Monday, April 12, 2021

Spotlight: Jim Cullen - Mathematical Topics

Spotlight:  Jim Cullen - Mathematical Topics 


On today's blog I want to feature Jim Cullen, who has a mathematical web page:


Mathematical Topics Index Page - Associated Calculator Programs


Topics include:


Pi and several series to approximate π

Random Normal Number Generators

Generalized Fibonacci Sequences

A Comparison between Casio fx-115ES and Sharp EL-W516 (2 pdf files)

Diophantine Equations



Cullen also has a page of family's genealogy:  http://members.bex.net/jtcullen515/CullOrig.htm


Check it out,  


Eddie


All original content copyright, © 2011-2021.  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. 


Sunday, April 11, 2021

Retro Review: Hot Rod Calculator

 Retro Review:   Hot Rod Calculator








Quick Facts:


Model:  8703, Hot Rod Calc

Company:  Mr. Gasket Co/Calculated Industries

Years of Production: 2009 - 2020*

Memory Registers:  1

Batteries:  2 LR-44

Operating System:  Chain

Display:  8 digits, unit indicators 

New Price: $80 retail; can be found on sale or clearance


* I can no longer find the Hot Rod calculator as a new calculator on the Calculated Industries website.  However, the Hot Rod app for both iOS and Android.  


Ladies and Gentlemen, Start Your Engines!


The Hot Rod Calc is a specialty calculator that emphasizes on automotive mathematics, with solvers and applications including:  


*  Air Temperature, Relative Humidity (Moisture), Elevation

*  Vehicle Weight, Elapsed Time (1/4 mile traveled in seconds), MPH

*  Bore, Stroke, RPM, Torque, Engine Displacement

*  Tire Ratio, Gear Ratio

*  Engine Volumetric Efficiency

*  Carburetor Size

*  Vehicle Weight, Horsepower, Elapsed Time

*  Conversions including length, area, volume, temperature, mass, velocity (speed)


You can download a PDF version of the manual here: 


https://documents.holley.com/mr_gasket_instructions_hot_rod_calculator_8703.pdf


The manual has several reference tables:


*  Drag Coefficients depending on the automobile type

*  Holley Jet Chart

*  Jet Orifice Area Conversation Chart


Keyboard


The calculator comes in a bright red Armadillo Gear case.   The keys are bright and colorful, with most of them sporting a warm color palette (red, orange).  The keys are responsive, but have a rubber feel to them.  I believe the keys are made to handle dirt and oils given the target audience of the Hot Rod Calc.


The case has a quick reference guide.


Example Calculations


The calculator is set to U.S. units (default)


Example 1:


Calculate Air Temperature given:

Elevation:  1,284 ft

Air Pressure:  30.12 inHg

Humidity:  33%


1284 [ Elev/ADI ]

33 [ Moisture ]

30.12 [ Conv ] [Air Temp] (Pressure)

[Air Temp],  Result:  55.4211 °F


Example 2:


Find the weight of a vehicle given:

It's horsepower:  426 HP

It's elapsed time:  9.73 sec to run 1/4 mi


426 [ HP ]

9.73 [ ET ]

[ Vehicle Wt ],  Result:  1999.7337 lb


Example 3:


Find the speed, in miles per hour, for an automobile traveling with the following specifications:

1st Gear:  3.26

Final Drive Gear: 3.03

RPM: 5800 (revolutions per minute)

Diameter of the tires: 26 inches


3.26 [ × ] 3.03 [ Gear Ratio ]

5800 [ RPM ]

26 [ Conv ] [ Gear Ratio ] (New Tire Dia)

[ MPH ],  Result:  45.417902  mph


Verdict


If you are into racing, hot rods, and automobiles, and you need a quick mathematics tool, the Hot Rod calculator is worth the investment.  Its user manual is a well written.  Now may be the best time to purchase one before the calculator becomes a rare item.  


Eddie


All original content copyright, © 2011-2021.  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. 


Saturday, April 10, 2021

Fun with the HP 20S (April 10, 2021 Edition)

 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 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 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 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 


All original content copyright, © 2011-2021.  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.


Spotlight: Jim Cullen - Mathematical Topics

Spotlight:  Jim Cullen - Mathematical Topics  On today's blog I want to feature Jim Cullen, who has a mathematical web page: Mathematica...