Casio fx-CG 50: Solar Panel Calculations

 Casio fx-CG 50: Solar Panel Calculations

Note:  The calculator programs can be modified for the monochrome Casio graphing calculators by removing the Color commands (Black, Blue, etc.).  The programs use ClrText and Locate to generate a result screen.

Optimum Tilt of a Solar Panel

The program SLRPANEL estimates the optimum tilt of a solar panel given your latitude (North/South), time of day, and day of the year.  The program assumes a 365 day year.   

For the time of day, enter the time in hours before noon.  Example:  For 9:00 AM, enter 3.   For 3:00 PM, enter -3.   

The declination of the sun is estimated at:

δ ≈ -23.44° * (cos(360°/365° * (n + 10)))

n = number of days from January 1, n = 0 for January 1.  

The program is listed in text file mode.

Casio fx-CG50 Program: SLRPANEL

(464 bytes)

'ProgramMode:RUN

Deg

ClrText

Locate 1,1,"SOLAR PANEL TILT"

Yellow Locate 1,3,"EWS 2022"

For 1->I To 750:Next

ClrText

"365 DAY YEAR ASSUMED"

"MONTH"?->M

"DAY"?->D

"HOURS FROM NOON"?->T

"LATITUDE (N//S)"?->L

0->X

M>2=>Int (0.4*M+2.3)->X

31*(M-1)+D-X-1->N

(-)23.44*(cos (360/365*(N+10)))->E

sin^-1 (sin L*sin E+cos E*cos L*cos (15*T))->H

sin^-1 (sin (15*T)*cos E/cos H)->Z

Z=0=>1Exp(-)9->Z

2/3*(tan^-1 (tan H/tan Z)-30)->P

ClrText

Black Locate 1,1,"MONTH:"

Blue Locate 8,1,M

Black Locate 11,1,"DAY:"

Blue Locate 16,1,D

Black Locate 1,3,"DEC:"

Blue Locate 7,3,E

Blue Locate 21,3,"_deg_"

Black Locate 1,5,"TILT:"

Blue Locate 7,5,P

Blue Locate 21,5,"_deg_"

Example:

April 30, 11:30 AM, at Latitude 40°20'11"

Inputs:

Month:  4

Day:  30

Hours From Noon:  0.5

Latitude:  40°20°11°   ( [ OPTN ], [ F6 ] ( > ), [ F5 ] (ANGLE), [ F4 ] ( ° ' " ))

Result Screen:

MONTH:  4   DAY: 30

DEC:  14.18251427 °

TILT:  34.39287954 °

Solar Energy Reflected

Given an incidence angle and the type of material, the program SOLARENG estimates the ratio of solar reflected.   The program offers three types of material:

Glass, average index of refraction of 1.52 is used

Silicon, average index of refraction of 3.45 is used

Diamond, average index of refraction of 2.417 is used

The program is listed in text file mode.

Casio fx-CG50 Program: SOLARENG

(324 bytes)

'ProgramMode:RUN

Deg

"INCIDENCE ANGLE"?->I

Menu "MATERIAL","GLASS",1,"SILICON",2,"DIAMOND",3

Lbl 1:1.52->R:Goto 4

Lbl 2:3.45->R:Goto 4

Lbl 3:2.417->R:Goto 4

Lbl 4

sin^-1 (sin I/R)->W

0.5*((sin (I-W))^<2>/(sin (I+W))^<2>+(tan (I-W))^<2>/(tan (I+W))^<2>)*100->P

ClrText

Black Locate 1,1,"AT ANGLE "

Black Locate 10,1,I

Black Locate 21,1,"_deg_"

Green Locate 1,2,"INDEX="

Red Locate 9,2,R

Green Locate 1,3,"REFLECT="

Red Locate 9,3,P

Red Locate 21,3,"%"

Example:

Incidence Angle: 6°, glass

Inputs:

INCIDENCE ANGLE: 6

MATERIAL: 1: GLASS

Result Screen:

AT ANGLE 6 °

INDEX = 1.52

REFLECT = 4.25820312 %

HP 32S and HP 32SII Week:  May 2, 2022 - May 6, 2022

Source:

Rosenstein, Morton.  Computing With the Scientific Calculator Casio 1986  ISBN-13:  978-1124161433

Eddie

All original content copyright, © 2011-2022.  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. 

