# Problems of Scale with Scale Models

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Another one for the brains trust after another wet weekend.

I was looking at the equations for flywheel weight for steam engines. If the same equations hole for scale models then the flywheel would have inadequate mass for smooth motion of a model running at original speed and the model would have to run faster - e.g. 12 times faster for a 12th scale model, or the motion would be jerky or stop.

But then I started to think about bearings. The mass of a 12th scale model is reduced by 12 X 12 X 12, the bearing area is reduced by 12 X

1. So the bearing area on the model is 12 times larger than is actually needed to support the mass (good), but that means 12 times the viscous drag, and if the model is running 12 times faster too, then 144 times the viscous drag.

And then I started to think about flyball governors ....er.... and rapidly decided to give up and ask the newsgroup if there have been any ME articles or books published on the problems of scale? Its fairly fundamental stuff that must have effected everyone making scale models - but I don't think I have ever seen a nice clear article on the topic.

Steve

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Cheshire Steve wrote: ...

I will echo that interest. It's something that makes modelling a challenge - you can have a model that looks good or you can have a model that works well, but how do you achieve the two together. Peter

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I have no problem with scale flywheels on my 1 1/2" Alchin, 2" Thetford Town showman's and 3" Foden lorry. All models run smoothly at low speeds. As all the motion work is scaled down the masses may well be quite OK when rotating. However the question is are they then running at scale speed? which begs the next question what is that? If you expect a 1/12 model to run at 1/12 the speed then a full size traction engine sitting ticking over at around 60 rpm would result in a model running a 5 rpm ........ it will not readily do that. Its all perception though as a 1/12 model running at 60 rpm looks fine (to me) and not out of place.

Now look at road speed, because all the wheels are scaled down the model will not run as fast as the full size prototype even though the engine may be running at the same speed ...... so pays yer money and take your choice.

• posted

What you say is encouraging. I was after making a beam engine model that would run close to normal rpm to allow you to see the Watts linkage working, and wondering if I could make a working governor using a variable cut-off. Do yours have governors ?

Some things change by area (1/12x1/12) and some by volume (1/12x1/12x1/12). So for example the force on a piston is proportional to the area (assuming the pressure stays the same), the weight of the piston is proportional to the volume. The moment of inertia of the flywheel is I think proportional to the mass (which is proportional to the volume) multiplied by the diameter (which is yet another 1/12th), so goes down by a further factor of 12 even compared to the weight of the piston.

Maybe a lead flywheel rim will make for a more realistic model, that will tick over slower and allow you to see the gubbins at work. The calculations for the governor will need me to decide on the speed first.

I hoped this would have been discussed in one of the modelling magazines - it is so fundamental to everything to do with scale modelling.

Steve

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In message , Cheshire Steve writes

[snip]

The late Lillian Lawrence (a.k.a.LBSC) wrote, "You can't scale nature". I believe that no one has yet proved him wrong by producing a true small scale working centrifugal governor.

• posted

Exactly - it would be hard for a mag to cover 'everything', while many articles may have discussed particular cases where scale effects are important. In any case there often won't be any 'correct' solution.

Consider a fire-tube boiler, for example. If you tried to make a model with the same number of tubes as in full size, it would not work. Many years ago Keiler did some research (measuring boilers that worked) and came up with a formula that seems to work satisfactorily that relates tube length to the area of its bore. That formula is completely empirical.

If you are really interested in this then you have to get to grips with the engineering science for yourself, and where the science doesn't help you have to experiment. A good pre-war text book such as D A Low's 'Heat Engines' should contain a chapter on governors.

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Re governor: Increase its RPM, use lead weights, make a bit out of scale longer levers.

If you want a working model, you have to accept physics. Meaning bigger tubes than scale, higher rpm, less power etc.

Nick

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No, mine are not governed although two have scale governors that are not used.

I would have thought a beam engine with its large scale flywheel would easily rotate around 40 rpm (maybe less) and at less than one rev per sec the Watts linkage would easily been seen. Should be controllable with the steam throttle valve at that sort of speed without too much variation if a decent boiler capacity is behind it.

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Thanks guys, I'll proceed with my model, and run it before finalising the governor design. Its not just the speed but the ability to get enough force out of a tiny governor to operate a valve or linkage. I thought the variable cut-off might take less force.

The technical problem of scale-up is the same as that of scale-down. The only engineering texts I can locate relate to scale-up from pilot plant to full scale production of chemical reactors. These days I assume scale protypes of mechanical items are rare as its all done on computer, but I still hear arguments about the ability to scale up

10kw wind turbines to 1 MW wind turbines, and that one design will overtake another at large scale (horizontal axis versus vertical axis).

