----- Original Message -----
Sent: Tuesday, September 26, 2000 3:52
AM
Subject: [PSUBS-MAILIST] Velocity and
Acceleration
"My two cents on the speed and power of personal submersibles:
A submerged body has the inertia of its displaced volume of water. Wet,
dry or anywhere in between, the mass of a submerged boat is equal to the
mass of the water it displaces. This mass has a large effect on the
acceleration (how quickly it starts or stops), but has no effect on the
velocity. The velocity is determined by thrust and drag. Velocity is hard to
calculate with certainty because of the many and mysterious elements of drag
(profile, skin, wave, parasitic), and the complex interactions of hull, prop
and water. Authors of cookbooks tend to present their formula without showing
their homework, which is unsettling for those of us without the gift of faith.
If I have enough cookbooks to compare, I'll eventually develop some
confidence in a common thread. But we have the additional disadvantage of
dealing in an obscure cuisine (small, low powered displacement hulls.) I'm
always on the lookout for applicable formulae, but I haven't found anything
short and sweet. - Joe"
Thanks Joe, that was well said.
We'd have to compare thrust to drag in determining the velocity at which
acceleration would cease and the vessel would achieve equilibrium in
motion. Calculating the drag coefficient of a multi-faceted hull over a
range of velocities is the hard part. Like you, I haven't found any
"short and sweet" way of doing that, either.
So far, with the small E-motor sub designs I've worked on,
thrust/velocity calculations haven't been too important: no matter what I do,
thrust is low and speed is slow. So, I just get the biggest DC motor I
can find, and expect performance to be underwhelming.
But I've got a Hi-Perf sub on paper; I've built a model of it that moves
pretty well through the water; and I wonder how fast a real one might go
with a large amount of thrust. I've got the basics of a hull and
drivetrain downstairs, but finishing the boat will be expensive; and I don't
want to do all that if she's not going to set a speed record. So now I
wish I could accurately determine how fast a certain hull would go given a
known amount of thrust. And right now, my math just aint that
good.
I'm hoping the calculations page Mike is sending me might give me at
least a ballpark guesstimation of what the sub might do. This is where
it really starts to get tough, though.
And another thing concerns me, too. Accurately estimating the crush
depth of a homebuilt hull is hard enough, but what about the effect of
dynamic pressures on the hull at high speed in shallow water? The
hydrodynamic impact-pressure is going to build up against the leading surfaces
of the hull as she accelerates. When we're talking about a propulsion
source similar to those used in drag boats, the possibility of extremely high
speeds for short periods of times exists, and that means a LOT of pressure on
the hull. I would sure feel more secure if I were able to compute
not only the sub's potential speed; but also to know that the hull's not going
to disintegrate if I ever get her going that fast.
Isn't there some kind of computer program that does this sort
of calculation? I sure hope so, because it's way beyond me and
my little calculator; and the lack of this information is keeping me from
proceeding with a project I have most of the components for downstairs in
the shop at this time. Considering the risks involved, maybe
that's just as well. But still, I'd like to develop the math skills
necessary to figure these sorts of things out.
Pat