How do solar panels work?

A solar panel converts sunlight into electricity through the photovoltaic effect, the semiconductor cousin of the photoelectric effect Einstein won the 1921 Nobel Prize for explaining. In both, a photon (a particle of light) striking a material can knock an electron loose if the photon carries more energy than the material's binding threshold (called the bandgap, in semiconductors). The two effects differ in what happens next: in the pure photoelectric effect, the electron is ejected entirely from the material into vacuum or another medium: the principle behind night-vision tubes, photomultiplier detectors in PET scanners and airport gamma-ray scanners, and old vacuum phototubes. In the photovoltaic effect used by solar panels, the electron is freed *inside* a thin silicon wafer that's been doped to create a P-N junction. The junction's built-in electric field sweeps the freed electron toward the N-side and the matching 'hole' toward the P-side, separating the charges before they can recombine. Connect a wire between the two sides and you have current, DC electricity, at roughly 0.5–0.6 volts per cell. A typical 'solar panel' wires 60–72 cells in series to reach the usable 18–40 V range. From there: a charge controller (MPPT or PWM) regulates voltage and current to match the battery's needs, the battery stores excess energy for night-time or cloudy days, and an inverter converts the battery's DC back to AC for household loads (or DC loads run straight off the battery). This calculator models every step of that chain (irradiance reaching the panel, the panel's STC-rated conversion, controller efficiency, round-trip battery losses, inverter losses, and final load delivery) so you can see exactly where energy is lost between sunshine and the outlet.

How much battery do I need for my off-grid system?

It depends on your daily load in watt-hours, your target depth of discharge (DoD), and how many days of autonomy you want. A common starting point is: divide your daily load by your DoD to get the minimum usable capacity, then add a safety margin. For example, 1,000 Wh/day at 80% DoD requires at least 1,250 Wh of nominal battery capacity. This calculator sizes both battery and solar together against real monthly irradiance data so you can see which months fall short.

What is depth of discharge (DoD) and why does it matter?

Depth of discharge is the percentage of a battery's capacity that has been used relative to its total capacity. Discharging a battery too deeply too often shortens its lifespan; lithium chemistries typically allow 80–100% DoD, while lead-acid batteries are usually limited to 50% for longevity. Setting a conservative DoD target in the calculator gives you a buffer above the hard cutoff, so the system flags months where your battery would dip into that buffer zone.

How does cloud cover affect solar panel output?

Cloud cover reduces the amount of solar irradiance reaching your panels. In the Scenario Planner's geometric mode, the sky-condition slider sets a clearness index (Kt) at the front of the physics chain: SKC ≈ 0.75 (clear), SCT ≈ 0.475 (scattered, ~63% of the clear-sky ceiling), OVC ≈ 0.15 (overcast, ~20% of the ceiling). These are midpoints of the METAR Kt bins (Iqbal/Reindl), so you can stress-test your system against any sky state without re-fetching irradiance. The other three weather modes (PVGIS-monthly, TMY-hourly, Forecast) use real observed irradiance and ignore the slider.

What's the difference between PVGIS and PVWatts data?

Both are free, government-backed datasets of historical solar irradiance, but they draw on different satellite and ground-station sources. PVGIS (from the EU's Joint Research Centre) has strong coverage for Europe, Africa, and Asia. PVWatts (from NREL) is optimized for the Americas and also supports tracking array types (1-axis, 2-axis). This calculator lets you choose which source to use per panel plane, and supports hourly TMY data from PVWatts for 8760-hour simulations.

Can this calculator size an RV or cabin solar system?

Yes, it's designed for exactly that. Enter your location (or any location you'll be traveling to), your panel array wattage and tilt, and your electrical loads with their daily hours. The calculator returns month-by-month results showing whether your system is adequate, approaching your DoD limit, or undersized for that month. The Scenario Planner can also simulate a specific trip duration under chosen weather conditions.

