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General Calculations 28

Engineering 4

Factor of Safety (load) ⚠Margin of Safety ⚠Reliability Factor ⚠Temperature Derating ⚠

Monte Carlo 3

Sample Normal ⚠Sample Uniform ⚠Sample Weibull ⚠

Reliability 14

Availability ⚠B10 Life ⚠Bathtub Curve ⚠Exponential Reliability ⚠Failure Rate From Mtbf ⚠Hazard Rate Ratio ⚠Mtbf From Failure Rate ⚠Reliability Growth ⚠Unavailability ⚠Weibull Failure Rate ⚠Weibull Mean ⚠Weibull Median ⚠Weibull Mode ⚠Weibull Reliability ⚠

Statistics 3

Normal Distribution PDF ⚠Process Capability (Cpk) ⚠Weibull Distribution PDF ⚠

Uncertainty 4

Coverage Factor ⚠Expanded Uncertainty ⚠Gage Rr Percent ⚠Relative Uncertainty ⚠

Aerospace 131

Aerodynamics 13

Downwash Angle ⚠Drag Force ⚠Dynamic Pressure ⚠Induced Drag ⚠Lift Curve Slope ⚠Lift Force ⚠Lift-to-Drag Ratio ⚠Mach Number ⚠Moment Coefficient ⚠Parasite Drag ⚠Pitching Moment ⚠Prandtl Glauert ⚠Reynolds Number ⚠

Atmosphere 12

Density Altitude ✓Dynamic Pressure ⚠Geopotential Altitude ⚠ISA Density ✓ISA Pressure ✓ISA Temperature ✓Mach Number ⚠Pressure Altitude ✓Reynolds Number Atm ⚠Speed Of Sound ⚠Stratospheric Temperature ⚠Wind Shear ⚠

Controls 12

Aileron Roll Rate ⚠Autopilot Heading Hold ⚠Control Power Moment ⚠Control Surface Hinge Moment ⚠Dutch Roll Damping ⚠Elevator Deflection (trim) ⚠Load Factor (pull-up) ⚠Pid Controller ⚠Pitch Rate Damping ⚠Rudder Yaw Rate Coeff ⚠Sideslip Due To Rudder ⚠Stability Derivative Cm Q ⚠

Navigation 7

Barometric Altitude ⚠Cross Track Error ⚠Gps Dilution Of Precision ⚠Great-Circle Distance ⚠Initial Heading ⚠Magnetic Heading ⚠Time To Go ⚠

Orbital 15

Circular Orbit Velocity ⚠Delta V Rendezvous ⚠Eccentricity Vector ⚠Escape Velocity ⚠Ground Track Velocity ⚠Hohmann Transfer Dv1 ⚠Hohmann Transfer Dv2 ⚠Inclination Change Delta V ⚠Nodal Precession ⚠Orbital Period ⚠Orbital Velocity ⚠Sun Synchronous Inclination ⚠Time Since Perigee ⚠True Anomaly From Radius ⚠Vis Viva Energy ⚠

Performance 14

Best Climb Speed ⚠Ceiling Density ⚠Endurance ⚠Energy Height ⚠Excess Power ⚠Glide Ratio ⚠Landing Distance ⚠Range Breguet ⚠Rate of Climb ⚠Rate Of Climb Ft Min ⚠Specific Range ⚠Stall Speed ⚠Time To Climb ⚠Turn Radius ⚠

Propulsion 13

Chamber Pressure Ratio ⚠Characteristic Velocity ⚠Combustion Chamber Temperature ⚠Ideal Delta-V (Tsiolkovsky) ⚠Mass Flow Rate ⚠Nozzle Efficiency ⚠Nozzle Expansion Ratio ⚠Propellant Mass Fraction ⚠Ramjet Efficiency ⚠Rocket Nozzle Thrust ⚠Specific Impulse ⚠Thrust-to-Weight Ratio ⚠Turbojet Thrust ⚠

