Engineering Before Computers

At the Matriculation Dinner each year, one of my opening gambits for chatting to the newly arrived engineering students is to point to one of the pictures in the Hall and ask 'What's he holding in his left hand?. The object in question resembles a white stick. Very few students have identified it correctly, especially in recent years. Finally I say 'It's a slide rule!' and get a response like 'Oh, of course, that's what it is!' About four years ago, for the first time, my victim looked blank, hesitated and finally said 'Please sir, what is a slide rule?' I still can't decide if he really was the first one who didn't know or whether some the earlier students had merely pretended to recognise it.

However, it comes as a bit of a shock to realise that only 50 years ago (circa 1955) engineers had no personal computers or pocket calculators (a handful of big 'main-frame' computers existed but at that time they had had virtually no impact on engineering). All engineering design calculations relied on slide rules, the occasional mechanical calculating machine, or the basic approach of pencil, paper and maths tables. Even mechanical calculators had only been available since the early 20^th century (round about 1910) and before that the slide rule had been the only aid to engineering design calculations. It must be difficult for present day students to understand what it was like to be an engineer fifty years ago. The previous generation of engineers would have had just as much difficulty in understanding how their predecessors managed before they had slide rules.

Approximation and Precision

Before we move on there is a closely associated problem that must be mentioned. Computers and electronic calculators can perform high precision calculations very quickly. Even my cheap basic Casio calculator manages 10 significant figure multiplications, evaluation of sines etc. in under a second. In 1955, using a slide rule, similar calculations could be carried out to 2 to 3 significant figures in a few seconds. If higher precision was essential the 1955 engineer could use a mechanical calculator, but each step in the calculation then took a minute or more. Before 1900 pencil, paper and maths table was the only way of performing a precise calculation, and each step could then take several minutes.

I personally knew electronic circuit designers who in 1955 took a month or more to design a single low-pass filter circuit using mechanical calculators. Their predecessors had not attempted precise design of filters at all, and had relied on simple approximate design techniques that could only roughly predict the performance of the circuits as finally constructed. They then ended up making experimental adjustments on the final filter circuits after they had been built.

However, in other fields of engineering even this approach was not possible. For example, it's not practical to make experimental adjustments on a bridge after it has been built. (Especially if it has already collapsed during a previous experiment!) Hence engineers resorted to inserting large 'safety factors' in their designs to cover the uncertainties.

Going back still further we reach a period before the slide rule had been invented, before logarithms had been discovered and before tables of logarithms had been worked out. This was the period when no numerical engineering design work was possible. Even then, major engineering works were successfully completed. Consider the Egyptian Pyramids, Greek Temples, Roman Aqueducts and Norman Cathedrals. The only design technique available was the 'rule of thumb'. i.e. 'We did it this way last time and it worked!' (or didn't work!).

This seems to be a good point to start our exploration of Engineering Design.

Designing a Pyramid

One of the features of pyramids is the remarkable precision in which they have been laid out. They are usually perfectly level, face exactly due north and have accurate right angle corners etc.

This is in fact quite easy to achieve if you use your brain. The Egyptians would start off by clearing the site, building an earth wall round it, and then filling the enclosure with water. Next they would drive in wooden stakes and cut notches in them at the water level. This provided a very accurate level reference plane and they could then level out the interior and start laying the base. (Egyptian Pyramids are, fortunately, built on rock plains with only a thin cover of earth or sand.) An accurate north bearing could be obtained by noting the points at which certain stars rose and fell below the horizon, and then bisecting the angle between them. Finally the Egyptians knew about the 3,4,5 right-angled triangle. The actual structure raised very few problems, provided they didn't make the sides slope too steeply. The Egyptians soon found out by trial and error how far they could go in this respect.

Erecting an Obelisk

This is another type of structure that the Egyptians were noted for. But how do you erect a large (100 ft or more) stone column weighing several hundred tons on top of a base pedestal when you don't have a big crane? In fact we are still not sure how the Egyptians did it with only ropes and slaves to hand, but recently a way of putting up an obelisk has been found, which the Egyptians could have used with their available resources. This is how you can do it.

You first cut your obelisk lying horizontally out of the rock in a suitable quarry, shape it and use lots of slaves to drag it up a ramp built at the point you intend to erect it. The base pedestal is carved out and installed and you end up as shown below.

Now comes the clever part. A wall is built round the site of the obelisk (i.e. The pedestal and high end of the ramp) and filled with fine sand (egg-timer quality). The obelisk is slid up over the top of the sand until it projects by a length equal to the vertical drop to the pedestal. It is also necessary for its centre of gravity to be beyond the end of the ramp. The trap door at the bottom of the wall is then opened so that the sand starts to pour out. As this happens the obelisk drops down, tilting about the end of the ramp, and if all goes well it should end up more or less vertical resting on the pedestal in its correct position. Slight adjustments on the guide ropes then ease it into a vertical position.

A test of this scheme was carried out in America a few years ago. It worked perfectly first time!