TMY stands for Typical Meteorological Year, a synthetic dataset assembled from many years of historical weather records to represent a statistically typical year at a given location. It provides hourly values for solar irradiance, temperature, and wind. Using TMY data gives a more realistic picture of annual system performance than a single year of measurements, but it is not a forecast; actual production in any given year will vary. This calculator uses TMY data for both its monthly irradiance lookups and its optional 8760-hour hourly simulation mode.

Can I add a wind turbine to my off-grid solar system?

Yes, this calculator lets you add a wind turbine alongside your solar panels. Enter your turbine's nameplate power, rotor diameter, cut-in and cut-out speeds, power coefficient (Cp), hub height, and local average wind speed. The calculator applies a wind shear correction to adjust the reference wind speed to hub height, then integrates the power curve over a Rayleigh wind-speed probability distribution to estimate daily and monthly energy production. Wind energy is added to the battery charging budget alongside solar and is not limited by the max charge rate cap, mirroring real micro-turbine behavior.

What is a wind turbine capacity factor?

Capacity factor (CF) is the ratio of a turbine's actual average power output to its nameplate (rated) power. A turbine rated at 400 W with a CF of 20% delivers an average of 80 W, or about 1.9 kWh per day. Small turbines at low-wind sites often have CFs of 5–20%, while well-sited utility turbines reach 35–45%. The Betz limit (CF_max ≈ 59.3%) is the theoretical ceiling no turbine can exceed. In this calculator the capacity factor is shown in the monthly wind-energy column and reflects the Rayleigh distribution of wind speeds at your entered mean wind speed.

What is the Betz limit?

The Betz limit (approximately 59.3%) is the theoretical maximum fraction of the kinetic energy in wind that any turbine rotor can extract, regardless of design. It arises because the turbine must leave some air motion downstream to keep wind flowing through the rotor disk. Real small turbines typically achieve a power coefficient (Cp) of 0.20–0.40, well below the Betz limit, due to blade aerodynamic losses, mechanical friction, and generator inefficiency. This calculator lets you enter your turbine's Cp directly; if you don't know it, 0.30 is a conservative default for small residential turbines.

Can I combine solar panels and a wind turbine in an off-grid system?

Yes, combining solar and wind is one of the most effective strategies for off-grid reliability. Solar production peaks midday in summer, while wind is often strongest at night and during winter storms. A hybrid system can significantly reduce the battery capacity needed to cover multi-day gaps in any single source. This calculator models both sources simultaneously: each contributes energy each hour, the battery absorbs surplus from either source, and deficit hours draw from the battery regardless of which source is offline.

How does a hybrid solar-wind system affect battery sizing?

Adding a complementary second source generally allows a smaller battery for the same reliability target. When solar and wind production are anti-correlated (windy nights, calm sunny days), the combined daily output is more uniform, so shorter autonomy windows are needed. Use this calculator's scenario planner to compare a solar-only, wind-only, and hybrid configuration side-by-side: it runs a full 8,760-hour simulation and reports the worst-month state of charge for each scenario so you can size the battery to your actual shortfall.

Why does a 100 Ah battery deliver less than 100 Ah at high current?

The Ah rating on a battery is measured at a slow, standardized discharge rate, typically C/20 (5 A for a 100 Ah battery, drained over 20 hours). At higher currents, internal resistance, electrolyte concentration gradients, and the chemistry's ion-transport speed all limit how much of the stored charge you can actually pull out before the voltage collapses. This is the Peukert effect: a 100 Ah lead-acid battery discharged at 50 A might only deliver ~75–80 Ah before hitting cutoff. The Peukert exponent k captures how steeply capacity falls off: k ≈ 1.05 for lithium (small effect), k ≈ 1.10–1.30 for AGM/flooded lead-acid. This calculator applies a Peukert correction whenever your average load current exceeds the rated-hour discharge rate.

Should I get an MPPT or PWM charge controller?

