Biographical notes

After working for a few months doing statistical tests for a chemical manufacturer I applied for a position designing gas turbine engines for aeroplanes, being hired as a Research Mathematician by Armstrong Siddely Motors in Coventry (UK).

The problems assigned were interesting and offered scope to actually use the mathematics I had studied at University. One was to design a test bed to measure the thrust of an engine, achieved by placing the engine on a table supported by four cantilever legs, pushing against pressure absorbing devices enabling the thrust to be measured. Another involved analysing why bearings in some of the engines kept fracturing. It turned out on analysis that the design of the bearing holder was such that under certain conditions the bearings would be subjected to something that could be considered like hammer blows, and the bearing would eventually disintegrate, potentially causing engine failure. I redesigned the bearing to eliminate the problem but as there was a limited market for engines the bearing manufacturers were not overly interested in building the new bearing housing, which was somewhat disappointing.

The problems, of course, involved a fair amount of calculation, and the only tools available at that time were devices called slide rules and a hand cranked (later electric) calculating device. In general we had support staff who handled the mechanical and electric calculators.

A company called the British Tabulating Machine Company then sent us a brochure suggesting that we might be interested in something called a computer that they were now offering for sale, so my boss (Head of the Stress Department by the name of David R Evans) and I went down to investigate. We had the sales presentation and came back armed with literature. Nothing was done with computers at that time.

One of the next problems I investigated was that of engine noise, with a view to seeing if it could be reduced. An early consideration was to break up the shear between the rushing jet and the outside air by inserting little pins around the circumference of the tail pipe.

A turbine has a number of rotating blades which are whizzing very close to the outer casing of the engine. Some of these are for the compressors, others for the turbines. If the tolerances are too loose at this outer periphery then some of the energy goes to creating turbulence around the edge of the blade, called 'secondary flow', which of course reduces the thrust available for driving the aeroplane. I worked on calculating the dissipated energy in secondary flow turbulence. Another problem involved resonance. In early engines, the pilot had to rev quickly through what was known as the 'critical whirling speed', which in those days occurred between start-up and operational speed. Staying too long at the critical whirling speed could damage the engine.

This brings me now to the most interesting problem I had to solve. Most of our work involved engines for military planes, (bombers and fighters), but the problem applied equally well to civilian aircraft. When a fighter plane makes a rapid turn the engines act like a huge gyroscope and try to keep the plane in the direction it was originally going. This creates a severe loading on the turbine and the problem was to find out how big such a load might be. At that time nobody had solved the problem.

When I examined the problem it became evident that a combination of the theory of elasticity (the subject I had found most difficult at University), combined with an approach based on the calculus (in which an area or surface is divided in to very small segments) would probably work. For the mathematically oriented the stresses and strains are handled by fourth order partial differential equations. Within a few days I came up with a solution that would have been relatively easy to compute with any of today's computers, but did involve our electric calculator person in a fair degree of computation.

The solution I arrived at appeared to have wider potential than to our company so I was allowed to submit it to the Journal of the Royal Aeronautical Society, for possible publication in their Journal. A paper was prepared and sent to the Journal editors. The paper title and abstract were:


Symmetrically loaded circular plates of constant thickness are dealt with adequately in several of the standard textbooks on the strength of materials. The problem of non-uniformly thick plates subjected to asymmetric loading has been discussed by M. Donath and more recently, by D.C Boston. So far very little has been done on the problem of a circular plate of varying thickness subjected to an asymmetric load. A tabular method approximating to the solution is outlined in this note. A typical example of the problem arises in certain manoeuvres of a jet aircraft in flight, the rotor discs of the engine being then subject to gyroscopic moments.

This paper was published in 1953 and I received a cheque for a few guineas, with an accompanying letter saying that the Royal Aeronautical Society Journal considered the paper one of the most significant developments of the year.