OPEN METHODOLOGY · MATHEMATICAL DERIVATIONS

Testing Methodology & Core Formulas

In alignment with our commitment to engineering accuracy, we publish the exact mathematical derivations, physical constants, and bench testing procedures that govern all calculations on 90daypoweroutage.com.

1. Battery Capacity & Inverter Sizing Formula

The gross daily electrical energy consumed by household appliances is derived as:

E_gross = Σ (Watts_running,i × DutyCycle_i × Hours_i)

To account for real-world inverter losses and the continuous 24/7 internal control circuitry tare drain, usable DC energy is calculated as:

E_usable = (E_gross ÷ η_inverter) + (Watts_tare × 24 hours)

Where η_inverter = 0.88 (default 88% efficiency) and Watts_tare = 20W continuous ($480\text{ Wh/day}$). Total nameplate battery capacity required is:

Capacity_nameplate = (E_usable × ReserveMargin) ÷ DepthOfDischarge

Where DoD = 0.90 for LiFePO4 cells and ReserveMargin = 1.25 (25% engineering safety headroom).

2. Solar Array Seasonal Sizing Derivation

Required photovoltaic solar array wattage is derived by dividing daily energy demand by geographic Peak Sun Hours (PSH) multiplied by combined system efficiency:

Array_Watts = E_daily_Wh ÷ (PSH × η_sys)

Where total system efficiency accounts for four cascading thermodynamic derates:

η_sys = η_mppt (0.95) × η_batt_accept (0.96) × η_temp_soiling (0.85) × η_cable (0.97) ≈ 0.751 (75.1%)

3. Small Engine Generator Oil Service Equation

Small air-cooled engines rely on splash lubrication and experience rapid thermal breakdown. Mandatory oil change intervals are modeled as:

Total_Run_Hours = Hours_per_day × Outage_Days Oil_Changes = ⌊(Total_Run_Hours - 25_hr_breakin) ÷ 100_hrs⌋ + 1 Oil_Stockpile_Quarts = (Oil_Changes + 1) × 0.6_quarts

4. Hardware Bench Testing Standards

Before an inverter or generator is recommended on our platform, it undergoes laboratory evaluation:

Reviewer Sign-off: Marcus Vance, Master Electrician (#ME-884920). Formulated in compliance with IEEE 1547 and ANSI/UL 2201 standards.