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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