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Spherical painted chickens in a vacuum

Hi everyone, it’s been a little while since I last posted, I’d say I’ve been busy, but I don’t think I’ve been unusually busy so I guess there’s no excuse. 

Tomorrow the whole Bianco company is meeting for the first time which will be very fun. Lots of new people to meet and old friends to meet again. The new exciting news is in the form of new tour dates being announced with exciting additions like the Edinburgh and Brighton Fringe Festivals!!! 

The past week has been a time for fun parkour, with lots of scary jumps, wall trampoline and singing (I say no more…) and it’s all going very well (including the hem, hem, LA-LA-LA!!! singing…) We have been gradually increasing in numbers and tomorrow will see us joined by everyone so it’s probably going to feel very crowded all of a sudden. 

In other exciting news, I’m getting two meals a day at the moment because we’re in rehearsals and it is AMAZING. Especially days like today, when we got Sunday dinner. While I do kind of miss cooking in the evenings, it is very nice to be able to finish training, go and sit down, socialise and eat, then just go home and put my feet up. Something I’ll definitely be able to get used to in the weeks to come. 

My current project is that of decorating the room in the bunk wagon (aka Nofit5) that I will be staying in over the summer. I haven’t started yet but I am starting to pull together a few ideas for a bit of colourful brushwork to brighten it up a little. It’s nice that I’ve got until the end of next month to get it sorted out and how I want it before I move in to go to London. 

On the decorating front however, it has however made me (not that I was unwilling) do some maths, unfortunately someone thought it was clever to only include coverage (11-13m squared per 2.5ltr) on the big tins, so I had to do some scaling to see how far the smaller tub will go. Although it did make me thing about whether there is more wastage in a small tub to corners and the stuff stuck to the sides compared to large tubs. I mean I know it’s a tiny amount but someone please confirm or correct my logic as applicable. Small containers must have a higher surface area to volume ratio then large containers.

Taking spherical chickens in a vacuum for example… a chicken of radius ‘r’ will have 4*Pi*r^2 square metres of feathers and (4/3) *Pi*r^3 cubic metres of chicken stuff in them. 

Now at this point it is tempting to just say cubed growth is faster then squared growth, so the volume is getting bigger faster then the surface area and so I’m done. However I kind of feel there is more then that going on so I’m going to get a pen and paper and do it properly.

Back in a minute.

Here is something to listen to while I’m gone.

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Ok, sorted. 

So, if we assume chicken stuff sticks to the feathers to the depth of ’d’. 

Therefore, the amount of chicken stuff stuck to the edge is given by (4/3)Pi*r^3 - (4/3)Pi(r-d)^3       =       (4/3)(r^3 - (r-d)^3)

And so the percentage of chicken stuff stuck to the feathers is given by - Amount stuck to edge/total amount  Which is

(4/3)Pi(r^3- (r-d)^3) / (4/3)Pi*r^3 = r^3-(r-d)^3  / r^3

expand the (r-d)^3 and cancel gives

3(d*r^2-r*d^2)+d^3 / r^3

A quick stare at this and you will see it disappears to 0 as r goes to infinity. This shows fairly neatly that the percentage of paint, I mean chicken stuff at edge goes to zero as the container, I mean chicken gets larger. 

Fun isn’t it! My paint hypothesis was right, small containers do have more wastage. 

This however is not good for my painting plans….