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Boats/Submarines and the HP of the motor to speed of the craft

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Ash Small

Fri Dec 12 2014, 11:33PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Uspring wrote ...

It follows (to me at least) that the drag must be similar.

Tend to agree, if the volume of water displaced by the kayak has the same shape as a submerged vessel. There are some differences, though,
a) the submerged vessel has a top on which friction can occur and
b) a kayak can displace water to rise above sea level, a submerged vehicle can't.

Interesting is the part on page 10 and 11 of the doc, where it says, an optimal hull width to length ratio is 1:7. I believe that depends much on the speed, since friction effects rise linearly with speed, whereas pressure drag with its square.

A kayak can also rise out of the water itself at speed, thereby reducing it's displacement.

I'm also uncertain of the context of the 1:7 ratio. Payload, propulsion unit and manouverability all play a part here. Pressure is another factor, a cylinder generally has great strength. I believe the paper also mentions the theoretical optimum shape, where the parabolic curves continue to the midpoint. but then settles on a cylindrical centre section. The paper I read recently on Australian nuclear subs seemed to go into more detail. I'll try and find a link. It was the replacement for the 'Collins class', if I recollect correctly, if anyone else wants to look.

klugesmith

Fri Dec 12 2014, 11:59PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Steve Conner wrote ...
A 100kg submarine must displace the same volume as a 100kg kayak, 100 litres of water.

I think the same applies to the water displacement of a 100kg hovercraft. It would be interesting to compare the water surface shape of a stationary hovercraft with that of one under way.

klugesmith

Sat Dec 13 2014, 12:19AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Some Internet searching for hovercraft displacement led me indirectly to this cool chart, which omits submarines and hovercraft.

How about expanding the low end of the chart to show human-powered boats and model boats? I think the forces of inertia and gravity would still be vastly larger than viscous forces.

Steve Conner

Sat Dec 13 2014, 03:40PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

An interesting question. I tried calculating the Reynolds number for my single scull at race speed and it works out well over 1 million, so that would certainly suggest that inertia forces are the main source of drag and friction is negligible.

However as far as I know that is not the case. A good deal of the drag is due to friction in the boundary layer between hull and water. This is the fundamental tradeoff in the design. The longer and finer you make the hull, the less the drag due to inertia forces because it takes more time to move the same mass of water out of the way. But on the other hand, the further you go from a sphere, the greater the surface area to volume ratio and the more drag due to friction on the wetted surface for a given displacement. I got the impression that boat designers try to optimise things by making these two forms of drag about equal.

There is also the matter of wave-making drag which is characterised by the Froude number. A long fine hull makes less wake for the same reason that it suffers less drag from inertia forces, indeed you could say that the wake is the manifestation of the lost energy. I saw one source that claims that submarines don't have wave-making drag.

The pressure under a hovercraft skirt is typically a few inches of water. So, I guess when it is hovering over water, the water underneath must be pushed down a few inches.

Ash Small

Sat Dec 13 2014, 05:53PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

That's a pretty old chart, Rich, but it demonstrates the point. Cigarette was an offshore racing powerboat from around the late sixties, maybe early seventies, which, if I remember correctly, averaged just under 70mph in the Cowes Torquay-Cowes race, I'm guessing in '69.

Offshore powerboats today can get to twice that speed, due to new materials and catamaran design, but mainly due to the huge increases in power due to engine development over the past forty years. The same can be seen in drag racing.

Submarines can still create turbulence, which is the same as wave making drag. Parabolic curves and laminar flow are what is required to minimise this.

Also, a sphere is a lot more manouverable than a harpoon.

klugesmith

Sat Dec 13 2014, 07:47PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Yes, an old chart. We could pencil in modern mega-cruise ships and mega-cargo ships. The Emma Maersk has one of those 14-cylinder Wartzilla engines (109,000 HP at 102 RPM).

I used to think cigarette boat was just a generic term for a long, overpowered speedboat. Named not for its shape but for its utility in the smuggling trade. Just learned that it's also a brand, still in business. Their ads today put a bit less emphasis on hot babes along for the ride.

1418499885 2099 FT167684 420wallp Tiger 2

p.s. What Steve said supports my claim that a stationary hovercraft displaces its own weight of water, just like any other floating body. On water that is shallower than the "draft", land will be exposed and carry the load.

Ash Small

Sat Dec 13 2014, 08:42PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

I think they were all designed by Don Aronow, of the USA. I was right about '69 being the year. Speed was 66.5mph, so I was pretty much spot on there too. I was a kid then, that was one of the first races I saw, really record breaking speed for that course at the time, but it was a calm day.

1418503340 3414 FT167684 The Cigarette 1969

Obviously not displacing much water here.

Uspring

Mon Dec 15 2014, 11:03AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
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Posts: 711

Steve Conner wrote:

I tried calculating the Reynolds number for my single scull at race speed and it works out well over 1 million, so that would certainly suggest that inertia forces are the main source of drag and friction is negligible.

However as far as I know that is not the case.

I've tried to get behind the discrepancy. A very rough estimate of the involved forces would be:

a) Inertial force: The volume displaced per unit time by a moving object with cross section A at speed v is A*v. Its mass is rho*A*v. Assuming this mass is accelerated to speed v the inertial force is:

Fi = v * rho * A * v = rho * A * v^2

b) Viscous drag: The idea is, that you have several layers of flow around the side of the object. The one closest to the object will stick to it and move at speed v. Further out layers will move slower. The drag is then proportional to the area of the layer and the rate at which speed decreases outward, i.e.

Fv = mu * A * dv/dx

Assuming the flow will drop to 0 at a distance L to the object:

Fv = mu * A * v/L

The ratio between inertial and viscous drag is then

Fi / Fv = rho * v * L / mu, which is Reynolds number.

This derivation shows, why a streamlined hull could have friction drag of about the same size as inertial drag:
a) a pointed hull has a much wider area looking from the side than looking from the front, i.e. the A in the inertial equation is not the same as the A for viscous drag.
b) it will displace the water mostly sideways at a much slower speed, than the speed of the hull
c) the characteristic length L, which describes the drop of speed of dragged water further away from the hull is probably only centimeters instead of meters, which reduces the Reynolds number significantly.

Andy

Tue Dec 16 2014, 03:28AM

Registered Member #4266 Joined: Fri Dec 16 2011, 03:15AM
Location:
Posts: 874

Hi Uspring, do those equation match to center of pressure? Havn't looked in a long time, but what you explained seemed to describe that.

Ash Small

Tue Dec 16 2014, 02:26PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

I'd start by deciding what's the biggest thing that needs to go inside, then draw a circle around it, allowing room for mountings, wiring, plumbing, etc. This circle gives you the inner diameter of the cylindrical bit.

You then need suitable parabolic bow and turtle back sections, and then just adjust the length of the cylindrical bit until everything else fits in.

At least it's a reasonable start.

As for propulsion, you effectively have a tug, so you'll want excess power, although I expect there will be a characteristic 'hull speed'.

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