Power and energy#
Sunwake SW-15 · SW-PWR Rev 1 · August 2026
This document explains the powering model, its limits, and the resulting power curve, operating points, battery endurance and Maine seasonal balance. Read it before relying on any speed or range figure elsewhere in the repository — including the ones in the design brief, which are summaries of what is derived here. Everything is produced by calc/sunwake/resistance.py, michell.py, solar.py and energy.py, and exported to data/power_curve.csv, data/endurance.csv, data/generator_range.csv and data/solar_monthly.csv.
1. Model scope and limits#
The model treats three resistance components separately.
Friction is computed. ITTC-1957 correlation line on the 48.4 m² wetted surface generated by the table of offsets, for both canoe bodies, with a form factor of 1.10, a roughness allowance, and a +15 % appendage margin carrying the skegs, shafts, struts, rudders and line cutters. That margin is the price of the lobster-gear protection the mission demands, and it is not optional on a Maine boat.
Air drag is computed, from 15.5 m² of above-water frontal area at a bluff-body coefficient. At 8 knots it is about 7 % of total resistance; at 15 knots about 6 %. Although small, it must be included for a boat with this much roof area.
Residuary resistance is calibrated. It is backed out of the design basis power curve and stored as a smooth coefficient against Froude number. This is deliberate. On a hull of this slenderness at these Froude numbers, neither thin-ship theory nor a series regression deserves to be believed to better than a quarter, and the design basis curve already embodies a blend of two validated full-scale curves. Calibration is the more defensible basis at this stage.
Bus power is tow power divided by a propulsive efficiency of 0.58 and a drivetrain efficiency of 0.90. Every drive rating, operating point and battery C-rate check in this project is stated on that same plane: DC electrical input at the bus. The implications are explained in §4.
Uncertainty#
Absolute powers carry roughly ±25–30 % uncertainty, widening near the hump. Comparisons between design variants are far tighter — a percent or two. That is why this document runs two models: a calibrated one for absolutes, and a Michell thin-ship model for deltas. CFD or a tank test before lofting, as the open questions register says.
The independent check#
calc/sunwake/michell.py implements Michell's 1898 thin-ship integral with catamaran interference. It is validated against the Wigley parabolic hull, where it returns a wetted surface of 0.1488 L² against the published 0.1489 and reproduces the canonical hump-and-hollow structure of the wave-resistance curve. Both checks are asserted in the test suite.
The Michell model is not used for the published power curve. It runs 25–35 % hot against the design basis at 9–9.5 knots. At s/L 0.33 this boat sits in a strong interference regime, and thin-ship theory overstates the effect. The model is used for comparisons: the facet ladder in the hull form study, the hull-spacing question and beam sensitivity.
2. The power curve#
Half load, 12.70 t, calm water, clean bottom.
| Speed | Fn | Friction | Residuary | Air | Bus power | Energy | Wave share |
|---|---|---|---|---|---|---|---|
| 4 kt | 0.170 | 388 N | 62 N | 32 N | 1.9 kW | 0.47 kWh/nm | 13 % |
| 5 kt | 0.212 | 588 | 72 | 50 | 3.5 | 0.70 | 10 % |
| 6 kt | 0.254 | 826 | 99 | 72 | 5.9 | 0.98 | 10 % |
| 6.5 kt | 0.276 | 960 | 220 | 85 | 8.1 | 1.25 | 17 % |
| 7 kt | 0.297 | 1,102 | 336 | 99 | 10.6 | 1.51 | 22 % |
| 7.5 kt | 0.318 | 1,253 | 325 | 113 | 12.5 | 1.67 | 19 % |
| 8 kt | 0.339 | 1,414 | 347 | 129 | 14.9 | 1.86 | 18 % |
| 8.5 kt | 0.361 | 1,584 | 623 | 145 | 19.7 | 2.32 | 27 % |
| 9 kt | 0.382 | 1,762 | 961 | 163 | 25.6 | 2.84 | 33 % |
| 9.5 kt | 0.403 | 1,950 | 1,490 | 181 | 33.9 | 3.57 | 41 % |
| 10 kt | 0.424 | 2,146 | 2,067 | 201 | 43.5 | 4.35 | 47 % |
| 11 kt | 0.467 | 2,565 | 2,698 | 243 | 59.7 | 5.43 | 49 % |
| 12 kt | 0.509 | 3,020 | 2,982 | 289 | 74.4 | 6.20 | 47 % |
| 15 kt | 0.636 | 4,588 | 2,265 | 452 | 108.0 | 7.20 | 31 % |
Chart: drawings/chart-power.svg, which also shows where the drag goes.
