Download the nomograph with the instructions
Nomograms, slide charts and volvelles
In 1844 Leon Lalanne created the Abaque Compteur, introducing the nomography.
Nomograms and later slide charts were the equivalent of modern apps.
These basic calculators made calculations available to all.
Leon Lalanne envisioned many copies of his Universal Calculator posted in public squares and business meeting places for popular use but today is very rare.
The original "Abaque Compteur"
In the Abaque the product of x and y is found from their intersection with the 45 lines. Here is a simplified example, but the original plot can also handle squares, cubes, roots, and various engineering and chemistry equations.
Remember that, as in the slide rule, on abaques and nomograms 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.
Download the original Lalannee`s Abaque
Even though they are still utilized for specific computations, abacuses never reached the expected level of success. The history progresses with the advancement of nomography, which proved to be even more straightforward and understandable
Abaque for the determination of the take-off space, 1965
The nomography was invented, as an easier replacement of the a abaques, in 1884 by Maurice d'Ocagne who replaced the Cartesian Coordinates with a system of parallel scales. The term originates from the Greek roots nomos (law) and graphein (to write).
The nomogram, or nomograph, essentially comprises three scales. The two externals ascertain the values of the issue to address, and by connecting them with a ruler, you can determine the outcome of the intersection with the central staircase. The scales can be either linear or logarithmic. Basic computations are depicted on straight lines, but occasionally it is useful to represent them in a circular format.
The nomography enabled anyone to carry out calculations effortlessly. One can simply draw one or more lines without needing to know the equation being solved. A significant assistance prior to the arrival of electronic calculators.
Nomograms continue to be extensively utilized for military applications in both medicine and aviation. They are simple to use, producing sufficiently precise results and remain unparalleled for numerous applications. The illustration below is very straightforward: simply connect the points representing our weight and height with a ruler to determine if we need to start a diet!
Height and weight nomogram
How to calculate with the nomography
To multiply, align with a ruler the two factors A and B on the outer scales and observe the outcome on the central scale. To separate, undo the method. You can also find the square and cube of a number (or calculate the square and cubic root). In the examples the red line is 2x5=10 or 10/2=5 or 10/5=2. The blue line is 6x3=18 or 18/3=6 or 18/6=3.
Now we can try this operation: √350 / 1,51
- to the left of 3.5 of the A2 scale we find on the A scale the square root of 350: 18.7;
- we connect 18.7 on the AxB scale with 1.51 of the A scale: on the B scale we can read the answer: ca. 12.39. A calculator would have been just a little more precise, finding 12.3896.
This small approximation did not stop Von Braun from designing space stations and sending people to the Moon. Using this system for calculations is actually easier than it seems; the key is to be precise and to practice regularly.
This table is designed to calculate the take-off space and is faster to utilize than the earlier abaque.
The manual states a 500-meter takeoff distance under standard conditions: a runway at sea level and a temperature of 15 degrees Celsius (59 degrees Fahrenheit).
Greater elevations and temperatures reduce air density, necessitating a longer runway
We're at 1,000 feet (300 meters) and 29°C: by combining the altitude and temperature with a ruler, it indicates we require an additional 35% runway, totaling 675 meters.
In the morning, with a temperature of 15°, the air will be more dense and 550 meters will suffice.
Additional details are available on the technician's nomograms section
Slide charts are nomograms placed within a cardboard cover and designed to perform particular calculations. They resemble contemporary smartphone applications, and when designed in a circular form, they are referred to as Volvelles.
Slide chart for calculating the strength of timber beams, 1902
Fluid velocity and pressure loss calculator, 1947
Promotional slide graph to assess fuel usage, 1979
Takeoff slide chart, 2010
Slide chart for lathe works, 2020
Additional details are available on the technician's slide charts section
The volvelle
The "volvelle" is a historical method for predicting cyclical astronomical occurrences, with its name coming from the Latin volvere (to rotate). It actually consists of a stationary disk over which one or more movable disks turn, featuring the scales or data intended for comparison.
Matthew Paris, a 13th-century English Benedictine monk, was the pioneer in employing revolving scales to determine the date of Easter in his work Chronica Majora. The system gained popularity in the 16th century with Petrus Appianus' work Astronomicum Caesareum, showcasing a collection of volvelles to forecast the planets' positions.
Volvellas are perfect for astronomical purposes and are favored over slide charts when the circular scales facilitate simpler reading.
Paris Chronica Majora, 1245 and Apianus Astronomicum Caesareum, 1540
John Emslie Sheppard's Clock, 1844: display the global time and
the stars observable on various dates and hours
Medical volvelle and masonite panels sizer, 1945-55
Star finder and body mass calculator, 2025
At one time, technicians had difficulty using slide rules, which required engineering training. Instead, graphical methods enable to intuitively see connections between variables and solve equations without necessarily knowing them, helping to avoid major mistakes.
They performed the function of modern "apps", anyone interested can download the classic text First Course in Nomography and a collection of historical nomograms of great visual impact.
Other nomograms, slide charts and downloadable texts can be found in the technician's nomograms section.
links:
The Nomogram on Wikipedia
Slide chart on Wikipedia
Volvelle on Wikipedia
The Nomography on KASS
International Slide Rule Museum
IREM La Reunion
Steve's Antique Technology
TakeOff Performance Computer
The Volvelle: a Smartphone App?
© 2004 - 2026 Nicola Marras Manfredi - IS1EH
