2006 | 1 comment

So after my induction meeting yesterday, I decided to go and get my registration form from the department, and sort out tuition fees and the like. At least, that was the plan…

I didn’t have a form. Apparently this is not surprising, and SPA (the centre that handles our registration process) don’t seem to be very good at their job. Richard seems to be in a similar situation, finding out first-hand about the general incompetence of the graduate school. Still, hopefully the department are on top of it! Looks like I’ll have to wait around for a bit. I’m off to see my office tomorrow!

After yesterday’s musings on Walkabout, I didn’t go for very long, and In fact was the only one of our lot to go, at about 1am. Since Walkabout was going to be full of Collingwood freshers, we planned to spend some time with the Hild Bede lot, who were heading to Rixies/DH1/The Loft. Now, I know that Klute is famous for its walls dripping with sweat (and I have incidentally just found the Urban Dictionary entry for it), but last night Rixies smelled particularly badly of stale beer and sweat — how lovely!

Walkabout was a refreshing change, and I got to catch up with Caroline and Reg. Caroline, remind me why you weren’t drinking?

To top it all off, Reg broke his watch by hitting me with it, and then decided to blame me. Nice one!

Back in Durham

2 October 2006

I got back to Durham yesterday afternoon. I haven’t unpacked anything, except my computer — important things first!

Today I get to enjoy an induction meeting that lasts for 95 minutes, followed by going to pick up my registration papers. Maybe I’ll also get to see my office today…

It’s good to be back. Let’s see what Walkabout’s like tonight!