Go Back   ModernMuscleCars.net
User Name
Password
Register FAQ Members List Calendar Mark Forums Read Home

Welcome to ModernMuscleCars.net.
If this is your first visit, be sure to check out the FAQ. You have to register before you can post. Registration is free! Click the register link above to proceed.
Our Sponsors
Advertise with us! Grundy
Collector car financing
J. J. Best
Collector car financing
Mecum Auctions
Collector car auction house.
Performance Restorations
Car restoration experts.

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
                  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



All times are GMT -5. The time now is 09:04 AM.




Powered by: vBulletin Version 3.0.5
Copyright ©2000 - 2018, Jelsoft Enterprises Ltd.
Copyright ModernMuscleCars.net