Scales

[Wagon173]

Okay so I've wikipedia searched and google searched the scaling factors and it seems very vague to me. In both sources they have explained that it's a dimension based scale but given a volume based example. So which is it? For example, If I build a 1/3 scale go cart off an existing car that is 144" x 60" x 48" For a total volume of 414,720 CuIn. A volume based third scale would put my dimensions somewhere in the neighborhood of 69-70% of the original dimensions (100.8" x 42" x 33.6" @ 142,249 CuIn). A dimensional 1/3 scale would put me at 1/27 (48" x 20" x 16" @ 15,360 CuIn) of the original volume. Am I over-thinking this?

 

[thayer]

Scale is traditionally considered a linear relationship in the modeling world, so it would be your second example. As you have found, volume scales as a function of the cube, scaling 1:3 gives a volume reduction of 1:27. Area scales as a square function, so the shadow cast by your model will be 1/9 the area of that cast by the prototype.

Thayer

 

[MachineTom]

One interesting thing about scaling, is that the strenght of the material remains the same as the model is scaled down. So in effect the model becomes stronger as it gets smaller. This allows all sorts of things to be done to a model that could not be done to a full size piece.

 

[MuellerNick]

So in effect the model becomes stronger as it gets smaller. This allows all sorts of things to be done to a model that could not be done to a full size piece.

Outch! You shouldn't try this!

Say for a 1:4 scale, area reduces to 1/16. So longitudinal stress is 4 times higher when you also scale forces by 1:4.
Things get even worse with bending forces. Stiffness is a power of 4 function. So at just half the scale, stiffness will be only 1/16.


Nick
Nick

 

[Wagon173]

Okay that takes care of that. Thanks Thayer. Tom, that sort of makes sense when I think about it. Nick, unfortunately so does that...oh the humanity :wall: