Solar Power and Scale Factor

You Did not get the answer to your question?? What??

From Alan Craig, post #11.......... "All the rest - I give up. I didn't ask the question you seem to want to answer."

Well Alan, evidently you did not read an early post that exactly answered your question. The question you were asking:

"Should a solar powered vessel be big or small?"

And the answer that was clearly given in post #5: "Bigger is more economic, a fundamental property. This was well known for the last 200 years, when coaling stations limited the economics of steamships".

 

This statement is incorrect for a solar vessel, and has been shown to be so due to scaling laws permitting less surface area per unit of displacement as the vessel increases in size. This means as a vessel gets larger it becomes impossible for the power generated by panels to provide the required energy for the ships displacement increase, which rises exponentially in comparison to the available area for panels. To put it another way, as the ship gets bigger the sun does not increase its output to compensate, and the area available for panels does not go up linearly with displacement.

I even provided a link to those who do not understand the effect of scaling laws and how they apply in this case.

http://www.boatdesign.net/forums/boat-design/solar-power-scale-factor-57148-2.html#post796771

 

Actually, that kinda assumes that the vessel is to be used as similar Fn since power needs to not increase linearly. A slow solar ship may sorta work.

But as I mentioned earlier a slow ship has other issues, and payroll probably isn't the deal breaker that issues with cargo would be, as some cargos might be time sensitive in and of themselves while others, shipped for industry using the just in time manufacturing, would require more cargos be at sea at any given time to keep things moving, meaning a lot more of their money doing something cost related rather than profit related at any given time.

But if the cargo is instead (probably rich) people wanting to look down their noses at ordinary cruise passengers for being on fast non-solar boats I say to them: go for it!

Just think, such a slow cruise liner may help keep such folks away from the rest of us for extended periods of time.

(here I'm assuming that since the power to size density of a solar ship is low it would mean that the number of passengers with power hungry lifestyles would be limited, upping the size of accommodations per passenger, a vicious cycle that means fares would be very pricy)

 

These are fast cargo ships or reefer vessels carrying perishable cargo. Definitely not a candidate for solar ships. Speed is important, fuel consumed is secondary.

 

Look up just a few posts and I did the analysis. Emma Maersk operates with 13 people, to move the same volume of cargo by clipper ship would take about 20,000 people. Yes the labor costs would be a deal breaker.

The largest and fastest solar vessel in the world averaged 5kn on her transatlantic record run with no cargo. And minimal crew. That is about 20% the cruising speed of the QE2. The QE2 takes 8 days to cross the Atlantic, so we can hypothesize that a solar cruise ship would take 32 minimum. Thought the extra food, staff, and other supplies likely means you would have to slow down even further.

 

Ah, but I wasn't talking sailing.

Though, btw, the rig used on the Maltese Falcon was originally designed for cargo use and with its high degree of automation, now sorted out, we can no longer say that payroll need be the deal breaker for use of sailing cargo ships.

 

Seriously? You are going to compare a modern designed sailing cargo ship (which is what I recommended that research/designing efforts be focused on) to the Flying Cloud, a clipper from 1862 as your rationalization that sail isn't the answer?

Please, how about modern rigs (or at least more modern than square rigging) with modern materials for ships designed to hold TEUs. There is nothing stopping anyone, and no they wouldn't need 100 crew members...oish...please dude.

 

Here is one by Tad.
http://www.boatdesign.net/gallery/showphoto.php/photo/24825/ppuser/287

 

What existing ship would you prefer to base the calculations on? I don't really care, I just used the FC because her data is easy to come by. But pick any sailing vessel with a registered tonnage and I will be happy to do the same.


I was thinking about this, and at least initially it would be far easier to apply a sailing rig to bulk liquid carries instead of containers. Jus because you eliminate the entire crane issue at no additional complexity. So why I doubt it will make any difference a better comparison than the EM is probably a VLCC. With less installed hp and a lower cruising speeds these are even likelier candidates for conversion. So as a base I am going to assume the Exxon Valdez (23,000kw engines, a cruising speed of 16.5kn and 214,000 DWT capacity).

But working from the Maltese Falcon, which to my knowledge is the largest rig of its type ever built... Th MF carries 2,400m^2 of sail to move her 1,250 ton displacement or 1.92m^2/ton.

The Valdez has a total displacement of 250,000 tons. So assuming you keep the same Sa/d that works out to about 480,000m^2 of sails. You would want (ithink to preserve the three masted nature of the rig, and carry sails all the way out to max beam.

So 480,000m^2/3 masts = 160,000m^2 of sail area per mast.

Since the Valdez is 51m wide, you would need to go up 160,000m^2/51m= 3,137m (10,500 feet, or 1.98 miles) tall to carry all the sail.

Now I am not by any means an expert on rotating, carbon, free standing masts, but I am doubtful that it is possible to build a mast this big. Though you could probably go a little lower, after all at altitudes higher than the cruising height of small aircraft you should have more wind.

 

This is why I said there is a limit to where sail gets more expensive than diesel. I have heard even on megga pleasure yachts with sail its far cheaper to motor due to the horrendous expense of maintaining the sailing rig. At this size its status and pleasure, not money saving. Now look at the displacement difference between the MF and EV which is 200 times higher.

A sailing assist ship would have the largest rig before costs blow out of control, this rig is much smaller than required for sail only propulsion so diesel engines will still be required.

