How to Size a 48 V DC Feeder: Voltage Drop, Loss, and Current Density
A worked 48 V DC feeder example showing conductor resistance, voltage drop, I²R loss, current density, and why those checks do not replace code ampacity.
Read worked guideEngineering Guides & Worked Examples
Detailed, hand-checkable engineering examples that explain the model before sending you into a calculator or simulator. Each guide publishes the equations, numerical steps, interpretation, sanity checks, limitations, and related tools.
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Use the calculator after you understand the model
These guides are intentionally different from a one-line formula page. The worked numbers are exposed so you can reproduce them independently, compare the result with the linked tool, and see where the simplified model stops being sufficient.
Voltage Drop and Wire Sizing Explained: A Practical Design Method
Learn how voltage, current, distance, conductor area, material, temperature, and allowable drop interact when choosing a feeder conductor.
Read worked guidePID Response Basics: Overshoot, Rise Time, and Settling Time from a Second-Order Model
A worked control-system example connecting damping ratio and natural frequency to overshoot, peak time, rise time, and settling time.
Read worked guideBeam Stress and Deflection: Simply Supported Center-Load Worked Example
Calculate reactions, bending moment, bending stress, and midspan deflection for a simply supported steel beam with a center point load.
Read worked guideReynolds Number and Pipe Pressure Loss: Darcy–Weisbach Worked Example
A water-pipe example that calculates velocity, Reynolds number, friction factor, head loss, and pressure loss using Darcy–Weisbach.
Read worked guideHohmann Transfer Worked Example: 7000 km Orbit to Geostationary Radius
Calculate circular speeds, two Hohmann burns, total delta-v, and transfer time from a 7000 km Earth-centered orbit to geostationary radius.
Read worked guideSeries RLC Resonance: Frequency, Q, and Bandwidth Worked Example
Calculate resonant frequency, quality factor, impedance at resonance, and bandwidth for a practical series RLC circuit.
Read worked guideBattery Runtime: Why Amp-Hours Alone Do Not Tell You Runtime
Estimate runtime from battery voltage, amp-hours, usable depth of discharge, inverter efficiency, and load power using a 48 V battery example.
Read worked guideGear Ratio, Speed, and Torque: A 12-Tooth to 60-Tooth Worked Example
Calculate gear ratio, driven speed, rotation direction, and efficiency-adjusted output torque for a simple external gear pair.
Read worked guideOff-Grid Solar and Battery Sizing: A 3 kWh/day Worked Example
Size a first-pass battery bank and solar array from daily energy, autonomy, usable depth of discharge, peak-sun-hours, and system derating.
Read worked guideThree-Phase Current and Power Factor: From kW to Feeder Current
A worked balanced three-phase example converting real power, line voltage, power factor, and efficiency into line current and apparent power.
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