Friction dominates the whole cruising range. It is 78 % of total resistance at 8 knots and does not fall below half until past 9.5. That is why wetted surface, and therefore the facet count and the weight ledger, matter. The residuary component is not smooth: the shoulder at 6.5 kt and the step at 8.5 kt are the twin-hull interference pattern showing through the calibration. §6.
Planning margin: add 15–25 % for weather and fouling. The free-miles arithmetic in §7 uses 25 %.
3. Operating points#
Continuous speed available from each power source.
| Available power | Continuous speed |
|---|---|
| 5.7 kW — haze or shoulder season | 5.9 kt |
| 8.6 kW — ordinary bright day | 6.6 kt |
| 11.7 kW — clear noon, 15 kWp array alone | 7.3 kt |
| 16 kW — one generator at its sweet spot | 8.2 kt |
| 20 kW — one generator at rating | 8.5 kt |
| 32 kW — two generators at 16 kW each | 9.4 kt |
| 40 kW — two generators at rating | 9.8 kt |
| 50 kW — drives at continuous rating | 10.4 kt |
| 52 kW — two generators plus noon sun | 10.5 kt |
| 120 kW — sprint, two-minute peak | 15.5 kt |
The sustained ceiling is set by the drives, not by the hull. Fifty kilowatts of continuous drive rating holds 10.4 knots; two generators plus noon sun would hold 10.5. The source and drive ratings are closely matched; adding generator capacity would have no effect without uprating the drives.
Weight sensitivity: about 0.11 knots at solar noon per 500 kg. That number is computed properly — the waterline is re-solved for the lighter displacement, so the wetted-surface reduction is counted alongside the reduction in wave-making. It is the exchange rate that makes the weight ledger a performance instrument.
4. Rating reference plane#
Every power figure in this project is DC electrical input at the high-voltage bus. Vendor catalogues split: Danfoss Editron and Cascadia rate shaft output, ePropulsion rates DC input.
On this boat the difference is decisive:
| Reference plane | Bank draw at sprint | C-rate on 128 kWh | Against the ≤ 1C limit |
|---|---|---|---|
| DC input at the bus (spec intent) | 120.0 kW | 0.94C | passes, thinly |
| Shaft output | 133.3 kW | 1.04C | over the limit |
If the selected drives turn out to be shaft-rated at 60 kW each, the two-minute sprint breaks the battery constraint. The drive RFQ must state the reference plane and the quote must answer on it. Confusing the two bases would lead to a costly drive-selection error, so it is carried in open questions as a gating item. The check itself is energy.sprint_c_rate_check(), and both cases are asserted in the test suite so the failure mode cannot be forgotten.
