John
i emailed a copy to you too Evil. you should post it on the articles page!
These equations are taken from Auto Math Handbook by John Lawlor
- For further explination of equations, please refer to the book published by HPBooks.
- These equations are pretty much self-explanatory. There is necessary explinations 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 th following nomeclature 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 Rato - 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 (yeilds 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 lage 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 vraiety or reason 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 tranmission 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
25.4 100
- 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
These equations are taken from Auto Math Handbook by John Lawlor
- For further explination of equations, please refer to the book published by HPBooks.
- These equations are pretty much self-explanatory. There is necessary explinations 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 th following nomeclature 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 Rato - 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 (yeilds 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 lage 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 vraiety or reason 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 tranmission 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
25.4 100
- 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