WIXLIB

Engineering Formula SheetStatisticsModeMeanPlace data in ascending order.Mode most frequently occurring value xinμ µ mean valueΣxi sum of all data values (x1, x2, x3, )n number of data values xi - μnMedianPlace data in ascending order.If n is odd, median central valueIf n is even, median mean of two central valuesStandard DeviationσIf two values occur at the maximum frequency thedata set is bimodal.If three or more values occur at the maximumfrequency the data set is multi-modal.2n number of data valuesσ standard deviationxi individual data value ( x1, x2, x3, ) mean valuen number of data valuesRangeRange xmax - xminxmax maximum data valuexmin minimum data valueProbabilityIndependent EventsP (A and B and C) PAPBPCFrequencyfx nxnPx fxfaP (A and B and C) probability of independentevents A and B and C occurring in sequencePA probability of event Afx relative frequency of outcome xnx number of events with outcome xn total number of eventsPx probability of outcome xfa frequency of all eventsBinomial Probability (order doesn’t matter)Pk n!(pk )(qn-k )k!(n-k)!P (A or B) PA PBP (A or B) probability of either mutually exclusiveevent A or B occurring in a trialPA probability of event AΣxi sum of all data values (x1, x2, x3, )n number of data valuesConditional ProbabilityPk binomial probability of k successes in n trialsp probability of a successq 1 – p probability of failurek number of successesn number of trialsPLTW, Inc.Mutually Exclusive Events P (A D) probability of event A given event DP(A) probability of event A occurringP( A) probability of event A not occurringP(D ̶ A) probability of event D given event A did not occurEngineering FormulasIED POEDECEAAEBECIM EDD1

Plane GeometryEllipseCircleArea π a bRectangle2bPerimeter 2a 2bArea ab2aCircumference 2 π rArea π r2BTriangleParallelogramhArea bhbArea ½ bhaa2 b2 c2 – 2bc cos Ab2 a2 c2 – 2ac cos Bc2 a2 b2 – 2ab cos CCRight TriangleRegular Polygonsc 2 a2 b2Area nsin θ cos θ acacbchAbsfs( f)2n number of sidesθcbatan θ baTrapezoidArea ½(a b)hhbSolid GeometryCubeSphereVolume s3Surface Area 6s2ssrVolume π r3Surface Area 4 π r2sRectangular PrismVolume wdhSurface Area 2(wd wh dh)CylinderhdwrhVolume π r2 hSurface Area 2 π r h 2 π r2Right Circular Coneπr2 hVolume 3Surface Area π r r2 h2hIrregular PrismrhVolume AhA area of basePyramidVolume Ah3A area of basePLTW, Inc.hConstantsg 9.8 m/s2 32.27 ft/s2G 6.67 x 10-11 m3/kg s2π 3.14159Engineering FormulasIED POEDECEAAEBECIM EDD2

ConversionsMassAreaForce21 acre 4047 m 43,560 ft2 0.00156 mi21 kg 2.205 lbm1 slug 32.2 lbm1 ton 2000 lbm1N1 kipEnergy 0.225 lbf 1,000 lbf1J 0.239 cal 9.48 x 10-4 Btu 0.7376 ft lbf1kW h 3,600,000 JPressureLength1 atmVolume1m1 km1 in.1 mi1 yd 3.28 ft 0.621 mi 2.54 cm 5280 ft 3 ft1L1mL 0.264 gal 0.0353 ft3 33.8 fl oz 1 cm3 1 cc1psiTemperature UnitEquivalentsTime1d1h1 min1 yr1K 24 h 60 min 60 s 365 d 1 ºC 1.8 ºF 1.8 ºR 1.01325 bar 33.9 ft H2O 29.92 in. Hg 760 mm Hg 101,325 Pa 14.7 psi 2.31 ft of H2ODefined Units1J1N1 Pa1V1W1W1 Hz1F1HPower1WSee below fortemperature calculation 3.412 Btu/h 0.00134 hp 14.34 cal/min 0.7376 ft lbf/s 1 N m 1 kg m / s2 1 N / m2 1W/A 1J/s 1V/A 1 s-1 1 A s / V 1 V s / VSI PrefixesNumbers Less Than OnePower of 10PrefixAbbreviationNumbers Greater Than OnePower of aYotta-MGTPEZYEquationsMass and WeightTemperatureTK TC 273M VDmTR TF 460W mgTF 59Tc 32W VDwV volumeDm mass densitym massDw weight densityg acceleration due to gravityPLTW, Inc.ForceF maF forcem massa accelerationEquations of Static EquilibriumTK temperature in KelvinTC temperature in CelsiusTR temperature in RankinTF temperature in FahrenheitEngineering FormulasΣFx 0ΣFy 0ΣMP 0Fx force in the x-directionFy force in the y-directionMP moment about point PIED POEDECEAAEBECIM EDD3

