One of the very first boats I built as a teenager, was one using narrow overlapping solid-wood boards (attached with copper rivets and roves) and at the time it was called 'clinker' construction. Rather than re-write what's already been well said, I'll attach two URLs of companies working regularly with this system, that cover the basics and claimed advantages.
Particularly since good clear marine wood (such as planks of mahogany) have become hard to obtain and that most other woods tend to split easily as they dry, there's been a move to replace the solid planks used for clinker-build with strips of plywood that effectively solve both the availability and splitting issues.
It's that method that I now refer to under 'Lapstrake'. Many small boats of the rowing type (like Wherry's and rowable Adirondacks etc) can now be built like this and even larger monohulls of the Folkboat type also.
One can also combine this method with the use of wider sheets for the flat-of-side and lower bottom, as was done very attractively in the design of the UK 17' 6" sailing dinghy 'Osprey'.
I personally liked the way the combination gives clean lines to a boat and stiffens the bilge area without internal framing being required, that I used it for a small series of 13‑footers called the Canadian Beaver, about 20 years back.
The method requires that sufficient temporary transverse frames be erected on a sturdy base-frame (similar to that for the ply+frame system), and after the transom and stem are attached and all accurately aligned, the ply strakes are fitted - starting at the keel, one each side. The outer (or upper) edge of each strake then needs to be beveled off to receive the next strake with a fair overlap (commonly about 19 mm on a small boat) and each strake is held in place with specially-made long-reach clamps that reach over the width of each added plank, after applying somewhat thickened epoxy to the joint area. After curing, another pair of planks are added until the shell is complete.
See www.duck-trap.com/gluedlap.html for more info.
Design-wise, a fairly round bilge can be achieved and the overlapping of each strake adds longitudinal stiffness to the hull. The so-called 'lands' of each plank do give some added resistance to a hull but as the article above notes, there is also some cushioning effect on the waves and I also remember enjoying the glick-glick-glick noise they create as the boat moves forward. The lands also add some slight roll resistance to a monohull and overall, these boats are enjoyable to use. However, it's doubtful that this method will ever be used much for a multihull, with so many more suitable methods being available. For narrow multihull shapes and faster speeds involved, the proportion of added resistance caused by the many 'lands' would likely be unacceptable high.
And without any need for added hull roll-resistance on a multihull, that benefit would also not be valid in such a case. One interesting development of the original clinker build, was the use of a reversed clinker—where the hull was built starting at the gunwale and the added strakes were overlapped as one built towards the keel. The few designers who used this approach way-back, claimed that the overlapping 'lands' caused less resistance—and in fact it's very likely that planing boats built to this reverse-clinker method actually had less resistance than those with pure round-bilge, as the water could separate away from the bottom surface very cleanly and lower the surface contact, rather in the same fashion as does a racing hull with multiple steps. So I submit that this reverse-clinker concept may still have some future on a multihull after all.
You can also click here to see this process explained in The Philosophy of Shipbuilding.
Although a 24' monohull, here is an example of a lapstrake hull for a fine prize-winning traditional design 'Stir Ven' by Francois Vivier of France. Strakes are laid out and pre-cut on a numerically controlled (NC) machine.
Advantages are enjoyment of construction in small steps; economy of wood; a stiff, rugged hull without need of much internal stiffening; attractive appearance; round bilge design. Laps make boat more resistant to rolling and add a cushioned ride. Also, well made epoxy-glued lapstrake boats rarely leak.
Disadvantages for a multihull are: increased resistance due to plank edges; concentration of narrow strips mostly under the waterline in order to achieve desired shape; slightly heavier overall weight than several other options.
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