Why are larger hulls heavier than smaller ones?

When looking at the displacements of boats of different sizes, you can notice that larger hulls are often somewhat heavier compared to their approx. waterplane area, than smaller hulls.

Bottom loading http://marine.marsh-design.com/content/bottom-loading

This article says that larger hulls can support significantly more weight for their waterplane area without too much compromising planing performance.
Why is that?
Let's say that we have a hard chine variable deadrise planing monohull with these specs:
LWL: 12.8m/42ft
BWL: 3.65m/12ft
Displacement: 10 000kg/22 000lbs
L/B ratio: 3.5:1
Bottom loading: 237kg/m2 / 48lbs/sqft

Waterplane area used for bottom loading calculation is my very inaccurate formula: (LWL x BWL) x 0.90

Now let's make a half scale version of that hull.
This boat will have a LWL of 6.4m/21ft and a BWL of 1.82m/6ft
If we keep bottom loading at the same 237kg/m2, it will have a displacement of 2490kg or 5500lbs.
Assuming that LCG, VCG, COB and other points are roughly in the same place, is there any reason why the smaller hull would be less efficient compared to the larger one?
And if yes, why?

 

One would be the structural needs of a bobbing ship. I think there is a correlation between waterline length increases speed and lessens bobbing, but the structural needs of a larger vessel increase because the ship is larger, heavier AND traveling faster. "the light object has less rest mass resistance againt the changes in buoyancy than the heavier object, "

 

Look no further than the Square-Cube Law.
Square–cube law - Wikipedia https://en.wikipedia.org/wiki/Square%E2%80%93cube_law#:~:text=The%20square%E2%80%93cube%20law%20can,the%20cube%20of%20the%20multiplier.

 

Aye yes, of course. A lot of interesting mathematical topological and volume phenomena with that. Very cool.

 

Thank you for your answers. I was somewhat aware of the square cube law, but I have never really thought about it as a factor in boat design.
But i still couldn't find an answer to my question.
Quotes from the article that i linked above:

"About 200 kg/m2 (40 lb/ft2)- For boats in the 4 to 7 metre range, this is the point where getting up on plane needs a bit of effort, and there may be a range of "no-go" speeds where the boat plows around with its bow in the air. Once up, planing can be easily sustained."

" About 300 kg/m2 (60 lb/ft2)- For a boat in the 4 to 7 metre range, overloading is indicated, and the boat probably won't plane very well. Given enough power, it may run OK at high speed, but will be a dog from 8 to 20 knots or so. In boats from 10 to 15 m LOA, bottom loadings in this range are typical and indicate reasonable performance."

Sdo according to that article, my larger (42ft) hull would have better than "reasonable performance" and the smaller (21ft) hull would have worse than "a range of "no go speeds" where the boat plows around with its bow in the air" even though they have the same amount of weight/load for their surface area. So what about the smaller hull makes it perform worse?

 

Just guessing, but could it be the faster displacement speed of the longer hull before it gets on plane produces more dynamic lift, so can support more weight?

 

Just a speculation, at displacement speeds the water moves aside and flows around the hull.

When planing, the hull is going too fast for the water to get out of the way, so for a given speed a wider hull makes it harder for the water to escape to the sides.

 

The cube square law as it applies to boats.
Consider a boat like mine: looks like a brick from above. 25' long, 10' wide, 10' high. Double the proportions. You have 4 times as much bottom area to plane on. But 8 times the weight. In my boat every square foot of botyom has 10' of boat and contents above it. In the scaled up boat, every square foot of bottom has 20' of boat to support. But it's the same water, same velocity, same physics. There's an upper limit on how big a planing boat can be. Power has the same kind of limitations. A prop is limited by disk loading. A propeller can only handle so much power per square foot, or square meter or whatever. It gets harder to efficiently delivery power through props as power goes up.

 

In general, it is my understanding that displacement stats are given without crew and gear on board. For a small boat (21 feet) under way, the crew, say a pilot of about 200lbs. That is a significant difference from that same pilot bringing a 40+ footer up onto a plane.

