Engineering Formula Sheet

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Transcript of Engineering Formula Sheet
Project Lead The Way, Inc. Copyright 2010
Engineering Formula Sheet  Page 1
Engineering Formula Sheet
Circular Shapes
Formulas Variables
C = Circumference
C d π = 3.14
d = Diameter 2A r A = Area
r = Radius
Electrical Systems
Formulas Variables
V = Voltage
V = IR I = Current R = Resistance
Right Triangle Ratios
Formulas Variables opposite
Sinhypotenuse
adjacentCos
hypotenuse θ = Angle
oppositeTan
adjacent
Simple Machines
Formulas Variables
R
E
FAMA
F
AMA = Actual Mechanical Advantage FR = Resistance force FE = Effort force
E
R
DIMA
D
IMA = Ideal Mechanical Advantage DR = Resistance Distance DE = Effort Distance
LE
LeverIMALR
LE = Length from fulcrum to effort LR = Length from fulcrum to resistance
Wheel and Axle W
A
rIMA
r rw = Wheel radius
ra = Axle radius
Pulley IMA = Total number of strands supporting the load
Inclined Plane L
MAH
L = Slope length H = Height
Wedge L
IMAH
L = Base length H = Height
C
ScrewIMAPitch
C = Circumference
1Pitch
TPI Pitch = Screw pitch
TPI = Threads per inch
Project Lead The Way, Inc. Copyright 2010
Engineering Formula Sheet  Page 2
Properties of Materials
Formulas Variables
σO
F
A σ = Stress
F = Axial force
εOL
Ao = Crosssectional area
ε = Strain
δ O
O
FL
A E δ = Deformation
Lo = Original length
σE=
ε
E = Modulus of Elasticity
E
δ δ2 1 O
2 1 O
F F L
A
Fluids
Formulas Variables
FPA
P = Pressure F = Force
1 2
1 2
V V
T T A = Area
V = Volume
1 1 2 2P V P V
Gear Ratios
Formulas Variables
in
out
GR
GR = Gear ratio ωin = Driver gear, rpm ωout = Driven gear, rpm
out
in
NGR
N
Nin = Number of teeth on driver Nout = Number of teeth on driven din = Diameter of driver
out out outin
in in out in
N d
N d
dout = Diameter of driven τin = Torque of driver, ftlbs τout = Torque of driven, ftlbs
Kinematics
Formulas Variables
g
2
iV *Sin 2
X
X = Range Vi = Initial velocity
g
ixVSin 2
g = Acceleration due to gravity θ = Initial trajectory angle from the horizontal
ix iV V cos Vix = Initial horizontal velocity
iy iV V sin Viy = Initial vertical velocity
Project Lead The Way, Inc. Copyright 2010
Engineering Formula Sheet  Page 3
Statics
Formulas Variables
M F d M = Moment about a point F = Force d = Perpendicular distance
XF 0 X(right) X(left)
∑ = Sum of X = Force in xdirection Y = Force in ydirection
YF 0 Y up Y down CCW = Counterclockwise moment
M 0 CCW CW CW = Clockwise moment
RMJ 2 J = Number of joints M = Number of members R = Number of reaction forces
Rectangular Sections
XXI3bh
12
IXX = Moment of inertia about xx axis b = Base dimension
h = Height
Work and Power
Formulas Variables
W F D
W = Work F = Force D = Distance
WP
t
P = Power W = Work t = Time
P V I
V = Volts I = Current
QP
t
P = Rate of heat transfer Q = Energy transfer Δt = Difference in time
TP kA
L
k = Thermal conductivity A = Area of thermal conductivity L = Thickness ΔT = Difference in temperature
P UA T U = Thermal transmittance (Ufactor)
1UR
R = Resistance to heat flow (Rvalue)