R100 Airship from 1954 Neville Shute Book – Slide Rule

R100 Airship

Engineering Wonder of the Early Aviation Age Circa 1925

25-r100-cardington-1938The R100 design was a remarkable tale of engineering, circa 1925. First it should be pointed out that two airships were designed and built in competition: the R101 by a government backed team (chief engineer: Lieutenant-Colonel Vincent Crane Richmond) and the R100 by a private venture (chief engineer: Barnes Wallis) – backed by a subsidiary of Vickers. The intention of the Air Ministry was to adopt the winning airship design for mail and passenger transport within the British Empire (in particular Canada, Australia and India). Notably the lead stress engineer on the Barnes Wallis team was Neville Shute Norway who subsequently published novels and the autobiography – Slide Rule – in which he described his experiences in this project.

R100cutawaydrawThe R101 was constructed in Cardington and the R100 in Howden Yorkshire in an adapted air station. The R100 was flown to Cardington on its maiden test voyage and modifications were made in in Cardington. The R100 was then flown to Canada, with Neville Shute Norway on board; docking in Montreal and then returning to Cardington. Under pressure from the air ministry after the successful flight of the R100, the more troubled prototype of the R101 was flown, despite reservations from some parties, and crashed in France on 4th October 1930 with many killed, including the Air Minister, Lord Thompson of Cardington.

R100_Howden_ConsThe  book Slide Rule by Neville Shute is well recommended, written by an engineer, with first hand experience of this project, following also his subsequent career in aircraft design and manufacture prior to World War II. Wikipedia is a good source of background history to the R100 and R101.

Key Dimensions and Structure

r100plnl

A geodesic framed structure with a series of circular (16 sided polygon) transverse frames and longitudonal frames at each of the corner points of the polygon.

The total length was 700ft (212m) and maximum diameter 130ft(40m). The transverse girders were constructed from a form of aluminium (Duralium), which were restrained by 16 radial cables (diameter not known – assumed 1 inch or 25mm diameter) per frame. The transverse frames were spaced at circa 45ft (13.5m). The longitudonal frames were similar in section as triangular trusses.

The airship gas bags were Hydrogen filled. It was powered by three mounted gondolas and steered by means of a rudder at the rear. The gross weight was in the order of 156 tons.

The air frame was covered with a fabric skin.

The sketchup file below shows the incredible size of the airship against a human figure