Reentry 13

Ablation Rate ⚠Ballistic Coefficient ⚠Lift To Drag Reentry ⚠Peak Heating Altitude ⚠Reentry Deceleration ⚠Reentry G Load ⚠Reentry Heat Load ⚠Reentry Range ⚠Reentry Time ⚠Reentry Velocity ⚠Skip Reentry Delta V ⚠Stagnation Heat Flux ⚠Thermal Protection Thickness ⚠

Stability 9

Control Power Cm Delta ⚠Dihedral Effect ⚠Dutch Roll Wn ⚠Longitudinal Trim Moment ⚠Phugoid Damping ⚠Roll Mode Time Constant ⚠Spiral Mode Time Constant ⚠Static Margin ⚠Weathercock Stability ⚠

Structures 23

Buckling Load Factor ⚠Buckling Stress ⚠Composite Longitudinal Modulus ⚠Composite Transverse Modulus ⚠Composite Wing Stiffness ⚠Crippling Stress ⚠Euler Buckling Load ⚠Fuselage Hoop Stress ⚠Fuselage Longitudinal Stress ⚠Margin Of Safety ⚠Max Principal Stress ⚠Min Principal Stress ⚠Panel Flutter Speed ⚠Reentry Heat Flux ⚠Sandwich Core Shear Strength ⚠Shear Flow ⚠Stringer Crippling Load ⚠Thermal Moment ⚠Thermal Stress ⚠Tresca Stress ⚠Tsai Wu Failure ⚠Von Mises Stress (2D) ⚠Wing Bending Stress ⚠

Electrical 90

AC 10

Apparent Power ⚠Impedance Capacitor ⚠Impedance Inductor ⚠Impedance Resistor ⚠Power Factor ⚠Power Factor Correction ⚠Quality Factor ⚠Reactive Power ⚠Resonance Frequency (LC Circuit) ⚠Three-Phase Power ⚠

Basic 11

Capacitive Reactance ⚠Capacitor Energy ⚠Inductive Reactance ⚠Inductor Energy ⚠Ohm's Law (solve for current) ✓Power Factor ⚠Rc Time Constant ⚠Resistor Voltage Divider ✓Rl Time Constant ⚠Three Phase Power ⚠Watt's Law ✓

Filters 14

Active Filter Gain ⚠Butterworth Cutoff ⚠Damping Ratio ⚠Filter Order Rolloff ⚠Highpass Passive Cutoff ⚠Lowpass Passive Cutoff ⚠Notch Filter Frequency ⚠Q Factor ⚠RC High-Pass Cutoff ⚠RC Low-Pass Cutoff ⚠RL Low-Pass Cutoff ⚠Rlc Bandwidth ⚠Rlc Series Resonant ⚠Sallen Key Lowpass ⚠

Motors 16

Back Emf ⚠Cogging Torque ⚠Efficiency Map ⚠Maximum Torque ⚠Motor Current ⚠Motor Efficiency ⚠Motor Inertia ⚠Motor Power ⚠Motor Thermal Time Constant ⚠Motor Torque ⚠Slip ⚠Speed Constant ⚠Starting Torque ⚠Synchronous Speed ⚠Temperature Rise ⚠Torque Constant ⚠

Power 15

Apparent Power ⚠Boost Converter Duty Cycle ⚠Buck Boost Duty Cycle ⚠Buck Converter Duty Cycle ⚠Conduction Loss ⚠Power Factor ⚠Reactive Power ⚠Rectifier Average Voltage ⚠Rectifier Ripple Factor ⚠Switching Loss ⚠Three Phase Power ⚠Total Harmonic Distortion ⚠Transformer Current Ratio ⚠Transformer Efficiency ⚠Transformer Turns Ratio ⚠

