Design Details

Open points and design decisions for the balanced rigid solar panel sail, numbered for reference. Values mentioned here come from the factsheet and the 3D viewer.

open points

  1. structural foundation (in progress)
    An unstayed column puts a large bending moment into the bridge deck, which the original fore-mast foot (built for a stayed mast) was not designed for. Wharram’s lashed beams also flex by design.
    done: two foundation options modelled (twin spars, pyramid, or both combined, switchable in the viewer), design loads and forces in the factsheet.
    left: the connections into beams 4 and 5 (the beam closer to the pivot takes most of the load; with the pivot 3.66 m forward of the aft mast that is beam 5), and how they work with the lashings. See also the assumptions below.

  2. weight budget and trim
    A mass list for the whole installation and its effect on fore-and-aft trim. The weight sits about m forward of the aft mast, well forward of the middle of the hulls, which puts the bows down and may increase pitching. It also comes out of the payload margin between light (3,000 kg) and full cruising displacement (5,000 kg). Rough estimate, calculated in the page from the masses in sail/params.json and the removed fore rig in boat/params.json, comparing the same modules as a fixed sun roof in about the same place with the two-axis sail; the fore-mast foot rebuild is assumed to be weight neutral:

    The two degrees of freedom add about – kg on top of a fixed roof, depending on material choices. The missing fore rig gives back about kg, most of it high up: the mast alone reaches 10 m above the deck, while the sail’s weight sits 2–3 m above it. It also stood about 3.6 m forward of the aft mast, close to the sail’s pivot, so the relief works on trim in the same place. The mass list also informs those choices: glass or lightweight panels, steel or carbon for the column. Stability against capsize is probably not an issue: the rough heeling moment of the sail in a 45 kn gust (~29 kNm) matches that of the original rig at its 21 kn reefing limit.

  3. storm procedure
    When to secure the array with stays, and when to remove the panels.

  4. anchor chain through the pivot base: clearance against bulkhead strength
    With the anchor gear at beam 4 (decision 9), the chain leaves the roller at about 37° and passes the pivot base box’s aft bulkhead just above its lower edge: at the default pivot about 1.17 m above the waterline. A V notch in the bulkhead’s lower edge (opening at 120°, its tip 6 cm above the chain) gives it room, and raising the box 10 cm above the spars leaves about 27 cm of bulkhead plus the plywood top above the notch. But the notch sits right in the middle of the bulkhead, where the bulkhead, working as a deep beam between the spars, carries the largest part of the sideways tipping moment (assumption 5). The two pull against each other: a wider, higher notch gives the chain more room when the boat surges or the pivot moves, and leaves less bulkhead where it matters most. Options to weigh: a steel strap or plywood doubler around the notch, thicker bulkheads, a deeper or higher box, a chain guide or roller in the notch, or a chain lead that passes below the box. Not solved yet.

Assumptions

Rough hand calculations to size the concept, not a structural sign-off. They use the ultimate design loads from the factsheet (40 kNm tipping, 18 kNm twist, 10 kN vertical; the upright sail in a 45 kn gust plus boat motion, with a safety factor of 2), and the box between the twin spars (1.0 m long, spars 1.10 m apart and 0.35 m deep, 24 mm plywood) with the pivot 3.66 m forward of the aft mast.

  1. twist about the vertical axis is uncritical
    The plywood top of the box works as a shear panel between the spars and the bulkheads. Spread over the box, the twist gives only about 0.3 MPa of shear in the top.

  2. the spars are comfortable
    Each spar sees about 21 kNm of bending, roughly 10 MPa in a 100 × 350 mm epoxy-laminated spar.

  3. steel plate to plywood is the critical joint
    The 0.40 m drive plate has to pass the full moment into the wood over a short distance: a force pair of the order of 100 kN at its edges, and the twist concentrated around the bolt circle. Bolts through 24 mm plywood alone would crush or tear it. The plate is therefore bonded to the top with epoxy over its whole area, bolted through to a steel backing plate under the plywood, and tied down with steel rods from its corners to the bottoms of the spars, so that the wood never has to take the pull.

  4. internal webs are needed
    Two fore-and-aft webs directly under the plate’s edges, from bulkhead to bulkhead, carry the plate’s loads into the bulkheads and spars.

  5. the bulkheads must be thicker than 24 mm
    The sideways tipping moment travels through the two bulkheads as deep beams between the spars. At 24 mm that is about 20 MPa of bending, marginal for plywood. Two layers of 18 mm (36 mm), or 24 mm with hardwood caps along the edges, filleted and taped to the spars.

