Submitted by: JohnThese 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

5

- 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

**Overboring**

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**

Stroke = __
displacement__

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

**Bore**

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__

5252

**Calculating Torque**

Torque = __(5252 x
horsepower)__

rpm

**Power Loss due to Elevation**

bhp loss = __elevation
in feet__ x 0.03 x bhp at sea level

1000

**Air Capacity (yields Cubic Inches per Minute)**

Air Capacity = __rpm x
displacement__

2

**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

3456

Race Carb cfm = __rpm x
displacement__ x 1.1

3456

**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

weight transfer = __weight
x cg height __ x
g-Force

wheelbase

**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__

rpm

**Tire Sizing**

*- Metric Tire
Diameter*

Tire Diameter = __2 x
section width x aspect ratio__ + rim diameter

2540

*- 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**

*- MPH*

miles per gallon = __
miles__

gallons

*- Miles*

miles = miles per gallon
x gallons

*- Gallons*

gallons = __
miles__

miles per gallon

*- Average Miles Per
Hour*

miles per hour = __
miles__

hours

*- Miles*

miles = miles per hour x
hours

*- Hours*

hours = __
miles__

miles per hour

*- Raceway Miles Per
Hour*

RMPH = __miles x 3600__

seconds

*-Seconds*

seconds = __miles x
3600__

miles per hour

**Blood Alcohol
Concentration**

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

body weight