Introduction to Nanotechnology
  • Introduction to Nanotechnology
  • About
  • The Nanoscale
  • Scaling Laws
  • Scaling Law Calculations
  • History of Nanotechnology
    • Nanotechnology Discoveries
  • Nanotechnology Today
  • Risks vs Benefits
    • Critique
  • Contact

Scaling Law CALCULATIONS

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The implementation of simple scaling law calculations, can also show how different ratios of properties (force, weight, volume, area, etc) change when scaled down. Scaling laws with positive exponents become more important as things get larger, for example weight being proportional to volume D^3, or force ( working on an area D^2. Scaling laws with negative exponents become more important as things get smaller D^-1. So with this in mind different ratios of measurements which have a negative exponent increase as dimensions get smaller.

sTRENGTH TO WEIGHT

Strength(force) to weight, D^2/D^3 = D^-1. With scaling down comes a better strength to weight ratio. Strength to weight gets 10 times better as an organism gets 10 times small. 

A real life example of this would be how ants are able to carry up to 100 times their own weight, and humans are only able to carry up to twice their weight. Some of us not even that.
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pOWER DENSITY

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Power density, power per volume D^2/D^3 = D^-1, increases with miniaturization. 

For example: A battery of 1m dimension produces power of 1,000 watts. Another battery one tenth in size .1 m produces 1/100 of the power(power is a function of D^2), 10 watts. However, in the volume occupied by the large 1 m engine, there is room for 1000 of the smaller 0.1 m batteries which combined produce 10,000 watts. So you can get 10 times as much power out of the same amount of space and material.
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