  6. wider spacing and a longer box relieve everything
    The sideways force pair on the spars is the tipping moment divided by their spacing: 36 kN at 1.10 m, 27 kN at 1.5 m. A longer box (1.2–1.5 m) gives the webs more room and lowers the force pair from fore-and-aft tipping. With the pivot position fixed, the box can be as long as the space allows.

  7. the beams remain the weak link
    With the pivot 3.66 m forward of the aft mast, most of the load goes into beam 5 instead of beam 4: about 23 kN into beam 5 and 13 kN into beam 4, alternating up and down. How the spars attach to the beams, and how the lashings take that load, stays with open point 1.

Design decisions

  1. power through the rotating axes: a cable loop, no slip rings
    The sail never needs more than about half a turn. Its smaller part always points forward, both faces are bifacial modules, and the tilt works both ways (±80°), so every sailing position and every sun-facing position can be reached within ±90° of turn from fore and aft; ±100° leaves some margin. A cable loop through or beside the column only has to follow that range. End stops or limit switches enforce it, so the cable can never over-twist, and no slip rings are needed. The tilt axis (±80°) is even easier. What remains is ordinary marine electrics: flexible cable, strain relief, a drip loop, and the choice between a high-voltage string across the joint or a charge controller on the rig with lower voltage down the column.

  2. implement controls and safety
    End stops and limit switches on both axes: turn ±100° (see decision 1), tilt within the range of the cable loop (tilt_limit in sail/params.json; mechanically, nothing limits the tilt). A torque limiter or slip clutch between each drive and the sail, so that a gust makes the sail slip instead of breaking something, since a self-locking worm drive cannot be let go like a sheet. A manual release or override for when the power or the controls fail.

    Pinch points: tilting towards upright closes the drive gap between the sail halves around the column. A hand, a line or a fender caught there is crushed by a self-locking drive that does not give way. The full-width ribs at the drive gap and the brush seals keep the gap closed along the sail; in addition the tilt slows down in the last degrees before upright, and a contact edge or a current limit on the tilt motor stops it when it meets resistance.

  3. follow a tilting and turning procedure to clear the aft mast (superseded by decision 8)
    With the pivot close to the aft mast, some positions between roof and sail touched the mast, and the sail needed a tilt-then-turn procedure to get past it. With the pivot where the balance puts it (decision 8), the 4 × 2 sail clears the mast in every position, so no procedure is needed.

  4. strong-wind mode: reef by tilting, lean to leeward upwind
    Turning is the sheet and tilting is the reef: between upright (full power) and the roof (depowered), a partly tilted sail keeps its full area but splits its force into a horizontal part (drive and side force) and a vertical part; at 45° each is about 70 % of the total. The catamaran heels about its lee hull, so the direction of the vertical part decides whether the lean helps. With the centre of effort about 4 m above the lateral resistance and 2.3 m from the centreline to each hull, for the same total force F:

    sail position heeling moment
    upright about 4.0 F
    leaned 45°, top to windward (force up) about 2.8 F + 1.6 F = 4.4 F, worse than upright
    leaned 45°, top to leeward (force down) about 2.8 F − 1.6 F = 1.2 F

    Upwind and reaching, the sail is therefore leaned to leeward: its downforce reduces the heeling moment, a gust adds downforce just as the heel increases, and the column and the plywood box stay in compression. Downwind, where the side force is small and burying the bows is the risk, the lean goes the other way, so that the force points forward and up and lifts the bows. Either lean keeps the camber bulging to leeward, because tilts of t and 180° − t bulge to the same side. The mode reefs the boat, not the structure: the loads on the column and the foundation stay about the same, since the vertical force acts ahead of the pivot. Above strong but manageable wind, the sail goes to the roof, turned across the boat (see open point 3).

  5. close the drive gap with brush seals; the sail area includes it
    The two sail halves leave a gap for the column and the tilt drive (drive_gap in sail/params.json). Upright, the column fills the lower half of that gap, but not the upper half, and which half points down depends on the sign of the tilt; tacking through the roof uses both. So neither half can be closed permanently. Brush strips along the two inner frame edges meet in the middle of the gap and bend around the column wherever it is, like the brush seals on garage doors or dinghy centreboard slots: cheap, light, and tolerant of frame flex. The gap then counts as sail, so the sail area is the frame’s full outline, and the viewer weights the solar sail’s centre of effort with the gap included. An open gap would work as a slot between two wing elements, which only helps with a lot of camber at large angles of attack, too little to design for. The gap itself is kept as small as the column allows: the column (0.15 m) plus a few centimetres on each side.