Retro Review: Texas Instruments TI-57 LCD

Retro Review:   Texas Instruments TI-57 LCD

Quick Facts:

Model:  TI-57 LCD

Company:  Texas Instruments

Years:  1982-1984

Type:  Programming

Batteries: 2 x LR44

Operating Mode:  AOS

Memory Registers: Minimum of 1, Maximum of 8

Program Steps:  Minimum of 0, Maximum of 48

Similar to many Texas Instruments programming calculators of the 1970s and 1980s, the memory can be partition between memory steps and program steps by the [ 2nd ] [ Part ] key sequence.  Each register has 8 program steps.  

Some Partitions:

Part 1:  1 register (R0), 48 steps

Part 2:  2 registers (R0, R1), 40 steps

Part 3:  3 registers (R0, R1, R2), 32 steps

Part 4:  4 registers (R0, R1, R2, R3), 24 steps

Features 

* trigonometric functions and inverses

* polar/rectangular conversions and degrees/degrees-minutes-seconds conversions

* integer part (Intg), fractional part (Frac), absolute value ( |x| )

* logarithms (log, ln x)

* storage arithmetic ([STO] followed by +, -, ×, ÷, y^x, INV y^x)

INV Key combinations

[ INV ] [ sin ]:  arcsin

[ INV ] [ cos ]: arccos

[ INV ] [ tan ]:  arctan

[ 2nd ] [ INV ] (P<>R):  rectangular to polar

[ 2nd ] [ INV ] (DMS-DD):  degrees to degrees-minutes-seconds

[ INV ] [ y^x ]:  y^(1/x)

[ INV ] [ log ]:  10^x

[ INV ] [ ln ]: e^x

[ 2nd ] [ INV ] (SBR):  RETURN - this ends subroutines

[ 2nd ] [ INV ] (Dsz):  Decrement R0 by 1 and skip if R0 ≠ 0

Polar to Rectangular:

r [ x<>t ] θ [ 2nd ] [ P<>R ]:   y [ x<>t ] x

Rectangular to Polar:

x [ x<>t ] y [ 2nd ] [ INV ] [ P<>R ]:   θ [ x<>t ] r

Keystroke Programming

The TI-57 LCD is a keystroke programmable calculator.   However, programming steps are at a premium with a maximum of 48 steps (allowing for one memory register) to 0 (yes, zero) if you use all 8 registers (R0 to R7).  

Programming commands include:

*  Test with the t register:  x=t,  x≥t, and inverses

*  Decrement and Skip:  either skip on zero or not on zero.  This command works on register 0.  

*  Labels and Go to commands:  labels 0-9

*  Pause command

*  Subroutines (SBR)

*  Go to step zero (RST)

Thankfully some steps are merged, mainly with the [ INV ] key, [ GTO ] key (GO TO command), [ 2nd ] key, and storage arithmetic.  

What is interesting is that there are no statistical functions on the TI-57 LCD.   See the One Variable Statistics section for a 25-step program to add one-variable statistics.  

Keyboard

We need to talk about the keyboard.  The keyboard looks good.  I have the United States edition of the TI-57 LCD and I like the blue, gray, black, and white color scheme.   

Unfortunately, some keys are hard to press and other keys can produce a double-stroke.  With the calculator I got, one wrong press gives a double number (22 instead of 2, 00 instead of 0) while some keys pressed in the "wrong" way do not register.  This does not allow for fast typing.   I think I found the keys "sweet spots":  the right side of the keys.    

The keyboard difficulties are a common complaint with the TI-57 LCD.   They are corrected with the TI-57 II released in 1986.  

TI-57 LCD Program:  One Variable Statistics

Memory Registers Required: 3  (Part 3)

00  23.01     LBL 1   // data entry

01  61.85.01 STO+ 1

02  34 x^2

03  61.85.02 STO+ 2

04  1 1

05  61.85.00 STO+ 0

06  13 R/S

07  22.01     GTO 1

08  23.02     LBL 2   // calculation

09  71.01    RCL 1

10  55 ÷

11  71.00     RCL 0

12  95 =

13  13 R/S   // sample mean

14  71.02     RCL 2

15  55 ÷

16  71.00     RCL 0

17  75 -

18  53 (

19  71.01     RCL 1

20  55 ÷

21  71.00     RCL 0

22  54 )

