scaling for work

[miner49r]

I am sure there is no quick and dirty answer to this. OK. We are building scale (to size) models of some very interesting machinery. These creations look great and if built properly will actually run. That's fine and dandy.
Let's say that the full size unit puts out "x" amount of work and the model is to 1/20 scale of the original. Will the models output be 1/20x amount of work?

Being new to the hobby I don't have any knowledge or experience to say yes or no, but if I were to make a guess I would have to say no and I would even guess that the amount of work output to much less than the scale.
Alan

 

[jtrout13]

You are right. I can guarantee that if you scale an engine down 1/20, you will get MUCH less than 1/20 the power output.

For any type of cylinder engine, the power is dependent upon displacement and speed. Displacement will scale down with the square of the diameter of the piston. For the same stroke, if you half the diameter, you get 1/4 the displacement. So in your case, a 1/20 scaling of bore will take you down to 1/400 the displacement, not considering the scaling of the stroke. All of the engines built here work off the premise of displacement, so this applies to the sort. You might gain back some of the 'lost power' by the fact that our small machines often run faster than large steam engines, but very much.

For other mechanical devices which make up more complex machinery, you'll find that it's the same way. Almost never will power output scale linearly with the size of the device.

 

[Jasonb]

Everything will reduce by the inverse cube unless you are measuring output in length or area, really depends on what the machine doesso for example displacement will be:

1/20 x 1/20 x 1/20 = 1/8000

and just to prove the theory lets say its a 10" bore and 10" stroke.

Full size would be 5x5x3.142x10 = 785cu in

Model would be 0.25 x 0.25 x 3.142 x 0.5 = 0.098cu in

Which is near as dam it 1/8000th of the full size

J

 

[steamer]

Jason's got it.

Dave

 

[Ken I]

As Steamer says - Jason's got it.

I used to confound my students with this question - If you take a 2.0 litre engine and scale it up 2:1 what do you get ? (most say 4.0 litres - wrong !)

8 times the capacity = 16.0 Litres (2 x 2 x 2)
8 x Torque
0.5 the rpm (if max piston velocity is not to be exceeded)

So only 4 x the power (8 x Torque x 0.5 x Revs)

So the specific HP is reduced 50% by scaling up 2:1

So if we build a 1/4 size version it will be 31.25 cc (1/64th)
with 1/64 the torque - but in this case the revs can be increaced 4 times for the same max piston velocity so the power is 1/16 and the specific power per litre is increaced 4 times.

(All other things being simplistically equal.)

Now you see why really high performance engines use lots of small cylinders.

Theoretically a 2.0 litre V8 is capable of producing 26% more power than a 4 cylinder of the same capacity.

(edit - I originally said twice the power - woke up in the middle of the night realising its the third root of 2 - ie 1.2599 - glad I spotted it before Marv did.)

A lot of my students had a really hard time wrapping their head around this.

Ken

 

[Tin Falcon]

when scaling liniar measurements are proportional. areas are rportional to the square or inverse of the square. and volumes proportional to the cube.
the cube also come in to play with mass of material double the sise of a 1 pound engine and the new one will be 8 pounds.
Tin

 

[Lew Hartswick]

the cube also come in to play with mass of material double the sise of a 1 pound engine and the new one will be 8 pounds.
Tin

Only if it's solid.
...Lew...

 

[RonGinger]

Only if it's solid.
...Lew...

I dont think so. Note Tin said the original engine was 1 pound. If you double its size in every dimension then the weight will in fact cube.

 

[Ken I]

Only if it's solid.
...Lew...

Doesn't matter what shape or complexity - if you scale up 2:1 - and make it from the same (density) materials it will weigh 8 times as much.

Ken

 

[steamer]

2 cubed is 8.... ;D


YUP

Dave

 

[JorgensenSteam]

I am not sure about all that math, but I do know there is a law of physics that states that the cost of the project is always 2-4 times what you thought it would be. That I understand.

 

[Tin Falcon]

and take 8 times as log as expected . LOL
Tin

 

[miner49r]

Great information. Where do I send my tuition? OK. Let's see if I have my brain around this.

At 1/20th scale the model is 1/8000th this size of the original as far as size and cylinder displacement. Does this correlate to the model putting out 1/8000th the amount of torque? Once again, I don't think the answer is so simple.
It was stated above that due to the lower mass of moving parts that the model will be capable of reaching greater RPM's, thus creating more power. This raises the question of whether this increased power is considered torque or horse power.
Damn! I should have gone to college.

 

[ShopShoe]

Sidetrack warning:

In my high school physics class we had to show the math to prove why the giant insects of the 1950s science fiction movies would not be possible. (I still remember that we did it, but I can't do all the math now.)

--ShopShoe

 

[mu38&Bg#]

No, the answer isn't so simple. When you get to very small engines the efficiency drops. 1/20th size would definitely see this. RPM can be increased and that helps, but it also depends on engine design. A two stroke could run fast and make a lot of power. 1/20th four stroke would be difficult. Of course, the power output only matters if you have a need for the engine to do something other than just start and without a load.

power=torque x RPM

So more of either torque or RPM makes more power. Now, if you have a real load you will be trying to pull with this scale engine you can determine if it's possible or scale your load so it's possible.

1/20th scale would be tiny for all but the largest engines, so what the heck is it you're modeling?

Greg

 

[Ken I]

Sidetrack warning:

In my high school physics class we had to show the math to prove why the giant insects of the 1950s science fiction movies would not be possible. (I still remember that we did it, but I can't do all the math now.)

--ShopShoe

I remember doing the same thing in college strength of materials class - a movie called "IT" IIRC was about ants which had mutated in the desert after the atomic testing which were 30' long - not posible given the structure of an ant - its own mass would crush it.

Even a mountain can't be infinitely large - for each doubling of size its mass increaces 8 times but the area to resist its mass only 4 times so for each doubling of size there is a 2:1 reduction in strength to weight.

This is what makes children so full of beans at half your height they have twice your power to weight ratio (not strictly true as they are "scaled" differently).

I made an error in my earlier post which I have edited...

Theoretically a 2.0 litre V8 is capable of producing 26% more power than a 4 cylinder of the same capacity.

(edit - I originally said twice the power - woke up in the middle of the night realising its the third root of 2 - ie 1.2599 - glad I spotted it before Marv did.)

Ken

 

[miner49r]

Hey Greg, It looks like we're almost neighbors.
That's just it. Everybody asks me what my engines do. I would like to be able to run something with a reasonable load. I see Brian Rupnow is enjoying some success with his donkey winch. Maybe an alternator powered by a three horse power engine. Possibly twin mill engines somewhere in the ball park of 1-1/2" bore and 2" stroke ought to be close.

 

[steamer]

Most naval Architects caution about home builders building too big....a 32 footer is 8 times the cost and labor as a 16 footer.


A fact often overlooked by the amateur builder....and why there are so many half built boats out there!

Dave