This gives you some idea of hows things were done before any formal design was possible. It was largely a case of building up knowledge by trial and error coupled with common sense and clever thinking. No doubt lots of trials were needed before to get a scheme just right, but thereafter it was a case of following the procedure that was known to work.

As time went by new techniques were added. The Romans made a major contribution through the invention of the arch, but they did not realise that arches need not be mere semicircles. When the Roman Empire collapsed round about 400 A.D. the so called 'dark ages' followed in which much knowledge was lost. However, as far as engineering was concerned this does not seem to have happened. Although there are no records, accumulation of techniques that worked and new innovations seems to have continued throughout the dark ages, so that when civilisation returned to Western Europe (circa 1000 A.D) spectacular developments suddenly appeared. The Norman conquest of England was followed by a virtual epidemic of cathedral building and these cathedrals were truly magnificent structures. As examples consider Durham and Ely.

The idea of using scale models to test out designs had developed, and this had in turn made it practical to erect very large buildings with a good chance that they would not fall down. (i.e. Fewer trials and fewer errors = more and faster development.) Use of models also helped to reveal new principles in structure design so that at about this time it was realised that arches need not be semicircular. This finally led to the design three dimensional arches. The nature of the forces on structures began to be understood, so that the right ways to use flying buttresses or weighted columns to stabilize structures became apparent. We have a very good example in Cambridge, Kings College Chapel, started in 1450. This is probably one of the finest buildings in Europe and if you compare it with the remains of Roman buildings you can see how far knowledge had advanced during the 'dark' and middle ages.

I've concentrated on structures, but similar advances were taking place in other areas, such as ship building. (Compare a Spanish Galleon with Roman merchant ships as an example.) Of course, military techniques had also been improved, specifically through the use of gunpowder.

However, almost all of this was still being carried out on a trial and error basis.

Numerical Design

The really big step in engineering was the move from designs based on trial and error to designs based on numerical analysis. This involves a number of innovations. We have already mentioned one of these, the availability of easy ways of making complicated calculations, but a calculation is pointless until you have the basic data to use in it, the mathematics to set it up, and the theory to specify a formula for it. So far I've used structures as an example but for a change, let's consider the design of a power transformer. Clearly I will need data on the magnetic properties of the iron core and on the resistance of the copper used in the windings. I will need the mathematical theory for manipulating complex numbers and the differential calculus. Finally I will need the electrical circuit theory that relates the number of turns in a coil to the magnetic flux in the iron core and the induced voltage in a coil, which in turn will lead to mathematical expressions relating flux density, number of turns in a coil, core dimensions, and voltages and currents.

The first item to appear was the differential calculus, early in the 17^th century, followed closely by the invention of the slide rule. Electromagnetic properties of copper and iron became known in the early 19^th century, followed finally by complex number theory and an understanding of electromagnetic induction. Hence in this area numerical design only became possible in the latter part of the 19^th century. However, in other areas use of numerical design methods became possible much earlier. We will now look into these various steps in detail.

The First Steps

Progress seems to occur in intermittent bursts. In fact what is happening is that little bits of new knowledge are continually accumulating and ultimately enough of these little items are available to reveal patterns and then a big forward leap (often several leaps) seem to occur within a very short time. This happened at the end of the 16^th century and a member of Caius College (Edward Wright) was involved in this particular set of leaps (See the article on the History of Engineering in Caius.) The man who started this was John Napier, a Scottish mathematician.

(See http://www.electricscotland.com/history/other/john_napier.htm )

John Napier was born in Merchiston, Edinburgh in 1550.

His father was a fairly wealthy protestant landowner, with the result that John never had to earn his living and spent his entire life pursuing his main interests, religion and mathematics. He entered St Andrews University at the remarkably young age of 13, and later studied in Paris and travel led to Italy before returning to Scotland to marry at the age of 21. Thereafter he spent most of his time at his family estates at Merchiston and Gartness, studying mathematics and religion. He had a thick black beard, habitually dressed in a black robe, and his neighbours were convinced that he dabbled in sorcery. Much of his work involved multiplication, which in those days was a very tedious process and this led to his two major discoveries, Logarithms and Napier's Bones.

Since we all know what logarithms are (I hope!) I will only describe his 'Bones'. These were a set of vertical sticks, each one corresponding to one digit of a number to be multiplied. The number is placed at the top and below it the results of multiplying it by the digits 1 to 9. As you will see, these products are arranged with their two digits in diagonally opposite corners of a square with a diagonal line between them. To form a product by any digit we then merely add the adjacent numbers separated by the vertical lines in the corresponding row, starting from the right.. For example, to multiply 187 by three we form:

3+2 4+2 1 = 561, and:

187 x 7 is 7+5 6+4 9 = 1309 (note the carry's)

Obviously 187x73 is 13090+561 = 13651.

This might not look exciting at this level, but for 15 digit numbers it represents a considerable saving in mental effort and was most welcome to mathematicians of the late 16^th century. The idea of turning multiplication into addition by a sort of table probably helped to lead Napier on to the discovery of logarithms as a tabular means of turning multiplication into addition. As I mentioned earlier, a Fellow of Caius College, Edward Wright, was known to have been in correspondence with Napier and was also an earlier user of logarithms in some of his own work.

