TI-55 (1977) Programs: Wind Turbine, Mile/Kilometer Conversion, 2D Vectors
Time for the classic TI-55 calculator from the 1970s. My spotlight on this calculator from November 2024: https://edspi31415.blogspot.com/2024/11/spotlight-ti-55-from-1977.html
TI-55: Power Generated by a Wind Turbine
The power generated by a wind turbine can be calculated by:
P = (π * r²) / 2 * ρ * v³ = area / 2 * ρ * v³
P = power generated by the wind turbine (W, Watts)
r = length of an arm of the turbine (radius) (m)
ρ = density of air (kg/m³). Typically, ρ = 1.225 kg/m³
v = velocity of the air (m/s)
Inputs before running the program:
r STO 1, R1 = r
v STO 2, R2 = v
ρ STO 3, R3 = ρ
Note: This formula and program does not take efficiency factors into account. The theoretical maximum power is calculated.
Code:
Step |
Key Code |
Key |
|
Step |
Key Code |
Key |
00 |
49 |
π |
|
10 |
02 |
2 |
01 |
55 |
× |
|
11 |
35 |
y^x |
02 |
61 |
RCL |
|
12 |
03 |
3 |
03 |
01 |
1 |
|
13 |
45 |
÷ |
04 |
32 |
x² |
|
14 |
02 |
2 |
05 |
55 |
× |
|
15 |
85 |
= |
06 |
61 |
RCL |
|
16 |
86 |
R/S |
07 |
03 |
3 |
|
17 |
87 |
Rst |
08 |
55 |
× |
|
|
|
|
09 |
61 |
RCL |
|
|
|
|
Examples:
r → R1 |
v → R2 |
ρ → R3 |
Result (P): |
5 |
7 |
1.225 |
16500.234 |
6.1 |
13.3 |
1.225 |
168449.82 |
4 |
10 |
1 |
25132.741 |
Sources:
Sharp Electronics Corporation Conquering The Sciences: Applications for the SHARP Scientific Calculator EL-506A Sharp Corporation. Osaka, Japan. 1986. pp.75-77
“Wind Turbine Calculator – Calculating Wind Turbine Power Output” CTRLCalculator.com 2024. Retrieved December 5, 2024. https://ctrlcalculator.com/ecology/wind-turbine-calculator/
TI-55: Miles/Kilometers Conversions
This program uses the in⋅mm conversion function. The results are stored as follows:
R1: x mi to km (first result)
R2: x km to mi (second result)
1 km ≈ 0.6213712 mi
1 mi ≈ 1.609344 km
Code:
Step |
Key Code |
Key |
|
Step |
Key Code |
Key |
00 |
51 |
STO |
|
14 |
76 |
Prod |
01 |
01 |
1 |
|
15 |
01 |
1 |
02 |
51 |
STO |
|
16 |
21 |
INV |
03 |
02 |
2 |
|
17 |
76 |
Prod |
04 |
06 |
6 |
|
18 |
02 |
2 |
05 |
03 |
3 |
|
19 |
61 |
RCL |
06 |
03 |
3 |
|
20 |
01 |
1 |
07 |
06 |
6 |
|
21 |
86 |
R/S |
08 |
00 |
0 |
|
22 |
61 |
RCL |
09 |
67 |
in⋅cm |
|
23 |
02 |
2 |
10 |
45 |
÷ |
|
24 |
86 |
R/S |
11 |
06 |
6 |
|
25 |
87 |
Rst |
12 |
29 |
10^x |
|
|
|
|
13 |
85 |
= |
|
|
|
|
Examples:
X |
R1: X mi → km |
R2: X km → in |
55 |
88.51392 |
34.17542 |
103 |
165.7624 |
64.00123 |
24.75 |
39.831264 |
15.378937 |
TI-55: 2D Vectors: Norm and Dot Product
Let there be two vectors defined as: [R1, R2] and [R3, R4].
Norms:
| [ R1, R2] | = √(R1² + R2²): stored in R5
| [ R3, R4] | = √(R3² + R4²): stored in R6
Dot Product:
[ R1, R2 ] ⋅ [ R3, R4 ] = R1 * R3 + R2 * R4
This program takes all 32 steps available on the TI-55. When this program terminates, the number in the display flashes. In order to use the number, press [ CE ].
For example, to calculate the angle between vectors, use the following keystrokes:
[CE] (to make the number stop flashing) [ ÷ ] [ ( ] [ RCL ] 5 [ × ] [ RCL ] 6 [ ) ] [ = ] [ INV ] [ cos ]
Code:
Step |
Key Code |
Key |
|
Step |
Key Code |
Key |
00 |
61 |
RCL |
|
16 |
36 |
P→ R |
01 |
01 |
1 |
|
17 |
31 |
x<>y |
02 |
31 |
x<>y |
|
18 |
51 |
STO |
03 |
61 |
RCL |
|
19 |
06 |
6 |
04 |
02 |
2 |
|
20 |
61 |
RCL |
05 |
21 |
INV |
|
21 |
01 |
1 |
06 |
36 |
P→ R |
|
22 |
55 |
× |
07 |
31 |
x<>y |
|
23 |
61 |
RCL |
08 |
51 |
STO |
|
24 |
03 |
3 |
09 |
05 |
5 |
|
25 |
75 |
+ |
10 |
61 |
RCL |
|
26 |
61 |
RCL |
11 |
03 |
3 |
|
27 |
02 |
2 |
12 |
31 |
x<>y |
|
28 |
55 |
× |
13 |
61 |
RCL |
|
29 |
61 |
RCL |
14 |
04 |
4 |
|
30 |
04 |
4 |
15 |
21 |
INV |
|
31 |
85 |
= |
Example:
[ R1, R2 ] = [ 19, -38 ]
[ R3, R4 ] = [ 32, 64 ]
19 STO 1
38 +/- STO 2
32 STO 3
64 STO 4
R/S
Results:
Norms:
| [ R1, R2] | = R5 = 42.485292
| [ R3, R4] | = R6 = 71.554175
Dot Product: -1284
Find out the angle between the vectors: [19, -38] and [ 32, 64]
After the program is ran:
[CE] (to make the number stop flashing) [ ÷ ] [ ( ] [ RCL ] 5 [ × ] [ RCL ] 6 [ ) ] [ = ] [ INV ] [ cos ]
Angle: 126.8699°
Enjoy!
Eddie
All original content copyright, © 2011-2025. 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.
