**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

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