Matters of scale

[nigel jones 5Participant @nigeljones5]

Im building a 71/4 gauge using 31/2 gauge drawings, basically doubling everthing with a few compensations, Ive just machined the water pump eccentric to twive the size, and thus throw, and then it dawned on me. If I double the throw and then double the piston diameter I will be getting a lot more than twice the original delivery volume – but having said that, if I apply the same principal to boiler and pistons will it all balance out? Suggestions please!

[nigel jones 5Participant @nigeljones5]

[Sub MandrelParticipant @submandrel]

Volumes and weights/masses will increse by the cube – 8 times.

Areas and cross sections will increase by the square – 4 times

Lengths will double.

Lots of opposing effects.

Bigger wheels mean less rolling resistance, lets (crudely) assume that it will take the same force per unit of mass to keep you moving at a scale speed regardless of scale.

You have four times the heating surface, but as work done = force x distance moved the work required will be a good 16 times as much (very crudely). So you need four times the heat transfer…. but wait, you have 8 times the fire volume.

But resistance to gas flow drops by the fourth power for doubling the bore of a pipe so the restrictions on gas flow & the losses will be much less.

Thermal loses will be much less as arae has increased less rapidly than valaum AND insulartion will be twice as thick.

Probably lots of other effects.

I expect you can prove anything by choosing to use the right estimates… I bet it works though.

Neil

[nigel jones 5Participant @nigeljones5]

Thanks Neil,

Are you saying it will be ok???

Nije

[MICHAEL WILLIAMSParticipant @michaelwilliams41215]

Hi Fizzy ,

Probably be OK but not the best way to go .

Cylinders , valve gear and everything related will just about do though since original design was a bit shaky in the first place I'd be very tempted to borrow a cylinder and valve gear design off another engine designed more recently and more nearly consistent with the scale you are building . The borrowed cylinder and valve gear design need not be copied in all respects – its the essential proportions that matter .

Boiler you basically have to design from new . Some 5 inch gauge boilers will give you a guide to the proportions needed for a very small engine in 7-1/4 inch gauge .

As for pumps – LBSC's pump designs were awful and to get them to work at all he designed them very much over size on pumping capacity .

If you use the 5 inch gauge boiler as your guide then copying the matching pump would be a good bet .

Hi Neil ,

Engines and many other technical devices can often be scaled up or down quite successfully but not by simply scaling the dimensions .

Any engine has a large number of variables that define its form and function . In changing the scale of the engine each of these variables has to be multiplied by a different factor to get a new size of engine .

So :

More obvious things like the general outline dimensions of the engine scale by the primary scale factor – times K for example where K could be 2, 3 , 4 etc

More subtle things like pipe sizes , heating surfaces , orifice jets , safety valve bores , blade heights in turbines and bearing surfaces scale by the primary scale factor to some power – times K to the power x for example where x has a value to suit the particular technology of each component .

x is often in the range 1/(root 2) to (root 2) but it can have any value . Strictly the multiplier could be a long equation with many terms but in practice its difficult to deal with more than a few terms so reasonable approximations are usually used .

To be strictly accurate there could also be a set of constraints which restrict some dimensions to be within certain limits to avoid impossible combinations and to meet practical limitations of size .

It is easiest in practice to think in terms of transform operators and to use matrix methods for the actual calculations .

An extension of these methods can give a quite good performance prediction for the scaled engine and by deliberately scaling some dimensions while leaving others untouched performance can also be optimised .

May all sound a bit over the top but such methods are routinely used in the top end of engineering design . Sometimes for actual scaling up or down but more commonly for optimisation .

Regards ,

Michael Williams .

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