Was this difference accounted for when measuring the relative difficulties in coming up onto a plane?

 

While I don't know the engineering, there are others things that wouldn't scale well, such as external waveheights, updraft and downdraft speeds, material stiffness, motor and propellor efficiency.

On the same portion of the same body of water, the external waves (I'm not talking about wakes generated by the boat) are the same height, regardless of boat length. OK, that's not quite true - a short boat can simply ride over the waves without spanning between waves or sometimes burying the bow underwater - but if the boat is longer than the wavelength (or the projection of the wavelength that the boat going in a particular encounters), the bow may sometimes bury itself into an oncoming wave if it isn't high enough above it.

(On the other hand, a sufficiently large ship may not need to plane to be fairly efficient in somewhat rough seas, because the waves are a small portion of the size of the ship. Perhaps that explains part of why large ships tend to be displacement hulls??)

I assume downdraft and updraft wind induced force that tends to make it bounce is roughly proportional to the surface area (i.e., the square of the linear size). But since the weight is roughly proportional to the volume (i.e., roughly the cube of the linear size), the bouncing component from downdrafts and updrafts is less important on a larger boat.

Another thing that adds to the complexity of the calculation might be material stiffness, though that might be very complicated. You might think the weight of a boat is proportional to its volume (cube law), but if you scale the thickness with the linear size, and make a material too thin, it can become too flexible to be practical. I'm not sure how important that is at normal boat and ship sizes. But in very small lightweight boats, material stiffness, not just strength, is sometimes a significant factor. It may even change the material composition you need to be stiff enough, which in turn changes its density. Obviously, that could get very complicated, and I admit I haven't tried to think through whether it makes it easier or harder for a small boat to plane.

BTW, very small engines tend to be inefficient. I don't know the physics behind that, but they are. So, if you half the size of the boat, you might more than half the power output of the motor. But I'm not sure if that is relevant here, because you only need to lift about 1/8 the weight (ignoring stiffness factors mentioned above). But it is also my impression, which might not be correct. that small propellers waste a larger fraction of their power generating turbulence and cavitation. But, I'm not sure to what extant that matters.

That said, at a very small scale, little water bugs can float above the water on surface tension alone. So maybe a very, very small boat the size of a water bug could plane very easily, on perfectly flat water??

Also - I don't think it isn't completely true that it is harder to bring small boats to plane. Small short whitewater playboats (certain kayaks, canoes, some short surfboards) are usually now designed to plane a little when you paddle very fast for short bursts of power, and to plane a lot when front surfing waves. For the most part, longer kayaks, canoes, and I think (surfing) longboards are displacement hulls. But that may be because a human generates the power when they aren't front surfing a wave, and human power doesn't scale with the length of the boat. (Except perhaps when the greater length lets you put more than one person in the boat.) I admit that politics play a part too - in most racing organizations, kayaks and canoes that fully hydroplane are currently banned, even on short sprint races where they might be used. I presume politics and racing organization rules play a part in sail and power boat racing too, and might distort how hard it is to bring those boats to plane.

 

Small point. Flat calm water (glassy) creates more drag than small waves. (Landing a flying boat on glassy water is dangerous because, amongst other things, the nose can get pulled down by the drag.)

 

What you say, Chris, may be true. I don't know, but it doesn't make sense to me. If a planing boat is more likely to nose dive on flat calm water, it seems likely for other reasons. A boat that starts pitching while running on a uniform surface will most likely represent a driven harmonic system and the nose dive would likely result from the increase in pitching motion as the boat is driven along. Eventually the pitch would become so pronounced that the bow gets grabbed by the water from the increased angle when driving forward.

I'm not an engineer, but that scenario makes more sense to me.

 

Hi Will,
Probably not an engineer's bag, more for a hydrodynamicist. Glassy water has qualities all of its own. It's a well known phenomenon for seaplane and float plane pilots.

 

Another factor to consider is that a small boat may have one deck. A ship will have several decks. In general, a small boat will have more empty volume.

 

I can definitely picture that being a bigger problem for sea planes and float planes, when landing. Glassy water would mean greater instantaneous contact with more wetted surface at once.