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Old 01-27-2009, 09:30 PM   #1
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Formulas, Constants, and Conversions.

Round 2. This is formulas, constants, and conversions. These mainly apply when designing an engine so you know how to safely and properly build it before buying the first part.


Predicting Power
BHP = PLAN/33,000
P is brake mean effective pressure, in PSI
L is piston stroke, in feet
A is the area of one piston, in square inches
N is the number of power strokes per minute


Piston Speed
Cm = .166 x L x N
Cm is mean piston speed, in feet per minute
L is stroke, in inches
N is crankshaft speed, in RPM


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

Temperature
F = 9 / 5 x C + 32
C = 5/9 (F - 32)
K = C + 273.4

Pressure (boost)
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

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

You can see my other two threads for Engine Formulas and Turbo Mapping as well.


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