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 / 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 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