23  34 x^2

24  95 =

25  35 √

26  13 R/S  // population deviation

Registers used:

R0 = number of data points = n

R1 = sum of the data points = Σx

R2 = sum of the data points squared = Σx^2

Mean:

x-bar = Σx / n

Population Deviation

σx = √( Σx^2/n - (Σx/n)^2 )

Instructions:

1.  If necessary, partition memory to fit 3 memory registers (R0, R1, R2).  [ 2nd ] (Part) [ 3 ].

2.  Enter the first point, press [ GTO ] [ 1 ], then [ R/S ].  1 is displayed when data points are entered.

3.  Enter each subsequent point, press [ R/S ].  Repeat until finished.  

4.  To calculate the mean and population deviation, press [ GTO ] [ 2 ].   The mean is displayed first, press [ R/S ] to display population deviation.  

[ RCL ] [ 0 ]:  number of points

[ RCL ] [ 1 ]:  sum of data points

[ RCL ] [ 2 ]:  sum of squares of data points

Example 1:

Data Set: 4, 5, 9, 8, 6

Results:

n = 5

Σx = 32

Σx^2 = 222

x-bar = 6.4

σx = 1.854723699

Example 2:

Data Set: 11058, 12360, 12445, 12761, 13002, 13360

Results:

n = 6

Σx = 74986

Σx^2 ≈ 9.40 * 10^8

x-bar = 12497.66667

σx = 725.9110757

Closing Thoughts

I wish the TI-57 LCD had both more memory and functions.   Honestly, Texas Instruments could combine the functions of the TI-57 LCD (tests, labels, go to, decrement and skip), the TI-55 III (better keyboard, linear regression, integrals, unit conversions, signum function, permutations, combinations), and the later TI-60 (the TI-55III with base conversions) with a total of 188 steps.  The programming set up with the TI-57 LCD wins with it's merged steps with INV, STO, LBL, and GTO.   

Overall, I like the appearance of the TI-57 LCD, despite the keyboard's set backs. That, the lack of functions and statistics, and the sometimes slow execution and we can see why the TI-57 LCD was not a best seller.  

HP 32S and HP 32SII Week:  May 2, 2022 - May 6, 2022

Until next time,

Eddie

All original content copyright, © 2011-2022.  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. 

TI-84 Plus CE (Python): Using SciTools for Conversions and Constants

 TI-84 Plus CE (Python):  Using SciTools for Conversions and Constants

SciTools 

SciTools is a complementary application that comes with the purchase of the TI-84 Plus family.   The SciTools offers four tools:

1.  SIG-FIG Calculator:  calculate using a designated number of significant digits

2.  UNIT CONVERTER:  conversions and constants, which will be this blog entry's focus

3.  DATA/GRAPHS WIZARD

4.  VECTOR CALCULATOR:  vector mode

Converting Units in SciTools

The Unit converter has two screen:  upper screen has the units to be selected, bottom screen is where the conversion happens.   

1.  Press [ apps ] and select SciTools, you may have to scroll.    

2.  Select option 2: UNIT CONVERTER.

3.  You will be prompted for a Unit Category, either arrows or the number keypad can be used.

4.   Enter the value to be converted.  

6.  Use the arrow keys to select, by pressing [ enter ] to select the "from" unit and the "to" unit.   Results will be shown in scientific notation.

Example:  70 ft to m:

1:  LENGTH, 70, select ft, [ enter ] select m, [ enter ]

7E1 ft > 2.1336E1 m  (21.336 m)

To copy the results to the home screen, press [ zoom/f3 ] (EXPT).  You will have to leave the app entirely to use the export as the result starts a new calculation in Home mode.

Copying a Scientific Constant

The numeric value of a scientific constant can be copied from SciTools to the Home Screen (unfortunately this can be done to a programming editing page) by the following:

1.  Press [ apps ] and select SciTools.  

2.  Select option 2:  UNIT CONVERTER

3.  To get to the list of constants, press either [ y=/f1 ] or [window/f2].   

4.  Use the arrow keys to select the scientific constant.  The name, it's value, and units will be displayed at the bottom of the screen.

5.  Press [ zoom/f3 ] (EXPT) to export the constant to the Home screen.  

6.  Press [ 2nd ] [ mode ] (QUIT) three times to get back to the home screen.  

7.  To use the constant in operations, either press [ enter ] and use Ans, or store the value in a variable (A-Z, Θ) for future calculations.

