dougies, PLAINLY you don't have a clew what the word "asymptote" means.
PLAINLY.

Now, KINDLY knock it off.

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.

Next thing you know, each increased bit of speed, down to hundredths of
knot increments, require many hundreds of horsepower to attain. Is this
asymptotic enough for you?

No?

Okay, let's keep going... we have hypothetically infinite horsepower
If we were adding millions of horsepower for each hundredth of a knot
increase in speed, is *that* asymptotic enough for you?

No?

How far do we continue this trend? We're inventing new universes to
contain the number of added horsepower for each increased femto-knot.

For the last umptysquintillion trillion horsepower we've added, we have
not seen a 1/8 knot increase.... Let me guess, you don't consider that
asymptotic?

I would, and so would most mathematicians & most yacht designers. YMMV

Fresh Breezes- Doug King