PPRuNe Forums - View Single Post - OK, all you heliGods out there. I seek your wisdom.
Old 8th Feb 2009, 16:36
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ramen noodles
 
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The hidden factor is the "squared-cubed" law, which we see in every Godzilla flick. When the monster picks up a train car and eats the passengers like candy from a box, it seems ok, but in reality, the car would fall apart if picked up by its roof and sides at real scale because the materials do not change in strength, but the weight of the item and the stresses in the material go up by orders of magnitude. In effect, little things can be thought of as if they were made of steel and big things as if they were made of cheese.

Why? Because the stresses created in the materials of big things are many times higher than the stresses of smaller things, the materials have one given stress capability, big or small, and the weight of the whole item goes up by its general volume, which is the cube of the length (length times the length times the length.)

The "squared-cubed" law goes like this: The size of the item grows so that any given cross section of the beams that make it up gets bigger by the square of the length of the item. If the railroad car goes from one foot long (a toy) to 50 feet long, then each beam element that makes up the car gets greater area and greater load bearing capacity by a factor of 2500. In other words, if the roof beams are 1/25th of an inch across in the toy (1mm) then they would be 2" on a side in the real, 50 foot long car. But the weight of the beam and car go up by the cube (third power) of the length, so the 50 foot long car and its beams see the stresses go up by a factor of 125,000. Thus, the big 50 foot car is 50 times weaker than the toy, and crumbles when Godzilla grasps it in his hands.

This "squared-cubed" law pervades everything we see and do, but is now obvious to us. If a bridge must carry a road bed and train that weighs 5,000 tons, and we double the length of the span, the bridge might need to be 5 times deeper in its main box structure to carry that load across the longer span.

Thus, little RC models do wild things, but if we translate them to full-sized stuff, they would crumble.

Here is a small discussion of the beam equations. Notice that the force bearing capability of the beam goes down by the cube of the length, so that the beam gats weaker very fast as it gets longer:
www.brushwellman.com/alloy/tech_lit/march01.pdf
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