Rockwell 61R
-.,
"
"
Rockwell International
..where science gets down to business
2520·Q-62-R2-407
Litho in U.S.A.
Welcome to the world of
Rockwell reliability!
If your problems involve trigonometric and logarithmic functions,
now you have The Answer-the
Rockwell 61 R Advanced Slide Rule.
1. Degrees/Radians selection switch
2. Display/Register and Display/
Memory exchange key
3. Clear/Entry Correction and
Clear Function key
4. Equal/Memory Display key
5. Change Sign/Store Display key
6. Add/Add to Memory key
7. Subtract/Subtract from Memory
key
8. Function/Data Recovery key
9. On/Off switch
10. Overflow indicator
11. Negativ:e number indicator
Copyright 1974, Rockwell International
Your Rockwell 61 R has been designed not only to perform the four
basic functions of arithmetic but
also to compute natural and common logs and anti-logs, trigonometric and inverse trigonometric
functions, square roots, roots and
powers for any real numbers, and
reciprocals. The constant pi may be
recalled for use at any time, and
there is an addressable memory for
storing data or accumulating results.
Your Rockwell 61 R uses one of
the most sophisticated electronic
devices on the market: a single
microelectronic silicon chip. This
device is no bigger than a fleck of
confetti, yet it is programmed to
provide the capabilities for solving
many types of complex problems.
Rockwell International has had
more experience with these remarkable devices than anyone else in the
industry.
1
.'
This instruction manual will assist
you in understanding the various
key functions and the operation of
your calculator.
CONTENTS
General Information _ _ _ _
Before Operating Your
Calculator
.
Operating Power
__
Battery Charger. . . . . . . .
Special Care and Precautions
Getti ng Started . . . . . . . ..
Display. _
_
Explanation of Switches
and Indicators - . .
. . . ..
Operation .. -
5
5
5
5
6
7
8
9
10
Basic Operations .. _
13
Repeat Operations. _
__
Constant Operations
_
Clear Operations
Overflow Conditions .
Wrap-Around Decimal ....
Computations With Very
Large or Very Small
Numbers . . . . . . . . .
Change Sign Operation __ ..
Register Exchange Operation
Key Secondary Functions ..
Memory Operation
_ ..
Constant 1T Key
17
18
23
27
28
30
31
32
33
33
37
Trigonometric Functions
(SIN), (COS). (TAN). _ . _ 41
I nverse Trigonometric Func-
tions (ARC) (SIN), (ARC)
(COS). (ARC) (TAN) ... 46
2
3
J
-------~~----.....
Square Root (vx>. . . . . ..
Reciprocals (l/x) Common Logarithms
Function (log X) . . . . ..
Natural Logarithms
Function (In X) - - - . - _.
Antilogarithms Function
(exl. (lOX) . __
Exponential Function (XY) .
Recovery Techniques .....
Sample Problems. . . . . . . .
Mathematics
_. _. _
Statistics . . . . . . . . . ..
The Pythagorean Theorem
50
52
54
54
55
56
60
63
63
63
68
Rectangular to Polar Coor-
dinates Conversion. ..
Law of Sines. . . . . . . ..
Law of Cosines . . . . . ..
Hyperbolic Functions __ .
Inverse Hyperbolic
Functions. . . . . . . ..
Engineering
_
Parallel Resistors . . . . . .
RC Network. . . . . . . ..
Simply Supported Beam .
Shaft Stress
Sound Pressure . . . . . ..
Range of Accuracy ... . . . . .
Consumer Warranty
69
71
73
75
78
82
82
83
85
87
90
92
96
GENERAL INFORMATION
BEFORE OPERATING YOUR
CALCULATOR
Your Rockwell 61 R Advanced
Slide Rule calculator is supplied
with rechargeable internal batteries
and a battery charger. Part No.
328R07·001. DO NOT OPERATE
YOUR CALCULATOR WITHOUT
THE CHARGER UNTIL YOU
HAVE CHARGED THE BATTERIES FOR FIVE HOURS. Failure to
do so can damage the batteries.
OPERATING POWER
Your calculator operates from nickel
cadmium rechargeable batteries. You
may use the calculator while the
nickel cadmium batteries are being
charged; however, your battery
charger is not an AC adapter and
should not be left plugged in
indefi nitely.
BATTERY CHARGER
To charge the nickel cadmium bat·
teries, simply plug the charger into
the jack provided in your calculator
and a standard 120-volt wall outlet.
With ihe calculator turned off, allow
4
5
-----~_.-
approximately five (5) hours for the
batteries to be fully charged. Your
calculator CAN be used while the
batteries are being charged, but the
time required for the batteries to
become fully charged will increase.
The nickel cadmium batteries will
provide a minimum of three (3)
hours operating time when fully
charged. The nickel cadmium battery life will be prolonged by recharging the batteries after approximately three (3) hours operating
time. The need for recharging is
indicated by the display becoming
2. Do not charge the batteries
continuously as battery degradation could occur after
approximately 72 hours.
3. Avoid exposing your calculator
to extreme cold or heat. Keep it
out of direct, intense sunlight
and away from heating devices.
4. Keep your calculator away from
moisture and liquids.
5. Do not drop or subject your
calculator to heavy shock or
vibration.
6. When not in use, turn the calculator off and place it in its
carrying case for maximum
protection.
dimmer. Do not continue to use
your calculator on battery power
once the display becomes dim. The
nickel cadmium batteries may be
permanently damaged by overuse
without charging.
7. Never use a dry or wet cleaner
of any kind on the case. Simply wipe the case with a clean
dust cloth.
8_ Do not attempt to repair the
calculator yourself. The parts
SPECIAL CARE AND
PRECAUTIONS
are replaceable, but not
repairable.
Observance of the following will
prevent damage to and assure
GETTING STARTED
trouble-free service from your
Your machine has a feature that
automatically clears all registers
when power is turned on. Place the
power switch in the ON position,
and a zero appears in the right hand
digit position. The calculator is now
calculator and the charger and
nickel cadmium batteries supplied
with it.
1. Use only the charger furnished with vour calculator.
6.
J
7
1
ready to accept key entries and per·
form calcu lations.