I'll admit that this is cumbersome.  Unfortunately, a constant's value cannot be copied directly to a program editing screen.  It's better than nothing...

HP 32S and HP 32SII Week:  May 2, 2022 - May 6, 2022

Eddie 

All original content copyright, © 2011-2022.  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. 

Applications: Sharp EL-5150

Applications:  Sharp EL-5150 

Note:  spaces included for readability

Fan Laws

AER Equation:

1; f(BCDI) = B * ( C ÷ D ) Y^x ( 1 ÷ I  )

Variables:

Calculate CPM_new

B = CPM_old

1st Fan Law:

I = 1

C = RPM_new

D = RPM_old

2nd Fan Law:

I = 2

C = SP_new

D = SP_old

3rd Fan Law:

I = 3

C = BHP_new

D = BHP_old

Example 1:

Fan Law 2:

CPM_old = B = 4000 CPM

SP_new = C = 48 

SP_old = D = 36

I = 2

Result:  4618.802153

Example 2:

Fan Law 3:

CPM_old = B = 3500 CPM

BHP_new = C = 59

BHP_old = D = 52

I = 3

Result:  3650.488072

Ideal Shockley Diode Equation

I = I0 * e^((VD/(n* VT) - 1)

where VT = K * T/q

I = diode current (amps)

I0 = saturation current (amps)

VT = thermal voltage (V) - see notes below

VD = voltage across the diode (V)

n = ideality factor, in ideal situations, n = 1

Notes:  

*  The equation below assumes the ideal diode, n = 1

*  The equation uses a ratio of scientific constants:  k/q 

*  k = Boltzmann's Constant = 1.380649 * 10^-23 J/K

*  q = Charge of an Electron = 1.602176634 * 10^-19 C  (on some calculators, like the Casio fx-991EX, this constant is labeled e)

*  k/q = 8.617332385 * 10^-5 J/(K*C) = 8.617332385 * 10^-5 V/K  (volts/degrees Kelvin)

AER Equation:

1; f(IDE) = 8.617332385E-5 × E STO A, I ×(e(D ÷ A) - 1)

Calculate VT (stored in A), the I 

I = I0

D = VD

E = temperature in Kelvin

Example 1:

I = 4E-6 A 

D = 0.08 V

E = 280 K

Results:

A = 0.024128531, (I) 0.00001061

 

Example 2:

I = 4E-6 A 

D = 0.06 V

E = 300 K

Results:

A = 0.025852000, (I) 0.00003674

Dot and Cross Product of Two 3D Vectors

For the two vectors [A, B ,C] and [D, E, F]:

AER Equations:

1; f(ABCDEF) = A × D + B × E + C × F ◣

2; B × F - C × E, C × D - A × F, A × E - B × D

Example 1:

[ A, B, C ] and [ D, E, F]

[ 4.5, -2.5, -8 ] and [ 1.6, 3.9, 6 ]

Dot Product:  -50.55

Cross Product:  [ 16.2, -39.8, 21.55 ]

Example 2:

[ A, B, C ] and [ D, E, F]

[ 4, 3, 2 ] and [ 2, 7, 0 ]

Dot Product:  29

Cross Product:  [ -14, 4, 22 ]

Law of Cosines

Sides with lengths A, B, C with D as the angle opposite of A.  Equation 1 finds the length of side A, while Equation 2 finds the angle D.

AER Equations:

1; f(BCD) = √(B^2 + C^2 - 2 × B × C × COS D) STO A ◣

2; f(ABC) = cos^-1 ((B^2 + C^2 - A^2) ÷ (2 × B × C)) STO D

Example 1 - find A:

Degree Mode Set

Input:  B = 4.5, C = 3.7, D = 30°

Run 1:

Result:  2.258617731

Example 2 - find D:

Degree Mode Set

Input:  A = 40, B = 56, C = 38

Run 2:

Result:  45.5579132°

Note:  Due to the incredible amount of spam comments that get sent on this blog, which I moderate so the readers don't see them, I have decided to turn comments off.  I will review whether to turn comments back on at a later time.  My apologizes to those who leave legitimate comments.  

Eddie 

All original content copyright, © 2011-2022.  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. 

