A friend of mine was recently doing research, and she told me she had to compare aluminium brake caliper pistons against steel brake caliper pistons. She said it was almost impossible, so I offered to try and help, but safe to say after an albeit rather quick search, I couldn't seem to find much either. So, I figured the next best place would be to ask here as there's quite some knowledgeable and technically minded posters (I'll be the first to admit I was a tad out of my depth whilst searching myself). Anybody out there have the faintest idea where to begin?

The big thing will be the weight v thermal transfer properties comparison. The approach I would use is to initially specify the materials I am comparing, identify their properties and then contrast them. From this you will be able to identify the parameters within which each material would be the ideal choice. As example, a light weight low speed vehicle, I.e a child's pram may be perfectly suited to Alu Alloy but this may not be acceptable on a freight train.

Metal companies often have specs online, as do automotive companies, so you can get a lot of data from the Internet.

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I should think it would depend on many factors. Thermal and weight as above, but also combinations of materials.

For instance, if it is considered 'best' to have Ally bodies, and Steel pistons, Ally expands at a higher rate than steel, so clearances will need to be calculated for uses at different temperatures and the loss of efficiency at either end of the range. It may well be the best option not to go with the 'best' as another option may be better over the whole range.

Not so much with F1 where cost is seemingly ignored, but cost and availability, reliability and life cycle also have to be considered.
Without considering all the options and ranges, not a single answer.