EXPLANATION OF SWITCHES
AND INDICATORS
DISPLAY
ON/OFF SWITCH
Numbers with an absolute value of
0.0000001 to 99999999 can be dis·
played. Negative entries and results
are indicated by a minus symbol at
the far left of the display. Results
The ON position applies power to
your calculator and clears it of all
previously entered data.
in excess of eight digits are indicated
by the overflow indicator, a large
dot in the far left of the display.
The eight most significant digits are
displayed with the decimal adjusted
eight places to the left of the
correct position (see Wrap-Around
Decimal). For fractional numbers
less than one, a zero is displayed to
the left of the decimal point. No
leading zeros are displayed for
numbers greater than one. The results of the calculations are displayed
DEG/RAD SWITCH
Refer to page 41 .
OVERFLOW INDICATOR
\e187.65432\ elights if the answer
exceeds 8 digits to the left of the
decimal point. The e indicator also
lights if memory accumulation
exceeds eight whole digits (no fraction). (See Overflow conditions, page
27 and Wrap-Around Decimal, page
28 for detailed information on calculator overflow_)
instantaneously for most calculations.
NEGATIVE NUMBER INDICATOR
NOTE: Computations using very
large or very small numbers
may be performed on your
I
1.2451 - lights when negative numbers are displayed.
slide rule calculator by
utilizing appropriate
scal ing (see page 30).
9
OPERATION
The Rockwell 61 R Advanced Slide
Rule has 20 keys, including a unique
"second function" key that allows
each key to have two separate uses.
The first (primary) use is identified
on the face of the key; the second
(secondary) use is identified above
the key. In this manual, the first
use is represented (except for digits)
by enclosing the identification in a
box, 0; the second use, by enclosing
the identification in parentheses, ( ).
The following explanation will help
you understand the operation and
TIPLY, G DIVIDE: Depressing any
of these four keys selects the next
operation to be performed by the
calculator and causes the previously
selected operation to be executed.
During calculations, intermediate
results are automatically displayed
after these keys are depressed.
ANSWER KEY
0:
Depressing the
0
key causes
your answer to appear in the dis-
play, then terminates the calculation.
The answer can be retained as the
first number for your next calcu-
uses of each key.
lation (see page 16).
DIGIT ENTRY KEYS
CLEAR KEY
[Q] THROUGH ffil: Depressing any
digit key enters that digit and causes
it to appear in the displaY.,. To enter
the number 24, depress W first,
then @1
~: Depressing the ~ key clears
DECIMAL POINT ENTRY KEY
0: Depressing the 0 key places
the display of erroneous entries,
cancels overflow conditions, or
clears the calculator of stored numbers and functions. (See Clear Operations, page 23, for detailed instructions on use of the ~ key.)
the decimal point in your entries.
CHANGE SIGN KEY
ARITHMETIC FUNCTION KEYS
1+/-1: Depressing the 1+/-1 key changes
the sign of a displayed number.
[±] ADD,
EJ SUBTRACT, Ii] MUL10
11
~
..
REGISTER EXCHANGE KEY
>-
8: Depressing the 8 key inter-
'"Q.
changes the contents of the display
and the working register.
o
~
FUNCTION KEY
[£]: Depressing the [£] key conditions the calculator to interpret the
next key depressed in accordance
with the function identified above
the key.
NOTES: The secondary functions
of the keys are described
under Key Secondary
F unctions, page 33.
Techniques for recovery of
data following unintentional depression of the wrong
arithmetic function key or
the [£] key are given under
Recovery Techniques, page
60. Recovery of data with
the (DR) key is also de-
r-Ii
<0"
scribed under Recovery
~
<:
+ w
Techniques.
M
..
C
Eo
~.-+::
-
."
to
0
...0:
.0'-
>-
01)
"
~
:>..
-0
0.«
12
-
13
r--- t.n
N
Problem:
Multiplication 3 x 5 = 15
Keyboard Entry
3
~
Display
3.
05
...
Problem:
Division 36 -;. 4 = 9
Display
36.
36
84
5.
o
Keyboard Entry
4.
o
15.
9.
Mixed Calculations
The following example shows how the calculator is used to solve complex
mathematical problems with a minimum of key depressions. The examples also
illustrate how the arithmetic function keys execute preceding operations and
cause intermediate results to be displayed.
_.. --_.
Problem: (4
+ 61
8- 7
8
Keyboard Entry
4
86
0
~
<I1
8
G
7
8
8
0
= 9.125
Display
4.
6.
10.
8.
80.
7.
73.
8.
9.125
Comments
(4 + 6) executed
(4 + 6)8 executed
(4 + 618 - 7 executed
Final result
If you want to use an answer in further calculations, there is no need to re·enter
the number. Just depress the desired arithmetic function key for the next oper·
ation and enter another number.
-
(j)
Problem:
Answer Re-entry: 17.4 + 3.7 ~ 21.1
21.1 + 32.4 ~ 53.5
Keyboard Entry
17.4
[±] 3.7
0
[±]
32.4
0
Display
17.4
3.7
21.1
21.1
Comments
Not necessary to
re·enter 21.1
32.4
53.5
REPEAT OPERATIONS
The repeat operation capability of your Rockwell 61 R is a time-saving feature
that enables you to add, subtract, multiply or divide a series of identical numbers
without re·entering the numbers each time.
Problem: ((((6 x 61 - 6) -;- 6),. 6)
:::j
~
11
Keyboard Entry
Display
6
6
6.
IZI
B
EJ
[±]
o
36.
30.
5.
11 .
Comments
Not necessary to
re-enter 6
~
00
CONSTANT OPERATIONS
The automatic constant is another time·saving feature of your Rockwell 61 R.
This feature enables you to add, subtract, multiply, or divide by the same num·
ber repeatedly without re·entering the number for each new calculation. The
number entered after the last arithmetic function key depressed is always saved
as the constant laddend, subtrahend, multiplier or divisor). The constant function
is the last function key depressed before depressing the 0 key. To perform mul·
tiple operations with this constant, si.r!Ply enter a new augend, minuend, Inulti·
plicand or dividend, and depress the l=J key for an answer.
Problem:
Constant Addend: 6 + 3 = 9 8+3='1
Display
Keyboard Entry
6.
6+3= 9
6
3.
III 3
~
'"
8+3=1'
13
9.
8
8.
13
11.
