The following tables define equations for four stroke reciprocating engines.
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Power
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- 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
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Piston Speed
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- 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
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Brake Mean Effective Pressure (BMEP)
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- 2-Stroke BMEP = (HP x 6500)/(L x RPM)
- 4-Stroke BMEP = (HP x 13000)/(L x RPM)
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L = Displacement in Liters
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- i.e., 80 cc = .08 Liters
- 1 ci. = 16.39 cc
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Piston Acceleration
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- 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
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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
- or
- sin X = R/L sin Z
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Piston Travel vs. Crank Rotation
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- 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
- OR
- 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
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Exhaust Systems Tuned Length
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- 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
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Port Open Time
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- 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
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Compression Ratio
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- CR = ( V1 + V2 ) / V2
- CR is compression ratio
- V1 is cylinder volume at exhaust closing
- V2 is combustion chamber volume
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Carburetor Throttle Bore Diameter
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- 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
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Crankcase Volume
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- Primary compression ratio =
- Case Volume @ TDC / Case Volume at BDC
- or
- CRp = V1 + V2 / V1
- CRp is the primary compression ratio
- V1 is crankcase volume @ BDC
- V2 is piston displacement
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Resonance Effects
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- 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
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Average Exhaust Temperature
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- Exhaust gas temperature in Kelvin
- (k = C + 273.15). This is usually a function of the engine's BMEP.
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