## 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

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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