Introduction

I have four "electrical" rules in my collection, a Unique "Electrical", a Faber Castell 378, a PIC 4866 and a Faber Castell 1/98 "Elektro". The Unique has a series of special gauge marks and the latter three operate in similar ways to each other, but a different way to the Unique, with scales in the well of the stock Of these four only the Faber Castell 1/98 and Unique will be described in detail.

In the case of the Unique there are two scales of temperature on the stock, shown highlighted below. These can, incidentally, be used to convert from Celsius (formerly Centigrade) to Fahrenheit, but their main use is to calculate the variation in resistance at different temperatures. Their range is from 0 to 300 ° C and from 32 to 600 ° F. The rule also has three special gauge points marked V, N and W. One of these, W, is also highlighted in the image below. There are also CF and DF (pi displaced) scales which can used for other calculations. On the Unique these are marked d and c.

The Faber Castell also has a temperature scale which goes from 32 to 167 ° F, shown highlighted below. (Which is both shorter than the Unique equivalent and without the possibilities of conversion of units.).

Its most unusual feature is the two scales in the well of the stock. These give dynamo and motor efficiencies (in black) and a scale of volts (in red). The scale of volts represents the voltage loss per 10 yards for a wire of 10 000 circular mils diameter and a current of 10 amps. The slide also has a "tongue" which can used to read values of these scales (seen to the right of this image).

With both rules it is necessary to perform a simplified calculation to estimate the position of the decimal point.

The explanation and examples for the Unique rule are based on Teach Yourself the Slide Rule by Burns Snodgrass.

Background

Voltage drop is given by the formula:

    V = (I x L )/ (c x A)
Where:
    V is voltage drop (volts)
    I is the current (amps)
    L is the length (yards)
    C is the conductivity of copper
    A is the section of the conductor. Typical units for this are square inches, square millimetres and circular mils. Circular mils is calculated from the diameter of the wire in thousandths of an inch squared.

The calculations all assume copper wire.

Most efficiencies are in the range of 80% to 100%.

Variation of resistance with temperature

To solve:
   A copper wire has a resistance of 2.8 ohms at 20 ° C (68 ° F). What is its resistance at 5 ° C (41 ° F) and 104 ° F (40 ° C).

Unique Electrical
   Set cursor to 20 ° C on lower temperature scale.
    Set 28 on C scale to cursor.
    Move cursor to 5 ° C on lower temperature scale.
    Read 2.63 ohms under cursor on C.
    Move cursor to 104 ° F on upper temperature scale.
    Read 3.01 ohms under cursor on C.

Faber Castell Elektro
   Set the cursor to 2.8 on the A scale.
    Set 68 ° F on the temperature scale to the cursor.
    Move the cursor to 41 ° F (= 5 ° C).
    Read 2.63 ohms under cursor on A.
    Move the cursor to 104 ° F.
    Read 3.01 ohms under cursor on A.

Dynamo Efficiencies

To solve:
   Calculate the efficiency of a dynamo which gives an output of 33.4 kW for 51.6 H.P.

Unique Electrical
   Set 33.4 on D scale against 51.6 on C scale.
    Read the efficiency, 86.6% on the d scale, opposite the gauge point N on the c scale.

Faber Castell Elektro
   Set 5.16 on the B scale against 33.4 on the A scale.
    Read the efficiency, 86.6% on the Dynamo efficiency scale.

Motor Efficiencies

To solve:
   Calculate the efficiency of a motor which develops 161 H.P. for 137 kW.

Unique Electrical
   Set 137 on the C scale against 161 on the D scale.
    Read the efficiency, 87.5% on the d scale, opposite the gauge point W on the c scale.

Faber Castell Elektro
   Set 1.61 on the B scale against 137 on the A scale.
    Read the efficiency, 87.5% on the Motor efficiency scale.

Volt drop

To solve:
   Calculate the volt drop in a copper conductor 208 yards long, 0.18"diameter, carrying a current of 20.4 amps.

Unique Electrical
   Area is 180² = 32400 circular mils.
    Set 1 on C against 2.04 on D.
    Move cursor to 2.08 on C.
    Move 3.24 to the cursor.
    Read volt drop, 39.9, above V on the c scale.

Faber Castell Elektro
The units on the rule are 10 yd, 10 amp and 10000 circular mils. This has to be taken into account when setting the scales.
   Move 1 on B scale to 2.04  (20.4 / 10 amps) on A scale.
    Move cursor to 20.8 (208 / 10 yds) on B scale.
    Move 3.24 (32 400/ 10 000 circular mils) on B scale to cursor.
    Read volt drop 39.9 (3.99) on (red) Volt scale.