(42S) Solvers: Automobiles

[Eddie W. Shore]

Blog Entry: http://edspi31415.blogspot.com/2019/06/h...lvers.html

Download files for Free42/DM42: https://drive.google.com/file/d/1N4wpO9Q...sp=sharing

1. Displacement, Bore, Strokes (File: displacement.raw)


Code:

00 { 79-Byte Prgm }
01▸LBL "DISPMNT"
02 MVAR "DISPMNT"
03 MVAR "BORE"
04 MVAR "STROKE"
05 MVAR "#CYLIN"
06 PI
07 4
08 ÷
09 RCL "BORE"
10 X↑2
11 ×
12 RCL× "STROKE"
13 RCL× "#CYLIN"
14 RCL- "DISPMNT"
15 .END.

Variables:

(DISPM): displacement of the a cylinder (cubic inches)
(BORE): diameter of the cylinder (inches)
(STRO): distance traveled by the piston (inches)
(#CYLI): number of cylinders

Equation:

π/4 * bore^2 * stroke * #cylinders - displacement = 0

Example:

Bore = 4 in
Stroke = 3.5 in
4-cylinder engine

Result: Displacement = 175.9292 in^3

2. Gear Ratio, MPH, RPM (File: gearratio.raw)

Code:

00 { 74-Byte Prgm }
01▸LBL "GEARRTO"
02 MVAR "RPM"
03 MVAR "MPH"
04 MVAR "TIREDIA"
05 MVAR "GEARRAT"
06 PI
07 RCL× "RPM"
08 RCL× "TIREDIA"
09 RCL÷ "MPH"
10 1056
11 ÷
12 RCL- "GEARRAT"
13 .END.

Variables:

(RPM): the tire's revolution per minute
(MPH): speed of the vehicle (miles/hour)
(TIREDI): diameter of the tire (inches)
(GEAR): gear ratio = transmission ratio * final drive ratio

Equation:

(RPM * π * tire_diameter) / (MPH * 1056) - gear_ratio = 0

Example:

RPM = 3,400 rpm
Tire Diameter = 28 in
Gear Ratio = 3.85

Result: MPH = 73.5635 mph

3. Quarter Mile Estimation: Elapsed Time, Car's Weight, Horsepower
(File: quartermile.raw)

Code:

00 { 52-Byte Prgm }
01 ▸ LBL "QRTMI"
02 MVAR "ET"
03 MVAR "WEIGHT"
04 MVAR "HP"
05 5.825
06 RCL "WEIGHT"
07 RCL÷ "HP"
08 3
09 1/X
10 Y↑X
11 ×
12 RCL- "ET"
13 .END.

Variables:

(ET): elapsed time for the car to travel 1/4 mile (seconds)
(WEIG): weight of the car including passengers, drivers, fuel, and other items carried (pounds)
(HP): horsepower

Equation:

(weight/horsepower)^(1/3) * 5.825 - elapsed_time = 0

Note: MPH = (horsepower/weight)^(1/3) * 234 = 1363.05/elapsed_time

Example:

Weight: 3,540 lb
HP: 215 hp

Result:

ET: 14.8190
(MPH = 91.9802 mph, [SHIFT] (TOP.FCN) ( 1/X ) 1363.05 [ * ])

4. Tire Sizes (file name: tiresize.raw)

Code:

00 { 87-Byte Prgm }
01 ▸ LBL "TIRESZE"
02 MVAR "SECWDTH"
03 MVAR "RIMDIA"
04 MVAR "ASPECT"
05 MVAR "TIREDIA"
06 2
07 RCL× "SECWDTH"
08 RCL× "ASPECT"
09 2540
10 ÷
11 RCL+ "RIMDIA"
12 RCL- "TIREDIA"
13 .END.

Variable:

(SECW): section width (millimeter)
(RIMDI): rim diameter (inches)
(ASEPC): aspect ratio
(TIREDI): tire diameter (inches)

On a side of a tire, we can get three of the four values by from a code that looks like this:

P235 / 75R17

P: passenger car (L for light trucks)
235: section width
75: aspect ratio
R: radial tire
17: rim diameter

Equation:

(2 * section_width * aspect_ratio) / 2540 + rim_diameter - tire_diameter = 0

Example: Use the stats of the tire above to calculate tire diameter.

Result: 30.8780 in