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Automotive Math

Automotive Math

Thought you'd get away from that cursed math book when ya headed out to the garage to play with yer Bronco eh? Think again! From calculating your compression ratio to degreeing the cam you're gonna need math. Here you'll find formulas I've run across to simplifiy some of the questions that sometimes arise and supply some general info I've found. This area is constantly going to change as I find new information.

Air Filter Selection:

An average foam filter will flow 4.38 cfm/sq-in. A good paper filter will flow 4.95 cfm/sq-in. An oiled cotton gauze (K&N) will flow 6.03 cfm/sq-in.

To get your required filtered surface area for a oiled cotton gauze filter use the following formula:

A = CID * RPM/ 20839

where A=
effective filtering area (square inches)

CID =cubic inch displacement

RPM =
rev./min. at max power
Then using the following modifying factors if using an alternative filter media:

A * 1.3767 = required surface area for foam element

A * 1.2181 = required surface area for paper element

Horsepower and Torque:

Horsepower comes from torque. Torque is a result of the combustion process forcing the piston downward and rotating the crank. This output is measured as Torque. The idea is to generate high enough pressure on each stroke often enough (rpm) to generate the necessary Horsepower.

Horsepower = Torque * RPM/ 5252

Torque = Horsepower * 5252/ RPM

Horsepower and Torque, incidentally, are always equal at 5252 rpm.

Wanna figure out what that factory horsepower rating is at your height above sea level?
Corrected BHP = BHP * (1 - ((elevation/1000) * .03))

Horsepower, ET, and Weight:

A quick calculation for horsepower based on your 1/4 mile trap speed:

HP = (TS/234)3rd power * race weight
or
HP = (TS * 0.00426) 3rd power* race weight
where

HP = Horspower (of course)

TS = 1/4 mile trap speed
This horsepower output is the minumum required for the specified trap speed. It assumes ideal track conditions, weather conditions, traction, and vehicle aerodynamics. It will understate horsepower required at speeds exceeding 100 mph.

Here's some more:

ET = (3) square root of (wght/hp) *5.825
or maybe you want

Weight = (ET/5.825)3rd power* HP
Or try:

HP = weight /(ET/5.825)3rd power
or for a quick idea of ideal ET assuming good street rubber and decent traction....
ET = 1353

mph

Horsepower:

Calculation assuming sea level and known Volumetric Efficiency

Horsepower =

AP * CR * VE * CID * RPM /792001.6

where AP = atmospheric pressure in psi

CR =compression ratio

VE =volumetric efficiency

CID =cubic inch displacement

RPM =revolutions per minute
Most use Barometric pressure which is in measured in inches of mercury. To get the equivalent pressure in psi:

Pressure psi = pressure Hg * 3376.85 /6894.757

Cubic Feet per Minute:

Theoretical CFM = CID * RPM /3464

and
Actual CFM = CID * RPM * VE /3464

Carburetor Cubic Feet per Minute:

Required CFM = CID * RPM * VE/ 2820

This seems to figure the requirement
a bit larger than you'd think necessary.

Volumetric Efficiency:

Engines are occasionally defined as simply an air pump. While this is definitely an oversimplification, your engine's output is based on how much air and fuel it can burn. It's proficiency at burning the air/fuel mixture is defined as it's Volumetric Efficiency. If you know the amount of air your engine can move at a specific rpm you can use this calculation to estimate volumetric efficiency.

Volumetric Efficiency = Actual CFM * 1728 /CID * RPM
or

Volumetric Efficiency = Actual CFM/ Theoretical CFM * 100
Or, if you know your horsepower at a given rpm (the point of peak tq is going to be your max VE) you can approximate your Volumetric Efficiency at sea level by using a variation of the previous Horsepower calculation:

VE = HP * 792001.6 /AP * CR * CID * RPM

Cubic Inch Displacement:

CID = Number of cylinders * 0.7854 * bore * bore * stroke
All measurements in inches.

Rev Limits:

There are some rough standards for RPM limits. These are based on pistion speed measured in feet per minute. Cast crank and rods should aim for under 3500 fpm. Forged crank, rods, and beefed main caps can handle closer to 3800-4000 fpm. Rmember...these are rough ....talk with your engine builder or an expert.

Piston speed (fpm) = stroke * RPM/6

and
RPM limit =

Piston speed (fpm) * 6 /stroke

RPM vs. MPH:

An optimum set-up will put you thru the traps at the rpm your engine's peak hp. These calculations are useful in selecting rear tire diameters and rear gear ratios. .

MPH = Tire Diameter in inches * RPM /336 * Diff Gear ratio * Trans Gear Ratio

RPM = 336 * Diff Gear ratio * Trans Gear Ratio * MPH /Tire Diameter in inches

Rearend Ratio = Tire Diameter in inches * RPM /336 * MPH * Trans Gear Ratio

Tire diameter in inches = 336 * Diff Gear ratio * Trans Gear Ratio * MPH /RPM

Fuel Injectors:

Just as the wrong sized jets in a carb can cause decreeased performance and driveability problems, so can incorrectly sized injectors. The following calculation can be used for approximating fuel flow per injector based on horsepower (HP) and Brake Specific Fuel Consumption (BSFC).

Note:
1) Engine HP must be a realistic estimate.

2) BSFC is determined from engine dyno measurements. It typically ranges from 0.4-0.6 for gasoline engines. A BSFC of 0.5 is a safe initial estimate.

BSFC = Pounds of fuel per hour/ Brake Horse Power

3) The 0.8 multiplier fo the "Number of Injectors" helps derive a practical "Max Injector Flow Rate" for each injector based on an effective real world injector operating pulse time and fuel flow. It is unrealistic to establish the fuel flow to an engine based on an injector operating pulse time of 100% (wide open all the time). This calcuation uses an injector operating cycle of 80%. Some full race engine management systems may operate at 85-95% duty cycle, but extended operation may eventually overheat the injectors and cause irregular flow rates and poor low rpm operation.

Injector Flow Rate (lbs/hr) = HP * BSFC /number of injectors * 0.8

With a known injector fuel flow rate you can get a rough estimate of the systems capacity by using:

HP = IFR * number of injectors * 0.8 /BSFC

where IFR = Injector Flow Rate (lbs/hr)
Increasing the fuel pressure can often provide increased fuel flow and better atomization. If you know an injector's static (non-pulsed) fuel flow at one system pressure you can find its static flow at another pressure with this:

F2 = (the squere root of (p2/p1))* F1
where

F2 is the calculated injector static flow (lbs/hr) at the higher pressure

P2 is the fuel system pressure (psi) you want to use

F1 is the injector's static flow (lbs/hr) at it's rated fuel system pressure (psi)

P1 is the fuel system pressure (psi) the injector is rated for

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