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SCIENTIFIC  INSTRUMENTS  CO.
» ELECTRO  HYPER - VECTOR  LOG-LOG «
( 10" / 25 cm Scales )


SCIENTIFIC INSTRUMENTS CO., Berkeley, California / USA             (1961)
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Made in Japan  by  RELAY (= Model 158 )                        SN = 40007

S C A L E S  of  the  » E L E C T R O  HYPER-VECTOR LOG-LOG «  Model 1580
=========================================================================
Front Side                [ inverse / RED ]                     Back Side
=========================================================================
                               left ; right  symbols               domain

Sh2   SinH(X)      <0.85 .. 3>    X2   Sh22X               <0.88 .. 1.15>
Sh1   SinH(0.1X)  <0.1 .. 0.9>    X1   Sh12X                <0.1 .. 0.88>
Th    TanH(0.1X)    <0.1 .. 3>    P2   X22                    <1 .. 1.42>
A     X2                          P1   X12                     <0.1 .. 1>
-------------------------------------------------------------------------
[BI]  [1/X2]                      Q    -X2                     <1 .. 0.1>
S     sin(0.1X) ; [cos(0.1X)]     Y    Cos2X                 <π/2 .. 0.1>
T     tan(0.1X) ; [cot(0.1X)]     L    X                         <0 .. 1>
[CI]  [1/X]                       /_X  /_thX          <0.1 .. 3 _______ >
C     X                           [I]  [X-1]                 <[104 .. 40]>
-------------------------------------------------------------------------
D     X                           [I]  [X-1]                 <[104 .. 40]>
LL3   exp(X)                      /_Θ1 /_tg1Θ   <0.5 .. 45 ; [89.5 .. 45]>
LL2   exp(0.1X)                   /_Θ2 /_tg2Θ   <45 .. 89.5 ; [45 .. 0.5]>
LL1   exp(0.01X)                  /_Y  /_tgX                <0.1 .. 1.48>

R E M A R K S :
=========================================================================
This » HYPER-VECTOR LOG-LOG « Slide Rule is designed for engineers in the
field of ELECTRO TECHNICS with  AC & HF  Calculating Problems:  4-POLES,
ELECTRICAL & MAGNETICAL FIELDS, ANTENNAS, CONDUCTORS & ATTENUATORS,   
FILTERS, ...  because  "Vectors & Hyperbolic Functions"  are involved ...

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This model is made of bamboo with scales on celluloid veneer.  The cursor
windows have the scale symbols engraved - a good idea!  Observe the mis-
sing B-Scale: There is instead a [BI]-Scale - an interesting idea!  The
slide rule came in a brown leather case with SIC-Logo & "Made in Japan".

The GAUGE MARK  f = 1/2π  on the C/D-Scales is for calculating
INDUCTIVE (XL) & CAPACITIVE (XC) REACTANCES, and RESONANCE FREQUENCY (FR)

  XL = 2πFL ;   XC = 1/( 2πFC ) ;   FR = 1/( 2π*sqrt(LC) )

The formula for DECIBEL Calculation is     db = 20*lg(V2/V1)

The DEFINITIVE FORMS for the HYPERBOLIC FUNCTIONS are:

CosH(X) = ( exp(+X) + exp(-X) ) / 2   <==  this is the "Chain Line"
SinH(X) = ( exp(+X) - exp(-X) ) / 2       ( eg. suspension bridge )
TanH(X) =  SinH(X)  / CosH(X)
 exp(X) =  SinH(X)  + CosH(X)
      1 =  CosH2(X) - SinH2(X)

CosH(X) =  SinH(X) / TanH(X)  =  sqrt( 1 + SinH2(X) )

(A) How to use the Hyperbolic Functions on the  F R O N T   S I D E :
-------------------------------------------------------------------------

Start with value on the Sh-Scales    ==>>  reading SinH on D-Scale,
  start with value on the D-Scale    ==>>  reading ArcSinH on Sh-Scale.
Start with value on the Th-Scale     ==>>  reading TanH on D-Scale,
  start with value on the D-Scale    ==>>  reading ArcTanH on Th-Scale.

Calculate CosH(X)  ==>>  Move hairline to X on Sh , set
                         right or left index of CI-Scale under hairline,
                         move hairline to X on Th-Scale,
                         read CosH(X) under hairline on CI-Scale.

(B) and the Hyperbolic- / Vector Functions  on the   B A C K   S I D E :
-------------------------------------------------------------------------
    Used for Calculating  HYPERBOLIC FUNCTIONS OF COMPLEX QUANTITIES
        Vector in Cartesian Coordinates:              V = a + jb
    Changing from CARTESIAN- TO POLAR-COORDINATES:
        R = |V| = sqrt(a2 + b2) ;   /_Θ = arctan(b/a)
    Changing from POLAR- TO CARTESIAN-COORDINATES:
        a = |V|*cos(Θ) ;   b = |V|*sin(Θ)

Addition and Subtraction of Vectors is easy in CARTESIAN COORDINATES:

    ADDITION of Vectors:        V1 + V2 = ( a1 + a2 ) + j( b1 + b2 )

    SUBTRACTION of Vectors:     V1 - V2 = ( a1 - a2 ) + j( b1 - b2 )

Multiplication and Division of Vectors is easy in POLAR COORDINATES:

    MULTIPLICATION of Vectors:  V1 * V2 = |V1|/_Θ1 * |V2|/_Θ2
                                        = |V1|*|V2| /_( Θ1 + Θ2 )

    DIVISION of Vectors:        V1 / V2 = ( |V1|/_Θ1 ) / ( |V2|/_Θ2 )
                                        = |V1|/|V2| /_( Θ1 - Θ2 )

How to use the Scales of the Back Side:
=======================================

(=1=)
Start with value on the Sh2 scales   ==>>  reading SinH on X2 scales,
  start with value on the X2 scales  ==>>  reading ArcSinH on Sh2 scales.

