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Engineering Wiki

Engineering Wiki

A plain-English guide to the formula, variables, assumptions, and named standard behind every PhDino calculator, on the same page as the calculator itself. Original writing from general engineering knowledge — no textbook text is reproduced.

Structural

  • Beam Deflection — How much a beam sags under a uniform load, and the bending moment that causes it.
  • Bolted Steel Connections — Checking whether a group of bolts can transfer a shear load, considering both bolt shear and plate bearing.
  • Column Buckling — How much axial load a steel column can carry before it buckles: Euler's elastic formula, with the AISC reduction for stocky columns.
  • Concrete Strength Development — Estimating how much of its 28-day design strength concrete has gained at an earlier age.
  • Continuous Beam Moments — Estimating support and span moments for a two-span continuous beam under uniform load.
  • Footing Design — Sizing a square spread footing so the pressure it puts on the soil stays within what the soil can safely carry.
  • Stress Concentration — How a geometric discontinuity like a hole or notch locally raises stress well above the nominal average.
  • Truss Member Analysis — Checking whether a truss member can carry its axial tension or compression force.

Mechanical

  • Bearing Stress — The contact pressure where one surface presses directly against another, and the safety factor against crushing.
  • Fatigue Analysis (Goodman) — Checking whether a fluctuating (cyclic) stress will cause fatigue failure well before a single overload would.
  • Gear Ratio — How tooth count determines the speed and torque relationship between two meshing gears.
  • HVAC Cooling Load — A rough-order cooling load estimate for sizing air conditioning equipment.
  • Motor Sizing — Choosing an adequately rated motor for a known mechanical load, with margin for starting and real-world losses.
  • Pipe Flow — Velocity, Reynolds number, and friction pressure drop for flow through a pipe.
  • Shaft Torsion — Shear stress and angle of twist in a circular shaft carrying torque.

Electrical

  • Cable Sizing (Voltage Drop Method) — Choosing a conductor size large enough to keep voltage drop within an allowed percentage over a given run.
  • Ohm's Law — The fundamental relationship between voltage, current, and resistance in a DC circuit.
  • Real, Reactive and Apparent Power — Real, reactive, and apparent power in a single-phase or balanced three-phase system, and how power factor relates them.
  • Transformer Sizing — Rating a transformer for a known load, and finding the resulting primary and secondary currents.
  • Voltage Drop in Conductors — Checking whether the voltage drop along a specific conductor run stays within NEC-recommended limits.

Geotechnical

  • Consolidation Settlement — How much a clay layer compresses over time as a new load squeezes pore water out of it, and roughly how long that takes.
  • Pile Capacity — How a deep foundation pile carries load through a combination of side friction and end bearing.
  • Retaining Wall: Earth Pressure — The lateral thrust a retained soil mass exerts on a wall, and the overturning moment it creates.
  • Slope Stability — A simplified factor of safety against a slope sliding, comparing resisting shear strength to driving gravity forces.
  • Soil Bearing Capacity — The maximum pressure a shallow footing can safely put on the soil beneath it, before shear failure of the soil.

Civil / Construction Materials

  • Asphalt Thickness — A simplified planning estimate for how thick a driveway or parking-lot pavement section needs to be.
  • Concrete Mix Design — Turning a volume of concrete into bags of cement, sand, gravel, and water using a simple proportion mix.
  • Concrete Volume — Converting a slab or footing's dimensions into the cubic yards ready-mix concrete is actually sold in.
  • Culvert Flow — Checking a circular culvert's full-flow capacity using Manning's equation.
  • Excavation Volume — Working out cut volume and how many truck loads it takes to haul the spoil off site.
  • Masonry Block Count — Estimating concrete block and mortar quantities for a block wall.
  • Rebar Sizing — Estimating bar count and total steel weight for a two-way reinforcing grid in a slab.
  • Soil Compaction Check — Comparing a field density measurement against the lab-established maximum to check compaction adequacy.
  • Stormwater Runoff — Estimating peak runoff from a small drainage area using the Rational Method.

Chemistry

  • Buffer Solutions — How a mix of a weak acid and its conjugate base resists changes in pH.
  • Ideal Gas Law — The relationship between a gas's pressure, volume, amount, and temperature.
  • Molar Mass and Solution Preparation — Converting a target molarity and volume into the actual mass of solid to weigh out.
  • Molarity and Dilution — Combining a concentrated stock solution with water to reach a target, more dilute concentration.
  • Percent Yield — How a reaction's actual, measured output compares to the maximum stoichiometry predicts.
  • pH and pOH — Converting a hydrogen or hydroxide ion concentration into the pH scale.
  • Reaction Half-Life (First-Order Kinetics) — How long it takes a first-order reaction to use up half its remaining reactant, and how much is left after any elapsed time.
  • Stoichiometry and Limiting Reagents — Finding which reactant runs out first, and how much product a reaction actually produces.
  • Titration — Finding the volume of titrant needed to exactly neutralize a known amount of acid or base.

Renewable Energy / Solar

  • Battery Bank Sizing — How much battery capacity an off-grid or backup solar system needs to ride out days without sun.
  • Charge Controller Sizing — Sizing the device that regulates power flowing from solar panels into a battery bank.
  • Inverter Sizing — Sizing an inverter for both its steady running load and the momentary surge a motor draws on startup.
  • Net Metering Savings — How solar production that doesn't match consumption in real time still shows up as bill savings.
  • Off-Grid Autonomy — How many days a battery bank can supply a site's energy needs with zero solar input.
  • Solar Array Sizing — How many solar panels it takes to cover a daily electricity need.
  • Solar Panel Tilt Angle — A latitude-based rule of thumb for angling a fixed solar panel toward the sun.
  • Solar Payback Period — How many years of electric bill savings it takes to recover the cost of a solar installation.
  • Wind Turbine Output — Estimating the electrical power a small wind turbine produces at a given wind speed.

