Re: [PSUBS-MAILIST] Bouancy (please read)

["Captain Nemo" <vulcania@interpac.net>]

----- Original Message -----
From: "Carsten Standfuß" <MerlinSub@t-online.de>

"Unfourtunatly the scale problem with your model and the original cover
(maybe) the small amount of effect. (means for your model the atoms of the
water are bigger in scale than for the original scale ship. So its creates
other geometry of waves than the orignial ship.) Lot work if you figures
with so small effects.."

Carsten's right; this becomes pretty complicated.

First of all, SCALE SPEED can be thought of as the velocity a scale model
might move in relationship to a scale environment, and the calculation used
to determine it would be relative to, say, a scale time and distance
problem.

CORRESPONDING SPEED is a concept devised by a German engineer named Froude
in his work LAW OF COMPARISON,  (where he also refers to it as "wave form
speed"): basically, the speed a scale model must move through water to
create a realistic hydrodynamic effect: bow wave, wake, control reactions,
etc.

SCALE SPEED and CORRESPONDING SPEED are not the same; the formulas used to
determine both are different; and which one you'd use depends on what you
want to determine.

As Carsten points out, in your case, you're looking for realistic
hydrodynamic effects of the scale model running in full-sized water
molecules, so Mr. Froude's CORRESPONDING SPEED formula is what you'd use.
(This is what they use in hull testing tanks to examine the hydrodynamic
characteristics of scale models.)


If you wanted to determine SCALE SPEED (as in a scale time-and-distance
problem) the formula would be:
(Where): Vk = Actual Velocity in Knots,
                 S= Scale, and
                Vs= Scale Velocity ("scale speed" expressed in inches per
second)

Vk X 1.15 X 5,280 -:- 60 -:- 60 -:- S X 12 = Vs        (or, expressed in
terms,)

Actual Velocity in knots, multiplied by 1.15, multiplied by 5,280, divided
by 60, divided by 60, divided by Scale, multiplied by 12, equals SCALE SPEED
expressed in inches per second.



However, if you wanted to determine CORRESPONDING SPEED, the formula (harder
to type) would be:

Vc = Vk -:- (--v-- S)            (or, expressed in terms,)

CORRESPONDING SPEED  equals Actual Speed divided by the square root of the
Scale.  (The --v-- symbol is what I've typed to simulate the square root
sign, because I don't have easy access to the actual square root emblem on
my computer).



Let's consider the difference between SCALE SPEED and CORRESPONDING SPEED
calculations.  For our example, we'll be talking about a 1:96 scale Los
Angeles 688 Class submarine; actual length 360 feet; scale length 45 inches.
We'll compute SCALE SPEED and CORRESPONDING SPEED for an actual LA  sub
moving, say, 30 knots.

SCALE SPEED:

30 kts X 1.15 X 5,280 -:- 60 -:- 60 -:- 96 X 12 = 6.3 IPS.

What this means is, if the real sub is moving 30 knots in relation to the
real coastline; and you want to simulate the movement of a scale model
relative to a scale coastline, the model will be moving a SCALE SPEED of
about 6.3 inches per second.
That's if you wanted to, say, simulate the time it would take for the model
sub to, say, move past a model bridge or other fixed surface feature, you'd
move the model at about 6.3 inches per second.



But if you wanted to simulate the scale effect of how the sub interacts with
water (how it generates a wake, a bow wave, or responds to hydrodynamic
control inputs), then you'd use the formula for CORRESPONDING SPEED (this is
more like what you want for your purposes).

CORRESPONDING SPEED:

We'll divide the actual speed in knots by the square root of the scale to
determine CORRESPONDING SPEED:

The Scale is 96; the square root of 96 is 9.79795897.  So:

30 kts -:- 9.79795897 = 3.06 kts CORRESPONDING SPEED.

In other words, if we want the 1:96 scale LA sub to generate bow wave that
looks the same relative size as that produced by the full sized sub moving
at 30 knots, we'll have to move our model at 3.06 knots (about 3.5 MPH, or
61.6 IPS.)


So, you can see there's a big difference between 30 Knots in SCALE SPEED and
CORRESPONDING SPEED in this case: SCALE SPEED is about 6.25 inches per
second, while CORRESPONDING SPEED is about 61.6 inches per second.

Like I said, a little complicated.

Katie, one thing you want to keep in mind: engineers use CORRESPONDING SPEED
equations with reference to very exact scale models operated in a controlled
environment (hull testing tank) where conditions can be regulated with
extreme precision.  I've given you these formulae as something to think
about and learn from; but it's going to be pretty hard to apply them to your
own homemade sailboat models with enough precision to determine the
minuscule differences were talking about in your freshwater versus saltwater
experiment.

But I don't want to discourage you.  Keep studying, experimenting, and
learning in every way you can.  .

Good luck to you, and I hope this has been of some help.

Very best regards,

Pat Regan
vulcania@interpac.net