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What is a "power law index"

My son, studying at Plymouth University asked me today thinking I might know from my boat building days.

That was a while back, I have been a marine artist for almost 30 years.

How should I know???
I thought the idea of Uni was to learn things parents don’t know, or have I missed some thing here?

Do you have any info or any thoughts on what is a Power Law Index?

He wrote, it’s the kind of thing that comes up on some coursework on hull dynamics and he is not quiet sure what this turn means and didn’t really understand it when he looked it up.

It’s in relation to hull resistance.

Resistance = C x Vn   (C = variable coefficient depending on hull form       and      n = power law index         V = boat speed

If you know more kindly point us in the right direction, thank you?

I replied as best I could ~

Power Law ~
2 web sites that may be helpful:

I’m not sure and can research further for you if that saves you time.

A Power Law seems to be a statistical (mathematical) way of charting unusual events.

Americans use it re casualties in a terrorist war for example, where a normal bow chart would not serve well.
The intention being to see patterns and predict the likely hood of future unusual events.

In this case it seems related to hull resistance and water flow over the hull in varying sea conditions thus useful for predicting handling characteristics and predicting theoretical boat speed in all weathers.

I currently have a marine art enquiry for a commission from an American who says his 40′ yacht (a Cutlass 40) clocked 26 knots on one occasion and that with a broken bow sprit.
I’d have thought give the conventional water line length data for hull speed, that would be impossible.
A Power Law calculation might have predicted this?

Given most sailors are by training quite careful and realistic about information I’d say his yacht probably did make 26 knots even if conventional science does not know how to predict such an event.

Thus my guess is a Power Law Index is a mathematical way of trying to predict events like the exceptional possible boat speed of the Cutlass 40.
It would of course be very useful with boats like the Vendee Globe yachts enabling designers and crew to know they can get more out of a boat.

In my youth I was taught boat and ship building by people who had built boats on a beach, things have moved on!

I’ll blog this interesting question. I am amazed by who replies to some of my blogs. We may be lucky

I also found:

What is a power law?

A power-law is a particular type of statistical pattern.

It is very different from the more familiar bell curve typically associated with random incidents.

The main practical implication of a ‘power-law war’ is that big incidents,  are always quite likely to happen.

If the distribution of exceptional events were a Bell curve rather than a power law, then such big events would be theoretically virtually impossible.

A power-law, with its associated power-law index, represents a particularly potent indicator.

The presence of a power-law has important practical implications concerning future risk: for example, the risk that future attacks will be of a particular intensity or larger.

It should be possible to build up a toolbox of such indicators in order to fully characterize the spatio-temporal behavior of such incidents and hence fully characterize a series of extra ordinary and apparently random event evolutions and the associated risks.