Power Electronics 21

Boost Converter Duty Cycle ⚠Buck Boost Duty ⚠Buck Converter Duty Cycle ⚠Buck Inductor Ripple ⚠Capacitor Energy ⚠Conduction Loss ⚠Core Loss Steinmetz ⚠Current Limit Sense ⚠Dead Time Loss ⚠Diode Forward Loss ⚠Efficiency Total ⚠Gate Drive Power ⚠Inductor Stored Energy ⚠Magnetizing Inductance ⚠Output Voltage Ripple ⚠Pwm Duty From Voltage ⚠Snubber Rc ⚠Switching Loss ⚠Synchronous Rectifier Loss ⚠Thermal Resistance Jc ⚠Transformer Turns Ratio ⚠

Signals 3

Signal-to-Noise Ratio ⚠SNR to Decibels ⚠THD to Decibels ⚠

Mechanical 261

Beams 11

Beam Bending Stress ⚠Beam Buckling Load ⚠Beam Moment At X ⚠Beam Natural Frequency ⚠Beam Strain ⚠Continuous Beam Moment ⚠Moment Of Inertia I Beam ⚠Plastic Section Modulus ⚠Rectangular Moment of Inertia ⚠Section Modulus ⚠Shear Deflection ⚠

Bearings 13

Bearing Life (hours) ⚠Bearing Life Modifier ⚠Bearing Misalignment Moment ⚠Bearing Preload Deflection ⚠Bearing Rating Life (L10) ⚠Bearing Stiffness Radial ⚠Equivalent Dynamic Load (Bearing) ⚠Film Thickness Parameter ⚠Heat Generation Bearing ⚠Life Reliability Factor ⚠Minimum Required Dynamic Capacity ⚠Static Equivalent Load ⚠Viscosity Required ⚠

Clutches Brakes 17

Band Brake Actuating Force ⚠Band Brake Tension Ratio ⚠Band Brake Torque ⚠Brake Energy ⚠Brake Fade Factor ⚠Brake Stopping Distance ⚠Brake Thermal Capacity ⚠Clutch Engagement Time ⚠Clutch Facing Pressure ⚠Clutch Slip Power ⚠Clutch Torque Capacity Uniform Wear ⚠Clutch Wear Volume ⚠Cone Clutch Torque ⚠Disk Brake Heat Flux ⚠Disk Clutch Heat Generation ⚠Disk Clutch Torque ⚠Multiple Disk Clutch ⚠

Columns 10

Beam Column Moment ⚠Critical Slenderness ⚠Euler Buckling Load (column) ⚠Euler Buckling Stress ⚠Interaction Formula ⚠Intermediate Column Load ⚠Reduced Modulus Load ⚠Secant Formula Stress ⚠Slenderness Ratio ⚠Tangent Modulus Load ⚠

Composites 14

Composite Density ⚠Fatigue Life Composite ⚠Fiber Volume Fraction ⚠Halpin Tsai Modulus ⚠Hygrothermal Strain ⚠Interlaminar Shear Stress ⚠Longitudinal Strength ⚠Micromechanics Shear ⚠Poisson Ratio Nu12 ⚠Rule of Mixtures (longitudinal) ⚠Rule of Mixtures (transverse) ⚠Shear Modulus Inplane ⚠Transverse Strength ⚠Tsai Hill Criterion ⚠

Fasteners 11

Bolt Fatigue Endurance ⚠Bolt Preload from Torque ⚠Bolt Proof Load ⚠Bolt Shank Stiffness ⚠Bolt Tensile Strength Area ⚠Bolt Tensile Stress Area ⚠Bolt Thread Stiffness ⚠Bolt Torque Preload ⚠Bolt Yield Torque ⚠Nut Height Minimum ⚠Thread Stripping Strength ⚠

Fatigue 12

Asme Elliptic ⚠Endurance Limit (steel) ⚠Fatigue Life (cycles) ⚠Fatigue Stress Concentration ⚠Gerber ⚠Marin Endurance Limit ⚠Modified Goodman Factor ⚠Notch Sensitivity ⚠Reliability Factor ⚠Size Factor ⚠Soderberg ⚠Temperature Factor ⚠

