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# Disc Calculator Bezel

The bezel may be used for various arithmetic operations as well as conversions especially for flying. It is bidirectional and can be moved by use of the crown on the left side.

The disc calculator with adjustable outer bezel is arranged according to the principle of a slide rule. It serves the determination of times, distances, fuel consumption and other sizes on the basis of known values.

It takes some time and practice to fully master its functions.

The motile bezel represents the first scale. The number 10 may be any of the values 1, 10, 100 etc., depending on the dimension.

Three more scales are located inwards. The scale on the very inside is the minute scale (gray). It is not used for calculations.

The middle scale (third scale) serves the conversion of minutes into hours, if the calculation results in more than 60 minutes (e.g. 90 minutes = 1:30 hours).

The actual counterpart to the motile scale (bezel) is the immotile second scale. This is the scale that is meant by “second scale” in the descriptions to the subsequent examples. It has a white arrow labeled MPH (marked red in the picture above). This arrow is the reference mark for all speed calculations.

Furthermore, markings at the values 10, 33, 36 and 38 are present on the second scale. They (as well as the red markings at 10, 36 and 60 on the moveable scale) will be explained in the following text.

The first and the second scale of the disc calculator correspond to the scales C and D of a slide rule.

Multiplication, division and the rule of three are therefore calculated the same way as with a slide rule.

At least two scales are needed in order to calculate arithmetic operations. If you lay two rulers (metrical scales) together you are able to easily add or subtract two values (distances).

Addition and subtraction are easily calculated but unfortunately multiplication and division are not. However, if you use logarithmic scales instead of metrical scales, addition becomes multiplication and subtraction becomes division.

To commemorate:
The disc calculator (slide rule) gives account of the order of the numerals of a result. The proven rough calculation (estimation of dimension and result) is an essential necessity before every operation. The number 10 for example may express 1, 10, 100 as well as 1.000.

Multiplication

In order to multiply look for the first multiplier on the first scale and adjust it opposite the reference mark of the second scale (red marked 10 just above 3 o’clock).

Then look for the second multiplier on the second scale.

The result may be found on the first scale opposite the second multiplier.

Example 1
5 x 13 – Adjust position 13 on the first scale opposite the reference mark (red 10) on the second scale.

Result = 65 on the first scale, opposite position 5 of the second scale.

Division

In order to divide adjust the dividend in such a way that it is opposite the divisor on the second scale.

The result is to be found on the first scale opposite the reference mark of the second scale (red 10).

Example 2
180 : 3 - Adjust position 18 on the first scale opposite position 3 on the second scale.

Result = 60 on the first scale, opposite the reference mark of the second scale.

Alternative: Adjust the divisor on the first scale opposite the dividend on the second scale.

Result: On the second scale, opposite the reference mark (red 10) of the first scale.

Speed (per Hour), Distance and Time

In order to calculate speed again both scales need to be used.

Two of the values time, distance and speed are known, the third is demanded.

Example 5
A distance of 105 km (MI) is covered during 36 minutes.

How fast is the speed?

Known: Time (36 minutes) and distance (105 km or MI)

Demanded: speed

Solution: Adjust position 105 on the first scale opposite position 36 on the second scale.

Result = 175 km/h (MPH) on the second scale, opposite the white MPH arrow on the second scale.

Fuel Consumption

Of the three values time, amount in liter (Gal) and consumption in liter per hour (Gal/h) again two are known.

Example 10
The flight time is 2 ¾ hours and the average consumption is 20 l/h (Gal/h). How much is the total consumption?

Known: time (2 ¾ h) and consumption (20 l/h or Gal/h)

Demanded: amount

Solution: Adjust position 20 on the first scale opposite the white MPH arrow on the second scale.

Result = 55 l (Gal) on the first scale, opposite position 2:45 (hours) on the third or position 165 (minutes) on the second scale.

Climb and Decline

Again, two of the three values height, time and average speed are known.

Example 13
The airplane climbs with 200 m/min (ft/min). At which level is the airplane after 48 minutes?

Known: Speed (200 m/min or ft/min) and time (48 minutes)

Demanded: level

Solution: Adjust position 20 on the first scale opposite reference mark of the second scale (red 10).

Result = 9.600 m (ft) on the first scale, opposite position 48 on the second scale.

Conversion Nautical Mile (NM), English Mile (Statute) and Kilometer (km)

On the second scale there are red marks at 33, 38 and 61 with the labels NAUT, STAT and KM.

They are used for the conversion of the units nautical mile (NM), English (statute) mile (MI) and kilometer (km).

Example 17
Which value of nautical miles corresponds to a distance of 70 English miles (MI)?

Known: Distance (70 MI)

Demanded: Distance in NM

Solution: Adjust position 70 on the first scale opposite red mark STAT on the second scale.

Result = 60,8 NM on the first scale, opposite red the mark NAUT on the second scale.

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