Problem:
Constant Subtrahend:
9- 5=4
Keyboard Entry
9-5=4
9
EJ5
"o
§]
11 -5=6
11
§]
Problem:
Constant Multiplier: 12 x 4 = 48
Keyboard Entry
12x4=48
1
"
~
3x4=12
11-5=6
Display
9.
5.
4.
11 .
6.
3 x 4 = 12
Display
§]
12.
4.
48.
3
§]
12.
12
04
3.
Problem:
Constant Divisor:
10.;. 5 ~ 2
Keyboard Entry
10';'5~2
12';'5~2.4
Display
10
10.
5.
85
§]
'"'"
12 .;. 5
~
2.4
2.
12.
2.4
12
§]
Mixed Operations with Constants
Problem: (5 + 3? - 2 ~ 11
Keyboard Entry
'"w
Display
5.
5
[£)3
3.
EJ
24.
o
8.
2
2.
§]
22.
11 .
8
Comments
Undetermined
Constant = 3
Constant ~ 3
Constant ~ 3
Constant ~ 2
Constant ~ 2
Constant ~ 2
CLEAR OPERATIONS
1. One depression of the [£] key when there is no overflow condition clears the
displayed number but does not affect the stored constants or the operation:
Problem:
Entry Correction: 12 + 5.5 = 17.5
Keyboard Entry
Display
12
12.
5.6
5.6
[g
o.
5.5
5.5
m
iii
""
a
§
Comments
Error; wrong number
Cleared
17.5
2. A double depression of the © key clears any operation in progress and ciears
the calculator except the memory.
Problem:
Clear Calculator (Except Memory)
Keyboard Entry
Display
2
m
""
tn
Comments
2.
2.
[g'
O.
Entry cleared
[g
O.
Calculator cleared
3. Depressing the © key during an overflow (see Overflow Conditions) cancels
the overflow condition. The number in the display is correct if multiplied by
108 and may be used in further calculations. Chain and constant operations
are not affected by overflowing.
Problem:
Clear Error (Overflow): 12345678 x 9 = 111111102
Keyboard Entry
Display
12345678
09
EJ
12345678.
9.
_ 1.1111110
[£)
1.1111110
N
O"l
Comments
Overflow Indicator lights;
calculator accepts only
clear entry key
Answer must be multi·
plied by 10 8 (see page 281
4. Depressing the (CF) key after pressing the [fJ key clears the secondary function
operation and restores the previous conditions (see page 60).
5. Depressing the [£), [E] and (X .) M) keys clears the memory (see page 33).
OVERFLOW CONDITIONS
The following operations result in an overflow condition which causes the Overflow I ndicator._, to light and all keys except [£) to become inoperative:
...,
N
1. Any answer or subtotal exceeding 8 digits to the left of the decimal point,
re9ardless of its arithmetic sign (absolute value greater than 99,999l99.),
The 8 most significant digits are displayed as follows:I_XXXXX.X X [.
Calculations can be continued, if desired (see Wrap·Around Decimal).
2. Memory accumulation exceeding 8 whole digits to the left of the decimal
point, regardless of the arithmetic sign. The number used in the last memory
operation remains in the display: IXXX. [, Calculations can be
continued, if desired (see Wrap·Around Decimall.
3. Division by zero. A 0 is displayed:! []
4, Exceeding capacity or range of scientific functions (see pages 92 through 961.
WRAP-AROUND DECIMAL
The wrap·around decimal feature of your calculator lets you proceed when the
answer obtained in the display or memory exceeds the capacity of the calculator
(10 8 or greater), except when the overflow condition is the result of computing
a scientific function. The calculator automatically retains the 8 most significant
digits, places the decimal point 8 positions to the left of its true position, and
~ lights the Overflow Indicator. You may proceed with the problem solution after
depressing the [Q] key once to clear the overflow condition, but you must multiply the final problem answer by 108 (100,000,000) or move the decimal
point 8 places to the right. Any numbers subsequently added or subtr8cted must
be divided by 10 8 before entering. If two overfiows occur in the S8me problem,
the final answer must be multiplied by 10 8 X 10 8; 10 16 and so on. This same
feature applies to the numbers in memory.
Problem:
'"CD
98,000.000 x 2.000
0.04
_ 20 000,000
'
Keyboard Entry
Display
98000000
02000
[±]
[Q]
98000000.
2000.
• 1960.0000
1960.0000
.04
.2
0.04
49000.
0.2
§J
48999.8
EJ
=
4,899,980,000,000
Comments
Overflow Indicator lights
Displayed number times
10 8 equals true number
Number entered
(20000000';' 108 ) ; .2
This answer times 108
equals true answer
COMPUTATIONS WITH VERY LARGE OR VERY SMALL NUMBERS
Computations which may exceed the a·digit capacity of the calculator can be
scaled, entered as if they were expressed in scientific notation, and the appro·
priate power of 10 determined as a second step,
Problem: 2 x 10- 6 X 5 X 10- 5 = 10 X 10- 11
~
Keyboard Entry
Display
2
2.
05
5.
EJ
10.
Comments
Times 10- 6
Times 10- 5
Times 10- 11
CHANGE SIGN OPERATION
Depressing the Gl=1 key changes the sign of the nllmber in the display. The Rock·
well 61 R Advanced Slide Rule allows sign change at any point in a calculation,
2
4 (-31
Problem:
=-a
6
Keyboard Entry
4
w
~
o
o
3
m;:J
G:J
6
EJ
Comments
Display
4,
4.
16,
3.
3,
48,
6,
8.
Negative Number
Ind icator Iigh ts
REGISTER EXCHANGE OPERATION
Another useful feature of your Rockwell 61 R Advanced Slide Rule calculator is
the register exchange capability. Depressing the B key exchanges the data (number! in the display with the number in the working register (the previously dis·
played number or the constant).
w
'"
3 ~56
Problem:
~
1.6666666
Keyboard Entry
Display
3
3.
3.
m
6
6.
15
9.
15.
9.
8
B
El
1.6666666
Working Register Constant
Undetermined
3
3
6
9
15
9
KEY SECONDARY FUNCTIONS
Depressing the [f] key conditions the 61 R Advanced Slide Rule to perform the
second function of the next key depressed. The secondary function is cancelled
after execution of all second function operations except (ARC) (see page461 or
(DR) (see page61). Operation and uses of the keys in performing their second
function are described in subsequent paragraphs.
w
w
NOTES: The display is blank during many operations using the scientific function
keys. No keyboard entries should be attempted before the display turns
on again.