  6. fast tilt, a turn that is fast near the roof, and emergency depowering by tilting to the roof
    The wind puts little torque on the tilt axis: the sail is balanced across its span, and the centre of pressure across the span lies close to the axis. The large torque, from the chordwise centre of pressure at 25–35 % of the chord, acts on the turn axis. So the tilt drive can be geared for speed rather than force: less reduction in front of the worm and a faster motor give about 10–20°/s, a tack in roughly 10–20 s. The worm stays self-locking, since that comes from its lead angle, not from the extra reduction; the worm’s permitted sliding speed and its heating in repeated fast moves are to be checked with the supplier. Emergency depowering is then a fast tilt to 0° (the roof), which depowers the sail at any turn angle; the slow turn drive starts towards the depowered position (turned across the boat) at the same time and completes when it can. It runs on a dedicated circuit from the house bank with its own emergency button, and a hand crank or a cordless-drill adapter on the worm shaft works without power. Releasing the sail to swing freely is no alternative: with a balanced pivot it would not weathervane about the turn axis, and a flat plate free to rotate about the tilt axis tends to autorotate. A reference switch at tilt 0° recalibrates the tilt every time the sail passes the roof, on every tack; the sailor corrects the rest by eye.

    The turn drive stays geared for force: under sailing load it carries the large torque from the chordwise centre of pressure (roughly 2–9 kNm in strong wind), and turning that fast would take kilowatts through a worm of about 30 % efficiency. It only needs to be fast while the sail lies near the roof, where the wind puts almost no torque about the vertical axis. A tack therefore runs: a fast tilt towards the roof, a fast turn while the sail is flat (50° in about 5 s at 10°/s), and a fast tilt out on the other side. One DC motor does both, because it runs fast when lightly loaded and slows down as the torque rises: the turn drive is sized for the trimming torque at low speed, with a motor whose no-load speed allows the fast turn near the roof. Both drives need soft acceleration and deceleration ramps in their motor controllers: the sail’s moment of inertia is roughly 900 kg·m² about the turn axis and somewhat less about the tilt axis, and stopping it abruptly with a self-locking worm puts shock loads into the gear.

  7. 4 × 2 modules
    The static analysis of the centres of effort shows that a 4 × 2 solar sail, with its pivot near beam 5, brings the total centre of effort of solar sail and aft sail onto the same vertical line as the original working rig’s. That, its symmetry (the drive gap in the middle, so the sail is balanced and drags symmetrically when depowered, unlike 3 × 2 or 5 × 2) and its comfortable clearance from the aft mast make 4 × 2 the preferred size. The larger solar harvest of 5 × 2 does not justify the engineering problems that come with it: a pivot far forward, a long overhang towards the bows, and an asymmetric sail.

  8. the pivot follows the total centre of effort
    The pivot’s position along the boat is set by the balance: where the total centre of effort of solar sail and aft sail lines up with the original rig’s. Earlier attempts to keep the pivot close to the aft mast are not worth it: they need tricky tilt-and-turn procedures to avoid the mast (decision 3), and they leave the rig unbalanced. The default (pivot_from_mast in sail/params.json) is chosen this way with the 3D viewer’s “show all rig”.

  9. anchor gear moves from beam 5 to beam 4
    The windlass (Lofrans Caiman, 700 W) sat on the old fore-mast foot just aft of beam 5, where the solar sail’s foundation now needs the space. Windlass and roller form a fixed unit: the 35 lb plow’s shank spans the 0.75 m between the roller and the gypsy. Raising the solar sail over the windlass was rejected: it would enclose the windlass in the foundation box, raise the pivot by about half a metre, and still leave the anchor under the sail’s lower edge. Instead the whole unit moves one beam aft. The windlass stands almost on beam 4, bolted to a pad across the twin spars (not into the lashed beam); the chain falls straight down into a deep chain locker right under the gypsy, between the spars, with a V bottom so that the chain sorts itself, accepting occasional wave contact for automatic chain handling. The roller sits 0.75 m further forward, with an opening in the middle deck for the anchor; the rest of the middle deck stays free. Anchor work gets easier, inside the platform with deck on both sides; about 100 kg of anchor, windlass and chain move about 2.5 m aft, which offsets part of the solar sail’s weight near beam 5 (open point 2). A rubbing strip under beam 5 protects it from the chain when motoring up to the anchor; at anchor, a bridle to both bows takes the load. The dimensions are in boat/params.json (anchor_gear).