Electric Boat Range Calculator: Speed, Battery and Solar

Power and resistance. Water viscosity is entered in mm²/s and explicitly converted to m²/s for both Reynolds-number calculations.

The displacement option implements the normal-stern, no-bulb, no-immersed-transom subset of Holtrop–Mennen (1982), printed pp.166–168. Displacement volume is mass / water density; block and prismatic coefficients follow from the entered geometry. Wetted area and the 1982 form factor give viscous resistance using the ITTC-1957 correlation line. The explicit additional coefficient is an allowance chosen by the user, not the publication's full model–ship correlation formula. Wave resistance retains the exponential and cosine interference terms. In particular, the wave-amplitude coefficient uses draught / beam, not draught / length.

The planing option solves $C_{L\beta}=C_{L0}-0.0065\beta C_{L0}^{0.6}$ and $C_{L0}=\tau^{1.1}(0.012\sqrt{\lambda}+0.0055\lambda^{2.5}/C_v^2)$ at the supplied trim. Angles in these empirical relations are numerical degrees. Pressure drag is weight × tan(trim); friction uses wetted area $\lambda B^2/\cos\beta$, full boat speed and mean wetted length for the ITTC Reynolds number, with the horizontal trim correction. This is a prescribed-trim screening calculation, not a free-running pitch solution. Savitsky (1964), DOI below, and Tayeb et al. (2025), equations 4–13, describe the basis.

Theoretical electrical input is effective towing power divided by the product of open-water propeller efficiency, motor/shaft efficiency and the hull-interaction/relative-rotation factor. Propeller and motor efficiencies are validated individually between zero and one. The combined product compares separately towed-hull power with actual electrical input; it can exceed one and is not a thermodynamic conversion efficiency. MIT lecture 12, equation 156 and printed p.54 explain this quasi-propulsive towing-power basis. The open-water relation is $\eta_0=J K_T/(2\pi K_Q)$; supply an efficiency from the actual propeller's operating data. The factor labeled hull interaction includes relative rotation. Efficiencies are held constant over a sweep. The measured option instead interpolates attached source s3, page 2, with shape-preserving PCHIP and no efficiency correction.

Battery and solar. Available departure energy is $E_n H(SOC_0-SOC_r)$. Battery-only endurance is energy / total electrical demand, capped at the assessment horizon. Nominal battery sizing gives no solar credit. The solar model reuses NOAA/Meeus geometry, standard refraction, Kasten–Young air mass and the sea-level horizontal Ineichen model from the catalog's Sun Position tool. PV power is nameplate × irradiance / 1000 W/m² × the entered multiplier.

PV is sampled at intervals no longer than ten minutes. Between samples it is linear. The integrator splits charging/discharging transitions, enforces the full-charge ceiling and solves the first reserve crossing within an interval. Future sunlight cannot rescue a trip that already reached reserve. After that event the displayed SOC is held at reserve. Full-horizon solar energy is available irradiation-derived generation, not necessarily energy used by the trip.

Map and curves. A 31-point speed grid is supplemented with the exact selected speed. The planing grid expands beyond its usual Cv = 3.5 upper limit when needed to include a valid selected point, up to the Cv = 13 method boundary. Range gaps exclude invalid geometry and motor overload. Best speed is the best feasible sample within the time horizon and is shown in the schematic only when a feasible sample exists. An empty sampled comparison does not block selected-point results. Map rings use spherical destination equations and a local equirectangular projection, centred on departure coordinates. Natural Earth 1:110m coastlines are thinned for overview display. The dotted return radius is half the total solar-assisted travel distance. Rings above 300 km radius are hidden.

• Steady speed through water, calm deep water, no current, no acceleration or maneuvering energy, and constant hotel load. Loaded mass includes battery, people and payload.
• Holtrop: one conventional displacement monohull, normal afterbody, no bulb, no immersed transom and no appendages. Small-boat use remains an extrapolation of a ship-based regression, even inside the stated shape limits.
• Savitsky: one unstepped prismatic hard-chine hull, both chines wetted, deadrise 0–30°, prescribed trim 2–15°. Thrust-line and friction moments, trim equilibrium, spray drag, appendages and aerodynamic drag are omitted.
• Battery remaining-capacity factor is a fraction, as are states of charge and efficiencies. Battery energy availability is independent of discharge rate and temperature; motor and battery current/thermal limits need a separate check.
• Propeller and motor efficiencies are entered assumptions, each greater than zero and at most one. Hull interaction is a separate positive towing-power factor and may make the combined ratio exceed one. These factors are not propeller selection or an RPM-matching solution. The published test has its own fixed load, water and motor conditions.
• PV is horizontal at sea level with an unobstructed horizon. The output multiplier is constant and represents assumed derating, not forecast weather. Direct PV offsets demand and surplus can recharge to full capacity; no separate charging-power or charge-efficiency limit is modeled beyond the multiplier.
• Location is fixed for solar calculations throughout the trip. UTC offset is supplied explicitly, including any daylight-saving adjustment.
• Coastlines and rings are orientation aids. Return distance assumes the same speed and demand on both legs, unchanged weather model, and a straight unobstructed route.

Displacement screening: 0.55 ≤ prismatic coefficient ≤ 0.85, 3.9 ≤ waterline length / beam ≤ 9.5, 2.1 ≤ beam / draught ≤ 4.0, and 0.08 ≤ waterline Froude number ≤ 0.45. These limits restrict the implementation; they do not guarantee small-craft accuracy. Do not use this option for catamarans, foils, planing hulls or an immersed transom. The normal-stern 1982 form factor is used, without the 1984 replacement.

Planing screening: 0.6 ≤ beam speed coefficient ≤ 13, mean wetted length / beam ≤ 4, positive wetted chine length and wetted keel within the entered hull length. Running trim must come from a measurement or a separate design analysis. No porpoising or dynamic stability prediction is made. The planing grid normally ends at beam speed coefficient 3.5; it expands to include the selected speed, within the method's Cv = 13 limit. Every sweep also includes the exact selected speed. This is not a maximum attainable speed search.

The published Linder curve applies only inside 1.4–5.4 kn for that boat/motor/test load. Source s3 page 2 reports 915 Wh and a 1030 W / 50 min point; a constant-power energy balance gives 53.3 min instead. The lower-power rounded cruise times are the endurance references. No formula is adjusted to force agreement with that inconsistent high-power time.

Solar: Gregorian years 2000–2100, latitudes within ±70°, a 1–48 h assessment and a fixed horizon/weather multiplier. Clear-sky estimates are not guarantees of harvest. A horizon-limited result is a lower bound on depletion range. Chart/table axes stay in their labeled units; nautical-mile result cards are explicit numerical nautical-mile counts because the engine's unit system does not define nautical miles.

The map uses a spherical Earth, generalized public-domain coastlines and no land avoidance, inland lakes, hazards, depths, tidal data or route search. It is not a navigation chart. Distances depend on the energy assumptions; no safe-operating range or equipment suitability is certified. Battery, propulsion and PV installation work belongs to a qualified person.