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-CG50 and HP Prime: Azimuth/Bearing Conversions

Casio fx-CG50 and HP Prime: Azimuth/Bearing Conversions

Introduction

The programs A2B (Azimuth to Bearing) and B2A (Bearing to Azimuth) convert angles between two measuring systems that are commonly used by civil engineers and navigators.

The program uses an unusual approach: the use of the arcsine, sine, and cosine functions.   These functions are used on because on scientific calculators, the trigonometric functions return answers in specific ranges.

Let x be a real number.  then:

asin(x) returns answers in the range -90° to 90°  (-π/2 to π/2 radians)

acos(x) returns answers in the range 0° to 180°  (0 to π radians)

atan(x) returns answers in the range -90° to 90°  (-π/2 to π/2 radians)

This was used in the HP 33E program from the calculator book "HP 33E: Surveying Applications".  See Source below.

Formulas:

A = azimuth
B = bearing
Q = quadrant  (1,2,3,4)

Azimuth to Bearing:

B = abs( asin( sin A ) )
Q = int(A/90 + 1)

(Yes, the asin/sin is there for a purpose: to get an angle in the range of -90° to 90°)

Bearing to Azimuth:

A = 180° * int(Q/2) - B * cos(Q * 180°)

In the programs A2B and B2A, both input and output will be degrees-minutes-seconds format.

To enter degrees-minutes-seconds:

Casio fx-CG50:  [ OPTN ] [ F6 ] (more) [ F5 ] (ANGLE)  [ F4 ] (° ' ")

HP Prime:  [ Shift ] [ a b/c ] or [ Shift ] [ 9 ] (select °, ', or '' from the menu)

Azimuth to Bearing Program A2B

Casio fx-CG50 Program A2B (Azimuth to Bearing)

ClrText
Locate 1,4,"AZIMUTH TO BEARING"
Deg
"AZ: "? → A
Abs( sin^-1 ( sin A ) ) → B
"BEARING ="
B ▶ DMS ◢
Intg( A ÷ 90 + 1 ) → Q
"QUADRANT = "
Q = 1 ⇒ "NE"
Q = 2 ⇒ "SE"
Q = 3 ⇒ "SW"
Q = 4 ⇒ "NW"

HP Prime Program A2B (Azimuth to Bearing)

EXPORT A2B(A)
BEGIN
// Azimuth to Bearing
HAngle:=1;  // Degrees
LOCAL B, Q, L0:={"NE","SE","SW","NW"};
B:=ABS(ASIN(SIN(A)));
Q:=IP(A/90+1);
RETURN { →HMS(B), L0(Q) }
END;

Example 1:  220° 15' 36"
Result:  40°15'36". SW

Example 2:  184°00'14"
Result: 4°00'14"  SW

Bearing to Azimuth Program B2A

Casio fx-CG50 Program B2A  (Bearing to Azimuth) 

ClrText
Locate 1,4,"BEARING TO AZIMUTH"
Deg
"BEARING: "? → B
Menu "QUADRANT", "NE", 1, "SE", 2, "SW", 3, "NW", 4
Lbl 1: 1 → Q: Goto 5
Lbl 2: 2 → Q: Goto 5
Lbl 3: 3 → Q: Goto 5
Lbl 4: 4 → Q: Goto 5
Lbl 5
180 * Intg( Q ÷ 2 ) - B * cos( Q * 180 ) → A
"AZ ="
A ▶ DMS

HP Prime Program B2A (Bearing to Azimuth)

Arguments:  Bearing, Quadrant.  You can enter Quadrant by a string or numerical quadrant.  "NE" = 1,  "SE" = 2,  "SW" = 3, "NW" = 4

EXPORT B2A(B,q)
BEGIN
// Bearing to Azimuth
// q "NE", "SE", "SW", "NW"
// or 1,2,3,4
LOCAL A, L0:={"NE","SE","SW","NW"};
HAngle:=1;  // Degrees
// deal with strings
IF TYPE(q)==2 THEN
q:=POS(L0,q);
END;
A:= 180 * IP(q/2) - B * cos(q * 180);
RETURN →HMS(A);
END;

Example 3:  43°21'55"  SW (q = 3)
Result:  223°21'55"

Example 4:  13°14'56"  SE (q = 2)
Result:  166°45'04"

Source:

Hewlett Packard.  "HP33E:  Surveying Applications"  Hewlett Packard Company.  March 1978

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.