MPPT (Maximum Power Point Tracking) is almost always the better choice for off-grid systems. A PWM controller forces the panel to operate at the battery's voltage, typically well below the panel's optimal voltage, so you lose the difference. On a 100 W nominal panel feeding a 12 V battery, a PWM controller often delivers ~75 W while MPPT delivers ~95–97 W: a 25–30% harvest gap. PWM is cheaper and may make sense for very small systems (under ~100 W) where the controller cost difference matters more than the harvest difference. Never direct-connect a panel to a battery without a controller: you'll either overcharge lead-acid (gassing, water loss, damage) or trip a lithium BMS. This calculator's Charge Controller dropdown applies the appropriate efficiency factor.

Does panel tilt matter more than panel size?

Both matter, but tilt affects when you generate power, while wattage affects how much. A panel matched to local latitude maximizes annual harvest, but if your worst-month deficit is in winter, tilting steeper (latitude + 15°) can recover 20–40% more December production at the cost of summer output, sometimes a better trade than buying a bigger panel. A flat (0°) panel collects more in summer but loses heavily in winter when the sun is low. Azimuth matters too: a 30° east-of-south offset typically costs only 5–10% of annual harvest, but 90° (due east or west) can cost 20–30%. Use this calculator's Tilt Optimization helper to see annual-best, summer-best, and winter-best tilt angles for your specific latitude, then check whether tilt or panel size is the bigger lever for your worst month.

Why does my fridge show a 70 W draw when it's rated at 35 W?

Fridge nameplate ratings are usually an average over a full day, accounting for the fact that the compressor only runs about half the time (~50% duty cycle). When you measure with a Kill-A-Watt or clamp meter and the compressor is on, you'll see the actual instantaneous draw, roughly 2× the nameplate. So a fridge rated at 35 W average is really a 70 W compressor cycling on/off. Add another 1–3× brief surge at startup (motor inrush) and the peak can momentarily hit 150–200 W. This distinction matters: your battery sizing depends on the daily average (35 W × 24 h = 840 Wh/day), but your inverter has to handle the 70 W running peak plus the inrush surge. Sizing the inverter to just the nameplate will trip overload protection every time the compressor kicks on.

Off-Grid Electric Power Calculator

⚡ Location & Power Source Data

Search Address

Format:

Latitude

Longitude

Solar Panels

Tilt Optimization

Calculated from your latitude using NOAA solar position geometry. Click any value to apply it to the Tilt field below.

Fixed installation

Annual optimum

Summer (May–Aug)

Winter (Nov–Feb)

Adjustable mount — monthly optimum

For DIY adjustable mounts, change tilt monthly to maximize harvest.

How these recommendations are calculated

Panel Tilt °

Angle of your panel from horizontal. 0° = flat; 90° = vertical. Rule of thumb: match your latitude for the best year-round average.

Panel Azimuth °

Direction your panel faces, measured clockwise from north (true north). 180° = due south (optimal in the northern hemisphere). 0°/360° = north | 90° = east | 270° = west.

*Panel Array Rated Power W at STC

Rated wattage of your solar panel, or combined power of your array.

Temp. coefficient (γ) %/°C

Magnitude of your panel's power-vs-temperature coefficient (γ_Pmax), from the datasheet; enter it as a positive number (e.g. 0.40 for −0.40 %/°C). Typical crystalline silicon: 0.35–0.45 %/°C. Reduces output above 25 °C cell temp; slightly increases it below.

Leave blank to skip; no additional thermal derating is applied. Requires the 8760-hour TMY simulation toggle below to take effect. Affects hourly-panel results only. The monthly Daily Solar Wh/day and Scenario Planner do not yet incorporate temperature.

Mount Type

Data Source

Get Hourly Data

Enable 8760-hour simulation

Fetches a full year of typical hourly data from PVWatts and runs an hour-by-hour battery simulation. Typical Meteorological Year (TMY) data is observed historical weather drawn from many years; useful for sizing, not a forecast.

Monthly Irradiance (kWh/m²/day)

Fetched from PVWatts, PVGIS, or NASA POWER, or enter manually. PVWatts: Solar Radiation column. PVGIS: H(i) column. NASA POWER provides long-term horizontal irradiance; confirm against your tilt. from NASA POWER: confirm or override

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Solar Access (Shading Factor)

Fraction of irradiance that reaches your panel after near-field shading (trees, structures). Tilt & orientation are already accounted for by the fetched irradiance. 1.00 = no shading | 0.90 = occasional shade | 0.75 = significant shade.