Manufacturing / Machining

  • Bolt Circle Patterns — Laying out evenly spaced holes around a circle for a flange, wheel, or mounting pattern.
  • CNC Speeds and Feeds — Converting a material's recommended cutting speed into the spindle RPM and feed rate a CNC machine actually runs at.
  • Drilling Cycle Time — Estimating how long a drilling operation takes from spindle speed, feed, and hole count.
  • Metal Stock Weight — Estimating the weight of a length of round, square, flat, or tube metal stock.
  • Press Brake Tonnage — Estimating the tonnage a press brake needs to air-bend a given sheet metal thickness.
  • Sheet Metal Bend Allowance — Figuring out how long a flat sheet metal blank needs to be to fold up into a finished bent part.
  • Surface Finish (Theoretical Roughness) — How feed rate and tool nose radius set a theoretical limit on how smooth a turned surface can be.
  • Tap Drill Size — Choosing the right drill diameter to bore a hole before cutting internal threads with a tap.
  • Tolerance Stack-Up — Two different ways of combining several individually toleranced dimensions into one overall tolerance.

Aerospace

  • Circular Orbital Velocity — How fast an object must travel to maintain a stable circular orbit at a given altitude.
  • Escape Velocity — The speed needed to break free of a body's gravity entirely, never to fall back.
  • Hohmann Transfer Orbit — The most fuel-efficient way to move a spacecraft between two circular orbits using just two engine burns.
  • Mach Number — How fast something is moving relative to the local speed of sound, which itself depends on air temperature.
  • The Drag Equation — The resistive force air exerts on anything moving through it, and why speed matters so much more than shape.
  • The Lift Equation — How airspeed, wing area, and airfoil shape combine to produce the force that holds an aircraft up.
  • Thrust-to-Weight Ratio — The single number that determines whether a vehicle's engines can lift it off the ground at all.
  • Tsiolkovsky's Rocket Equation — Why a rocket needs to be mostly propellant, and how efficiently it converts that propellant into velocity change.
  • Wing Loading — How much weight each unit of wing area has to support, and what that implies about an aircraft's flight characteristics.

Biomedical / Clinical

  • Anion Gap — A calculated value from basic blood electrolytes used to help categorize the cause of a metabolic acid-base disturbance.
  • BMR and Caloric Needs — Estimating resting energy expenditure and total daily calorie needs from body measurements and activity level.
  • Body Mass Index (BMI) — A simple screening ratio of weight to height, and why it's a starting point rather than a diagnosis.
  • Body Surface Area (BSA) — Estimating total body surface area from height and weight using the Mosteller formula.
  • Creatinine Clearance (Cockcroft-Gault) — Estimating kidney filtration function from age, weight, sex, and a blood creatinine level.
  • IV Drip Rate — Converting a prescribed IV volume and duration into drops per minute for a gravity infusion.
  • Pediatric Dosage: Clark's Rule — A historical rule of thumb for scaling an adult medication dose down to a child's weight.
  • Target Heart Rate Zones — Estimating a maximum heart rate from age, and a moderate-to-vigorous exercise target zone from that estimate.
  • Weight-Based Drug Dosage — Scaling a medication dose to a patient's body weight using a per-kilogram dosing rate.

Motorsport

  • Aerodynamic Downforce — How a race car uses airflow to press itself into the track instead of lifting off it.
  • Braking Distance — How speed, braking deceleration, and reaction time combine to determine total stopping distance.
  • Corner Weight Balance — How a car's weight is actually distributed across its four tires, and why the diagonal split matters as much as front/rear.
  • Fuel Load Strategy — Working out how much fuel a race actually needs, how much weight it adds, and how many pit stops that requires.
  • Gear Ratio and Top Speed — Working out the theoretical top speed a given gear, tire size, and final drive ratio allow at redline.
  • Lap Time Delta — Estimating how much a lap time changes from a change in average speed around a fixed-length track.
  • Suspension Spring Rate — The difference between a spring's own stiffness and the stiffness it actually delivers at the wheel, and the ride frequency that results.
  • Tire Contact Patch — A tire's only actual connection to the road is a small contact patch, sized mainly by load and inflation pressure.
  • Weight Transfer — How braking and acceleration shift a car's effective weight between its front and rear axles.

Digital Logic / Computer Engineering

  • Addressable Memory — How the width of an address bus directly determines how much memory a processor can address.
  • Bit Width and Parity — How many bits a number needs, how many of those bits are 1, and what that means for a parity check.
  • Boolean Function Counting — How fast the space of possible logic functions explodes as the number of input variables grows.
  • Clock Frequency and Duty Cycle — The relationship between a clock signal's period, its frequency, and how long it spends high versus low each cycle.
  • Flip-Flop Setup and Hold Timing — The two timing checks that determine whether a synchronous digital circuit will actually work at a given clock speed.
  • Half and Full Adders — The basic building blocks that add binary digits together, and how they chain into multi-bit addition.
  • Karnaugh Map Position — Why Karnaugh maps arrange their rows and columns in Gray code order, and where a given minterm actually lands.
  • Logic Gate Propagation Delay — Why a chain of logic gates takes real time to settle, and what that means for how fast a circuit can run.
  • Minterms and Truth Table Rows — How a single number (a minterm) encodes one specific row of a truth table.
Educational tool — not a substitute for a licensed engineer or the official code text.