Flexible Elements 15

Belt Efficiency ⚠Belt Length Crossed ⚠Belt Power ⚠Belt Stress ⚠Belt Tension Ratio ⚠Centrifugal Tension ⚠Chain Sag Allowance ⚠Chain Velocity ⚠Chain Wear Elongation ⚠Maximum Belt Power ⚠Open Belt Length ⚠Timing Belt Pitch Diameter ⚠Timing Belt Tooth Load ⚠V Belt Contact Angle ⚠V Belt Speed ⚠

Gears 13

Backlash Allowance ⚠Bevel Gear Pitch Angle ⚠Gear Bending Stress (Lewis) ⚠Gear Contact Stress ⚠Gear Mesh Stiffness ⚠Gear Power Capacity ⚠Gear Scoring Index ⚠Helical Gear Thrust ⚠Helical Overlap Factor ⚠Lewis Form Factor ⚠Planetary Ratio ⚠Worm Gear Center Distance ⚠Worm Gear Efficiency ⚠

Joints 17

Bolt Fatigue Factor ⚠Bolt Load External ⚠Bolt Preload ⚠Bolt Spacing ⚠Bolt Torque from Preload ⚠Bolted Joint Stiffness Member ⚠Eccentric Weld Load ⚠Gasket Factor ⚠Interference Fit Torque ⚠Joint Stiffness ⚠Joint Stiffness Ratio ⚠Member Load External ⚠Press Fit Pressure ⚠Rivet Crushing Stress ⚠Rivet Shear Stress ⚠Weld Size ⚠Weld Throat Stress ⚠

Lubrication 16

Bearing Power Loss ⚠Contact Stress Herzian ⚠Elastohydrodynamic Film ⚠Friction Coefficient Boundary ⚠Grease Life Factor ⚠Hertzian Contact Pressure ⚠Hertzian Contact Radius ⚠Hydrodynamic Film Pressure ⚠Journal Bearing Load Capacity ⚠Lambda Ratio ⚠Minimum Film Thickness ⚠Petroff Friction ⚠Reynolds Number ⚠Sommerfeld Number ⚠Stribeck Curve ⚠Viscosity Temperature ⚠

Materials 17

Ashby Chart Index ⚠Corrosion Resistance Index ⚠Creep Resistance Index ⚠Cyclic Strain Hardening Exponent ⚠Damping Capacity Index ⚠Endurance Limit Unmodified ⚠Fatigue Strength Coefficient ⚠Fracture Toughness To Yield Ratio ⚠Hardness to Tensile Strength ⚠Material Performance Index Thermal Conductivity ⚠Material Selection Index Stiffness ⚠Material Selection Index Stiffness Thermal ⚠Material Selection Index Strength ⚠Material Selection Index Toughness ⚠Specific Modulus ⚠Specific Strength ⚠Thermal Stress Index ⚠

Power Screws 12

Acme Thread Torque ⚠Ball Screw Efficiency ⚠Collar Torque ⚠Power Screw Efficiency ⚠Power Screw Torque (raise) ⚠Preload For Backlash ⚠Screw Lead Angle ⚠Thread Bending Stress ⚠Thread Shear Stress ⚠Thread Stress Tensile ⚠Torque Lower Load ⚠Total Torque Raise ⚠

Pressure Vessels 13

Burst Pressure ⚠External Pressure Critical ⚠Head Thickness Ellipsoidal ⚠Head Thickness Hemispherical ⚠Hydrostatic Test Pressure ⚠Nozzle Load Area ⚠Nozzle Reinforcement Area ⚠Required Thickness Thin ⚠Spherical Vessel Stress ⚠Thin-Wall Hoop Stress ⚠Thin-Wall Longitudinal Stress ⚠Vessel Volume Cylinder ⚠Vessel Weight ⚠