Annual assumption 0–1

Additional Arrays

Add extra planes for split arrays (e.g. east + west roofs, or a boat bimini plus deck). Each plane can be fetched independently. Global Solar Access and irradiance overrides apply to all planes unless you opt into per-plane values.

Wind Turbine (optional)

Enable wind turbine

Axis type

HAWT = classic propeller (swept area = π(d/2)²). VAWT = Darrieus / H-rotor / Savonius (swept area = diameter × rotor height). VAWTs typically have a lower power coefficient; pick the type below to prefill a sensible C_p default.

Rated Power W

Avg Wind Speed (10 m ref.) m/s

Site Altitude (for air density) m

Looks up long-term average wind speed (NASA POWER) and site altitude (Open-Meteo) for the location entered above. Fills the two fields when blank; edit either to override.

Speed unit

Length unit

Rotor Diameter m

Cut-in Speed m/s

Rated Speed m/s

Cut-out Speed m/s

Power Coefficient (C_p) (optional)

Hub Height m above ground

Terrain / Roughness

Cp 0.30 is a conservative default for small turbines (Betz limit = 0.593). Hub height and terrain type correct the reference wind speed via the power-law shear model. Production is estimated from a Rayleigh wind speed distribution centered on the annual average; enter a higher value for an exposed coastal or ridge site.

🔋 Storage Setup

Battery Bank

*Fields with an asterisk are required

Chemistry

Capacity unit:

*Battery Capacity Wh

*Battery Capacity Ah at C/20

*Battery Voltage V DC

Use advertised, rated, or nominal output voltage.

Chemistry Parameters (auto-filled, overridable)

Peukert Exponent (k)

Round-Trip Efficiency %

DoD Design Target %

Hard Cutoff DoD %

Rated Hour H

Max charge rate (optional) W

Maximum power the battery can accept from all sources combined (solar surplus + chargers). Leave blank for no cap. Use “Suggest” to auto-fill from your battery chemistry's typical max C-rate × capacity.

External Charging (optional)

Top-off nightly

Battery supports pass-through charging

Pass-through on (default): charger charges the battery while loads run simultaneously; the battery is the central bus. Off: charger output first serves loads directly; only surplus reaches the battery (use for systems where the battery cannot simultaneously accept charge and supply loads, e.g. some isolated charging circuits or older lead-acid banks). Affects the 8760-hour simulation; the monthly model reports the same energy balance either way.

Shore or grid power refills the battery to 100% each night. Infinite duration shown when daily deficit stays within usable capacity; otherwise the row flags “Top-off insufficient” and duration remains finite.

Battery Voltage (optional) V DC

Enter your battery bank voltage if you have DC loads at a different voltage. Used to detect DC-DC conversion losses; leave blank if unknown or all loads are AC.

Battery Charging

Charge Controller

Load Management

Select the power conversion devices your loads run through. Inefficiencies increase the effective draw on your battery.

Inverter

Detailed Inverter Model

Real inverters waste a fraction of every watt, generally becoming more efficient at higher loads. Enable this to replace the single efficiency above with a 3-point partial-load curve plus a continuous no-load draw. Used by every calculation path (monthly, hourly, scenario).

Use detailed inverter model

Rated power W

Surge / peak W

Instantaneous peak rating (1–2 s, for motor inrush). For portable power stations, use the published "Surge" spec, not the longer "X-Boost" / sustained-boost rating (modeled separately below).

Sustained boost W

Boost time min/day

"X-Boost" / sustained boost: power above the continuous rating that the inverter can deliver for limited periods before thermal limits force a derate. Leave blank if your unit doesn't list one. Loads that fall between Rated and Sustained boost will trigger an amber warning when their daily duty-time exceeds the boost cap.

No-load draw W

Continuous 24/7 draw; additive to Standby Draw.