Range of accuracy of the Rockwell61R calculator is given on pages 92
through 94.
MEMORY OPERATION
Your Rockwell 61 R Advanced Slide Rule calculator has a completely independent memory which is unaffected by arithmetic or scientific operations. Through
the use of this memory, you can perform chain operations involving complex
mathematical problems with a minimum of key depressions. All of the memory
operation keys are activated by depressing the [£] key. The functions of the
memory operation keys are as follows:
Key
~
Function
(M+I
(M-)
(X <- MI
(X .... MI
Add to memory.
Subtract from memory.
Display number in memory.
Store displayed number in memory. Any number previously in
memory is destroyed.
(X - M) Exchange number being displayed with number in memory.
(M + X2) Add square of contents of displayed number in memory; display
is not altered.
The following example illustrates use of the memory operation keys and the
memory clearing procedure.
Keyboard Entry
Display
Memory
~
O.
[£] (X -> M)
O.
o
4
[£] (M+ J
4.
4.
4.
[£) (M + X2)
4.
20.
w
'"
o
Comments
Memory cleared: displayed number copied
into memory; display
not altered.
Displayed number added
to memory; display not
altered.
Square of displayed
number added to memo
ory; display not altered.
Keyboard Entry
Display
Memory
1Kl
4.
20.
3
(M-I
3.
3.
20.
17.
[±]
12.
17.
1Il (X+-M)
17.
17.
EJ
29.
17.
1Il
w
OJ
Comments
Multiply operation
established
Displayed number sub·
tracted from memory;
display not altered
3 x 4 executed and addi·
tion operation established
Contents of memory reo
called to display; original
number moved to work·
ing register
12 + 17 executed
•
[I] (X ++M)
17.
29.
Contents of memory
exchanged with dis·
played number
CONSTANT" KEY
The value of" may be entered into the display at any time by depressing the
...,w lIland (,,) keys. The display will be 3.1415926.
Problem: Area of Circle: Find area (A) of a circle 6 feet in diameter (D)
Formula: A = 11
~2
Keyboard Entry
~
A = 28.274332
Display
Comments
6
6.
[I]~
6.
36.
3.1415926
113.09733
o
o
Diameter
02
rr 02
4.
4
El
28.274332
Area
Problem: Degrees to Radians: Convert 200 degrees (d) to radians Ir)
Formula: r =
1:a
Keyboard Entry
200
w
CD
00 (~
180
§]
r = 3.4906584 RAD
Display
Comments
200.
3.1415926
628.31852
180.
3.4906584
Degrees (dl
Radians (r)
Problem: Radians to Degrees: Convert 10 radians Ir) to degrees Id)
Formula: d
...
a
= 180
r
11
d
= 572.9578'
Keyboard Entry
Display
Comments
10
0180
10.
180.
1800.
3.1415926
572.9578
Radians (r)
B
[£]~
Degrees Id)
TRIGONOMETRIC FUNCTIONS (SIN), (COS), (TAN)
Depressing the [£] key and then the ISIN), ICOS) or (TANI key causes the calculator to compute and display the trigonometric function for the value of the
angle that was displayed.
...
~
DEG/RAD SWITCH: The position of the DEG/RAD switch selects whether the
trigonometric functions are to be computed with angles expressed in degrees or
radians .
Problem: sin 30' = 0.5
Keyboard Entry
Display
30
30.
[£] lSI N)
0.5
Comments
DEG/RAD switch in
DEG position
'l·
,\
,
Problem: cos 300· = 0.5
Display
Keyboard Entry
i!3
300
300.
[£] (COSI
0.5
2
2.
[£] (TAN)
2.185042
Koyboard Entry
..
DEG/RAD switch in
DEG position
Problem: tan 2 radians = -2.185042
Problem: sin ;
w
Comments
radians = 0.5
Display
[£] (11)
3.1415926
86
§
6.
0.5235987
0.5
I:II (SIN)
DEG/RAD switch in
RAD position
Negative Number
Indicator lights
Comments
DEG/RAD switch in
RAD position
Problem: (2 x 3) + 3 (tan 15°) ~ 6,803848
Keyboard Entry
Display
2
2,
03
""
ElIIJ(X .... M)
3.
6.
""
15
[£](TAN)
0.267949
Comments
DEG/RAD switch in
DEG position
15.
03
III
3.
0.803847
•
Keyboard Entry
[£] (X +- M)
EI
•
Display
Comments
6.
6.803847
Some chain operations using scientific and arithmetic functions can be accom·
plished without the use of memory by rearranging the problem.
Problem: (2 x 3) + 3 (tan 15°) ~ (2 + tan 15°) 3 ~ 6.803848
""
(J'l
15
[£] (TAN)
1lJ2
III
3
13
15,
0,267949
2.
2.267949
3,
6.803847
DEG/RAD switch in
DEG position
INVERSE TRIGOI\IOMETRIC FUNCTIONS (ARC) (SIN), (ARC) (COS),
(ARC) (TAN)
+>
Ol
Depressing the [£]and (ARC) keys and then the (SIN), (COS) or ITAN) key
causes the number in the display to be interpreted as the value of a trigono·
metric function and the inverse trigonometric function (the angle) to be cal·
culated and displayed.
Problem: sin -, 10.5)
~
30°
Keyboard Entry
I£J (ARC)
Display
.5
0.5
(SI N)
30.
DEG/RAD switch in
DEG position
..
.
