Saturday, June 15, 2019

HP 42S and TI-60: Dimensions of a Race Track

HP 42S and TI-60:  Dimensions of a Race Track



We have a race track that consists of two rectangular tracks connected by a circular ring that is cut in half.  A half ring attaches to each end. 

Let the variables define the following measurements:

R0 = radius from the center of the circular ring to the outside of the track
RI = radius from the center of the circular ring to the inside of the track
C = length of the rectangular potion of the track
R0 - RI = width of the rectangular portion of the track

I am taking an imaginary line in the middle of the track (see the pink dotted line on the right side of the illustration).  The radius from the center of the ring to the pink dotted line is:
 RI + (R0 - RI)/2.

Area: 

Area
= area of the circular ring + area of the top rectangular portion + area of the bottom rectangular portion
= (π * RO^2 - π * RI^2) + C * (RO - RI) + C * (RO -RI)
= π * (RO^2 - RI^2) + 2 * C * (RO - RI)

Perimeter:

Perimeter
= circumference of the circle at the half way point between the outside and inside radius + length of the top rectangular portion + length of the bottom rectangular potion
= 2 * π * (RI + (RO - RI)/2) + C + C
= 2 * π * (RI + (RO - RI)/2) + 2 * C
= 2 * π * 1/2 * (2 *RI + RO - RI) + 2 * C
= π * (RO - RI) + 2 * C

Now that we have the calculations, let's put them to practice.

Input Variables (see above):

R0 = RO
R1 = RI
R2 = C

Ouput Variables:

R3 = area
R4 = perimeters

HP 42S/DM42/Free42 Program RACETRK

00  {68-Byte Prgm}
01  LBL "RACETRK"
02  RCL 00
03  X ↑ 2
04  RCL 01
05 X ↑ 2
06  -
07  PI
08  *
09  2 
10  RCL * 02
11  RCL 00
12  RCL - 01
13  *
14  +
15  STO 03
16  "AREA="
17  AVIEW
18  STOP
19  2
20  RCL * 02
21  RCL 01
22  RCL + 00 
23  PI
24  *
25  +
26  STO 04
27  "MID PERIMETER="
28  AVIEW
29  RTN
30  END

TI-60 Program Race Track

Format:   line number :  key code : key

00 :  91  :  π
01  :  65  :  *
02  :  53  :  (
03  : 71  : RCL
04  :  00 :  0
05  :  96  : x^2
06  :  75  :  -
07  :  71  :  RCL
08  :  01  :  1
09  :  96  :  x^2
10  :  54  :  )
11  :  85  :   +
12  :  02  :  2
13  :  65 :  *
14  :  71  :  RCL
15  :  02 :  2
16  :  65  :  *
17  :  53  :  (
18  :  71   :  RCL
19  :  00  :  0
20  :  75  :  -
21  :  71  :  RCL
22  :  01  :  1
23  :  54   :  )
24 :  95  :  =
25  :  61  :  STO
26  :  03  :  3
27  :  13   : R/S
28  :  02  :  2
29  :  65  :  *
30  :  71   :  RCL
31   :  02 :  2
32  :  85  :  +
33  :  91  :  π
34  :  65  :  *
35  :  53  :  (
36  :  71  : RCL
37  :  00  :  0
38 :  85  :  +
39  :  71  :  RCL
40  :  01 :  1
41  :  54  :  )
42  :  95  :  =
43  :  61  :  STO
44  :  04  :  4
45  :  13  : R/S
46  :  22  :  RST

Example

R0 = radius to outside ring = 12 ft
R1 = radius to inside ring = 8 ft
R2 = length of the rectangular portion of the trace = 45 ft

Results:

Area (R3) = 611.3274123 ft^2
Perimeter of the mid-line (R4) = 152.8318531 ft

Eddie

All original content copyright, © 2011-2019.  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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