Population vs Standard: Deviation and Covariance

 Population vs Standard: Deviation and Covariance

Population Deviation vs Standard Deviation

How is the population deviation related to the standard deviation?

Population Deviation (of a data set x_i):

σx = √( Σ(x_i - mean(x)) / n)

where mean(x) is the arithmetic mean of the data set over x_i

Standard Deviation:

sx = √( Σ(x_i - mean(x)) / (n - 1))

n is the size of the data set x_i.  

Suppose we can calculate the standard deviation by multiplying a factor (let's call it ß for the purpose of this example) to the population deviation.   

ß * σx = sx

ß * √( Σ(x_i - mean(x)) / n) = √( Σ(x_i - mean(x)) / (n - 1))

ß  * √( Σ(x_i - mean(x))) /  √n = √( Σ(x_i - mean(x))) / √(n - 1)

ß * √( Σ(x_i - mean(x)))  / √( Σ(x_i - mean(x))) = √n / √(n - 1)

ß  = √n / √(n - 1)

ß  = √(n/(n - 1))

Hence:

sx =  √(n/(n - 1)) * σx

and

σx = sx * √((n-1)/n)

Example:

x = {4, 7, 10, 16, 38}   

n = 5

σx = 12.16552506

sx = 12.16552506 * √(5/4) = 13.60147051

Population Covariance vs Standard Covariance

For the data sets x_i and y_i, population covariance:

cov_σ = 1/n * Σ((x_i - mean(x)) * (y_i - mean(y)))

And the sample covariance:

cov_s = 1/(n - 1) * Σ((x_i - mean(x)) * (y_i - mean(y)))

We will use the similar tactic above to find a relationship between population covariance and sample covariance:

ß * cov_σ = cov_s

ß * 1/n * Σ((x_i - mean(x)) * (y_i - mean(y))) = 

1/(n - 1) * Σ((x_i - mean(x)) * (y_i - mean(y)))

ß * Σ((x_i - mean(x)) * (y_i - mean(y))) / Σ((x_i - mean(x)) * (y_i - mean(y))) =

n/(n - 1)

ß = n/(n - 1)

Hence:

cov_ s = n/(n - 1) * cov_σ 

and

cov_σ = (n - 1)/n * cov_s

Example:

x = {4, 5, 6, 8}

y = {-2, -1, 2, 0}

n = 4

mean(x) = 5.75

mean(y) = -0.25

cov_σ = 1.1875

cov_s = 1.1875 * 4/3 = 1.5833333333

Hope you find this helpful,

Eddie 

All original content copyright, © 2011-2022.  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. 

Big Font Reference - 2022 Edition Available

 Big Font Reference - 2022 Edition Available

The big font reference update is here.   My blog is about to be 11 years old on April 16 and I provide this as a thank you.  

Topics include:

Conversions

Scientific Constants

Algebra

Boolean Algebra

Geometry

Finance

Statistics, Probability and Curve Fitting

Hyperbolic Functions

Calculus including Derivatives, Integrals, and Differential Equations

Laplace Transforms

Selected Applications:  Astronomy, Physics, Electronics, Solar Panels, Basic Automobile Math

Table of Mathematical Unicode Symbols

The reference documents is designed for smartphones, small tablets, and iPod Touches.  I created this document to have a to-go reference in a easy to read capacity.  

The document can be downloaded here or there is a link on the right side menu of this blog:

https://drive.google.com/file/d/1DZMhDf7rhLRBHzlsSfIkg9jJ14HQ4e-z/view?usp=sharing

Take Care,

Eddie

All original content copyright, © 2011-2022.  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. 

Retro Review: Calculated Industries NautiCalc Plus

 Retro Review:   Calculated Industries NautiCalc Plus

Quick Facts:

Model:  NautiCalc Plus

Company:  Calculated Industries

Years:  1996-1998

Type:  Nautical

Batteries: 1 x CR-2032

Operating Mode:  Chain

Memory Registers: 10

Features

For a company that produces specialized calculators, the NautiCalc Plus is a rare calculator.   I purchased mine from Calculator Source's eBay page.   Calculations that the NautiCalc offers are:

*  conversions of time

*  conversions of distance

*  conversions of speed

*  triangulation calculations:  course direction, 1st bearing, 2nd bearing, distance of the bearing object, distance abeam

*  solver:  speed, distance, time

*  solver:  tank capacity in gallons, fuel efficiency (statute miles per gallon), range (how far can you travel with a fuel tank)

*  paperless tape with the capacity of 10 entries, accessed by the [ Rcl ] [ = ], which is not marked on the calculator.   Scroll the entries by the plus and minus keys.  