•
Problem: cos -, (0.5) ~ 60°
Display
Keyboard Entry
0.5
.5
[£] IARC) ICOS)
Comments
Comments
DEG/RAD switch in
DEG position
59.99999
Problem: tan -, 111 ~ 45°
~
1
1,
[£] (ARC) (TAN)
44.99999
(Continued on page 50)
DEG/RAD switch in
DEG positon
Model lOR
8-digit Electronic Calculator*
Basic Answer features: 8 digits • 4
function (+ - x';-) • Algebraic logic
• Floating decimal • Repeat function
Model20R
Electronic Calculator with Memory
and Percent*
• All Basic Answer features PLUS
• Fully addressable memory • Automatic constants • % key • Automatic
fully addressable memories. 2-place or
floating decimal· Automatic constants
• Fraction calculations. 224 fixed conversions plus programmable conversion
• AC charger and case
~Model61R
Advanced Slide Rule
j Electronic Calculator
• All Basic Answer features PLUS
• Fully addressable memory. Automatic constants. Register exchange
• Sign change. Reciprocals. Sum of
squares. Square roots. Log functions
mark-on and discount
Model30R
Slide Rule Memory
Electronic Calculator*
• All Basic Answer features PLUS
• Fully addressable memory. Automatic constants· % key. Automatic
• Trig functions in degrees or radians
• Powers· AC charger and case
Model80R
lO-digit Printer
Electronic Calculator
• 4 functions • Commercial logic
mark-on and discount • Register
exchange • Sign change • Reciprocals
• Squares • Square roots
Model51R
Universal Converter
Electronic Calculator
• 10 digits plus 2 columns of symbols
• Thermal printer • Floating decimal
or dollar decimal with override • Auto~
matic constant and repeat • Subtotals,
\ group totals and grand totals
• All Basic Answer features PLUS
*Moael 01 R Accessory Kit (AC Adapter
and Carrying Case) Available at Extra Cost.
Problem: ;
+ tan -, (1) = 2.3561945 radians
Keyboard Entry
Display
1
gJ
[I] (ARC) (TAN)
[IJIX-+M}
I£] (rr)
02
[±]
[I] (X<- M)
EJ
Comments
1.
0.785398
0.785398
3.1415926
DEG/RAD switch in
RAD position
2.
1.5707963
0.785398
2.3561943
Radians
SQUARE ROOT (-IX)
Depressing the [I] and (-IX) keys causes the square root of the number being
displayed to be computed and displayed.
ProQlem: .J:]8f = 3
Keyboard Entry
81
[I](~I
WI.,[X}
Display
81.
9.
3.
The.,[X function can also be used in chain operations,
~
Problem:
V4 + V9
4
W I-./X}
[±] 9
WI";><I
EJ
= 5
4.
2.
9:
3,
5,
RECIPROCALS (l/x)
Depressing the 1£J and (l/x) keys causes the reciprocal of the number being
displayed to be computed and displayed.
Problem:
'"
IV
io
= 0.05
Keyboard Entry
Display
20
1£J(1/x)
20.
0.05
The l/x function can also be used in chain operations.
Probl,em:
iJ + -fcJ
Keyboard Entry
'"
w
20
m(l/x)
[±] 10
m(1/x)
G
= 0.15
Display
20.
0.05
10.
0.1
0.15
COMMON LOGARITHMS FUNCTION Ilog X)
Depressing the [£] and (log Xl keys causes the common logarithm of the displayed
number to be computed and displayed.
Problem: log,o 100 ~ 2
(J1
~
Keyboard Entry
Display
100
[£] (log XI
100.
2.
NATURAL LOGARITHMS FUNCTION lin X)
Depressing the [£] and lin X) keys causes the natural logarithm of the displayed
number to be computed and displayed.
Problem: In 132 3 ) ~ 3 In 32 ~ 10.397211
Keyboard Entry
32
[£] (In XI
03
EI
31
Display
32.
3.465737
3.
10.397211
ANTI LOGARITHMS FUNCTIONS lexl, (10 X )
Depressing the [£] and lex) or [£] 'and (1 OX) keys as desired causes the antilogarithms of the displayed number for the bases e (e ~ 2.718281) or 10 to be computed and displayed.
Problem: 10 2 ~ 100
Keyboard Entry
Display
Comments
2.
2
X
1IJ(10 I
100.
Problem: e- 3 = 0.049787
~
3
3.
1m
3,
[E) (eX)
0.049787
Negative Number
I ndicator lights
EXPONENTIAL FUNCTION (XY)
The exponential function raises X (first number entered) to the power y (second
number entered I for any real vaiues of y. Depressing the [E) and (XY) keys causes
the displayed number to be taken as the value of X and the natural log of X to be
com£!!ted and displayed. The function is completed by entering y and pressing
the L::J key,
Problem: 33
<11
-..J
~
27
Keyboard Entry
Display
3
Y
[l] (X )
3
3.
1.098613
3.
27.00005
EI
Comments
In 3
The (X Y) key may be chained with the (l/x), (11) or (v'X) key.
Problem: 5y'32 = 32 1 / 5 = 2
Keyboard Entry
Display
32
mil/xl
32.
3.465737
5.
0,2
§]
2.
m(X
y
)
5
g]
sin
Y
38
to
In 32
(x) can be computed easily.
Problem: sin 1/3 (38°) = 0,850708
Keyboard Entry
Display
(]1
Comments
[£] (51 N)
[£](X Y )
3
[£](l/X)
§]
38.
-
0.615661
0.485058
3.
0.3333333
0,850709
Comments
DEG/RAD switch in
DEG position
Negative Number
Indicator lights
RECOVERY TECHNIQUES
Occasionally you may unintentionally depress one of the function keys. The
following techniques allow easy correction without loss of the displayed
number.
~
Unintentional 0 or W: Depress 1, then G. If constant multiplication or division
is being performed, the constant is replaced by 1.
Unintentional [±] or B: Depress 0, then G. If constant addition of subtraction
is being performed, the constant is replaced by 0.
Clear Function (CF)
Depressing the (CF) key immediately after an unintentional [£J key clears the
calculator of secondary function operation,
Problem: 4 x 3 = 12
Keyboard Entry
(J)
~
Display
4
03
4,
3,
[£J
3,
(CF)
3.
13
12.
Comments
Error!! Did not want
to press [£J
Data Recovery (DR)
Depressing the III and (DR) keys immediately after a digit entry recalls the last
number displ2Yed. The selected function remains set. If only one digit has been
entered, the l.EJ (DR) key sequence recalls the previous result to the display, If
more than one digit has been entered, the III (DR) key sequence eliminates the
last digit, If more digits are to be entered or primary functions are to be executed,
the (CF) key must be depressed to clear the function.
Keyboard Entry
O'l
'"
Display
45
45.
(SIN)
451.
ill (DR)
(SINI
45.
0.707107
12346
IIJ(DR)
(CF)
5
12346.
1234.
1234.
12345.