Shafts 13

Combined Stress Shaft ⚠Interference Fit Pressure ⚠Keyway Stress Reduction ⚠Marin Modification Factors ⚠Polar Moment (solid shaft) ⚠Polar Moment Hollow ⚠Shaft Deflection ⚠Shaft Diameter (torsion) ⚠Shaft Diameter Bending ⚠Shaft Diameter Combined ⚠Shaft Fatigue Factor ⚠Shaft Thermal Stress ⚠Torsional Shear Stress ⚠

Springs 11

Belleville Spring Rate ⚠Helical Spring Deflection ⚠Helical Spring Rate ⚠Helical Spring Stress ⚠Leaf Spring Rate ⚠Spring Energy ⚠Spring Index ⚠Spring Natural Frequency ⚠Spring Set Removal ⚠Torsion Spring Rate ⚠Torsion Spring Stress ⚠

Stress Analysis 15

Biaxial Stress State ⚠Combined Loading Stress ⚠Elliptical Interaction ⚠Factor of Safety (yield) ⚠Factor Of Safety Ultimate ⚠Fatigue Notch Factor ⚠Goodman Line ⚠Mohr Circle Center ⚠Mohr's Circle Radius ⚠Octahedral Shear Stress ⚠Residual Stress Superposition ⚠Strain Energy Density ⚠Stress Concentration ⚠Tresca Stress ⚠Von Mises Stress ⚠

Vibration Analysis 17

Critical Damping ⚠Damped Natural Frequency ⚠Damping From Log Decrement ⚠Damping Ratio ⚠Fatigue From Vibration ⚠Force Transmissibility ⚠Half Power Bandwidth ⚠Logarithmic Decrement ⚠Magnification Factor ⚠Natural Frequency Mass Spring ⚠Quality Factor (Q) ⚠Random Vibration Rms ⚠Rayleigh Damping Alpha ⚠Rayleigh Damping Beta ⚠Response Spectrum Value ⚠Transmissibility ⚠Vibration Isolation Efficiency ⚠

Welds 14

Butt Weld Strength ⚠Eccentric Load Angle ⚠Eccentric Weld Primary Shear ⚠Eccentric Weld Secondary Shear ⚠Fillet Weld Capacity ⚠Fillet Weld Size ⚠Plug Weld Shear ⚠Slot Weld Strength ⚠Throat Thickness ⚠Weld Bending Stress ⚠Weld Fatigue Factor ⚠Weld Group Moment Of Inertia ⚠Weld Group Polar Moment ⚠Weld Torsional Shear ⚠

Physics 159

Acoustics 15

A Weighted Level ⚠Acoustic Impedance ⚠Critical Frequency ⚠Doppler Shift ⚠Insertion Loss ⚠Octave Band Center ⚠Radiation Efficiency ⚠Reverberation Time ⚠Sound Attenuation ⚠Sound Intensity ⚠Sound Intensity Level ⚠Sound Power Level ⚠Sound Pressure Level ✓Speed of Sound in Air ⚠Transmission Loss ⚠

Controls 15

Acceleration Error Constant ⚠Bandwidth ⚠Bode Magnitude ⚠Damping Ratio From Overshoot ⚠Gain Crossover Frequency ⚠Gain Margin ⚠Lag Compensator Attenuation ⚠Lead Compensator Phase ⚠Peak Overshoot ⚠Phase Margin ⚠Phase Margin From Damping ⚠Pid Output ⚠Rise Time ⚠Settling Time (2%) ⚠Velocity Error Constant ⚠

Electromagnetics 19

Coulomb's Law (force) ⚠Displacement Current ⚠Electric Field (point charge) ⚠Electric Potential ⚠Energy Electric Field ⚠Energy Magnetic Field ⚠Induced Emf ⚠Inductance Solenoid ⚠Lorentz Force ⚠Magnetic Field Wire ⚠Magnetic Flux Density ⚠Magnetic Force ⚠Mutual Inductance ⚠Parallel-Plate Capacitance ⚠Poynting Vector ⚠Radiation Resistance ⚠Self Inductance ⚠Skin Depth ⚠Wave Impedance ⚠