Memory Registers

The NautiCalc has ten memory registers, M0 through M9.   What is unusual is that the [ Stor ] key acts a memory-plus for M0.   For example:

[ Conv ] [ + ] (Clr Mem)

25 [ Stor ] 0  (M-0   25)

[ Stor ] 1    (M-1  25)

50 [ Stor ] 0  (M-0  50)

[ Stor ] 1  (M-1 50)

[ Rcl ] 0   (M-0 75)   75 is stored in M0,  50 and 25 were added together

[ Rcl ] 1   (M-1 50)   50 is stored in M1, 50 replaced 25 in M1

Miles

There are two measurements for miles:  statute miles and nautical miles.   Statue miles, also known as survey miles, are miles related to road distance, equal to 5,280 feet.   Nautical miles, which are used in sailing and air travel, are measure from 1% of 1 degree of the Earth's curvature (see source, "What Are Statute Miles?").   

Statue Miles:  [ Conv ] [ 7 ]

Nautical Miles:  [ Miles ]

1 nautical mile ≈1.1507794 statute mile

Entering Time 

Time can be entered with several ways:

*  [ AM ] and [ PM ] keys.  We can use the shortcut method hhmmss or hhmm format to enter time.

*  The colon [ : ] key.   

*  The use hours, minutes, and second keys ([ Hr ], [ Min ], [ Sec ]).  

The [ Conv ] [ : ] changes the time format between 12-hour and 24-hour military time format.  

If we want to enter degrees-minutes-seconds, we must use the [ d:m:s ] key.  

Stopwatch 

The stopwatch can be started and stopped with the [ Timer ] key twice.  The stopwatch also has a split/lap feature with the [ S/Lap ].  While the stopwatch is running, a clock icon is on the display.

Timer

The timer is started with pressing the [ Timer ] key, entering the time, then pressing the [ Timer ] key again.   The NautiCalc Plus has a buzzer, not very loud, that can be turned on and off.  While the timer is going, we see a clock and star on the display.  The entire display flashes when the timer is completed. 

Not many calculators as a whole have the stopwatch and timer, so to have it is a nice feature.  

Now let's demonstrate some of the main calculations that are done wiht the NautiCalc Plus.  

Example:  Fuel Efficiency

If a tank can carry 15 gallons and has an average efficiency of 30 miles per gallon, what is the range?

[ On/C ] [ On/C ]

15 [ Conv ] [ Speed ] (Cap) (display has GAL)

30 [ Conv ] [ Time ] (Eff)   (display has MPG)

[ Conv ] [ Dist ] (Range)

Result:  RNG:  450 MI S  (450 statute miles)

Example:  Distance of Objects and Abeam

Traveling with 30° course with bearings reading 45°12' and 58°42', respectively.   You have traveled 5 nautical miles.   Find the distance bearing from the bearing object and distance abeam.  

[ On/C ] [ On/C ]

30 [ Course° ]   (CRSE)

45 [ d:m:s ] 12 [ 1stϕ ]  (BRG1)

58 [ d:m:s ] 42 [ 2ndϕ ] (BRG2)

5 [ Miles ] [ Dist ] (DIST   5  N MI)

[ Dist ]    (Display:   TRVL 5  N MI)

[ Dist ]    (Display:  DOBJ 5.6156432 N MI)

[ Dist ]    (Display:  BEAM 3.1139547 N MI)

TRVL:  distance traveled

DOBJ:  distance from object

BEAM:  distance abeam

Example:  Speed/Time/Distance 

If a boat travels 13.5 nautical miles and it took 2 hours 23 minutes, what is the speed of the boat?

[ On/C ] [ On/C ]

13.5 [ Miles ] [ Dist ]

2 [ Hr ] 23 [ Min ] [ Time ]

[ Speed ] 

Display:  SPD 5.6643357 K NO T  (5.6643357 knots, 6.5184011 miles an hour)

Closing Thoughts

The keyboard is solid with the keys have a nice feel to them.  The NautiCalc Plus comes with a protective wallet, where the user guide can fit in the pockets.   