Comments
DEG/RAD switch in
D EG position
Error!! Forgot to press
IIJ
Error!! Did not want 6
SAMPLE PROBLEMS
Your Rockwell 61 R Advanced Slide Rule calculator is a versatile problem solving
tool. Several practical examples were chosen from different fields of interest to
familiarize you with your calculator. We recommended that you gain familiarity
with your Rockwell61R by working the sample problems.
O'l
W
MATHEMATICS
Many problems can be arranged so that two parallel calculations are performed
with one entry of data: one in the display, the other in memory. Some examples
of this procedure are shown on following pages.
Problem:
Statistics:
Find the mean (M), variance (V), standard deviation (SD), and standard error
(SE) of the mean olthe following values of X (10, 11, -3, 14, 181 I Note: n = 51
'ii,
a.
Formulas:
i
LX 2
LX,
n
M~
b. V ~
M ~ 10.
\
I
c. SO
~
SD
Keyboard Entry
~
LX I
(LX )2
I
-
11
n
7.9056941
Display
d. SE
~ ~
SE ~ 3.535534
Memory
Comments
o.
o
10m(M+X 2 )
10.
100.
Display and memory
cleared
X~ added to memory
10.
11.
21.
3.
100.
221.
221.
221.
ill
3.
18.
230.
230.
X~ added to memory
Xl + X displayed
2
Negative Number
Indicator lights
X~ added to memory
Xl + X + X 3 displayed
14 [£] 1M + X2 1
14.
426.
X~ added to memory
ill
32.
426.
18[£](M+X 2 )
18.
750.
X+X+X+X
I
2
3
4
displayed
X~, added to memory
2
)
31m
[fJ (M + X2 1
'"
--'
n
n- 1
[£]m IX-+ M)
m
11 [fJ (M + X
m
(LX.)2
V ~ 62.5
2
~
,-
-
(J1
(Continued on page 66)
2
Keyboard Entry
Display
Memory
13
50,
5,
10,
5,
50,
750,
750.
750,
750.
750.
13
500,
750,
III
5
W
EJ
tI
'"
'"
[I) (M-I
500.
250,
[I) (X .... MI
250,
250,
III 4
o
[I)(..fl(1
III 5
[I){v'X1
o
'"....,
4.
62,5
7.9056941
5.
2.2360679
3.535534
250.
250.
250.
250.
250.
250.
Comments
:EXi displayed
n
Mean (M) displayed
M. n = :EX., displayed
(:EX,I
M2 • n = - - n
displayed
,
(:EX 12
:EX n
subtracted from
memory
,
2
(n - 1)
Variance (VI
Standard deviation (SDI
n
..;n
Standard error (SEI
of the mean
B
Problem:
:;11
Given right triangle ABC with sides
3 and 4, find the hypotenuse c.
i
Ol
co
c
3
4
A
Formula:
C=----Cc='
c'= ;/3 2 + 42
c= 5
Keyboard Entry
Memory
Display
[£]
[£]{X--+ M)
3 I£J 1M + X2)
41£] 1M + X 2 1
O.
O.
o
3.
4.
9.
25.
I£J(X+-M)
25.
25.
I£J (y'X)
5.
25.
Comments
Memory cleared
3 2 added to memory
4 2 added to memory
Sum of squares recalled
from memory
Hypotenuse (c)
Problem:
Converting From Rectangular to Polar Coordinates:
Convert the point' (24,701 into polar coordinates.
Ol
<0
C
Formulas:
Magnitude of
Vector
V = y"'X"2'+"-y2"
angle
tan
(J=
-1
~~
)
Where x = 24 and
y = 70
(J = 71.07536"
V= 74.
Keyboard Entry
G
-...I
a
Display
Memory
C [I] (X---> M)
O.
0
70 [I] (M + X2)
24 [I] (M + X~
IIJ (X <- M)
70.
24.
2.9166666
71.07536
5476.
4900.
5476.
5476.
5476.
5476.
II] (v'X)
74.
5476.
II] (ARC) (TAN)
Comments
Display and memory
cleared
y2 added to memory
X2 added to memory
Y/X
Angle a (degrees)
y2 + X2recalled from
memory
Magnitude of
vector (V)
Problem:
Law of Sines:
A
b
Given the above triangle. find angle B.
-...I
~
Formula:
!!.-
sin A
~
b
c
sillB
sin C
or
sin B
=
b sin A
a
Where
A ~ 30"
a
~
b
~ 105
B ~ sin
75
(bSinA
-1
B ~ 44.42701°
a
~
Keyboard Entry
Display
30
I
30.
[EJdJS1N )
X 105
;\
I
75
N
DEG/RAD switch in
DEG position
sin A
Length of side b
b sin A
Length of side a
sin B
Angle B in degrees
0.5
105.
52.5
75.
0.7
44.42701
G
"
Comments
B
[EJ (ARC) (SIN)
B
Problem:
Law of Cosines:
c=5
a=3
Given three sides of the above
triangle, find angle A.
C
A
b=4
Formula:
"w
a2 = c2 + b 2 - 2cb cosA
2
2~~ -
A = cos -1(C +
Keyboard Entry
Display
Memory
[£][EJ(X-> M)
O.
0
3[R]
3.
(Continued on Page 74)
2
a
A = 36.8699°
)
Comments
Display and memory
cleared
a
Keyboard Entry
Display
Gill (M-)
9,
- 9,
4
4,
4,
5,
5,
20,
2,
40,
32,
- 9,
7,
7,
32,
32,
32,
32,
32,
40,
0,8
36,8699
32,
32,
32,
[I] (M + X2)
[K)5
ill(M
...,
+ X2)
[K)
2
.l>
G
illIX<-M)
EJ
o::J
G
(ARC) (COS)
Problem:
Hyperbolic Functions:
Formula:
sinh a =
Keyboard Entry
...,
(J1
2,1
ill (eX)
EJ
ill 11/Gj
ill
G
ea
Memory
Comments
a 2 subtracted from
memory
b
b 2 added to memory
c
c 2 added to memory
cb
2 cb
c 2 + b 2 - a 2 recalled
from memory
2 cb
cos A
Angle A (degrees I
sinh 2,1 = 4,021856
_
e- a
2
Display
2,1
8,166168
8,166168
0,1224564
8,0437116
2,
4,0218558
Comments
a
ea
e- a
ea _ e-a
sinh a
Problem:
Hyperbolic Functions:
Formula:
I
a ,.