William Oughtred

It is probable that the association with his work on the 'Bones' soon led others to turn their thoughts to the possibility of producing some sort of 'Bone' for logarithms. The first known attempt was made by William Gunter of Gresham College in Oxford. In 1624 he published a description of a single logarithmic scale which was employed for multiplication by using a pair of dividers. This was apparently used by seamen for navigation and Gunter also published work on the magnetic compass. These interests are strikingly similar to those of Edward Wright in Caius, and it seems highly likely that they were in touch with one another. At about the same time William Oughtred was a Fellow of Kings College Cambridge studying mathematics and again it seems likely that he also knew of the work of Wright and Gunter. Oughtred was the man who finally put it all together. He first invented a circular logarithmic scale, which got around the difficulty of passing from one decade to the next during multiplication and finally in 1632 he had the idea of using two sliding scales rather than one plus dividers. The slide rule had finally arrived!

However, at that time there was still no great demand for rapid easy calculations and the entry of the slide rule into science and industry was slow. In 1675 Sir Isaac Newton solved cubic equations using a slide rule with three parallel logarithmic scales and made the first suggestion for the use of the cursor. This idea failed to catch on at the time. Two years after Newton invented the cursor, Henry Coggeshall perfected a specialised version of the slide rule, the timber and carpenter's rule. This was still in common use 200 years later. Other applications followed, which moved the slide rule from being a device for mathematical research to use in common practical applications.

By 1790 James Boulton and James Watt were modifying slide rules to improve their accuracy and usefulness and their slide rules, which were used in the design of the early steam engines, helped to usher in the Industrial Revolution.

In 1815 Peter Roget, an English physician (and better known as the author of Roget's Thesaurus), invented the log log scale, which he used to calculate roots of numbers. Again at the time this seemed unimportant and was forgotten but fifty years later, advances in electrical engineering, thermodynamics, dynamics and statics, and industrial chemistry make these scales so necessary that they were rediscovered.

Amandee Mannheim

In 1851 a French artillery officer named Amedee Mannheim introduced a set of four scales for the most common calculation problems. These included two double length scales, named A & B, for squares and square roots and two single length scales, C & D, for multiplication and division. With the addition of the log-log scales, an inverse scale and a cursor this defined the standard design for slide rules which was used for the next 100 years and bears Mannheim's name today.

The slide rule's importance to the Industrial Revolution, and the impact of the Industrial Revolution upon the slide rule, are demonstrated by the proliferation of designs starting at that time. From 1625 to 1800, the first 175 years after its invention, a total of 40 slide rule types, including circular and spiral designs, were recorded. The next 100 years, from 1800 to 1899, saw the creation of 250 slide rule types and manufacturers. Over 90 designs were recorded in the first 10 years of the 20th Century.

The 20th Century

During the 20^th century the slide rule was the dominant tool used by engineering designers. Everything, from steam turbines and suspension bridges through to super-tankers and aircraft were designed using slide rules. In the period 1950-80 they were used by the designers of of the big rockets and slide rules were taken into space by astronauts as lightweight calculators that needed no power source. A typical 20^th century slide rule is shown below.

If you want to find out what it was like to actually use a slide rule you will find a very nice animated image of one in Derek's Virtual Slide Rule Gallery (Not me � another Derek!) at:

http://www.antiquark.com/sliderule/sim/

As a final example here is a picture of one of the last slide rules designed, a specialist slide rule for manipulating complex numbers, designed by a G.E.C. Engineer and produced for the G.E.C. During the 1960's.

Mechanical Calculating Machines

In parallel with the development of the slide rule there had been work on calculators based on mechanical schemes from the 17^th century onwards. Pascal is credited with being one of the first people to devise such a machine. However, this had proceeded much more slowly, possibly because precision engineering is needed to construct such devices. The first major attempt to make such a machine was the well known proposal for a 'Difference Engine made by Charles Babbage in the mid-19^th Century. At the time there was not a lot of interest shown in his proposals and his work was terminated by lack of financial backing. We now know that his proposed design would have worked � probably very well � and it is interesting to speculate on what might have happened if Babbage had been able to complete it's construction. Perhaps the 'Information Age' would have arrived a century ago. However, simple mechanical calculating machines capable of carrying out addition, multiplication and division to around 10 digit precision were available by the end of the 19^th century and in the mid 20^th century much faster versions of these machines, driven by electric motors appeared. A couple of these are shown below, a hand-driven Brunsviga calculator and a later electric machine.


Madas Electric Calculator	Brunsviga Calculating Machine

In the 1960's there was even a mechanical pocket calculator developed, the Curta Calculator, but this arrived too late too have any impact. However, there is also a nice working simulation of this machine on: http://www.vcalc.netcu.htm

The Curta Pocket Calculator

By this time the electronic pocket calculator was about to appear and the age of the slide rule and its associates was ending.

Derek Ingram.