Was there life before computer?

calculating instruments before the digital era

The aeronautical slide rule

The slide rules, invented in the early 17th century, were the only calculators available before the electronic age, arrived with the Apollo 11 on the Moon and, essentials on board aircraft for reckoning, are still needed as emergency instrument.

1937: the first aeronautical E6-B slide rule

The navigation's problems are always the same from immemorial time and a modern aircraft slide rule is not so different from the graphs drawn in the Middle Ages to determine the ship's position. The pilots have to find their location and perform various conversions of measures with great rapidity: in this task the slide rules are unbeatable. Mr. Spock used the E6-B on board Star Trek Enterprise: was considered an irreplaceable instrument even in a technological future. The interface of the aeronautical slide rule has no equal for dead reckoning and its graphic is used in several navigation software.


2266: the E6-B with Mr. Spock onboard Enterprise

Regolo E6-B

The classic E6-B slide rule, one of the most widely used in aviation

The classic interface of an E6-B navigation software

The aircraft slide rule, knows as E6-B flight computer, was invented in the '30s and its use is so instinctive that is often preferred to electronic calculators: solves all the problems of flight, finds the angle of drift caused by the wind and it is essential to convert the jungle of measures in which the pilots must unravel. In fact they use indifferently meters, feet, nautical miles, statute miles, kilometers, liters, gallons, etc.

Raxon de Martelojo     Regolo aeronautico moderno

Raxon de Martelojo, chart of 1430 to determine
the route, and modern aeronautical slide rule


The presentation of the E6-B in the 30s

Slide rule watches

Since the '50s the E6-B, in a simplified form, has been included in the ring of watches especially designed for pilots. The most popular models are the Breitling's "Navitimer" and "Cosmonaute", the last built for the NASA with the display divided in 24 hours as in space is impossible to distinguish day from night. It was the first watch to make an orbital flight, at the wrist of Scott Carpenter in Mercury-Atlas 7 mission of 1962, but it wasn't water-proof being soon replaced by the Omega Speedmaster. These watches today can be found at reasonable prices and in the next section you will found a template to build a working model of the E6-B, only the slide rule of course!).

Breitling Cosmonaute     Scott Carpenter

The 24 hours "Cosmonaute" and Scott Carpenter in a 1963 advertising

The paper "Easy E-6B"

The Easy E-6B is the reduced version of the slide rule designed in the 30s and still supplied to aircraft. Although it lacks of the graphic for the correction of the routes and of some specialized functions, such as determining the Mach number, is useful in solving problems of travel time, speed, fuel consumption and for make conversions between different units of measure or currency. Easy to build one: download and print the template and it will be ready in 5 minutes.

Download the template with instruction and virtual E6-B emulation


On the left a real areonautical slide rule, on the right the "Easy E6-B"

It has one mobile outer scale and a fixed inner one with the number 60 (Speed index) marked with an arrow; remember that, as in the standard slide rule, only the numbers are given: "0.9", "9", "90", "900", "9,000" are always read as "9" and how to locate the dot or how to add tenths or hundreds we must find by ourselves, but it is always instinctive to know if we are dealing with tens, hundreds or thousands. Here are some examples, useful in daily life. The complete instructions, with all the aeronautical functions, are included with the template.

1) Multiplication

Example: 12 x 15.

Align 12 on the outer scale with 10 on the inner scale. Then 15 on the inner scale corresponds to 18 on the outer scale. Take into account the position of the decimal point and add one zero to obtain 180.

2) Division

Example: 300/15.

Align 30 on the outer scale with 15 on the inner scale. Then 10 on the inner scale corresponds to 20 on the outer scale. Take into account the position of the decimal point to obtain 20.

3) Time required

Example: Obtain the time required for travel 330 kilometers driving at 55 km/h.

Align 55 on the outer scale with the Speed index (MPH). Then 33 on the outer scale corresponds to 36 on the inner scale. Thus the time required is 360 minutes (6 hours). Can also be calculated in miles instead of kilometers.

4) Average speed

Example: obtain the average speed (km/h) needed to travel 120 kilometers in an hour and 30 minutes.

Align 12 on the outer scale with 90 (minutes) on the inner scale. Then the Speed index (MPH) corresponds to 80. Thus the average speed is 80 kilometers per hour.

5) Rate of fuel consumption

Example: obtain the hourly rate of fuel consumption for 5 h running time and a total consumption of 35 liters.

Align 35 on the outer scale with 30 on the inner scale (300 minutes = 5 hours). Then the Speed Index (MPH) corresponds to 70. Thus the fuel consumption rate is 7 liters per hour.

6) Fuel required

Example: obtain the fuel required for a trip with 6 l/h of consumption and a running time of 5 h. Align 60 on the outer scale with the Speed Index (MPH). Then 30 on the inner scale (300 minutes = 5 hours) corresponds to 30 on the outer scale. Thus the fuel required is 30 liters.

7) Estimated running time

Example: obtain the estimated running time with 5 l/h of fuel consumption and a tank of 30 liters.

Align 50 on the outer scale with the Speed Index (MPH). Then 30 on the outer scale corresponds to 360 on the inner scale. 360 minutes = 6 hours thus the estimated running time is 6 hours.

8) Distance

Example: convert 45 miles into nautical miles and kilometers.

Align 45 on the outer scale with STAT on the inner scale. Then NAUT corresponds to about 39 and KM to about 72 km.

Try the virtual Easy E6-B

The paper E6-B is useful also on helicopters

The backside side of the E6-B

We have seen how the front of the aeronautical slide rule serves to calculate distances and make conversions, timing or power consumption. The back, inspired by the graphic Raxon de Martelojo * shown on the second page, is used to solve the problems of reckoning: we see how determine the changes of direction and speed needed to compensate the wind, although our paper model does not have these features.

Example: You have laid out a course on a chart and measured it to be 090░ true. The winds aloft forecast calls for the wind at your chosen altitude to be 230░ at 18 knots, and the performance data for the airplane says that you can expect a true airspeed of 125 knots at that altitude.

  • Set 230░ at the TRUE INDEX.
  • Using any convenient starting point, measure 18 units up from the grommet toward the True Index and make a dot at 18 units (Fig. 1).
  • Rotate the transparent disk to bring 090░ to the TRUE INDEX.
  • Move the slide until the wind dot falls on the arc for 125 knots (Fig. 2).
  • Read the ground speed of 138 knots under the grommet; the fact that the wind dot is below the grommet indicates a tailwind.
  • The wind dot is 5░ to the right, indicating that the true heading should be 095░. Now all you have to do is apply local magnetic variation to correct the compass.
  • We are a bit faster and we can slow down of 13 Knots to respect the time of the flight plan


Fig. 1                                                   Fig.2

Until the '70 on board the aircraft was only used the slide rule
and today is still required: always work in any situation!

Nicola Marras 2008


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