  P2 = sqrt( 1 + SinH12(X) ) = CosH(X)
                 SinH(0.7)  ==>>  CosH(0.7) = 1.255  (direct read-out!)

(=2=)
P1, P2 & Q scales are used for vector calculations:

  P2 = sqrt( 1 + P12 )      = 1.281  <<==  ( P1 = 0.8 )
   Q = sqrt( 1 - P12 )      = 0.600  <<==  ( P1 = 0.8 )

   Q = P1 inverted:   ( Q = 0.800 )  <==>  ( P1 = 0.6 )

  EX.A:  Calculate the ABSOLUTE VALUE of  V = 0.4 + j0.3  ==>>  |V| = 0.5
  *****
         Move hairline to  0.4  on P1,  set  0.3  on Q under hairline,
         opposite right index of Q read answer  0.5  on P1

  Why the PYTHAGORAS can be calculated with the P2, P1 & Q-Scales ???


(=3=)
Start with RADIANS on the  Y-Scale   ==>>   reading cos2(Y) on X-Scale
                                     ==>>   reading sin(Y)  on Q-Scale

(=4=)
(X =) L-Scale ( = lgX )    keyed to     C-Scale                  on front

(=5=) /_X
/_thX -Scale ( = TanH )    keyed to     A-Scale ( *0.1 )         on front

(=6=)
[I] ; [X-1] Scales to find THE SUM OF RECIPROCALS:

    The resulting value of parallel wired resistances is given by
        1/R1 + 1/R2 + ... + 1/Rn  =  1/R

  EX.B:  When   R1 = 200 Ω  &  R2 = 60 Ω  ==>>  R = 46.15 Ω
  *****
         1/200 Ω + 1/60 Ω  =  1/R  =  1/46.15 Ω

     Opposit  200  on I (on stock), set left index of I (on slide).
     Move hairline to  60  on I (on slide), read answer  46.15  on I.

(=7=) /_Θ1;2
BLACK Degrees of /_tgΘ1;2  keyed to     A-Scale ( *0.01 ;  *1 )   on front
  RED Degrees of /_tgΘ1;2  keyed to  [BI]-Scale ( *1 ;  *0.01 )   on front

  EX.C:  Calculate the PHASE ANGLE of  V = 0.4 + j0.3  ==>>  /_Θ = 36.9°
  *****
         Opposit  3  on A,  set left index of [BI],
         move hairline to  4  on [BI],
         under hairline read answer  36.9°  on /_tgΘ1 (BLACK)

  EX.D:  TRANSFORMING a VECTOR from CARTESIAN- to POLAR COORDINATES
  *****  is the combination of  EX.A  and  EX.C

(=8=) /_Y
Start w.RADIANS on /_tgX-Scale   ==>>  reading tanX on A-Scale   on front

  EX.E:  HYPERBOLIC FUNCTIONS OF COMPLEX QUANTITIES:
  *****  ( Examples taken of the SIC-1580 Instructions ... )

              SinH(0.43 + j0.68)  ==>>  0.769/_1.106  =  0.769/_63.4°

         Move hairline to 0.43 on X1,
              set 0.68 on Y under hairline,
              opposite right index of Q read answer  0.769  on P1.
         Move hairline to 0.68 on /_Y ,
              set 0.43 on /_X  under hairline.
         Move hairline to right index of /_X ,
              under hairline read answer as  1.106  on /_Y .
         Move hairline to left index of I (on slide),
              under hairline read answer  63.4°  on /_Θ2 (black).

              CosH(0.7 + j0.61)   ==>>  1.117/_0.4  =  1.117/_22.9°

         Move hairline to 0.7 on X1,
              set right index of Q under hairline.
         Move hairline to 0.61 on Y,
              under hairline read answer as 1.117 on P2.
         Move hairline to 0.61 on /_Y ,
              set right index of /_X under hairline.
         Move hairline to 0.7 on /_X ,
              under hairline read answer as 0.4 on /_Y.
         Move hairline to 0.61 on /_Y ,
              set left index of I (on slide) under hairline.
         Move hairline to 0.7 on /_X ,
              under hairline read answer  22.9°  on /_Θ1 (black).

Historical Remarks ...

Presented at the 3rd BERLIN-BRANDENBURGER SAMMLER-TREFFEN (BBST) in Berlin

impressum:
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© C.HAMANN        http://public.beuth-hochschule.de/~hamann       03/14/09