Engine Formulas for the Technically Minded

 

 

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 = ((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[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(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 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

or

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 Uusually 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

 

Determine the exhaust gas temperature in Kelvin

(k = C + 273.15). This is usually a function of the engine's BMEP.

Torque

 

1.00 lb-ft = 0.138 kg-m = 1.35 N-m

1.00 kg-m = 7.23 lb-ft. = 9.81 N-m

1.00 N-m = 0.102 kg-m = 0.737 lb-ft

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/sq-cm = 100 kPa

1.00 psi = 0.069 bar = 0.070 kg/sq-cm = 6.89 kPa

1.00 kg/sq-cm = 0.980 bar = 14.2 psi = 98.1 kPa

1.00 kPa = 0.010 bar = 0.145 psi = 0.010 kg/sq-cm

Temperature

 

F = 9 / 5 x C + 32

C = 5/9 (F - 32)

K = C + 273.4

Area / Volume

 

1.00 sq-in = 6.452 sq-cm

1.00 sq-cm= 0.155 sq-in

1.00 cu-in = 16.387 cc

1.00 cc = 0.0610 cu-in

Power

 

1.00 HP = 746 W

torque (lb-ft) = 5252 x hp / rpm

hp = rpm x torque (lb-ft) / 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 = (Temp-32.0) * 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 (U.S. fluid); 16.230664 minims (U.S.); 0.999972 milliliter

 

1 Cubic Foot - 0.803564 bushel (U.S.); 7.480520 gallons (U.S. liquid); 0.028317 cubic meter; 28.31605 liters

 

1 Cubic Inch - 16.387064 cubic centimeters

 

1 Cubic Meter - 35.314667 cubic feet; 264.17205 gallons (U.S. liquid)

 

1 Foot - 0.3048 meter

 

1 Gallon (U.S. liquid) - 0.1336816 cubic foot; 0.832675 gallon (British); 231 cubic inches; 0.0037854 cubic meter; 3.785306 liters

 

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 (U.S. liquid);0.0353157 cubic foot; 1.056718 quarts (U.S. liquid)

 

1 Meter - 1.093613 yards; 3.280840 feet; 39.37008 inches

 

1 Mile (statute) - 1.609344 kilometers

 

1 Ounce (U.S. fluid) - 1.804688 cubic inches; 29.573730 cubic centimeters

 

1 Ounce (avoirdupois) - 28.349523 grams

 

1 Ounce (apothecary or troy) - 31.103486 grams

 

1 Pint (U.S. liquid) - 0.473163 liter; 473.17647 cubic centimeters

 

1 Pound (avoirdupois) - 0.453592 kilogram; 453.59237 grams

 

1 Pound (apothecary or troy) - 0.3732417 kilogram, 373.24172 grams

 

1 Quart (U.S. dry) - 1.10119 liters

 

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