Fluids 13

Bernoulli Total Pressure ⚠Continuity ⚠Drag ⚠Dynamic Pressure ⚠Froude Number ⚠Lift ⚠Mach Number ⚠Mass Flow Rate ⚠Pipe Head Loss ⚠Reynolds Number ⚠Speed Of Sound ⚠Thrust ⚠Weber Number ⚠

Heat Transfer 17

1D Steady Conduction ⚠Biot Number ⚠Conduction Cylindrical ⚠Convection Heat Transfer ⚠Critical Radius Insulation ⚠Fin Efficiency ⚠Fourier Number ⚠Grashof Number ⚠Heat Exchanger Lmtd ⚠Heat Flux ⚠Nusselt Number ⚠Overall Heat Transfer Coefficient ⚠Prandtl Number ⚠Radiation Heat Transfer ⚠Reynolds Number Heat ⚠Thermal Resistance Conduction ⚠Thermal Resistance Convection ⚠

Materials 13

Column Slenderness Ratio ⚠Euler Buckling Load ⚠Factor of Safety ⚠Fatigue Endurance Limit ⚠Fracture Toughness ⚠Hooke's Law (strain) ⚠Hookes Law Strain Stress ⚠Poissons Ratio ⚠Section Modulus ⚠Shear Stress ⚠Strain Energy Density ⚠Stress Intensity Factor ⚠Von Mises Stress ⚠

Mechanics 21

Angular Momentum ⚠Centripetal Force ⚠Circular Orbital Velocity ⚠Conservation Of Momentum ⚠Elastic Potential Energy ⚠Escape Velocity ⚠Gravitational Force ⚠Impulse ⚠Kinetic Energy ⚠Moment Of Inertia Disk ⚠Moment Of Inertia Point Mass ⚠Momentum ⚠Newton's Second Law ⚠Parallel Axis Theorem ⚠Potential Energy ⚠Power ⚠Power From Force Velocity ⚠Reduced Mass ⚠Rotational Kinetic Energy ⚠Torque ⚠Work (constant force) ⚠

Optics 18

Brewster Angle ⚠Coherence Length ⚠Critical Angle ⚠Diffraction Grating ⚠Diffraction Single Slit ⚠Etendue ⚠Fresnel Reflection ⚠Lens Magnification ⚠Lens Power ⚠Lensmaker's Equation ⚠Malus Law ⚠Mirror Focal Length ⚠Numerical Aperture ⚠Optical Path Length ⚠Rayleigh Criterion ⚠Snell's Law (refraction angle) ⚠Thin Film Thickness ⚠Youngs Double Slit ⚠

Thermodynamics 16

Availability Change ⚠Availability Efficiency ⚠Brayton Efficiency ⚠Carnot Efficiency ⚠Cop Refrigerator ⚠Enthalpy Moist Air ⚠Entropy Change Ideal Gas ⚠Exergy ⚠Exergy Destruction ⚠First Law (ΔU) ⚠Heat Exchanger Effectiveness ⚠Otto Efficiency ⚠Psychrometric Wet Bulb ⚠Rankine Efficiency ⚠Second Law Entropy ⚠Thermal Efficiency ⚠

Vibration 12

Critical Speed Shaft ⚠Damped Natural Frequency ⚠Damping Ratio ⚠Equivalent Viscous Damping ⚠Logarithmic Decrement ⚠Magnification Factor ⚠Natural Frequency (mass-spring) ⚠Natural Frequency Cantilever Beam ⚠Quality Factor ⚠Resonance Frequency (damped) ⚠Transmissibility ⚠Vibration Isolation Efficiency ⚠

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