5. Battery and silent endurance#
128 kWh LFP nominal, two 64 kWh islands at 352 V (window 308–394 V), in sealed, insulated, heated trays under the berth platforms — low, and at the longitudinal centre of gravity, where the mass also calms a catamaran's characteristically quick roll. Usable window 80 %, from 95 % to 15 %: 102 kWh. Trays, cabling and protection sized for 192 kWh.
| Speed | Bus power | Dark, battery only | With about 8.6 kW of bright-day sun |
|---|---|---|---|
| 5 kt | 3.5 kW | 29.3 h · 146 nm | effectively unlimited |
| 6 kt | 5.9 kW | 17.4 h · 104 nm | effectively unlimited |
| 7 kt | 10.6 kW | 9.7 h · 68 nm | runs past daylight, about 358 nm |
| 7.5 kt | 12.5 kW | 8.2 h · 61 nm | 26 h · 196 nm |
| 8 kt | 14.9 kW | 6.9 h · 55 nm | 16.3 h · 130 nm |
| 8.5 kt | 19.7 kW | 5.2 h · 44 nm | 9.2 h · 78 nm |
| 9 kt | 25.6 kW | 4.0 h · 36 nm | 6.0 h · 54 nm |
| 10 kt | 43.5 kW | 2.4 h · 24 nm | 2.9 h · 29 nm |
Example cruising day. Eight hours at 7.5 knots is 60 nautical miles and 100 kWh of propulsion. Add 11.5 kWh of hotel load and subtract an August solar harvest of about 59 kWh, and the bank ends the day at 54 % state of charge.
The 128 kWh bank is not sufficient for an overnight passage under battery power alone. Those passages require a generator.
Charging#
| Source | Power | 15 % to 95 % takes |
|---|---|---|
| CCS DC fast charge (capped at 128 kWh) | 120 kW | 0.9 h |
| Both generators at rating | 40 kW | 2.6 h |
| Shore, two 12 kW on-board chargers | 24 kW | 4.3 h |
| One generator at its sweet spot | 16 kW | 6.4 h |
| Shore, single 50 A / 250 V leg | 12 kW | 8.5 h |
| Solar, clear noon | 11.7 kW | 8.8 h |
| Solar, ordinary bright day average | 8.6 kW | 11.9 h |
An overnight shore connection provides a full charge, and a CCS lunch stop adds most of a bank. Solar is the normal underway charging source.
6. Twin-hull interference#
At hull centres of 5.00 m on a 15.00 m waterline — s/L 0.33 — the two wave systems interfere strongly. The Michell model quantifies it:
| Speed | Wave resistance relative to two independent hulls |
|---|---|
| 6.0 kt | 1.40 |
| 6.5 kt | 1.09 |
| 7.0 kt | 0.76 |
| 7.5 kt | 0.80 |
| 8.0 kt | 1.31 |
| 8.5 kt | 1.48 |
| 9.0 kt | 1.45 |
| 10 kt | 1.31 |
| 12 kt | 1.11 |
A favourable dip of about 20–24 % sits exactly on the solar cruise; an interference penalty of about 45–48 % sits exactly on the single-generator passage speed. This is the first priority for CFD. Confirmation of either feature could change hull spacing or passage-speed planning.
Chart: drawings/chart-interference.svg. Discussion in the hull form study §7.
7. Solar and the Maine season#
15 kWp on about 63 m² of usable roof — 238 W/m², within the output density of modern glass or lightweight composite marine panels. A painted fascia surrounds the house and cockpit arrays so they appear as one dark roof plane. Strings are zoned across high-voltage MPPTs so mast and boom shading sacrifices no more than 2 kWp, about 13 % of the array.
The model uses monthly-average daily global horizontal irradiation for coastal Maine at 44° N with a single 0.80 annual-energy derate carrying soiling, cell temperature, mismatch, wiring and MPPT losses together. The array is modelled flat because the boat has a fixed array. Tilting panels are excluded by the 3.53 m air-draft requirement.