"
1.3
m(eX)
m
m(l/x)
ill
2
B
Problem:
Hyperbolic Functions:
""
= 1.970914
cosh a =e . 2e
Keyboard Entry
CJ)
cosh 1.3
-a
Display
1.3
3.669295
3.669295
0.2725319
3.9418269
2.
1.9709134
= 0.655794
a
e" - eFormula: tanh a =
e" + e- a
Memory
Display
Kp.yboard Entry
3.1415926
I£J (11)
4.
84
0.7853981
B
[f] (eX)
2.193279
2.193279
2.193279
l.E.]( X -> M)
2.193279
2,193279
B
2.193279
0.4559383
I£J (l/x)
2.6492173
0.4559383
{M+I
(Continued on page 78)
m
Comments
a
e·
e-·
e" + e- a
cosh a
tanh:
Comments
a
e·
e-·
Keyboard Entry
G
iIJIX+-MI
EJ
"
ex>
Display
Memory
1.7373407
2.6492173
0.6557939
2.6492173
2.6492173
2.6492173
Problem:
Inverse Hyperbolic Functions:
Formula:
sinh- 1 1.3356469=1.1
sinh- 1 a= In la + V a2 + 1
Keyboard Entry
m
IlJ IX ,- M)
IlJ h.!X~
IlJ lin XI
1.
1.
2.7839526
2.7839526
2.7839526
2.7839526
2.7839526
2.7839526
2.7839526
1.668518
3.0041649
1.1
Problem:
Inverse Hyperbolic Functions:
Formula:
Comments
Memory
Display
11.
IlJ IX-+MI
1.
1.3356469
1.3356469
[£] 1M + X2)
1.3356469
1.3356469
"<0
Comments
ea _ e- a
e a + a-a
tanh a
a
a2 + 1
~.-:.1_
a + va 2 + 1·
sinh- 1 a
cosh- 1 1.3374385 = 0,8
cosh- 1 a = In (a + va 2 -1
I£J IlJ IX"" M)
mllJ 1M-I
1.3374385
O.
1.
1.3374385
(Continued on page 80)
o
- 1.
- 1.
a
Keyboard Entry
Display
W(M + X~
1.3374385
1.3374385
0.7887417
0.8881113
2.2255498
0.800003
[fJ(X+-M)
[fJ (yx)
G
00
a
[fJ (In Xl
Problem:
Inverse Hyperbolic Functions:
Formula: tanh- 1 a = % In l'
00
-->
Keyboard Entry
19WIX-M)
1
[fJ (X --> M)
W
.7615942
[fJ (M-)
W
[fJ (X +- M)
G
[fJ (In Xl
W2
EJ
Memory
0.7887417
0.7887417
0.7887417
0.7887417
0.7887417
0.7887417
Comments
a2 - 1
ya 2 - 1
a+..(a2-1
cosh- 1 a
tanh- 1 0.7615942 = 1.
+ :
1.
1.
1.
0.7615942
0.7615942
1.7615942
0.2384058
7.3890576
2.
Memory
0
0
1.
1.
1.
0.2384058
0.2384058
0.2384058
0.2384058
0.2384058
2.
1.
0.2384058
0.2384058
Display
O.
Comments
a
1+a
1- a
(1+a)/(1-a)
In 1 + a
1- a
tanh-
1
a
ENGINEERING
Problem:
Parallel Resistors:
Three resistors of 5 ohms, 20 ohms and 10 ohms are can·
nected in parallel. What is the equivalent resistance?
Formula: Re
1
Re = 2.8571428 ohms
q
1
1
1
q
-+--+-R!
R2
Ra
00
'"
Keyboard Entry
5
o (1 Ix)
m
20
o (1 Ix)
m
10
o (l/x)
G
o (l/x)
0 isplay
5.
0.2
0.2
Comments
R,
l/R,
20.
0.05
R2
0.25
10.
l/R, + l/R 2
0.1
0.35
2.8571428
1/R 2
R3
1/R 3
l/R, + l/R 2 + 1/R 3
Equivalent Resistance
(Reo I
00
w
Problem:
RC Network:
A step voltage (V,) of 25 volts is applied across series RC network with
R = 50,000 ohms and C = 0.1 microfarads. What is the voltage (V I across the
capacitor after 15 milliseconds?
C
Vc = VI (1 _ e-t/RCI
Formula:
Keyboard Entry
Comments
0.015
1II.0000001
0.0000001
G
50000
150000.
50000.
ttQ
3.
EI
3.
I£JkX )
0.049787
El1
t (15
+ 1000) =
0.015 seconds
C(0.1+10 6 1=
0.0000001 farads
tiC
R
tlRC
- tlRC
a-t/R C
1.
El
0.049787
0.950213
25.
23.755325
o25
EI
U1
=23.755325 volts
Display
.015
~
'"
Vc
(1 _ e- t/RC )
VI
Voltage across
capacitor (V cl
Problem:
Simply Supported Beam:
A beam simply supported at the ends carries a uniformly distributed load (wi of
10 pounds per inch across its full length. Find the maximum deflection (Y cl.
~
Formula:
Y =
c
~n":: ~4.
E = .3
X
lOB psi
1=1.2in'·
I = 200 in.
Keyboard Entry
200
co
m
0
0
0
0
©
[[]
0
10
G
384
G
.3
G
1.2
co
....,
o
•
Display
Comments
200.
200.
40000.
8000000.
16.000000
Length (I)
I
16.000000
5.
80.
10.
800.
384
2.0833333
0.3
6.9444443
1.2
5.7870369
2
13
1
4
1 ;
overflow; answer to
be times 108
14 -; 10 8
5 X 14 -;. 10 8
Load (w)
5 x (w) 14 -;. 108
(5 (wi 14 -;. 108 ) 384
Entry scaled by 108
(5 (w) 14 ) -;. 1384 E)
Moment of inertia (I)
Deflection (Ye) in inches
Problem:
Shaft Stress:
A shaft 3 inches in diameter (d) has a 1000 inch-pounds bending moment
and a 2000 inch-pounds torque (T). What is the maximum stress?
IMI
16
Formula:
(J max
Keyboard Entry
E9[£J(X->M)
1000
[£JIM + X 2 1
(Xl
(Xl
[±]
2000
[£J(M+X2)
[£J~X<-M)
[£] (v'X)
IE]
16
Display
rJ max = 610.41323 psi
Memory
o
o
0,
1000,
1000,
1000,
2000.