Efficiency curve

Eff @ 10% load %

Eff @ 50% load %

Eff @ 100% load %

Below 10% load the curve extrapolates linearly toward zero (real inverters drop sharply at very light loads). Above rated power, efficiency is held flat at the 100% value. The surge field triggers an inrush-vs-surge warning when a load's startup inrush exceeds it.

DC-DC Converter

Backup Generator

Optional fuel-burning backup. Auto-starts when battery SoC drops below the trigger and runs until SoC reaches the target or the daily runtime cap is hit. Manual schedule entries fire unconditionally. Outputs are in Hourly Data.

Enable backup generator

Wiring

Wiring Loss %

Electrical Loads

*Fields with an asterisk are required

Advanced: Standby / Parasitic Draw

All real systems have a small continuous draw from the charge controller, BMS, clocks, and other standby electronics. Enabling this adds it to your load calculation and may change Charging/Deficit status results.

Standby Draw W (continuous)

Month	Irradiance kWh/m²/day	Solar Access	Typical Daily Charge Status	Daily Solar Wh/day	Wind Wh/day	Net Balance Wh/day	Recharge fraction/day	Days to Full from empty	Duration days, clear	Duration days, overcast	Load/Capacity %	Net DoD %	Solar vs Load %	Solar Noon 15th, std time

Scenario Planner — trip / event check

Stress-test a specific trip against a chosen month and sky&wind conditions. Uses the irradiance you’ve already fetched. Add an extra ad-hoc load (e.g. a portable air conditioner) and slide the cloud cover from clear to overcast or select a calm to strong wind condition to see when your battery hits the DoD cutoff.

Month

Start date

Duration (days)

Starting SoC (%)

Add an extra ad-hoc load

Power (W)

Start time (std)

Duration (h)

Geometric + Cloud Conditions Monthly average irradiance with sky-condition derate and cosine solar model. Works without fetching hourly data.

TMY Data Uses the 8760-hour dataset from your last hourly fetch. Real modeled weather; sky & sliders do not apply.

Forecast (next 7 days) Open-Meteo hourly forecast; real near-term weather. Limited to today through today + 6 days; max 7-day duration. Sky & wind sliders do not apply.

Sky condition (forecast)

Wind condition Moderate

Formulas & Sources

Daily Solar Input (Ah/day)

Panel Wattage × Irradiance × Solar Access × System Efficiency ÷ System Voltage

where:

Solar Harvest Efficiency = Controller Efficiency × (1 − Wiring Loss) × Round-Trip Efficiency

Effective Load = Raw Load ÷ (Inverter Efficiency × DC-DC Efficiency)

Irradiance in kWh/m²/day equals peak sun hours; a 1:1 equivalence at STC means Panel Wattage × kWh/m²/day = Wh/day directly.

Example: Panel = 200 W, Irradiance = 5.2 kWh/m²/day, Solar Access = 0.85, System Eff = 0.89 (MPPT 97% × wiring 97% × RTE 95%), Voltage = 12 V
→ 200 W × 5.2 kWh/m²/day × 0.85 × 0.89 ÷ 12 V = 786.8 Wh/day ÷ 12 V = 65.6 Ah/day

Peukert Correction (discharge only)

Effective Capacity = Rated Capacity × (Rated Hour ÷ (Load Current × Rated Hour ÷ Rated Capacity))^{(Peukert Exponent − 1)}

Applied to discharge only; charge correction is complex and rarely material. Load Current is approximated as the 24-hour average: total daily Wh ÷ System Voltage ÷ 24 hours. This is accurate for steady loads. Intermittent high-draw loads (e.g., a pump running 30 minutes) experience a higher instantaneous current and therefore a greater Peukert penalty than this average reflects; treat those results as optimistic.

Example: Rated capacity = 100 Ah, k = 1.05 (LiFePO₄), Rated hour H = 20, daily load = 1,200 Wh, Voltage = 12 V
I = 1,200 Wh/day ÷ 12 V ÷ 24 h = 4.17 A
→ 100 Ah × (20 h ÷ (4.17 A × 20 h ÷ 100 Ah))^0.05 = 100 Ah × 24.0^0.05 = 117 Ah (slow draw raises effective capacity above rated)

Source: Peukert, W. (1897). Über die Abhängigkeit der Kapazität von der Entladestromstärke.

