Car Math
I thought it would be nice to put together some of the interesting, and useful formulas, conversions and notes I've come across over the years. I will be editing and adding to this list as time permits.
ET (1.4 mi.) x 64% = approx. ET (1/8th mi.)
MPH (1.4 mi.) x 0.8 = approx. MPH (1/8th mi.)
optimum differential gear ratio setup for 1/8th mi. x 80% = optimum differential gear ratio setup for 1/4 mi.
HP = (TQ X RPM) / 5252
vehicle MPH = (engine cfm / scoop area in square inches) x (60 x 1/5280) / (1/144)
where: 60 = minutes (m) per hour (H)
1/5280 = miles (M) per foot (f)
1/144 = square feet per square inch
(60 x 1/5280) / (1/144) = 1.64
vehicle MPH = engine CFM x 1.64 / scoop area (square inches)
minimum WHP = (vehicle weight x 200) / (ET x ET x ET)
minimum WHP = vehicle weight x (MPH / 234) x (MPH / 234) x (MPH / 234)
Parasitic drivetrain losses can account for 10% - 20% hp loss at the driving wheels.
To maintain consistent performance, supercharged engines should avoid intake temperatures in the range of 180 to 220 deg. F and above.
Compression ratio calculation. When done correctly, this can be a complicated calculation. Stay with me.
Using my engine configuration (v3.1.5) as an example here.
Cylinder volume = pi/4 x bore squared x stroke.
To convert cubic inches to cubic centimeters multiply by 16.387064.
Deck clearance volume: -.020" = 3.98cc. Subtract 1.99cc for a deck clearance of -.010" which would come about from steel rod expansion (.010"). Use 0.00cc for aluminum rod expansion (.020").
Head gasket thickness volume: .039" = 8.36cc
Cylinder head combustion chamber volume: 50cc
Compression ratio calculation notes:
Cylinder volume = .7853982 x 15.5 x 3.06 = 37.251436 = 610.44166cc.
Cylinder head combustion chamber volume = 50cc.
Head gasket volume = 8.36cc.
Deck clearance volume = 3.98cc or 1.99cc w/rod expansion.
Top ring land crevice volume = 1cc.
Valve pocket volume = 2cc.
Piston dish (+) or dome (-) volume = 10cc
Total chamber volume [cylinder head combustion chamber volume + head gasket volume + deck clearance volume + top ring land crevice volume + valve pocket volume +(-) piston dish/(dome) volume] = 75.34cc. 73.35cc if rod expansion cuts deck clearance to -.010" (steel rods).
Compression ratio = Total volume (all volumes added together) / Total chamber volume = 685.78cc / 75.34cc = 9.10 to one (9.32 to one w/rod expansion).
Average compression ratio = 9.21 to one.
Optimum cylinder pressure peak at crankshaft angle: 12 to 17 degrees ATDC
(horsepower x brake specific fuel consumption) / (number of injectors x duty cycle) = fuel consumption in pounds per hour per injector.
Recommended BSFC for gasoline is .45 to .5 for naturally aspirated, .55 to .6 for supercharged, .65 and higher for turbocharged.
Recommended BSFC for methanol is .95 to 1.10 for naturally aspirated. Can be as low as .88 or as high as 1.2. 1.15 to 1.35 for supercharged and turbocharged. Even higher (into the 2s) in max CR/boost (12 to one CR, 3 atms. boost) applications where a massive amount of extra methanol is required to cool the intake charge (no aftercooler application) to below detonation/preignition limits.
Recommended maximum injector duty cycle: 80 to 85 percent. 80 percent is the industry norm. Beware, some electronic injectors may not be able to provide a stable, repeatable fuel delivery over 80 percent duty cycle.
square root of (new fuel pressure / old fuel pressure) x old flow rate = new flow rate
(lb/min of air) / .076 (some use .069) = cfm
Conversions
To convert from: multiply by:
atmospheres to kilopascals: 101.325
atmospheres to pounds per square inch: 14.695949
bars to atmospheres: 0.9869233
bars to kilopascals: 100.0
bars to pounds per square inch: 14.503774
cubic centimeters to cubic inches: 0.0610237
cubic centimeters per minute to pounds per hour: 0.09523809
cubic centimeters per minute to gallons per hour: 0.015873
cubic inches to cubic centimeters: 16.387064
cubic inches to liters: 0.0163871
feet to meters: 0.3048
gallons, ethanol (ethyl alcohol), to pounds: 7.6
gallons, gasoline, to pounds: 6.0 (can vary according to blend)
gallons, liquid propane, to pounds: 4.25
gallons, methanol (methyl alcohol), to pounds: 6.7
gallons, nitromethane, to pounds: 9.4
gallons, water, to pounds: 8.3449037 (at 4.0 degrees Celsius or 39.2 degrees Fahrenheit)
gallons, U.S., to gallons, imperial: 0.8326742
horsepower, SAE, to kilowatts: 0.7456999
inches to millimeters: 25.4
inches of mercury to kilopascals: 3.3863886
inches of water to kilopascals: 0.249074
kilometers per hour to miles per hour: 0.6213712
kilopascals to inches of mercury (Hg): 0.2952998
kilopascals to inches of water: 4.0148716
kilopascals to pounds per square inch: 0.1450377
liters to cubic inches: 61.023744
liters to gallons, U.S.: 0.2641721
meters to yards: 1.0936133
miles per hour to kilometers per hour: 1.609344
millimeters to inches: 0.0393701
pounds per square inch to kilopascals: 6.8947574
pounds per hour to gallons per hour: 0.1666666 (for gasoline). 0.14925373 (for methanol)
pounds per hour to cubic centimeters per minute: 10.5
Temperature Conversion
Celsius to Fahrenheit: multiply by 1.8 and add 32 degrees
Fahrenheit to Celsius: subtract 32 degrees and divide by 1.8
Misc.
25 inches of water to 28 inches of water: multiply by 1.06
In general, a turbocharged engine running on gasoline will develop 9.5 to 10.5 hp (some believe 10.86 to be a good number) for each lb/min of air flow. A turbocharged engine, properly prepared to take advantage of running on methanol fuel, will develop 10.5 to 11.5 hp for each lb/min of air flow.
Yes. Aftercooling does benefit a turbocharged engine on methanol to the same degree that it benefits the same engine on gasoline. It provides a denser intake charge and moves the fuel mixture further from detonation/preignition limits. Particularly in a high static compression ratio with high boost situation.
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Office phone: (619) 258-4240 Fax: (619) 258-9105
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