I really like this calculator and how Calculated Industries makes calculators for specific applications.  I would have loved to have seen the NautiCalc had a longer life than it did.   It's really cool to collect.  

I'm now retired from purchasing vintage calculators online.  I still will be posting retro reviews in the next few months, including the recently purchased the Texas Instruments TI-57 LCD (1982) and HP 45 (1973).  I am also going to include calculators that have been sitting in the garage that I didn't get a chance to do a review on, such as the Radio Shack EC-4026 (Casio fx-4500P equivalent) and TI-65.  

Source:

Bollman, Mark.  "NautiCalc Plus" April 21, 2013.   Last Accessed March 24, 2022.  http://mathcs.albion.edu/~mbollman/CI/NCalc+.htm  

Jones, Louise.  "What Are Statute Miles?"   Sciencing.  April 25, 2017.  Last Accessed March 27, 2022.  https://sciencing.com/statute-miles-8358166.html  

Until next time,

Eddie

All original content copyright, © 2011-2022.  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. 

Casio fx-CG 50 and fx-9750GIII: Regression Builder

Casio fx-CG 50 and fx-9750GIII:  Regression Builder

Introduction

The program LRBUILD lets the user fit bi-variate data (x,y) to a customized regression equation in the form:

y = C + Σ Cₙ * fₙ(x) 

where:

C = constant term.  This term is automatically calculated for by the program.

Cₙ = coefficient of each subsequent term of fₙ(x)

fₙ(x) = function, where the user can choose any of the following forms:

1.  x^A

2.  ln(A * x)

3.  e^(A * x)

4.  sin(A * x)

where A is a real number.  Angles are assumed to be in radian measure.  

For example, we can fit data by least squares method to this equation:

y = C + C_1 * x^2 + C_2 * e^(0.5 * x) + C_3 * sin(x)

You can add as many fₙ(x) terms as you like.

The program will give you the coefficients in a vertical matrix, starting from C and so forth, and the R^2 goodness of fit:

R^2 = 1 - SS_res / SS_tot

SS_res = Σ( y_observed - y_predicted)^2

SS_tot = Σ(y_observed - mean(y_oberserved))^2

Notes:

The characters _n (lower subscript n) and Σ (sigma symbol) are found on the CHAR (Character Select) on the programming editor menu (almost exit until the soft menu TOP, BOTTOM, SEARCH, ... displays).

The lines:

For 1 → I To 750

Next

are used to create a short pause.

There are two versions:  

Program files with the g3m extension is for the color Casio graphing calculators, such as the fx-CG50.   You can download this file here:

https://drive.google.com/file/d/1YidknrzjU_oRT3KLIzkEogbU_XFBCH0j/view?usp=sharing

Program files with the g1m extension is for the monochrome Casio graphing calculators, such as the fx-9750GIII (United States) and the fx-9860GIII (International).  You can download this file here:

https://drive.google.com/file/d/1GOO6VHGV_JRlNlbZB8ww3hK1qDqZaag_/view?usp=sharing

To transfer between Casio calculators, it is recommended to save them as text files.  Then transfer to the SAVE-F folder and load it on the home calculator.  Some editing may be necessary, such as <-1> with x^-1.

Casio fx-9750gIII and fx-CG50 (and probably most other Casio modern graphing calculators) Program: LRBUILD

(Extra spaces included for readability - this meant to be typed on the calculator)

Rad

ClrText

Locate 1,1,"LIN REG BUILDER"

Locate 1,2,"EWS 2022-01-17"

Locate 1,3,"Y=C+Σ(C_n×F_n(X))"   (n is the lower script n from the CHAR screen)

For 1 → I To 750

Next

"X DATA"? → List 1

"Y DATA"? → List 2

Dim List 1 → N

Dim List 1 → Dim List 3

{0} → List 4

{0} → List 5

Seq(1,X,1,N,1) → List 6

List→Mat(List 6) → Mat A

List→Mat(List 2) → Mat B

"CONSTANT TERM ADDED"

