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Engine Formulas for the Technically Minded |
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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 |
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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 |
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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 |
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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 |
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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 |
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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. |
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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 |
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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 |
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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 |
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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. |
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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 |
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Additional
Conversion Factors |
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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 (
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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 |