| Month | Irradiation | Solar | Hotel | Heating | Load | Net | Free miles/day |
|---|---|---|---|---|---|---|---|
| April | 4.75 kWh/m²/day | 57.0 kWh | 11.5 | 11.9 | 23.4 | +33.6 | 14.4 nm |
| May | 5.30 | 63.6 | 11.5 | 4.0 | 15.5 | +48.1 | 20.7 |
| June | 5.70 | 68.4 | 11.5 | 1.2 | 12.7 | +55.7 | 23.9 |
| July | 5.60 | 67.2 | 11.5 | 0 | 11.5 | +55.7 | 23.9 |
| August | 5.00 | 60.0 | 11.5 | 0 | 11.5 | +48.5 | 20.8 |
| September | 4.10 | 49.2 | 11.5 | 1.7 | 13.2 | +36.0 | 15.5 |
| October | 2.90 | 34.8 | 11.5 | 7.0 | 18.5 | +16.3 | 7.0 |
Free miles are calculated at 8 knots including the 25 % weather and fouling margin. Over the April-to-October season the array harvests about 12,200 kWh against a load of about 3,250, leaving roughly 9,000 kWh of surplus — some 3,900 free nautical miles a year.
November goes negative and the boat hauls out.
Two results are notable:
Maine summer solar runs within a few percent of the Bahamas. Long days at 44° N very nearly cancel the lower sun angle, and cool air keeps the panels a few percent more efficient than they are in the tropics. The Maine hotel load is also far lighter than a tropical one — no air conditioning, little watermaker use, and refrigeration working less in cool air.
Heating is cheap because the sea is warm relative to the air. Coastal Maine seawater holds 6–16 °C all season, which is an excellent heat-pump source: modelled COP 3.6–4.4 against 2.4–3.0 for an air-source machine, about 30 % less energy for the same heat.
Smart loads — water heating, battery-bay heat, and the watermaker if fitted — run automatically when solar power is surplus.
8. Generators and fuel#
Two 20 kW variable-speed DC sets, one per hull, HVO throughout, 600 L in two integral keel tanks at the LCG. Selection and noise strategy in generator selection.
Fuel converts at 2.9–3.2 kWh of DC bus energy per litre — roughly 30–33 % of HVO's 9.6 kWh/L thermal content through a small common-rail diesel, a PM alternator and an active rectifier. Values above about 3.5 kWh/L generally omit part of the conversion chain. Six hundred litres is therefore 1,740–1,920 kWh to the bus.
| Speed | Energy | Range on 600 L | Hours |
|---|---|---|---|
| 7 kt | 1.51 kWh/nm | 1,149–1,268 nm | 164–181 |
| 7.5 kt | 1.67 | 1,044–1,152 | 139–154 |
| 8 kt | 1.86 | 934–1,031 | 117–129 |
| 8.5 kt | 2.32 | 751–828 | 88–97 |
| 9 kt | 2.84 | 612–675 | 68–75 |
| 9.5 kt | 3.57 | 488–538 | 51–57 |
| 10 kt | 4.35 | 400–441 | 40–44 |
Against the 600 nm passage requirement: met with 56–72 % reserve at 8 knots, comfortably at 8.5, and with little reserve at 9. The resulting operating plan is 8–8.5 knot passages, with 9–10 knots reserved for shorter legs when needed. Ten knots does not meet the 600 nm passage requirement.
Tank volume available below z = −0.25 m is about 635 L per hull, so growth to 800–1,000 L total remains possible at a cost of a few thousand dollars and 160–320 kg if later passage planning requires it.
9. Model review priorities#
In priority order:
- The interference regime at s/L 0.33 (§6). Everything else is second order next to whether that dip and that hump are real.
- The calibrated residuary curve. It reproduces the design basis by construction, which means it inherits any error in that basis.
- The propulsive efficiency of 0.58. Big slow propellers behind partial skegs in a catamaran wake; the skeg wake into the propeller plane is an unmodelled noise and efficiency question and is on the CFD list.
- The +15 % appendage margin, which is a convention rather than a calculation.
- The 0.80 solar derate, which is a single number standing in for six effects, and the flat-array assumption underneath it.
- The heating load, which assumes a heat-pump COP the trials in SW-800 will measure rather than assume.