Power-speed graph displacement catamaran

Your friend is using the V^3 power law to support his arguments, which is not correct for all displacement vessels and all speeds. It is grossly correct for all vessels at very low speeds (low wave formation), but as soon as wave resistance starts playing a major role, humps and hollows is created in the power curve which invalidate the V^3 law.

If a hull follows (roughly) V^3 law it means that the predominant part of it's resistance is due to friction and that the wave resistance is a minor player. Kayaks are a good example of this behavior because of their low mass, as well as very slender mono and cat hulls (with length-displacement ratio L/D^0.333 above 7-8). regarding the cat vessels, the condition of low wave resistance is reasonably true if they are operating sufficiently far from the zone of hydrodynamic interference of the hulls.

You wanted to see some graphs. I think that this one will say it all very eloquently: http://www.boatdesign.net/forums/boat-design/frictional-resistance-15949.html#post125444

Cheers

 

Best way to resolve this is to examine the fuel usage of a displacement cat of the size that interests the OP, at the speeds he is interested in. There ought to be a rough equivalence between fuel use and resistance, that will suffice for his purposes. I would be amazed if fuel use at 20knots was 8 times that at 10 knots. It would be nowhere near it. Not within a bull's roar ! There should be some boat tests on the net that show fuel use Vs speed for vessel of the type that will confirm this.

 

Voila ! Just the very thing..............

http://www.argusboats.com/index.php

A claimed fuel use of 1 litre per nautical mile @ 8 knots, and 1.5 litres per nautical mile @ 16 knots, which by my calculation is triple the fuel flow at double the speed.

 

A pure case that the numbers coincide at those particular speeds.

Take a look at the graph in that page:


I have taken those values and put them into an excel spreadsheet. Then have plotted the LPM vs KTS and this is the result:

Definitely not a smooth 3rd-power curve, as expected. So evidently the V^3 law is not valid here.

Cheers

 

The curve is quite flat over the mid-range, which obviously is affected by the characteristics of the engines and props as well as the hull resistance, but is not at all supportive of a rapidly increasing resistance in that speed range. What surprises me about that boat is how much trim angle under power it shows, considering the hull type.

 

I have seen similar graphs as well but the conversation is centered on <5kn speeds which is where most of these graphs stop. Since the idea is to use 4kw torquedo outboards the top expected speed is 6kn.

 

A 35ft power cat driven by 4kw (5.5hp) outboard is really a non starter I'm afraid. Unless you are only using it on inland flat water canals you will literally go nowhere in any waves or wind irregardless of what the theory tells you. In flat water I would think a lightweight 35ft catamaran could do 6 knots with a 6hp outboard. But if it is solar powered it will not be light (sorry, accidental pun)

So what is the SOR of the boat??

Richard Woods

 

As Richard Woods said.
But, to answer the question in the OP, for speeds below 5 kts and for reasonably slender hulls around 35' long, most of resistance comes from viscosity-related sources. Hence, the V^3 relationship for power is very likely valid in that speed range.
Cheers

 

True, but not many people will want a boat that does 2.5knots, even on canals where speed is limited to the speed a horse can walk. Which of course implies 4mph needs 1HP on a canal

The OP may find this article interesting

http://www.passagemaker.com/articles/technical/power/the-science-of-hybrid-propulsion-part-2/

Richard Woods

 

The SOR is basically all all electric vessel capable of duration or love aboard cruising with ocean crossing capability.

The proposed plan is a 45' catamaran, twin torquedo 4kw's, (18) 700ah 3.2V LIFPO4 batteries, and (18?) 150watt flexable solar panels to generate power. Expected speed at infinite range is expected to be 4kn.

 

I can see a potential for a huge marketing success there...

Gives a new meaning to the term "pleasure boat".

 

Sorry, I'm missing something...

You say 8kw of engine power will be powered indefinitely by 2.7kw of solar power?

You will need more than 300W of solar to charge the domestic systems alone with no generator. That's what we have and it is minimal for a small fridge (no freezer) plus lights, computers etc. A 45ft cat will use a lot more power, as it will probably have a watermaker, anchor winch, freezer etc

As I said earlier, there is no way you can power a 45ft cruising catamaran off a lee shore into waves with two 4kw engines

Richard Woods

 

Lol. I should edit it, but.... I don't want to.

 

Appropriately made point, the safety aspect is dubious at best. There are a wide variety of circumstances where being restricted to a snail's pace is disadvantageous safety-wise, even down to the fatigue factor. It is more a raft than a boat.

 

Not my plan, I think it's a pretty stupid idea. I was attempting to show why it was stupid, but I don't think I am getting thru to them. The concept however is that by using the engines at less than full speed you could go forever, charging the batteries during the day, and using the power at night to achieve reasonable average passage speeds.

Personally I figure add a sail or two and save the headache.