Sunday, December 3, 2023

Casio fx-5000F: Auto Formulas

Casio fx-5000F:   Auto Formulas



The formula listing can apply to (almost) any calculator that can handle formula programming.


In November, there I want to a luncheon that a local car club had in Riverside.  Of course, this was an opportunity to bring a calculator and find something in common with the members.   I previously did this with a TI-68.


Except noted, US, imperial units are used.  


The source for all the equations are from The Auto Math Handbook, except for Gas Efficiency.  




Stroke of an Engine

(spaces added for readability)


S = D / ( π / 4 × B^2 × n ) = D / ( π / 4 × B² × n )


S = stroke (in)

D = displacement (in^3)

B = bore (in)

n = number of cylinders


Example:

D = 421

B = 4 

n = 6


Result: 

S ≈ 5.58369 in 



Engine Horsepower


H = R × T × 2 × π / 33000


H = engine horsepower (hp)

R = revolutions per minute (rpm)

T = torque (lbs-ft)


Example:

R = 5200 

T = 446


Result:

H ≈441.57465



Theoretical Air Capacity of an Engine


C = R × D / 3456


C = air capacity (in^3/min [cubic feet per minute])

R = revolutions per minute (rpm)

D = displacement (in^3)


Example:

R = 5200

D = 421 


Result:

C ≈ 633.44907



Estimated Elapsed Time in a Quarter Mile


The time is based off an engine's weight (really, mass) and horsepower.


E = 5.825 × ³√( W / H ) = 5.825 × ( W / H )^(1/3)


E = elapsed time in seconds (sec)

W = weight of the automobile/truck (pounds)

H = horsepower of the engine (hp)


Example:

W = 3676 

H = 440


Result:

E ≈ 11.81962



Gear Ratio 


This estimates the final gear ratio.  Note that 63360 ÷ 60 = 1056, allowing a simplified formula to be used.


G = R × T × θ / M / 1056


G = gear ratio

R = revolutions per minute (rpm)

T = tire diameter (in)

M = miles per hour (mph) (average)


Example:

R = 5200

T = 28

M = 57.8


Result:

G ≈ 7.49410



Tire Diameter


T = W × A / 1270 + R


Take the following measurements as they are marked on the tire:


[LT/P]  W / A  [R/B]   R


W = section width (mm:  yes, somehow U.S. tires measure this in millimeters)

A = aspect ratio (percentage difference between section height and section width)

R = rim diameter (in)


T = tire diameter (in)


Example:

W = 235

A = 75

R = 15


Result:

D ≈ 28.87795



Gas Efficiency


M = (B - A) / g


B = ending mileage (mi)

A = beginning mileage (mi)

g = number of gallons used


M = gas efficiency (mpg, miles per gallon)


Example:

B = 13695

A = 13385

G = 10


Result:

M = 31



Source


Lawlor, John.   Auto Math Handbook:  Calculations, Formulas, Equations and Theory  HPBooks  New York, NY 1992.



Eddie


All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


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