# On the Fractal Dimension of Rough Surfaces

Chapter

First Online:

## Abstract

Most natural surfaces and surfaces of engineering interest, e.g., polished or sand blasted surfaces, are self affine fractal over a wide range of length scales, with the fractal dimension \(D_\mathrm{f} = 2.15 \pm 0.15\). We give several examples which illustrate this and a simple argument, based on surface fragility, for why the fractal dimension usually is \(<\)2.3. A kinetic model of sand blasting is presented, which gives surface topographies and surface roughness power spectra in good agreement with experiments.

## Keywords

Power Spectrum Fractal Dimension External Object Capillary Wave Engineering Interest
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Notes

### Acknowledgments

I thank J. Krim for useful comments on the text.

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