Reciprocating Engine Formula Equations 4-Stroke

General Engineering Reviews
Engineering Applications and Design

The following tables define equations for four stroke reciprocating engines.

BHP = PLAN/33,000
P is brake mean effective pressure, in PSI
L is piston stroke, in feet
A is the area of one piston, in square inches
N is the number of power strokes per minute
Piston Speed
Cm = .166 x L x N
Cm is mean piston speed, in feet per minute
L is stroke, in inches
N is crankshaft speed, in RPM
Brake Mean Effective Pressure (BMEP)
2-Stroke BMEP = (HP x 6500)/(L x RPM)
4-Stroke BMEP = (HP x 13000)/(L x RPM)
L = Displacement in Liters
i.e., 80 cc = .08 Liters
1 ci. = 16.39 cc
Piston Acceleration
Gmax = ((N2 x L)/2189) x (1 + 1/(2A))
Gmax is maximum piston acceleration, in feet per second squared
N is crankshaft speed, in RPM
L is stroke, in inches
A is the ratio of connecting rod length, between centers, to stroke
Piston Stroke Motion
S = R cos X + L cos Z
S = the distance piston wrist pin is from center of crankshaft
R = the radius of the crankshaft wrist pin
L = the length of the connecting rod
X = the angle of the wrist pin
Z = the angle of the connecting rod
sin X = R/L sin Z
Piston Travel vs. Crank Rotation
d = ((S/2) + L) - (S/2 cos X) - L sin[cos-1 (S/2L sin X)]
S = Stroke (mm)
L = Connecting Rod Length (mm)
X = Crank Angle Before or After TDC (deg)
Note: (L) Rod Length is usually 2 times the (S) Stroke
For Spreadsheets and some Calculators
HT = (r + c) - (r cos (a)) - SQRT(c2 - (r sin (a))2)
r = s/2
dtor = PI/180
a = d x dtor
HT = The height of piston
r = The stroke divided by 2
c = The rod length
a = The crank angle in radians
d = The crank angle in degrees
dtor = Degrees to Radians
Exhaust Systems Tuned Length
Lt = (Eo x Vs) / N
Lt is the tuned length, in inches
Eo is the exhaust-open period, in degrees
Vs is wave speed in feet per second (1700 ft/sec at sea level)
N is crankshaft speed, in RPM
Length of Curved Pipe
L = R x .01745 x Z
L is length
R is radius of the pipe bend
Z is the angle of the bend
Diffuser Proportions
D2 = SQRT( D1^2 x 6.25 )
D2 is the diffuser outlet diameter
D1 is the diffuser inlet diameter
6.25 is the outlet/inlet ratio constant
Baffle Cones
Lr = Le/2
Lr is mean point of the reflection inside the baffle cone
Le is the length of the baffle cone
Port Open Time
T = ( 60/N ) x ( Z/360 ) or T = Z/( N x 6)
T is time, in seconds
N is crankshaft speed, in RPM
Z is port open duration, in degrees
Compression Ratio
CR = ( V1 + V2 ) / V2
CR is compression ratio
V1 is cylinder volume at exhaust closing
V2 is combustion chamber volume
Carburetor Throttle Bore Diameter
D = K x SQRT( C x N )
D is throttle bore diameter, in millimeters
K is a constant ( approx. 0.65 to 0.9, derive from existing carburetor bore)
C is cylinder displacement, in liters
N is RPM at peak power
Crankcase Volume
Primary compression ratio =
Case Volume @ TDC / Case Volume at BDC
CRp = V1 + V2 / V1
CRp is the primary compression ratio
V1 is crankcase volume @ BDC
V2 is piston displacement
Resonance Effects
F = Vs / 2 * the square root of A / Vc (L + 1/2 the square root of   A
Vs is the sonic speed Usually about 1100 ft/sec)
A is the cross-sectional area of the inlet
L is the inlet pipe length
Vc is the flask (crankcase) volume
Average Exhaust Temperature
Exhaust gas temperature in Kelvin
(k = C + 273.15). This is usually a function of the engine's BMEP.

MPH Calculate

To figure miles per hour, multiply the engine RPM by the Wheel Diameter in inches and divide this by the Gear Ratio times 336
MPH = RPM * wheel diameter (in inches) / gear ratio * 336

RPM Calculate

To figure engine speed (RPM), multiply by the Speed in MPH, by the rear axle gear ratio times 336. Divide this by the tire diameter in inches.


RPM = MPH * gear ratio * 336 / tire diameter

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