2000.
1000000.
1000000.
1000000.
5000000.
5000000.
2236.0679
3236.0679
16.
5000000.
5000000.
5000000.
5000000.
5000000.
5000000.
5000000.
3
3.
5000000.
G
ill
5493.7193
5000000.
1831.2397
5000000.
0
610.41323
5000000.
[I] (lTl
G
<0
1M + VT2 + M2
51777.086
3.1415926
16481.158
G
(Xl
:: rrd3
Comments
Memory cleared
Bending moment (M)
M2 added to memory
Torque (T)
T2 added to
memory
T2+ M2
+ M2
M + y'':T::=2'''+-M=2
02
161M + 0 2-+ M2 )
16
ViM
+ y'T2+
T2 + M2 )
Diameter Idl
1E.. 1M + VT2 + M2 )
(lTd)
~ (M + .Jf2+ M2 )
(lTd 1
Maximum stress in
shaft ( rJ ma)
~
o
Problem:
Sound Pressure:
What is the sound pressure (PI of a jet airplane taking off that was measured to
have sound pressure level of 133 decibels (db), where reference pressure (Pol is
2 x 10- 4 fl bar?
Formula: P ~ anti-log
(~g + log Po)
P ~ 893.367 fl bars
'0
Keyboard Entry
.0002
Display
0.0002
IIJ (log XI
3.69897
[£] (X"'" MI
133
3.69897
133.
820
20.
6.65
3.69897
EI
2.95103
- 3.69897
ill (1 OX)
893.367
- 3.69897
[£] (X +- MI
~
- 3.69897
- 3.69897
- 3.69897
- 3.69897
- 3.69897
[±]
~
Memory
-
Comments
Reference pressure
( J.l bar)
log Po; Negative Number
Indicator lights
db
db
20
Negative Number
Indicator lights
db
(20 + log Po)
Sound pressure
( fl bar)
RANGE OF ACCURACY
Your Rockwell 61 R Advanced Slide
Rule is capable of performing the
following scientific functions with
great accuracy. All calculations take
less than three seconds; in general,
functions rarely take more than 1.5
seconds. The six leftmost digits
displayed will be correct to within
±1 in the sixth digit displayed. including any suppressed zeros necessary to achieve six digits (except for
the few instances noted in the following paragraphs).
TRIGONOMETRIC FUNCTIONS
Sin X, Cos X, and Tan X may be calculated with X in degrees or radians
according to the position of the
DEG/RAD switch. The result will
have the correct algebraic sign. The
range of magnitude for sin and cos
functions is -360° LX L+360°
(211" radians). For values of X outside
of this range, the accuracy may be
less than six digits and the computation time greater than 3 seconds.
Tan X accuracy may be less than six
digits for 89.5° L lIXI-1800n)
L 90.5° (corresponding radians)
where n = 0, 1, 2, 3, _.. If X is
92
large enough to cause an overflow in
an intermediate result, the overflow
condition occurs and computation
is terminated.
INVERSE TRIGONOMETRIC
FUNCTIONS
For Arc Sin X and Arc Cos X. the
result is displayed in degrees or
radians (according to the position of
the DEG/RAD switch) with the
correct algebraic sign and the following principal angles: _90° (-11"/2
radians) L arc sin X L 90° (11"/2
radians). 0° (0 radians) L arc cos X
L 180° (11" radians).
The acceptable range of magnitude of X is IXI L 1. For values of
IXI> 1, the calculator will overflow.
Arc Tan X: The result will be displayed in degrees or radians (according to the position of the DEG/
RAD switch) with the correct
algebraic sign and with the following
principal angles: _90° (-11"/2 radians)
Larc tan X L90° (11"/2 radians). The
acceptable range of magnitude of X
is 0.0000001 L Ixi L99999999 and
X~O.
93
LOGARITHMETIC FUNCTIONS
NOTES
lin X and log Xl
Both natural and common logarithms may be calculated. The
acceptable range of the argument is
0.0000001 L X L99999999_ For
values of X La, the calculator will
overflow_
ANTILOGARITHMETIC FUNCTIONS
(eX and 10 X)
The range of the argument for ex is
0.000001 LX Lin 99999999
(approximately); the range of the
argument for 10' is -6 LX < 8_
It the value of X is outside of these
ranges, the calculator will overflow
or underf low.
SQUARE ROOT FUNCTION (y'Xl
The range of the argument is a L
X L99999999. If X is negative,
the calculator will overflow.
EXPONENTIAL FUNCTION (xY )
The range of X is 0.0000001 LX
£.99999999; the range of y is
In 0.000001 L
L In 99999999 _
In X
-y -
In X
The calculation is in two parts
according to the formula
XY = ey1n x.
94
95
Consumer
Warranty
Rockwell International
Corporation
Electronic Calculator
This electronic calculator from ROCKWELL
is warranted to be free from defects in
materials and workmanship under normal
use and service for one year from the date
of retail purchase. Rockwell will, free of
charge, repair or replace (at its option) any
part(s) which are found to have become
defective through normal use, provided
that the calculator and charger are returned
prepaid within one year to one of the
Rockwell Customer Service Centers.
(The original packaging is ideal for
this purpose.)
To assure proper handling.and servicing of your calculator under the one-year
warranty, you must send with your calculator a copy of the sales receipt (or
other proof of purchase date). Calculators
returned without proof of purchase date
will be serviced out-of-warranty at our
prevailing service rates.
96
This Warranty does not extend to any
article which has been subject to misuse,
neglect or accident, or if the Serial Number
has been altered or defaced, or if the calculator has been serviced by anyone other
than a Rockwell Consumer Service Center.
This Warranty contains the entire obligation of Rockwell and no other warranties
express or implied or statutory are given.
In no event shall Rockwell be liable for
consequential damages.
For service under this Warranty, send
your Rockwell electronic calculator prepaid, with copy of sales receipt or other
proof of purchase date, to your nearest
Rockwell Consumer Service Center.
Out-af-Warranty Service
If the calculator fails to operate satisfactorily beyond the one'year warranty
period, Rockwell International Service
Centers will repair and return the calculator to you for a nominal sum.
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