Mk 3 "ARROW' Hull Design Notes

There have always been many more considerations to the 4b hull design than the usual matrix for a fiberglas high-performance dinghy. Originally rowing performance was given as much weight as sailing, before it was realised how powerful a rig could be stowed in the box. The mk2 sailing performance suffers from the high rear rocker necessary for the coxed rowing mode, in which the stern of the mk 1 had dragged. Now that the sail area can be more than doubled on almost all lightwind points of sailing with the genaker, rowing is relegated to rarer use in utter dead calms. So the new hull design is freed of serious rowing considerations, but many others remain…

Firstly the principal boat concept is the 8’aft cockpit of flat plywood box bench, false floors, and transom with which the hull design must be compatible. The early hulls gave cockpits with wasted space and weight at the stern despite only a narrow traveller base, and lack of width at the front, such as for sleeping two or more typically light wind seating.

A second extra consideration has always been ease and economy of making at least the prototype hull itself of plywood. Plywood’s advantages are its low tree waste and economical high pressure phenolic bond , its thinness for light weight, its large width, and attractive face grain ; and its one weakness is its edge grain. Lapstrake is a very appropriate for the narrowness of solid lumber, but makes very little sense for plywood. Multiple chine joining of narrow plywood panels protects the edge grain better but uses even more expensive oil-derived epoxy especially with inappropriate biaxial glass tape.

So the 4b designs have consistently sought to minimise the number of ply panels and joints. Using a solid cedar hull bottom extending the bottom of the box, the first two prototypes got the maximum boat and good ply grain beauty out of just two sheets of marine ply, with a chine joint only on the last 4’ of each side. Fairness was high in the mk 1, but suffered a bit in the mk2, especially at the difficult runout of the jointed chine.

Since then it has been realised that the boil proof phenolic bond actually allows marine plywood to be hot bent to very sharp curvatures suitable for a radiused rather than joined chines for a typical rear section. Such a radiused bend is inherently better for all displacement flow and runouts more naturally. This hot bending is also suitable for a very lightweight, comfortable rolled gunnel which maximises hiking and trapezing moment with the big asymmetric spinnaker rig and reduces the weight and difficult fitting of a separate wide gunnel or racks.

Only such formed bends follow ruling lines. Free elastic bending of a sheet causes anticlastic opposite transverse curvature, and twisting of a sheet equal and opposite curvature. The constraint is on compound curvature and one can calculate how positive the product of the two curvatures can be to bring the wood to its elastic limit. For instance the ruling lines of a principal curvature radius 4' can elastically rocker 3/8" over a 8' length.

When bends for the aft chine and aft rolled gunnel were heat-formed from the edges of model birch ply, quite nice low rocker shapes of the rest of a model hull half were elastically developed from the single birch ply sheet for spectacular grain, only broken by scarfs and the keeline.

From near tumblehome at the transom, the sides progressively develop flare, whilst amidships the bottom starts to develop some transverse curvature, both running out the chine angle . Ahead of the cockpit, rocker and V progressively develop in the keeline and culminate in a sharp knuckle turn to a vertical stem. Transversely the knuckle is the final elastic trace of the chine.

The rolled gunnel is run out at the front of the cockpit just aft of the bend in beam from constant to straight convergence to the bow. This sharpish bend is well above the optimum unheeled waterline and should be camouflaged by the foredeck to cockpit transition. Such imperfections must be weighed literally against the assured performance enhancement of the lightness and stiffness of this construction, if not its ease and economy .

So there is now extra space forward with the flare for lightwind sitting low in the boat. Flare there also gives a wide structural diffusion of the mast loads at the front bulkhead to the hull and cockpit, without the stress concentrations of tight bends.

The gunnel delta ’wing’ for sitting up, out and back in a breeze will be supported by the wide traveller cross girder at the transom . Over its straight outer edge a slotted dowel will be fitted and terminated at the front bulkhead. On it will easily run a 3 “ length of slit aluminum tube with welded pivot for the hiking plank.

But does this shape match all-round flow requirements? In lightwind to shape the sails requires heel and then weight forward to stop the transom chine corner digging and to minimise the static wetted area. In Mk 1&2 this bow down mode was slightly unstable at moderate induced heel. Here the radiused chine helps to minimise the corner drag and the forward flare gives lots of heeled bow down stability.

In stronger winds, a dinghy is best sailed absolutely flat and as stern down as a clean wake permits. Planing will be improved by the very flat bottom (and lightness) of this design , and the higher prismatic coefficient. A recent trend is minimising rear (planing) wetted surface by transversely arcing the bottom between waterline chines. The current design allows some deadrise in the bottom between the box bench and the chines (matched at the ply transom by deadrise of the false floors). The flat center box bottom segment gives some beached upright stability , and the deadrise is limited to assure static stability of the empty boat at the dock. Imposing this deadrise with the transom helps to keep the aft chine parallel to the keel

The shape above the maximum displaced upright waterlines relates to waves and heeling, and amidships seems the correct location for stabilizing flare without pitch being excited by waves or the heeling itself…..