R100-Sketchupfile

Extract from Slide Rule by Neville Shute

A Stress Engineer’s Headache

"My own work in the calculating office led at times to a satisfaction almost amounting to a religious experience. The stress calculations for each transverse frame, for instance, required a laborious mathematical computation by a pair of calculators that lasted for two or three months before a satisfactory and true solution to the forces could be guaranteed.
To explain this for the benefit of engineers, I should say that each transverse frame consisted of a girder in the form of a stiff, sixteen-sided polygon with the flats at top and bottom; this girder was twenty-seven inches deep and up to a hundred and thirty feet in diameter. Sixteen steel cables ran from the centre of the polygon, the axis of the ship, to the corner points, bracing the polygonal girder against deflections.
All loads, whether of gas lift, weights carried on the frame, or shear wire reactions, were applied to the corner points of the polygon, and except in the case of the ship turning these loads were symmetrical port and starboard.
One half of the transverse frame, therefore, divided by a vertical plane passing through the axis of the ship, consisted of an encastré arched rib with ends free to slide towards each other, and this arched rib was braced by eight radial wires, some of which would go slack through the deflection of the arched rib under the applied loads. Normally four or five wires would remain in tension, and for the first approximation the slack wires would be guessed. The forces and bending moments in the members could then be calculated by the solution of a lengthy simultaneous equation containing up to seven unknown quantities; this work usually occupied two calculators about a week, using a Fuller slide rule and working in pairs to check for arithmetical mistakes.
In the solution it was usual to find a compression force in one or two of the radial wires; the whole process then had to be begun again using a different selection of wires. When a likely-looking solution had at last been obtained, deflection diagrams were set out for the movements of the various corners of the polygon under the bending moments and loads found in the various portions of the arched rib, and these yielded the extension of the radial wires under load, which was compared with the calculated loads found in the wires. It was usual to find a discrepancy, perhaps due to an arithmetical mistake by a tired calculator ten days before, and the calculations had to be repeated till this check was satisfied. When the deflections and the calculated loads agreed, it was not uncommon to discover that one of the wires thought to be slack was, in fact, in tension as revealed by the deflection diagrams, which meant that the two calculators had to moisten the lips and start again at the very beginning. The final check was to take vertical and horizontal components of the forces in every member of the frame to see that they equated to zero, that your pencil diagram was not sliding off the paper into the next room. When all forces were found to be in balance, and when all deflections proved to be in correspondence with the forces elongating the members, then we knew that we had reached the truth.
As I say, it produced a satisfaction almost amounting to a religious experience. After literally months of labour, having filled perhaps fifty foolscap sheets with closely pencilled figures, after many disappointments and heartaches, the truth stood revealed, real, and perfect, and unquestionable; the very truth. It did one good; one was the better for the experience. It struck me at the time that those who built the great arches of the English cathedrals in medieval times must have known something of our mathematics, and perhaps passed through the same experience, and I have wondered if Freemasonry has anything to do with this."

A Snapshot of the 3 Month Analysis

Problem

A transverse frame slice was modeled on GSA and backed up with a preliminary hand calculated check. The writer has no idea if the results or air pressures are any where near the actual answers that Neville Shute and his team obtained, but it at least shows how powerful a tool we have with computers to short cut the tedious process.

The most difficult task was to find naca-report-223.pdfappropriate pressures for design. Atmospheric pressure varies with height from 100kPa at ground level to around 72kPa at 300ft, reducing with greater altitude. The actual net pressures on the air frame fabric are much lower than this as the pressure inside and out tends to equalise.

But from a 1920s paper from Cranbrook a maximum measured pressure on the main body of an airship was measured at circa 3 pounds/sqft (circa 0.15kPa). Not knowing what pressures occur with gust and maneuvering net pressures were selected similar to buildings – 1kPa at or near ground level and a conservative 2kPa at higher altitudes. Pressure plots to the right show almost uniform pressures on the main body of the tested airship (reversible it appears).

An out of balance pressure on a quarter segment was given as 0.5kPa.

Forces and Parameters

 

CCI29016_uploadsheet_1The diagram to the right shows the overall parameters of a centre segment. Like Neville Shute the transverse frame was cut in half for simplicity.

On the GSA model the lattice girder was likened to a 635mm depth (as per the girder) but as a thin walled tube in aluminium.

Three load cases are shown.

 

 

 

 

 

 

CCI29016_uploadsheet_2

Ignoring the girders cable loads were estimated by distributing the loads into the cables……

 

 

 

 

 

 

 

 

CCI29016_uploadsheet_3Taking cases 1 and 2 the statically indeterminate problem was made difficult by the interaction of the girder stiffness with the cable axial stiffness.

As a rough estimate the expected deformation of each under full load was calculated and the net effect was that the cable load was halved from the previous sheet.

 

 

 

 

CCI29016_uploadsheet_4In summary the distortions are shown as an estimate …….

And finally some GSA output shown side by side.

The first is for the Load Case 1 – even distribution of pressure at ground level.

Load Case 2 shows the out of balance quarter segment output. Cables going into compression were removed in a similar way to the method by Neville Shute.

 

151117_airshipmodel3_slice

 

151117-airshipmodel3-slice-outofbalance1

 

 

 

 

 

 

 

 

 

 

 

Imagine having to spend three months doing this by hand and with graphical methods!

Leave a Reply

Your email address will not be published. Required fields are marked *