"DSK" wrote in message
...
Rodney Myrvaagnes wrote:
You are using "asymptote" in a metaphoric, rather than mathematical
sense.

Not at all.

Some realistic numbers, for example:

Let's say 1 horsepower (applied) will drive a given boat 4 knots.
2 horsepower will drive it 5.5 knots
3 horsepower will drive it 6.7
4 horsepower will drive it 7.5
6 horsepower will drive it 8.1
8 horsepower will drive it 8.5
12 horsepower will drive it 8.7
20 horsepower will drive it 8.8
50 horsepower will drive it 8.85

Now, is this a boat capable of planing? If yes, then we'll see an
increase in the amount increased speed for the next increase in
horsepower... then the trend will reappear.

These figures are not realistic. Up to the point of the hull speed they
resemble reality, but as soon as the hull starts planing, more 'ordinary'
rules of resistance/drag apply and as far as I know the function becomes
more like a square root function, which is mathematically definately not an
asymptote.

Meindert