Re: Small sailing ship help

In article
<e6b8d9f3-70c0-4678-a8a4-dd5fab48ad0a@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Bob Throllop <bobthrollop@xxxxxxxxxx> wrote:

On Nov 21, 1:52 pm, David Friedman <d...@xxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
In article
<9eb48fe6-2ddb-4c26-9454-68847f903...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Bob Throllop <bobthrol...@xxxxxxxxxx> wrote:



On Nov 21, 10:22 am, David Friedman <d...@xxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
In article
<d1147668-a766-4ef7-bbdc-f6dde5852...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Bob Throllop <bobthrol...@xxxxxxxxxx> wrote:

On Nov 20, 11:09 am, David Friedman <d...@xxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
In article <JrtIMw....@xxxxxxxxxxx>,
djhe...@xxxxxxxxxxx (Dorothy J Heydt) wrote:

Speed (in knots) = 1.4 * sqrt waterline length.
[...]

Did sailing ships typically move fast enough for this constraint to
become binding?

If you mean, did they routinely cruise around those speeds, I believe
the answer is no; only the very fastest ships (like clipper ships and
racing yachts) in strong winds could approach them.

But the principle that a longer hull moves faster still applies at any
speed and wind condition.

The conclusion might still apply, but I don't see how the particular
reason for it, having to do with the speed of water waves of different
lengths, would.

Okay, let's try this: the drag due to the bow wave is a function of
how far out of "phase" the stern is, which can in turn be expressed as
a function of speed and length. It reaches a minimum at the magic
speed, but it is a decreasing function at lower speeds, which means a
longer hull still gains an advantage.

I assume there's some speed below which it ceases to apply; the out-of-
phaseness is an oscillating function, as things associated with sine
waves tend to be,

That was the point that had occurred to me.

and other factors come into play, such as ordinary
parasite drag which is always greater for a bigger cross-section, and
the fact that a bigger ship probably has more power or more sail,
etc...at this point, I don't have numbers so I don't know what is the
actual speed range where the rule applies.

I had wondered about scaling effects in general--what went as the first
or second power and what as the third or higher.

The following is rather vague as I don't know how closely the basic
principles apply to real-life ships (and I rather suspect there aren't
any widely applicable rules-of-thumb), but here are some basic facts
of life from undergraduate fluid dynamics:

Power required vs. speed:

Drag force (the standard fluid dynamics equation, ignoring the bow
wave effect discussed above) is proportional to velocity**2. Since
power consumed = force X velocity, that means power required is
proportional to velocity**3. (That's water speed.) Force on the sails
follows the equation for aerodynamic lift, which tells us propulsive
force is proportional to wind speed**2.

Surely that's wind speed relative to the ship. If the ship is running
before the wind, that would be the difference between wind speed and
ship speed.

Now, a force needs to be
applied over a distance before it can do actual work; the upshot of
which is that power generated is proportional to wind**2 x hull speed,
another third-order formula.

It's first order in hull speed, second order in wind speed relative to
hull, which is a different variable. And it's a decreasing function of
hull speed, not an increasing function.

Poswer required vs. size:

Now when we scale for ship size, drag is also proportional to cross-
sectional area, which means that (assuming the same shape), drag is
proportional to length**2.

Only if the depth below the water line is proportional to length, which
it doesn't have to be. If you simply scale the ship up in all dimensions
it works, because displacement goes as the cube then too. But if the
hull thickness stays constant instead of increasing with the other
dimensions, then mass only goes up as the square, so displacement goes
as the square, so depth below the water line doesn't change. Off hand,
I'm not sure if thickness of the hull has to increase as you scale up or
not.

--
http://www.daviddfriedman.com/ http://daviddfriedman.blogspot.com/
Author of _Harald_, a fantasy without magic.
Published by Baen, in bookstores now
.

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