Heeling in a dinghy is unlike in a keelboat, an off-optimum and transient condition for which the prime design consideration can be stability and control especially with a big rig. A typical wipeout scenario is a large gust impinging on the spinnaker. The low boatspeed makes the apparent wind abnormally high and the planing bow lift low., and the boat can nosedive and heel . Nosediving shifts the CLR forward and heel shifts the rig CE to leeward, both increasing the weather helm. Particularly with a lot of aft flare, the boat goes even more nosedown with (static) heel and the rudder can ventilate and lose control for a complete broach and nosediving capsize to leeward.

Full Scale Engineering

To realise the above concept needs a way of hot-forming the bends at full scale, a way of joining prebent panels, and a practical displacement and center of bouyancy for the shape.

Hot bending plywood for radiused chine and rolled gunnel

The aft bends are formed over a 10" pipe (eg 3 truck mufflers welded end to end and on stands) heated with a propane torch to say 350F. To it are welded the ends of a 8.5' 'nosebar' of say 2" pipe with enough gap for the ply to be slid between them. The ply is pre-wetted in the area to be bent, especially on the inside of the bend. Hand pressure within the wetted area helps feel and prevent any fracturing as ply is formed over the hot mandrel. Also it helps to form each bend at least twice with the sheet turned end for end so the nosebar is on each edge of the curve. Then the ply is clamped down on the mandrel and within two minutes the heat transmission dries the outside enough for glassing the bend with unidirectional glass and polyester resin, exploiting the residual heat, if necessary. The ply should be sanded by hand first and any small fracture high spots can be held down by local sheet metal screws into he muffler pipe. The gaps between the scres are glassed first with unidirectional and then the main fabric deformed with a pen barrel to pass around the screw head. Polyester will resist the wet heat of the second nearby bend better and is cheaper for this provisional rough glassing and does not stain the wood. The glass weave must be filled and the resin must set hard and the ply be left on the mandrel overnight to set to the imposed shape. And then the screw heads must be cleared of any resin and the screws carefully removed, taking care not to lift the surrounding glass which is now holding the fracture down until at least epoxy glass can be applied to the inside of the fracture.

In forming the chine bend at the transom running out at the front bulkhead it is important to heat the final front 1/3 of the mandrel as well, despite the fact that litle final bend is required. Otherwise the handling and set up over the mandrel can cause fractures . Likewise be very careful not to overheat the transom end of the mandrel as scorching here on the inside is the one place on the inside of the bend which will be highly visible. The outside of the bend should always be wetted in the nosebar area so that any unintentional heating of the nose bar cannot burn the highly visible outside of the bend. It is very difficult to restore the appearance of areas easily scorched significantly into the thin top veneer.

The practical need for rocker

Whilst a full length strip has smoothed out the gunnel curve nicely, there was actually a big conflict between low rocker and the aft cockpit. With the static requirement that the transom not be immersed, no keel-line curvature inevitably makes the front of the boat deeply immersed and relatively too bouyant. The under-bouyancy of the cockpit is increased by the popular arcing of the transom between the chines, to reduce the wetted surface as the side stern waterline rises with hard planing. Many current duo dinghies require the crew to go ahead of the mast in light winds, but this is not practical for a singlehander and with my mast built in at the front bulkhead which even rises above the foredeck. So the transom had to be made flat between the chines and the keel curved strongly under the front bulkhead to bring it up to the waterline at the bow.

Extra compound curvature by broadseamed spline joint instead of scarf

To achieve this much rocker requires some curvature to be introduced at the ply panel joint by cutting the end of one of the panels on a slight curve before joining. This tends to make all the longitudinals fairly sharp bends between a bow wedge and a parallel run, but similar sharp bends are found on the Ian Murray Cherub, and the optimised Javelin, as well as the Swift Solo. The ply joint has to be made anyway and curving it is more effective and much less of a hassle than darting, back plating, filling, and glassing the plywood further forward on the keeline. This is analogous to the superior fairness of broadseaming a sail over darting which again requires the additional of material to bridge and smooth the cut. The resulting ply hull is fairer than the mk1 and especially the mk 2, and any discrete chine dinghy (variable waterlines and dynamic lift) and of course lapstrake. Both mk 1&2 had some strange disconcerting hollows as well as discrete aft chines, whose discontuity may admittedly become an advantage in the planing mode. Torturing of straight scarfed ply sheets tends to produce hollows as both curvatures cannot be significantly positive, and this only disappears with very fine hulls in canoes and multi hulls.

A scarf was already impractical because of the pre-curvature in the aft panel at least, and the idea is to mill out the large crossgrain centerply of the 1/8" 3 ply on the sheet end and insert a spline of 1/16" veneer to align the joint with full strength in tension.The milling is done with an anglegrinder attachment with a thin abrasive cutoff disc or a jewellers slitting circular saw blade before the sheets are bent at all.

