Differential Analysers

Marshall University - Prof Bonita Laurence - 2007

Based upon Arthur Porter Machine. See: Detailed write-up.

West Virginia Public Broadcasting article with explanation of benefits to students: Lab304: Math Machine (8m23)




University Of Illinois - Arnold Nordsieck Differential Analyzer -1956

Cursory views of exhibit at Computer Science Museum Silicon Valley by TilTuli:  Nordsieck Differential Analyzer -1956 (2m31)



Peter Holtam Differential Analyser - 2009

Silence footage of a very good home-brewed machine:  Meccano Diifferential Analyser



Simpson College Differential Analyzer Club 2011

Brief introduction to their Meccano machine at Science Centre Iowa: Differential Analyzer Club presents at Science Center of Iowa



General Electric Differential Analyser

News footage. See The Think Machine Tab UCLA -Samueli.

Since 1977 at the Smithsonian Institute:   UCLA's Mechanical Brain: 1948 (2m59)



Computer Animation 2011 - Planimeter

No commentary but animated phrases show the principle of operation: Differential Analyser  (2m04)



Life Story of Vannevar Bush

MIT commentary on the career of this amazing inventor who started Ratheon.

It’s worth doing a separate YouTube search on his name as there are a lot of videos about him out there -some good some very poor eg:  Vannevar Bush (4m39)

Disclaimer

Whilst some care has been taken to check externally linked websites no responsibility is offered nor implied for the suitability, legality or reliability of content therein.

What Is A Differential Analyser

Everywhere we look there is change and predicting change is fundamental to understanding any environment. Initial understandings of the changes taking place nature are innate to life’s survival: seeing night follow day and the return of good weather after a winter season. However man has always sought to go further in his prediction of the tides on the sea or movement of celestial bodies. However it wasn’t until 1631 when Newton, then Liebnitz and others, formalised the mathematics of so called dynamic systems to enable more complex problems to be easily solved.


If you are still unfamiliar with the idea take a look at: What Are Differential Equations



As Babbage had made a machine to perform repetitive mathematical operations in 1822 the desire to make a machine to solve real world natural problems became ever more pressing. In 1836 Coriolis made a simple machine to solve first order equations which was quickly developed by the stunning brothers James Thomson and then his younger sibling Lord William Kelvin in 1872.

How To Build A Differential Analyser

An extremely thorough explanation by William Irwin of the Auckland Meccano Guild. Read this before building one:  The Differential Analyser Explained



History Of Differential Analysers

Undergraduate student under Douglas Hartree Dr Jack Howlett (CBE in 1993) wrote this well researched potted history of DA’s:     Differential Analysers



Vannevar Bush's Differential Analyzer

MIT’s fairly basic introduction to his machine (adly the links to the videos don’t work):   Vannevar Bush's Differential Analyzer



Dr Michael Adler’s Fully Meccano Differential Analyser

A very succinct write up of how they work for the International Society Of Meccanomen:  Meccano Differential Analyser


Tim Robinson’s Wonderlist

A tremendous anthology of all the technology that Tim thinks important (in alphabetical order of author):  Bibliography

Differential Analysers Explained on Websites

Hartree&Porter with their Meccano DA

(Manchester 1935) Click for better picture.

Vannevar Bush with his giant programmable RDA2 with 18 integration tables (Maryland 1941)

Electronic Torque Amplified DA (Tokyo 1942)

A Differential Analyser is an analogue device for solving equations describing rates of change that are dependent upon more than one variable at the same time.


Equations like these appear in every area of natural change be that in growth, decay or waste; trade, in economics or in population growth; in Engineering such as structures, engines, in use of power generation or flight; in warfare, in space flight or the movement of stars or planets.

A simple integrator as devised by Hartree & Porter

Hartree Meccano Differential Analyser No 2

Silent footage during the restoration at MOTAT in New Zealand in 2008 by MeccaGazza

  1. Da1.mpg (2m28)

  2. Da2.mpg (3m15)

  3. Da3.mpg (5m38)

The starting gun had been fired and so many more machines were built to solve more and more complex problems. Speaking of which it must be said that it was the advent of war that finally made the necessity so acute that an accurate working real-time device became literally a matter of life or death. It is thus the equations of ballistics that some of the machines below were designed to solve.

Differential Analyser Videos On YouTube

Hartree Meccano Differential Analysers In The UK

Ian Henwood’s HDA at University Of Kent

       Recent Photographs 2018


Description by Matt Goodman & Ian Henwood:

       YouTube: Exploring how the differential analyser works in simple terms


Tim Robinson

Cursory introduction of Tim Robinson by Neil Fraser:

Close ups of machine running but no explanation by by Tim Robinson at Vintage Computer Festival:

Quick look by GeePeerces at Vintage Computer Festival 2016:

Differential Analyser Origins

Planimeter

Whilst these analysers may seem rather theoretical they all perform very practical tasks. For instance if a farmer wanted to plant seeds evenly over an irregularly shaped field how many seeds would he need ? Of course it would depend on the area. The same might apply if you needed to apply paint to an irregular shape. In 1854 the Swiss mathematician Jacob Amsler-Laffon built the first modern Planimeter which when traced around any irregular shape gave a value to the area inscribed. Very clever. Here we have another numerical output given a graphical input. Wikipedia describes:

     Wiki: Various types of Planimeter

Integraph

In 1836 the French mathematician Gaspard-Gustave de Coriolis first described a device for plotting integrals from a graph. Not surprisingly he called it his Integraph. The input to this was a point, guided by the user, that traced the differential curve to be solved. The output was a counter on a disk that rolled along the paper without slipping. One can see that development of this idea might lead a clever person to the continuously variable motorised device we know and love. The Integraph’s simple first order maths is described here:

   Wiki: The Integraph Device

Coriolis’ Integraph (1836)

Laffon’s Planimeter (1854)