Fun with the HP 20S (April 10, 2021 Edition)
In all the programs presented on the blog, all inputs are stored in the appropriate registers before the program is run.
The Power of a Windmill
This program calculates the power generated by a windmill, given the diameter and velocity of the windmill’s fans. SI units (meters, kilograms, seconds) are used. The general equations used are:
Area of the swept by the windmill’s fans (in m^2):
A = ( π * diameter^2 ) / 4
Power generated (in W (Watts), J/s, m^2 kg/s^3):
P = ½ * area * density * velocity^3
Density of air = 1.225 kg/m^3
Input:
R1 = diameter of the fans, m
R2 = velocity of the fans, m/s
Output:
R3 = area that the fans cover, m^2; press [ R/S ]
R4 = power of the fan, W
Program:
01 LBL A 61,41, A
02 RCL 1 22, 1
03 x² 51, 11
04 × 55
05 π 61, 22
06 ÷ 45
07 4 4
08 = 74
09 STO 3 21, 3
10 R/S 26
11 × 55
12 RCL 2 22, 2
13 y^x 14
14 3 3
15 × 55
16 . 73
17 6 6
18 1 1
19 2 2
20 5 5
21 = 74
22 STO 4 21, 4
23 RTN 61, 26
Example:
Inputs:
diameter = R1 = 6.65 m
velocity = R2 = 10 m/s
Results:
R3 = area = 34.7322702808 m^2
R4 = power = 21,273.515547 W
Source:
Sharp Electronics Corporation. Conquering The Sciences: Applications for the SHARP Scientific Calculators EL-506P, EL-510S, EL-515S Japan. 1984
Depth of a Well
This program calculates the depth of a well, which is determined by the time between a person drops a rock and the person hears the rock hit the bottom of the well. The program uses SI units (meters, kilograms, seconds) with the following constants:
Earth’s Gravitational Acceleration: g = 9.80665 m/s^2
g/2 = 4.903325 m/s^2
Speed of Sound, in dry air, 20°C temperature: s = 343.21 m/s
Equations:
X = (-B + √(B^2 + 4*A*B)) / 2
Y = g/2 * a^2
where:
B = s / (g/2) (see the above constants)
A = amount of time, in seconds, between the person drops the rock and hears the rock hit the bottom (input)
X = amount of time, in seconds, that it actually takes the rock from the time it was dropped until the rock hits the bottom of the well (output)
Y = depth of the well, in meters (output)
Input:
R1 = time until you hear the rock hit the bottom of the well (sec)
Output:
R2 = time until the rock actually hits the bottom of the well (sec), [ R/S ]
R3 = depth of the well (m)
Program:
01 LBL B 61, 41, B
02 3 3
03 4 4
04 3 3
05 . 73
06 2 2
07 1 1
08 ÷ 45
09 4 4
10 . 73
11 9 9
12 0 0
13 3 3
14 3 3
15 2 2
16 5 5
17 STO 0 21, 0
18 = 74
19 STO 4 21, 4
20 +/- 32
21 + 75
22 ( 33
23 RCL 4 22, 4
24 x² 51, 11
25 + 75
26 4 4
27 × 55
28 RCL 4 22, 4
29 × 55
30 RCL 1 22, 1
31 ) 34
32 √ 11
33 = 74
34 ÷ 45
35 2 2
36 = 74
37 STO 2 21, 2
38 R/S 26
39 x² 51, 11
40 × 55
41 RCL 0 22, 0
42 = 74
43 STO 3 21, 3
44 RTN 61, 26
Example:
Input:
time until you hear the rock hit the ground = R1 = 3 sec
Results:
R2 = time the rock travels to the bottom of the well = 2.8813865 sec
R3 = depth of the well = 40.70930098622 m
Source:
Saul, Ken. The Physics Collection: Ten HP-41C Programs for First-Year Physics Class Corvallis, OR. 1986
Thevenin’s Theorem
This program calculated the equivalent resistance and voltage of a linear network of two resistors and a capacitor.
Formulas:
R_TH = (R1 * R2) / (R1 + R2)
V_TH = V * R2 / (R1 + R2)
Inputs:
R1 = resistor 1 ( Ω )
R2 = resistor 2 ( Ω )
R3 = capacitor ( V )
Output:
R4 = equivalent resistor, R_TH, [ R/S ]
R5 = equivalent capacitor, V_TH
Program:
01 LBL C 61, 41, C
02 RCL 1 22, 1
03 × 55
04 RCL 2 22, 2
05 ÷ 45
06 ( 33
07 RCL 1 22, 1
08 + 75
09 RCL 2 22, 2
10 ) 34
11 = 74
12 STO 4 21, 4
13 R/S 26
14 RCL 3 22, 3
15 × 55
16 RCL 2 22, 2
17 ÷ 45
18 ( 33
19 RCL 1 22, 1
20 + 75
21 RCL 2 22, 2
22 ) 34
23 = 74
24 STO 5 21, 5
25 RTN 61, 26
Example:
Input:
R1 = 8 Ω
R2 = 9 Ω
R3 = 11 V
Results:
R4 = 4.23529411765 Ω
R5 = 5.82352941176 V
Source:
Gussow, Milton and William T. Smith Schaum’s Easy Outlines: Basic Electricity New York. 2012 ISBN 978-0-07-178068-1
Norton’s Theorem
This program calculates an equivalent resistance and current when any network connected to a positive and a negative terminal.
Formulas:
R_N = (R1 * R2) / (R1 + R2)
I_N = V / R1
Inputs:
R1 = resistor 1 ( Ω )
R2 = resistor 2 ( Ω )
R3 = capacitor ( V )
Output:
R4 = equivalent resistor, R_N, [ R/S ]
R5 = equivalent current, I_N
Program:
01 LBL D 61, 41, D
02 RCL 1 22, 1
03 × 55
04 RCL 2 22, 2
05 ÷ 45
06 ( 33
07 RCL 1 22, 1
08 + 75
09 RCL 2 22, 2
10 ) 34
11 = 74
12 STO 4 21, 4
13 R/S 26
14 RCL 3 22, 3
15 ÷ 45
16 RCL 1 22, 1
17 = 74
18 STO 5 21, 5
19 RTN 61, 26
Example:
Input:
R1 = 8 Ω
R2 = 9 Ω
R3 = 11 V
Results:
R4 = 4.23529411765 Ω
R5 = 1.375 A
Source:
Gussow, Milton and William T. Smith Schaum’s Easy Outlines: Basic Electricity New York. 2012 ISBN 978-0-07-178068-1
Eddie
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