My thinking is that a boat of this style, amount of superstructure and detail built to a scale giving a sub metre length is not a practical model in anything other then dead calm conditions - great for the shelf though.
Seems you're right. Unfortunately:
Not wanting to bore you with mathematical similarity laws,
just a rough calculation I just made and which I found quite
interesting:
All of you know that mass or displacement are scaled by the
power of three.
As the lever on which the righting forces act on a listing boat
is scaled simply with the scale of length. The righting torque
at a given list angle therefore is scaled by the power of four
(By the way, the same scale factor also applies to the torque
of the drive if we want to reach scale speed).
Now for the wind: The lateral area of the boat on which the wind
acts is scaled by the square of the length scale.
The listing torque caused by the wind and acting on the boat is
proportional to the lateral area (square of length scale)
times the height of of the center of that lateral area (length scale)
times the square of the wind speed.
The scale of the listing torque is therefore the cubic of the
length scale times the square of the scale of wind speed.
Pfff - so much for the theoretical background....
But now it gets interesting:
Every model ship builder knows the scale speed according to Froude,
which means that a speed scaling factor of the square root of the
length scale leads to a similar wave pattern.
If we assume a "Froude wind", for example only 1/7 of the original
wind speed for a 1:50 scale model, we would get an identical
listing angle as the prototype:
The listing torque caused by the wind would scale by the power
of four, just as the righting torque does.
So even the wind makes no exception to Froude's law regarding
the similarity of liquid behaviour.
But as we experience on our pond the SAME REAL wind speed
given by mother nature, a moderate 20 kph wind would act on a
1:50 model boat in the same way as a 140 kph gale on the real boat!
And I wouldn't like to be on the ocean on a high rising wooden
riverboat during such a gale!
Therefore, the theory can fully underline what you experienced
the hard way: High rising riverboats are very prone to wind
problems, which get worse with miniaturisation.
Small models of riverboats unfortunately seem to be restricted to
fair weather or even indoor use, even if measures such as very
light cabins or ballast keels are taken. Unless you find ways to
increase the righting torque by the factor of 50.
Looks like I will have to rethink my sternwheeler plans, and
concentrate on low sitting river carferries, providing a minimal
amount of lateral area and height.
So much for that, Moritz
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