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Car Math
Submitted by: John

These equations are taken from Auto Math Handbook by John Lawlor

- For further explanation of equations, please refer to the book published by HPBooks.
- These equations are pretty much self-explanatory. There is necessary explanations were needed.
- As with all mathematical equations, the rules, symbols and theories of math apply in all respects. symbols have been changed where necessary but a legend of changed symbols has been provided

Some nomenclature descriptions
- There are two ways to list division in this document
one is: 4/5 reads as Four Divided by Five
the other is: 4 which also reads 4 divided by five
- This ^ is called a carat. In these equations it is used to show that a number that follows another number or term is to be the power of that term.
for example: four squared will be written as so 4 ^ 2
six cubed will be written as so 6 ^ 2
stroke squared will be written as so stroke ^ 2
- Since my HTML editor does not support a square root symbol, I will use the following nomenclature for a square root symbol: SR/
for readability purposes, square roots will look like this (SR/ [4.5/6.2] *3)
this reads as follows multiply the result of the equation 4.5/6.2 by 3 and then take the square root of that result
a cubed root will be written as such 3CR/

Piston Displacement

Cylinder Volume = pi/4 x bore ^ 2 x stroke

Rounding Up or Down
- To figure out actual displacement and whether or not you have a 4.9L or a 5.0L

Displacement = 0.7853982 x bore ^ 2 x stroke x Number of cylinders


Displacement = 0.7853982 x (bore + overbore difference) ^ 2 x stroke x Number of cylinders

- the bore + overbore difference would look like this 3 in bore + .030 overbore = 3.03 which is then squared and multiplied by stroke and cylinder count


Stroke =                 displacement
              (pi/4 x bore ^ 2 x no. of Cylinders)


Bore = (SR/ displacement / (pi/4 x stroke x no. of cylinders) )

Calculating Compression Ratio

Compression ratio = Cylinder + Chamber Volume
                                        Chamber Volume

Calculating Chamber Volume

Chamber Volume =      Cylinder Volume
                               Compression Ratio - 1.0

Milling Heads

Amount to Mill = [(new disp. ratio - old disp. ratio) / (new disp. ratio x old disp. ratio)] x stroke

Mean Piston Speed

Piston Speed in fpm = (2 x stroke in inches x rpm) / 12

Rev Limits

RPM = (piston speed in fpm x 6) / stroke in inches

Calculating Horsepower (Brake)

Horsepower = rpm x torque

Calculating Torque

Torque = (5252 x horsepower)

Power Loss due to Elevation

bhp loss = elevation in feet x 0.03 x bhp at sea level

Air Capacity (yields Cubic Inches per Minute)

Air Capacity = rpm x displacement

CFM (Cubic Feet per Minute of Air Capacity)

CFM = rpm x displacement
                   2 x 1728

Volumetric Efficiency

V.E. =    actual CFM   x 100
            theoretical cfm

- to obtain the theoretical CFM figure, use the CFM calculation above.

Carburetor Size (Street and Strip)

Street Carb cfm = rpm x displacement x 0.85

Race Carb cfm = rpm x displacement x 1.1

Vehicle Weight Distribution
- This is applicable if you have access to a large enough scale.
- Use this equation to weigh the amount of weight on each axle by weighing one axle on the scale at a time. You can also use rough guesstimates but that sacrifices accuracy.
- This equation is also applicable for left/right distribution. To get the weight on wheels number, weigh only one side of the car at a time and perform the calculation.

Wheel Weight Percentage =  weight on wheels x 100
                                              overall weight

Adding Weight
- This can be used for a variety or reasons including off-roading, trailer towing, payload capacities and of course better weight balance for racing

Wheel Weight Increase = [(weight on wheels/wheelbase) x weight to be added] + weight to be added

Center Of Gravity

CG behind front wheels = (rear wheel weight / overall weight) x wheelbase

CG location off-center to heavy side = (track / 2) - (weight on light side / overall weight) x track

CG height = (level wheelbase x raised wheelbase x added weight on scales)
                                          distance raised x overall weight

- for the CG Height requirement, please refer to the book for better description.

Drive Wheel Torque

drive wheel torque = flywheel torque x first gear ratio x final drive ratio x 0.85

Wheel Thrust

wheel thrust =      drive wheel torque
                      wheel rolling radius in feet

Calculating g-Force

g-Force = wheel thrust

weight transfer = weight x cg height     x  g-Force

Lateral Acceleration

lateral acceleration = (2.0 x pi) ^ 2 x   radius
                                                        time ^ 2

- To find lateral acceleration directly in g-Force, the value of 1.0 g per second per second (32.174) must be entered into the above equation like so:

lateral acceleration =    (2.0 x pi) ^ 2     x    radius
                                        32.174             time ^ 2

Lateral Weight Transfer

lateral weight transfer =                  weight x cg height              x lateral g-Force
                                       average wheel track width in inches

Centrifugal Force

centrifugal force = weight x lateral g-Force

Shift Points

RPM After Shift =   ratio shift into  x rpm before shift
                              ratio shift from

Driveshaft Torque

driveshaft torque = flywheel torque x transmission ratio

1/4 Mile ET

ET = (3CR/ {weight/hp} ) x 5.825

Power or Weight from ET

HP =      weight
         (ET/5.825) ^3

Weight = (ET/5.825) ^ 3 x hp

Miles Per Hour

MPH = (3CR/ {hp/weight} ) x 234

Power or Weight from MPH

HP = (mph/234) ^ 3 x weight

weight = (234/mph) ^ 3 x hp

Gearing for 1/4 Mile Speed

Overall Gear Ratio (manual transmission) = tire diameter x rpm
                                                                        340           mph

Overall Gear Ratio (automatic transmission) = tire diameter x rpm
                                                                             335          mph

Instrumentation Error

- Speedometer Check

Actual MPH =        3600
                       seconds per mile

Speedo Error Percent = difference between actual and indicated speeds x 100
                                                              actual speed

- Odometer Error

Indicated Distance = reading at finish - reading at start

Percent Error = difference between actual and indicated distances x 100
                                               actual distance

MPH From Tire Size

MPH =   rpm x tire diameter
                gear ratio x 336

RPM From Tire Size

RPM = mph x gear ratio x 336
                    tire diameter

Overall Gear Ratio from Tire Size

Gear Ratio = rpm x tire diameter
                          mph x 336

Tire Diameter

Tire Diameter = mph x gear ratio x 336

Tire Sizing

- Metric Tire Diameter

Tire Diameter = 2 x section width x aspect ratio + rim diameter

- Effective Drive Ratio

Effective Ratio =  old tire diameter  x original ratio
                           new tire diameter

- Equivalent Drive Ratio

Equivalent Drive Ratio = new tire diameter  x original ratio
                                       old tire diameter

- Speedometer Correction

Actual MPH = new tire diameter x indicated mph
                        old tire diameter

Indicated MPH =  old tire diameter   x actual mph
                            new tire diameter

Average MPH and MPG


miles per gallon =  miles

- Miles

miles = miles per gallon x gallons

- Gallons

gallons =        miles
               miles per gallon

- Average Miles Per Hour

miles per hour =  miles

- Miles

miles = miles per hour x hours

- Hours

hours =       miles
            miles per hour

- Raceway Miles Per Hour

RMPH = miles x 3600


seconds = miles x 3600
                miles per hour

Blood Alcohol Concentration

BAC = (ounces consumed x %alcohol x 0.075) - (hours x 0.015)
                                body weight

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