The ply joint is clamped to the midships bulkhead in a progressive manner from the first central contact. Wood blocks are preattached to the outside of the 0 ply pieces at the gunnel and keel so that pipe clamps can be used to draw the edges together . The associated bending moment helps to stop the joint inflecting 1' wide 'rubber' ply backing pads are shimmed away from the joint on the outside of the bend. They are divided at least once to mimimise their own compounding. The shimming compensates for the tendency of the joint to inflect as the ply edges are brought together, and leaves space for ultimate and fair outside glassing across the joint. The inside clamping strips are preattached to the bulkhead in their middle and the ends screwed through the ply into the margins of the backing ply. Closure and flatness of the spline joint can be monitored in the gaps between the strips. Also in between at the ends, further screws are driven through the ply into the backing pad. These will hold the flatness once the splines have set and the clamping strips and bulkhead are unscrewed temporarily to insert a narrower piece of roll ply for bonding to the inside in the curved area below the false floor line and then rescrewed through the same holes to clamp that until it sets. Finally all screws are undone and the outside joint area bridged with unidirectional glass. The inside lap plate reduces the concentration of longitudinal bend at the joint, once the side of the boat is pulled into position.

Two sheets of paper joined at a seam of radius R deform into mirror circular cones with apexes 2R apart and on the centerline of the joined transverse curvature of the seam. Thus the angle of discontinuity across the joint decreases with that curvature. In practice the above clamping techniques prevent any such angle of inflection and spread this inflection into longitudinal curvature. In this longitudinal bending the normal force from the curved seam in seamwise compression balances the normal forces from tranverse 'hoop' tension on either side. Again the more the seam is curved transversely the more normal force is produced to enforce longitudinal continuity, so always favouring the more disparate the curvatures. This seamwise compression can cause local bulging of the seam unless it is held to the bulkhead curvature. Such average net stresses over the thickness of the sheet are a prerequisite of any compounding.

These broadseaming techniques have allowed the first "wide body" tortured ply hull, and others are possible for instance for a 2 person sailing dinghy. It should also make completely unecessary putting chines in any wide kayak design.

Design for Mast and Daggerboard at the Front Bulkhead.

The 4b's designs had evolved substantial mast cantilevering at the front bulkhead so the only rigging is trapeze wires and backstays for the masthead spinaker. The Arrow will use the same transverse detail to tie the mast securely to the inner and outer gunnels of the wings, and the backstaying and trapezing points there.

Longitudinally the 4b's used a deep box the full length of the cockpit with an "off-centerboard" built into one side capable of storing the entire rig as well as the spinaker, pole and oars. With the Arrow's CG concerns the latter 3 must be stowed under the longer foredeck, and under a shorter front seat. The stern-heavy centerboard is no longer ideal mainly the aft shift in CLR as it is raised which is the opposite of that required by the spinaker downwind. The ideal is in fact a strongly raked daggerboard whose CG is more forward and whose CLR moves that way as it is raised. Such a strong rake allows the boat if not the board to rise to lessen any bottom impact, and helps to shed weed from the board. Also here it provides an escape from the difficulty of the raised board interfering with the boom if not mast or at least obstructing forward sitting in light air which is an acute problem for a single-hander.By still having the board slightly offcenter it can be passed through the front bulkhead to emerge ahead of the mast through the empty foredeck.

Hydrodynamically ..

Design of False Floor

To strenghten the broadseam joint and make sure the longitudinal curvature it induces is spread out smoothly stringers run from the transom to forward of the joint and front bulkhead. Generally these make the hull fairest fore and aft as best, avoiding the “starved horse” unfairness of ribs next to the hull, and let any water drain forward on shore so it can be sponged out through the hatch inside the front console.

The false floor bears on the stringers through ribs, from cedar lath near the transom to cedar plywood towards the front bulkhead..

Finishing of the Outside of the Hull

There are 4 (developable) ply panels only and the outside of each one is glassed and varnished in a single operation with no sanding of the epoxy or varnish. For each panel, I cut  a wide roll of heaviest 6 mil .006"  polyethylene  “vapour barrier”  to overlap the (sanded) seam tapes and then lay it flat on a flat sheet of plywood and exterior latex varnish the inside avoiding air bubbles and dirt, but not worrying about brush marks or about a bit of dust on the surface. This then is placed ontop of a matching fiberglas sheet which has been impregnated on the hull panel with clear epoxy and the air bubbles squeeged out the airbubbles to the edge of the sheets. Surface tension then compresses the glass weave and fills it. The varnish film sticks to it and releases from the polyethylene once the epoxy is set, leaving a mirror of the very flat polyetheylene surface with all the surface impurites in the polyethylene varnish absorbed into the internal  interface with the epoxy,with very high glass to resin ratios.

Design of Rudder