Overcast Sky Factor: 3%

The monthly table's worst-case overcast-day column models a fully overcast day at 3% of the typical-day harvest for that month. The typical-day value already reflects the long-term cloud mix at your site (PVGIS climatology), so this is the overcast tail of that distribution, not 3% of a clear-sky ceiling. For a true clear-sky ceiling, use the Scenario Planner with the sky-condition slider at SKC.

Example: typical-day harvest = 200 W × 5.2 kWh/m²/day = 1,040 Wh/day
→ 1,040 Wh/day × 0.03 = 31 Wh/day on a fully overcast day

Source: field data from several hundred off-grid systems.

Temperature Derating (γ_Pmax)

PV panel output decreases linearly with cell temperature above the Standard Test Condition reference of 25 °C. The power temperature coefficient γ_Pmax (typically −0.30 to −0.45 %/°C for crystalline silicon) is printed on every module datasheet.

P(T) = P_STC × [1 + γ × (T_cell − 25 °C)]

where γ is the signed coefficient (negative for standard panels) and T_cell is the cell temperature in °C reported by PVWatts’ thermal model (accounts for irradiance, ambient temperature, and wind cooling).

PVWatts default replacement (Choice B): PVWatts already bakes in a default γ = −0.47 %/°C. Rather than stacking the user’s value on top (which would double-count), the calculator undoes the PVWatts default first and applies the user’s coefficient:

P_corrected(h) = P_PVWatts(h) × [1 + γ_user × (T_cell(h) − 25)] ÷ [1 + (−0.0047) × (T_cell(h) − 25)]

Example: July noon, Great Falls MT: T_cell = 58 °C, panel γ = −0.40 %/°C, P_PVWatts = 820 W/kW
PVWatts factor: 1 + (−0.0047) × (58 − 25) = 0.845
User factor: 1 + (−0.0040) × (58 − 25) = 0.868
→ P_corrected = 820 × 0.868 ÷ 0.845 ≈ 842 W/kW (less conservative than PVWatts’ default for this panel)

Source: IEC 61215 temperature coefficient definition; PVWatts V8 technical reference (NREL/TP-6A20-68586).

Day / Night Load Split

Switch to Advanced mode and set a load Operating Window to see the day/night split here.

Solar Noon (15th of month, standard time)

Solar noon is the moment the sun crosses the local meridian, its highest point in the sky that day, and the midpoint of the solar window. It is not the same as clock noon: it drifts by site longitude (4 minutes per degree east/west of your time-zone meridian) and by the Equation of Time (up to ±16 minutes across the year, from Earth’s axial tilt and orbital eccentricity).

Solar Noon (local min past midnight) = 720 − EoT(N) − 4 × (Longitude − 15 × TZ Offset)

where N is the day-of-year for the 15th of the month (epoch used for the monthly display). TZ Offset is the site’s standard-time UTC offset; DST is intentionally ignored so the displayed time is consistent year-round. Site time zone is resolved from your entered latitude/longitude.

Example: New York City: Lon = −74.0°, TZ offset = −5 (EST), Feb 15 (N = 46), EoT(46) = −14 min
→ 720 min − (−14 min) − 4 min/° × (−74.0° − 15 °/h × (−5 h)) = 734 min − 4 min/° × 1.0° = 730 min = 12:10 PM

Source: Equation of Time, NOAA Solar Position Calculator methodology.

Battery Duration (days)

Usable Capacity ÷ |Net Daily Deficit|

where Usable Capacity = Effective Capacity × DoD Target. Shown as ∞ when the system is in daily surplus (charging).