Maybe I am asking too much of science/engineering - and maybe the model engineering side has always done it in dribs and drabs - and no- one has ever pulled it all together. I was trying to understand what goes wrong so I can design around it in the first place (rather than build something and be disappointed, and have to adapt it). But this discussion has been helpful.

Thanks, Steve

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I don't know nuffink about steam engines but maybe a comparison with IC engines will help you.

If you build a 1/10th scale model then the following happens. Capacity reduces to 1000th but valve area only to 100th. As power is proportional to breathing ability then power drops to 100th but rpm increases by 10x to compensate because torque is only proportional to cylinder capacity. That's why model airplane engines run at 20,000 rpm or more and this only at 100.

The flywheel moment of inertia inertia reduces by a factor of 1000 due to the reduced mass and a further factor of 100 due to reduced diameter as it is proportional to the square of this. However the kinetic energy stored in it increases in proportion to rpm squared which compensates for the reduction in moment of inertia due to diameter. The kinetic energy stored therefore reduces in the same proportion as cylinder volume and everything stays copacetic because cylinder volume determines the energy needed to smooth the transition of the pistons over TDC during the compression stroke. Obviously if you tried to run the engine at the same rpm as the full sized version A) it wouldn't and B) even if it did the flywheel energy would be insufficient for smooth running.

Other things you need to look at include beam strength of components like conrods which can become progressively more 'spindly' looking as they get smaller and valve train dynamics where you have 3rd and 4th powers operating on the linear dimension to determine the valve spring rate but the loadings need to increase in proportion to the square of rpm to prevent valve bounce.

Most of it is actually fairly straightforward if you just perform the calculations on first principles.

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Thanks Dave,

Most scale models of stationary engines are run with no load, which buys some margin as regards breathing issues, and power delivery - but I think the big difference between steam and IC is that steam engines don't have a compression stroke (Aha - hadn't thought of that !). So maybe a steam engine can be run as slow as friction will allow, whereas an IC engine minimum speed is dictated by the balance between flywheel energy and gas compression.

So a scale IC engine will have to be run faster, but a double acting steam engine with small demands on power can be run closer to original speed. This will be aided by dropping the steam pressure via a throttle valve, rather than varying the cut-off and working it expansively.

My ability to calculate from basics is limited, I'll have to read up on flywheel inertia as I thought it would be the 4th power of the scale, and I don't really know where to start when it comes to friction in plain bearings and cylinders. However talking this through has been very helpful.

Steve

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HI!I am doing my proyect and is about wind turbines. I have to desing an aerodynamic wind turbine. Is NACA 4418. I would like to know if you Know wich is the best angle of atacc for those type of airfoils, ecause I have been searching information and i cant found it. thank you

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Is it homework season again already?

I thought that the idea of a project like that was to do your own research, rather than mooch it off others.

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He should find a good text on aerodynamics.

A good English as a second language course might help him to spell, and construct a coherent sentence.

Steve R.

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I find a good angle of attack is about 90 degrees to the computer, then using the keyboard (at 15 degrees or so) type NACA 4418 angle of attack into your favourite search engine. Alternatively you could saunter at about 75 degrees through the door of the library. What does this have to do with making small steam engines run at a leisurely pace?

Dave

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to desing an

you Know

Aren't all the wind turbine blades made somewhat like a propeller where the pitch changes from root to tip,or are they just a tapered airfoil and the angle of attack is varied according to the wind speed ?

At a guess,the thickness and airfoil alters from root to tip without the twist of a propeller.

Allan

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Come on guys we can do better that just be critical. The suggestion of getting a good text on aerodynamics is not helpful as this is a particular application so general aerodynamics information won't help much especially when you are new to it all. Wind generator blades are twisted like a propeller for the same reason of getting sensible angles of the blade section to the approaching wind when the rotor is turning. Typing 'wind turbine design' into Google will give the OP a lot of information. Much of it is of a practical nature.

Henry

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This is a (very) large subject and there isn't 'an' answer. As with most things there are a heap of trade-offs. For some fairly serious reading I would suggest either of these: The Theory of Flight by Richard von Mises or Theory of Wing Sections by Abbott & Doenhoff. I'm not sure what 'level' you're at, but the fact that whoever has set the question has specified a blade section seems to suggest that you should be able to cope with reasonably technical text. Get a dictionary and learn how to use it!

As a quick comment and given that you have been specified a wing (blade) section, you need a set of 'polars' for that section so you can assess it's characteristics at different Re's (ie wind speed in conjunction with the blade cord). If you email me off list I can provide an un-certified plot for you.

As a very broad rule of thumb, you can expect to be working at an AoA of not more than around 10 degs. and expect a stall at around 15 degs. This is NOT _the_ answer!!

Richard

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In article , Richard writes

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