For 1 → I To 750

Next

Lbl 0

Menu "TERM?", "X^A", 1, "ln (AX)", 2, "e^(AX)", 3, "sin (AX)", 4, "CALCULATE", 5

Lbl 1

"A"? → A

Augment(List 4, {1}) → List 4

Got A

Lbl 2

"A"? → A

Augment(List 4, {2}) → List 4

ln(A×List 1) → List 6

Goto A

Lbl 3

"A"? → A

Augment(List 4, {3}) → List 4

e^(A×List 1) → List 6

Goto A

Lbl 4

"A"? → A

Augment(List 4, {4}) → List 4

sin(A×List 1) → List 6

Goto A

Lbl A

Augment(List 5, {A}) → List 5

List→Mat(List 6) → Mat D

Augment(Mat A, Mat D) → Mat A

Goto 0

Lbl 5

Dim List 4 → M

(Trn Mat A × Mat A)^-1 × Trn Mat A × Mat B → Mat C

"COEFFS:" ◢

Mat C ◢  

For 1 → I to N

0 → Y

For 1 → J To M

List 4[ J ] → L

List 5[ J ] → A

Mat C[ J, 1 ] → C

List 1[ I ] → X

L = 0 ⇒  Y + C → Y

L = 1 ⇒ Y + C × X^A → Y

L = 2 ⇒ Y + C × ln(AX) → Y

L = 3 ⇒ Y + C × e^(AX) → Y

L = 4 ⇒ Y + C × sin(AX) → Y

Next

Y = 0 ⇒ 1E-7    (lower case 10 on the fx-CG 50)

Y → List 3[ I ]

Next

1 - (Sum (List 2 - List 3)^2)÷(Sum (List 2 - Mean(List 2))^2) → R

"R^2="

R ◢

List→Mat(List 1, List 2, List 3) → Mat D

Variables:

List 1:  X Data

List 2:  Y Data

List 3:  Expected Y Data (Calculated)

List 4:  Operation Types:  0 - constant, 1 - x^a, 2 - ln(a*x), 3 - e^(a*x), 4 - sin(a*x)

List 5:  A

Mat A:  X data matrix 

Mat B:  Y data matrix

Mat C:  matrix of calculated coefficients

Examples

Example 1:

Fit the following data:

x data = {10, 25, 34, 46, 65}

y data = {39.7, 100, 135.9, 183.9, 260}

to the curve y = C + C1 * x + C2 / x

Remember the constant term is automatic.   

On the TERM? menu, select 

1.  X^A with A = 1

1.  X^A (again), this time with A = -1

5.  CALCULATE

Calculated coefficients:

[[ 0.1012904425 ]

[ 3.99874051 ]

[ -3.775351133 ]]

y = 0.012904425 + 3.99874051x - 3.775351133/x

R^2 = 0.9999994909

y' predicted data: 

{39.71116043, 99.91878916, 135.947281, 183.9612811, 259.9613413}

Example 2:

Fit the following data:

x data = {-0.35, -0.16, 0.27, 0.84}

y data = {-0.64, -0.31, 0.58, 2.06}

to the curve y = C + C1 * sin x  + C2 * e^x

Remember the constant term is automatic.   

On the TERM? menu, select 

4.  sin(A*X) with A = 1

3.  e^(A*X) with A = 1

5.  CALCULATE

Calculated coefficients:

[[ -0.9847711767 ]

[ 1.023495272 ]

[  0.9854914931 ]]

y = -0.9847711767 + 1.023495272 * sin x + 0.9854914931 * e^x

R^2 = 0.9999986129

y' predicted data:

{-0.6412613439, -0.3080521531, 0.5791860102, 2.060127487}

Example 3:

Fit the following data:

x data = {2, 3, 4, 5, 6}

y data = {22.5, 34, 45.5, 57.5, 69.75}

to the curve y = C + C1 * x^1.2 + C2 * ln(3*x)

Remember the constant term is automatic.   

On the TERM? menu, select 

1.  X^A with A = 1.2

2.  ln(A*X) with A = 3

5.  CALCULATE

Calculated coefficients:

[[ -0.08646217016 ] 

[ 6.83429695 ]

[ 3.855357541 ]]

y = -0.08646217016 + 6.83429695 * x^1.2 + 3.855357541 * ln(3* x)

R^2 = 0.9999924407

y' predicted data:

{22.52250254, 33.92570965, 45.56537698, 57.50145068, 69.73496014}

Eddie

All original content copyright, © 2011-2022.  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.