Section PropertiesRectangle CentroidMoment of InertiahIxxxx3bh 12bIxx moment of inertia of a rectangular sectionabout x-x axisx Aiand y b2hand y 2Right Triangle Centroidx b3hand y 3Semi-circle CentroidComplex Shapes Centroid xi Aix x r and y yi Ai Aix x-distance to the centroidy y-distance to the centroidxi x distance to centroid of shape iyi y distance to centroid of shape iAi Area of shape i4r3πx x-distance to the centroidy y-distance to the centroidStructural AnalysisMaterial PropertiesBeam FormulasStress (axial)ReactionFσ AMomentDeflectionσ stressF axial forceA cross-sectional areaReactionMomentStrain (axial)Deflectionϵ δL0Reactionϵ strainL0 original lengthδ change in lengthModulus of ElasticityσE εE (F2 -F1 )L0)AE modulus of elasticityσ stressε strainA cross-sectional areaF axial forceδ deformationPLTW, Inc.PRA RB Mmax PL42(at point of load)3PL max 48EI(at point of load)ωLRA RB Mmax max 2ωL2(at center)85ωL4384EI(at center)RA RB PMomentMmax Pa (between loads)DeflectionPa max 24EIReactionRA MomentMmax DeflectionΔPb(at xLand RB PabLaaPaLa aa aTruss AnalysisFL0δ AE2J M REngineering Formulas(at center)(at Point of Load)Deformation: Axialδ deformationF axial forceL0 original lengthA cross-sectional areaE modulus of elasticity3L2 -4a2,when ab)J number of jointsM number of membersR number of reaction forcesPOE 5 AE 4 CEA 4

Aerospace EquationsForces of FlightCD 2DAρv2R e ρvlμ2LCL Aρv2M FdCL coefficient of liftCD coefficient of dragL liftD dragA wing areaρ densityRe Reynolds numberv velocityl length of fluid travelμ fluid viscosityF forcem massg acceleration due to gravityM momentd moment arm (distance fromdatum perpendicular to F)PropulsionOrbital MechanicsF N W vj - voI Fave t 1-Fnet Favg - Fga vf tT 2πFN net thrustW air mass flowvo flight velocityvj jet velocityI total impulseFave average thrust force t change in time (thrustduration)Fnet net forceFavg average forceFg force of gravityvf final velocitya acceleration t change in time (thrustduration)NOTE: Fave and Favg areeasily confused.Energy1GMm2RK kinetic energym massv velocityU gravitational potential energyG universal gravitation constantM mass of central bodym mass of orbiting objectR Distance center main body tocenter of orbiting objectE Total Energy of an orbitPLTW, Inc. eccentricityb semi-minor axisa semi-major axisT orbital perioda semi-major axisμ gravitational parameterF force of gravity between twobodiesG universal gravitation constantM mass of central bodym mass of orbiting objectr distance between center of twoobjectsBernoulli’s Lawρv22 Ps 1ρv222PS static pressurev velocityρ densityGMmRE U K aa 2πμ GMGMmr2Ps K 2 mv2U F b2a2Engineering FormulasAtmosphere ParametersT 15.04 - 0.00649hp 101.29ρ T 273.1288.085.256p0.2869 T 273.1T temperatureh heightp pressureρ densityAE 5

PLTW, Inc. Engineering Formulas f Numbers Less Than One Numbers Greater Than One Power of 10 Prefix Abbreviation Power of 10 Prefix Abbreviation 10-1 deci- d 101 deca- da 10-2 centi- c 102 hecto- h 10-3 milli- m 103 kilo- k 10-6 micro- µ 106 Mega- M 10-9 nano- n 109 Giga- G 10-12 pico- p 1012 Tera- T 10-15 femto- f 1015 Peta- P