Engine Formulas  


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