HP Prime & TI-84: Bearing and Azimuth Conversions

HP Prime & TI-84:  Bearing and Azimuth Conversions

Azimuth vs Bearing

AZ2BE (Azimuth to Bearing)

Note:  Bearings start clockwise from due north.  Bearings will be reduced to angles between 0° to 360°.

Three outputs will be returned:  bearing, direction string, and quadrant reference number (for reference).  The HP Prime version will return a list.  

HP Prime AZ2BE:

EXPORT AZ2BE(θ)

BEGIN

// Azimuth to Bearing

// EWS 2015-07-19

LOCAL q,b,s;

θ≔θ MOD 360;

q≔IP(θ/90)+1;

// Determining the Bearing Angle

IF q==1 THEN

b≔θ; s:=”NE”;

END;

IF q==2 THEN

b≔ABS(θ-180); s≔”SE”;

END;

IF q==3 THEN

b≔θ-180; s≔”SW”;

END;

IF q==4 THEN

b≔ABS(θ-360); s≔”NW”

END;

RETURN {b,s,q};

END;

TI-84+ AZ2BE:

Input "ANGLE:",θ

360*fPart(θ/360)+360*(θ<0)→θ

iPart(θ/90)+1→Q

If Q=1:Then

θ→B

"NE"→Str1:End

If Q=2:Then

abs(θ-180)→B

"SE"→Str1

End

If Q=3:Then

θ-180→B

"SW"→Str1

End

If Q=4:Then

abs(θ-360)→B

"NW"→Str1

End

Disp "BEARING",B

Disp Str1,Q

BE2AZ  (Bearing to Azimuth)

Note:  Bearings outside of range of 0° to 90° or quadrant numbers outside of 1 to 4 will result in an “UNEXPECTED RESULT” message. 

Quadrants:

Quadrant 1:  Northeast

Quadrant 2:  Southeast

Quadrant 3:  Southwest

Quadrant 4:  Northwest

HP Prime BE2AZ:

EXPORT BE2AZ(b,q)

BEGIN

// Bearing to Azimuth

// bearing, quadrant

// 1 = NE, 2 = SE, 3 = SW, 4 = NW

// 2015-07-19 EWS

LOCAL θ;

// Are b and q in the proper range?

IF b<0 OR b>90 OR q<1 OR q>4 THEN

RETURN “Unexpected Value”;

KILL;

END;

// Calculation

q≔IP(q);

IF q==1 THEN

θ≔b;

END;

IF q==2 THEN

θ≔180-b;

END;

IF q==3 THEN

θ≔b+180;

END;

IF q==4 THEN

θ≔360-b;

END;

RETURN θ;

END;

TI-84+ BE2AZ:

Input "BEARING:",B

Disp "1=NE"

Disp "2=SE"

Disp "3=SW"

Disp "4=NW"

Input "Q:",Q

If B<0 or B>90 or Q<1 or Q>4

Then

Disp "UNEXPECTED VALUE"

Stop

End

iPart(Q)→Q

If Q=1:Then

B→θ:End

If Q=2:Then

180-B→θ:End

If Q=3:Then

B+180→θ:End

If Q=4:Then

360-B→θ:End

Disp "AZIMUTH:",θ

Examples:

Azimuth:  68°, Bearing: 68° bearing NE (q=1)

Azimuth: 164°, Bearing:  16° bearing SE (q=2)

Azimuth: 224°, Bearing:  44° bearing SW (q=3)

Azimuth: 321°, Bearing:  39° bearing NW (q=4)

This blog is property of Edward Shore.  2015