Example: Battery = 300 Ah × 12 V = 3,600 Wh, DoD target = 80%, net daily deficit = 1,440 Wh/day
Usable = 3,600 Wh × 0.80 = 2,880 Wh
→ 2,880 Wh ÷ 1,440 Wh/day = 2.0 days

Detailed Inverter Model (partial-load curve)

Real inverters waste a fraction of every watt that passes through them, and the fraction depends on the load. Below ~10% of rated power they're inefficient (the conversion circuitry's idle losses dominate). Around 40–80% load they hit peak efficiency, then dip slightly at full rated power.

η(f) = piecewise-linear interp through (0, 0), (0.1, η₁₀), (0.5, η₅₀), (1.0, η₁₀₀)

where f = instantaneous load ÷ inverter rated power. Below 10% load the curve extrapolates from the origin but is floored at η₁₀ ÷ 2 so a very small draw (e.g. 5 W on a 2 kW inverter) never produces an unrealistically low efficiency that would double-count the no-load loss already captured by the idle-draw field. Above 100% load (within the surge headroom) the value is held at η₁₀₀.

When the largest steady AC load exceeds the inverter's rated power a red undersized warning fires; a real inverter would trip overload protection. When the largest load is below 10% of rated, an amber advisory points out that the inverter is heavily oversized for the system; the math will work but low-load efficiency dominates and a smaller inverter is usually the better fit.

No-load draw (the inverter's idle current when no load is present) is added as a continuous 24/7 baseline, additive to the existing Standby Draw field. Both feed every calculation path: the monthly table, the 8760-hour TMY simulation, and the Scenario Planner.

Example. 2 kW inverter with curve 75% / 92% / 88%, no-load 12 W. A 500 W AC load is at f = 0.25, so η = 75% + (0.25-0.1)/(0.5-0.1) × (92% − 75%) = 81.4%. Battery sees 500/0.814 = 614 W draw. Idle adds 12 W × 24 h = 288 Wh/day on top of all loads. A second 35 W load at f = 0.0175 hits the floor: linear extrapolation gives 13%, but η₁₀/2 = 37.5% wins, so battery sees 35/0.375 = 93 W for that load.

Surge / peak power (1–2 s instantaneous rating) triggers an inrush-vs-surge warning when a load's startup inrush exceeds it. Note: this is the short motor-inrush rating, distinct from the longer "X-Boost" / sustained-boost spec on portable power stations; sustained-boost modeling is a separate future feature.

Wind Power & Capacity Factor

P = ½ ρ A v³ C_p

where ρ = air density (kg/m³), A = rotor swept area (m²), v = wind speed (m/s), C_p = power coefficient (max 0.593, the Betz limit; real small turbines 0.20–0.40 for HAWTs, 0.15–0.22 for VAWTs). Output follows a three-zone power curve: zero below cut-in speed, cubic growth from cut-in to rated speed, flat at nameplate power from rated to cut-out, then zero above cut-out.

Swept area depends on axis type:

Horizontal-axis (HAWT, propeller): A = π (d/2)² (circular swept disc).
Vertical-axis (VAWT: Darrieus, H-rotor, Savonius): A = diameter × rotor height (the rectangular swept area traced by the blades around the central column).

For VAWTs the shear-law correction also uses an effective hub height of mount + rotor height / 2 (the swept-area centroid), since the rotor extends vertically rather than concentrating at a single hub.

Wind shear (power law): v_hub = v_ref (h_hub/h_ref)^α, where α ranges from 0.10 (open water) to 0.25 (forested terrain). Wind speed, and therefore power, rises quickly with height.

Rayleigh PDF & capacity factor: Real wind speed is variable. This calculator integrates P(v) over a Rayleigh probability density (1,000 bins up to max(2 × v_cut-out, 12 v̄)) to find the mean power. The capacity factor CF = P̄/P_rated shows what fraction of nameplate power is delivered on average.

Yosemite Valley example (15 W micro-turbine, v̄ = 1.5 m/s, cut-in 2.5 m/s, rated 8 m/s, C_p = 0.35, d = 1.0 m, ISA air):
CF ≈ 3.6% → P̄ ≈ 0.54 W → ~13 Wh/day, a low-wind site where solar dominates.

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