Engine Formulas for the Technically Minded 



Brake
Mean Effective Pressure (BMEP) 2Stroke
BMEP = (HP x 6500)/(L x RPM) 4Stroke
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 = ((N^2 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 or
sin
X = R/L sin Z 
Piston
Travel vs. Crank Rotation d
= ((S/2) + L)  (S/2 cos X)  L sin[cos1 (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(c^2  (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 exhaustopen
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 or
CRp = V1 + V2 / V1 CRp is the primary
compression ratio V1
is crankcase volume @ BDC V2
is piston displacement 
Resonance
Effects F
= Vs / 2¼ * the square root of A / Vc (L + 1/2 the
square root of ¼ A Vs
is the sonic speed Uusually about 1100 ft/sec) A
is the crosssectional area of the inlet L
is the inlet pipe length Vc is the flask (crankcase)
volume 
Average
Exhaust Temperature Determine
the exhaust gas temperature in Kelvin (k
= C + 273.15). This is usually a function of the engine's BMEP. 
Torque 1.00
lbft = 0.138 kgm = 1.35 Nm 1.00
kgm = 7.23 lbft. = 9.81 Nm 1.00
Nm = 0.102 kgm = 0.737 lbft 
Mass 1.00
lb = 0.454 kg = 4.45 N 1.00
kg = 2.20 lbs = 9.81 N 1.00
N = 0.102 kg = 0.220 lb 
Distance 1
in = 2.54 cm = 0.0000158 mi = 0.0000254 km 1
cm = 0.394 in = 0.00000621 mi = 0.00001 km 1
ft = 30.5 cm = 0.000189 mi = .000305 km 1
mi = 63,360 in = 160,934.4 cm = 1.609 km 1
km = 0.621 mi = 100,000 cm = 3281 ft 
Pressure 1.00
bar = 14.5 psi = 1.02 kg/sqcm = 100 kPa 1.00
psi = 0.069 bar = 0.070 kg/sqcm = 6.89 kPa 1.00
kg/sqcm = 0.980 bar = 14.2 psi = 98.1 kPa 1.00
kPa = 0.010 bar = 0.145 psi
= 0.010 kg/sqcm 
Temperature F
= 9 / 5 x C + 32 C
= 5/9 (F  32) K
= C + 273.4 
Area
/ Volume 1.00
sqin = 6.452 sqcm 1.00
sqcm= 0.155 sqin 1.00
cuin = 16.387 cc 1.00
cc = 0.0610 cuin 
Power 1.00
HP = 746 W torque
(lbft) = 5252 x hp / rpm hp
= rpm x torque (lbft) / 5252 
The
Weight of Air 14.7
lbs. per sq. inch at sea level. 
Air
Density Calculation StdAirDensity = 1.22556 and is defined
at 59.0F degrees, 0.0% humidity, and 29.92 inches on the barometer.
Temp_c = (Temp32.0) * 5.0 /
9.0; Temp_k = Temp_c
+ 273.0; Baro_mb = Barometer / (29.92 /
1013.0); Baro_pa = Baro_mb
* 100.0; SaturationPressure_mb = 6.11 * pow(10,(7.5*Temp_c)/(237.7+Temp_c));
VaporPressure_mb = Humidity * SaturationPressure_mb / 100.0; TempVirtual_k = Temp_k
/ (1.0  (VaporPressure_mb/Baro_mb)*(1.0.622)); //
D = P/(T*R) AirDensity = Baro_pa
/ (TempVirtual_k*GasConstant);
%
Std Density = AirDensity/StdAirDensity*100 

Additional
Conversion Factors 

1
Centimeter  0.0328084 foot; 0.393701 inch
1
Circular Mil  7.853982 x 10 to the negative seventh square inches; 5.067075
x 10 to the negative sixth square centimeters
1
Cubic Centimeter  0.061024 cubic inch; 0.270512 dram (
1
Cubic Foot  0.803564 bushel (
1
Cubic Inch  16.387064 cubic centimeters
1
Cubic Meter  35.314667 cubic feet; 264.17205 gallons (
1
Foot  0.3048 meter
1
Gallon (
1
Grain  0.06479891 gram
1
Gram  0.00220462 pound (avoirdupois); 0.035274 ounce (avoirdupois);
15.432358 grains
1
Hectare 2.471054 acres; 1.07639 x 10 to the fifth square feet
1
Inch  2.54 centimeters
1
Kilogram  2.204623 pounds (avoirdupois)
1
Kilometer  0.621371 mile (statute)
1
Liter  0.264179 gallon (

1
Meter  1.093613 yards; 3.280840 feet; 39.37008 inches
1
Mile (statute)  1.609344 kilometers
1
Ounce (
1
Ounce (avoirdupois)  28.349523 grams
1
Ounce (apothecary or troy)  31.103486 grams
1
Pint (
1
Pound (avoirdupois)  0.453592 kilogram; 453.59237 grams
1
Pound (apothecary or troy)  0.3732417 kilogram, 373.24172 grams
1
Quart (
1
Quart (liquid)  0.946326 liter
1
Radian  57.295779 degrees
1
Rod  5.0292 meters
1
Square Centimeter  0.155000 square inch
1
Square Foot  0.09290304 square meter
1
Square Inch  645.16 square millimeters
1
Square Meter  10.763910 square feet
1
Square Yard  0.836127 square meter
1
Ton (short)  907.18474 kilograms
1
Yard  0.9144 meter 