 

We definitely got sidetracked with the sailing. That's not really a solar question.

A larger vessel is more efficient from a cargo*speed/power standpoint. However, since solar power is a function of surface area you run into problems when you scale up. Even if you cut back the Fr massively by traveling well below hull speed it doesn't follow that a really huge ship will be able to carry enough solar to make a remotely practical amount of power.

If we look to nature there are a ton of motile photosynthetic organisms at very small scale, but as you get larger the organisms operating on solar flux get more and more sessile.

 

The scale factor for panel area VS displacement has been mentioned ad nauseam with links and explanations. The original question has been answered.

 

Bigger is better

From DennisRB, addressing the fredrosse statement "Bigger is more economic, a fundamental property.",

DennisRB indicates....."This statement is incorrect for a solar vessel, and has been shown ............I even provided a link to those who do not understand the effect of scaling laws and how they apply in this case."

In fact, this statement that bigger is fundamentally better is proven below, with simple math and a few fundamental relationships. I will not address all kinds of nebulous constraints such as crew size, unloading time, etc, just give a comparison of two hypothetical ships, one is 25% longer the other in all dimensions:

Let us start by stating the criteria, in this case, delivery of cargo from one place to another, the criteria is, which ship can deliver more tonnes of cargo to the destination, per hour of sea time. Of course, both ships are pure displacement ships.

Small Ship 100 Meters LWL, 18 Meters Beam, 6 Meters Draft, 8640 Tonne, hull speed = 13 knots, requiring 12960 Horsepower to make hull speed. Area for solar collectors = length x beam = 1800 Sq Meters

Big Ship 125 Meters LWL, 22.5 Meters Beam, 7.5 Meters Draft, 16875 Tonne, hull speed = 14.5 knots, requiring 25312 Horsepower to make hull speed. Area for solar collectors = length x beam = 2812 Sq Meters

Assuming 0.3HP per square Meter of collector area (or use whatever number you like), the Small Ship will travel at 4.51 knots, and deliver, on average, 19.5 tonnes per hour across the waterway, assuming half the displacement is cargo.

With the same assumptions, the Big Ship will travel at 4.68 knots, and deliver 39.5 tonnes per hour across the waterway. So the 25% longer solar ship would be capable of delivering twice the capacity of the smaller ship.

The inputs used here, hull speed = 1.3 * SQRT (LWL), and 1.5 HP per tonne required for hull speed. HP required is a cubic function of speed for actual speeds below "hull speed".

 

How are you calculating the speeds under solar power? Both of those ships will be grossly under powered with the available panel area and would probably struggle to make way in a headwind. The 25% longer ship has 25% less power per ton as per the scaling laws.

Below I used 0.3hp per m2. Generously assumed a rectangular array of LxB, generously assumed 25% of the 0.3hp would propel the ship over 24 hours with the fact of night time and conversion losses. In reality this would be even worse.

Small 540hp 8640t = 0.0156 hp per ton
Big 844hp 16875t = 0.0125hp per ton

That's less than the power of a fridge lightbulb per ton.

Does this level of powering seem adequate to anyone? How are you getting a higher speed with 25% less power? The real speeds here would be so low wave making / approaching hullspeed would not be much of a factor. Wetted surface has gone up even more per m2 of panels on the larger ship. Just a rough calc for wsa, the surface of the bottom of the ship has gone up the same as the panel area, BUT there is extra 25% extra depth so each m2 of wsa has less panel area AND it has an extra 25% of displacement!

 

From DennisRB: "How are you calculating the speeds under solar power? "
ANS: Per my last post, horsepower at 1.5 horsepower per tonne of displacement, at "hull Speed". For displacement ships of equal geometry, this is a common relationship. For speeds below "hull speed", the required power is a cubic function of speed: HPlowspeed = HPhullspeed * (Knotslowspeed/Knotshighspeed))^3 simple as that.


"Both of those ships will be grossly under powered with the available panel area and would probably struggle to make way in a headwind. The 25% longer ship has 25% less power per ton as per the scaling laws. "
ANS: All correct, but extraneous to the topic, we are not discussing the practicality of a solar ship, but just its theoretical performance difference according to size.

"Below I used 0.3hp per m2. Generously assumed a rectangular array of LxB, generously assumed 25% of the 0.3hp would propel the ship over 24 hours with the fact of night time and conversion losses. In reality this would be even worse."
ANS: All correct, but running the numbers with any conversion efficiency and utilization factor will give the same conclusion.

"Does this level of powering seem adequate to anyone? "
ANS: Power not adequate, that is why these are only being built by uninformed dreamers, but extraneous to the topic, we are not discussing the practicality of a solar ship, but just its theoretical performance difference according to size.

How are you getting a higher speed with 25% less power?
ANS: The fundamental relationships are clearly stated in the previous post. But notice, the small ship uses 540 Horsepower, the big one uses 844 Horsepower, not less power? What is your statement based on?

The real speeds here would be so low wave making / approaching hullspeed would not be much of a factor. Wetted surface has gone up even more per m2 of panels on the larger ship. Just a rough calc for wsa, the surface of the bottom of the ship has gone up the same as the panel area, BUT there is extra 25% extra depth so each m2 of wsa has less panel area AND it has an extra 25% of displacement!
ANS: Actually the small ship is 8640 ton, the large ship 16875 ton, the big ship has almost double the displacement.