Weights and measures

I'm sure some of you clever folks will put me straight with this one

So at a rally the other weekend I was discussing Scale with a MOP and that my Agri was a 4" or 1/3 scale engine, the topic moved on to how much it weighed. Of course we all know the standard 4" comes in around 500kg or 1/2 Ton, we then had a conundrum, if you scale up the weight to full size i.e. multiply 500kg by 3 you get 1500kg or 1.5 Tons. Now I'm sure we all realise a full size Agri weighs a heck of a lot more than 1.5 Tons so something somewhere is going wrong with our calculation ??
We chatted about this for a while and could only really come up with the fact it must have something to do with density and size, i.e. if you have a 1inch block of steel and double its size the weight wont double but be a lot more.

So can anyone shed some more light on this as I found it quite an interesting and unusual question from a MOP, compared to the normal one's which range from does it run on gas (when its running on good quality steam coal and not producing any smoke) or what was such a small engine used for back in the day

Hi Livesteam, When you say take the weight & x3 same as size there is something you are forgetting that is the plate thickness off all parts of the engine, this is where the weight would increase more than the scale size, e.g just think if the say horn plates on the full size were the thickness of our 4" scale, I think i,m right but I'm open to correction

Check the Square-cube Law this gives the idea of how volume increases more than surface area,https://en.wikipedia.org/wiki/Square-cube_law

Put simply, if you stand three 4" engines side by side you would have the correct width, but you would also have the have three rows to get the length right and three layers to get the height. So the correct factor is 27, which for half a ton gives you 13.5 tons. Anyone know if this is anywhere close to the real thing?

Mike

Nicely put Mike. Even I can follow that. The weight is probably a bit on the plus side but not that far out.

I have a Burrell book which has a copy of a certificate for Single Cylinder Traction Engine No. 3984 called Dolly which weighs in at 10Ton 10Cwt.

Jim

Well if you put a box around the engine there's empty above the tender so you could take away three engines for sure, over the motion work perhaps two in that area. Remember our engines a a third of the 2d drawing, a cube of a 3d so let's say 3 to the power of 3 would equal 27. 3×3×3=27. There would be roughly lets say 5 empty cubes roughly, so the maths does work out. Excuse me while I apologise to my maths teacher for saying we'll never use this....

Fantastic folks, I get it now

I knew you would come up trumps, some really useful info here and gives me some interesting extra facts to chat to folks about.

I think the reason why the weight is coming out on the heavy side at 13.5 tons is that the miniature engines are overbuilt so heavier than if they were truly built to scale. The boilers in particular are much thicker as someone once told me that rust doesn't rust to scale, you don't get miniature rust on a miniature engine! The full size boiler barrels are not much thicker than the STW ones having seen a tube plate replaced and been surprised at how thin they actually are.

I would always try and teach maths and geometry in the most practical way possible Keith and like you many of my students would say "now I know why we were taught that..."

Mike

That's certainly the best way to do it. I find nowadays however the maths is more theoretical and the practically minded folk cannot see the maths and work it out easily. Of course I would be happy to eat my words especially if it helps with engines