## Thursday, March 31, 2011

### Fall of France, 9: Manpower, Part 6, 3: Computers. Drilling Down.

There are ways and ways to make this argument. The unpersuasive way is to swan about making dubious connections. The more persuasive way is to drill down and show the stakes entailed in something obvious and every day, rather like Marc Van De Mierop pointing out the implications of Late Bronze Age sheep shearing.

Now, nothing was more obvious and everyday during the long nightmare of Europe's great bomber war. Most places in a big German city were not far from one of these:

That's an 88/56 (88 mm diameter barrel with a barrel length 56 times the diameter) 8.8cm FlaK 37, firing a 9.2kg shell with a muzzle velocity of 790 meters/second. It weighed 7,407kg in action, and, like all quick-fire guns, has a nominal rate of fire of 15--20 rounds, basically the ergonomic estimate of how many rounds an experienced crew could get off when working at top rate.

In a British city, it would be one of these (though hopefully in better shape):

This is the QF 3.7"AA, a 94/50, for comparison's sake. It fired a 12.7kg shell at a muzzle velocity of 2670 feet/second. Given that lengthening the barrel (in calibre lengths) will have the effect, all other things being equal, of increasing muzzle velocity while decreasing barrel life, we can see that there have been some nice ballistic achievements made here compared with the earlier and slightly smaller German gun.

Oh. And it weighed 9,317kg. Just to put this in perspective, the British army's standard field gun, the 25 pounder (88mm calibre, if you're interested in these things) weighed 1,633kg. The heaviest new British gun of World War II, the enormous 7.2" howitzer that rained 90kg shells on hapless enemies 15 kilometers away, was a 10 ton gun, and the 9.2" howitzer that was the BEF's standard siege gun at the outbreak of WWI weighed less than 6. That, alone, is an intimation of the social change this gun is going to enact. For this weapon to work as a means of national defence, we need a fleet of these, and the consequences of turning social logistics over to big trucks are still being worked out today. But it will probably turn out in the long run that it's something much more humble that leveraged all of this social change. That weight doesn't come from nothing. The nobby bits on this gun are machinery. Computery machinery.

(After the break, math.)
The original design concept of the QF 3.7" HA called for centrally aimed fire. A human-operated sight was laid on a plane passing overhead, and the operator(s) twirled one nob to track the plane, and another to keep it in focus in the sight. The first process was sampled to produce a radial velocity variable, while the second yielded a radial distance. From these, the future location of the aircraft could be calculated and an interception plotted by what is now called an "electromechanical computer," but which had any number of names at the time on account of the computer paradigm not yet existing. The director would then directly drive, through a device called a magslip, a pointer that told the individual gunlayer operating the individual gun's motor (no wonder they weighed so much!) where to point the gun. Meanwhile, shells would be fed by the gun detail into a hopper that took them to a fuzesetter, which also accepted an input from the computer and set the delay on the fuze.

The computer and the velocity-sampling sight have got their due share of attention over the years. Even the fuzesetter has been noticed, not least because the manufacture of mechanical fuzes for all of the shells to be fired proved problematic, and for several years most fuzesetters instead cut incendiary fuzes, and people could later complain about how British industry was unable to produce "precision clockworks." David Harmer, for all his limitations, even reminded us of the importance of the transition from follow-the-pointer to the final version of the technology (available from 1944), in which the computer directly told the gun's motor where to point the muzzle (Remote Position Control, although people can't seem to agree what the acronym "RPC" originally meant and "Power" is seen, too.)  He just gets it wrong. No great surprise; I can't believe that I'm about to talk about what I'm about to talk about now. The poor profs who tried to drill this stuff into my head as an undergrad are in no way to blame for any errors that follow.

Here's the thing: you have a muzzle that has to be displaced into a position. We give it an initial push, and it acquires a velocity. Now, we want it to stop on position, but smoothly. No backlash, no overreach. Mathematically, we can describe what we want as an equation of this general form:

Ax = -Cd2x/dt2. This is a differential equation, and quite a famous one, too. It's the "simple harmonic equation," and it appears all over the place from music to electronics. It is easily solved: $v(t) = \frac{\mathrm{d} x}{\mathrm{d} t} = - A\omega \sin(\omega t+\varphi),$
I'm stealing that from Wikipedia so that I don't have to spend time playing around with a math editor, so I guess that it is my fault that this expression lacks the vectoral formalism that I would prefer to see. I'm going to keep it, though, because the appearance of the sine function leads to the awesome experience of playing with an oscilloscope.  It's mind-blowing that an equation that we just wrote down to explain how we're going to make sure that a gun barrel stops moving pointed in the direction the computer tells it to point is the same one that that video is playing with, and, in fact, I am cheating a bit. There is friction involved, and perhaps other things as well, such as the viscous drag of oil passing around plungers in hydraulic equipment, or impedance in electrical circuits. So there is a velocity term as well:  Ax =Bdx/dt -Cd2x/dt2. Now there is no longer a neat solution. Now we're facing one of that vast majority of differential equations that can only be solved by numerical analysis. That is, by cheating, approximating, and, above all, by lots and lots of calculations.

Ironically, we've started with a computer telling a mechanism what to do, and ended up with a problem that we'd really like to have a computer to solve.

And there's more, because obviously the computer isn't some high-powered machine from which we can take off enough power to throw the barrel of a 10 ton gun around with. (Though if it were, that would be a great bit of Steampunk/dieselpunk technology, and the German navy tried an aspect of this solution.) The signal from the computer has to be amplified. The Admiralty Research Laboratory seems to have been in the lead in developing this kind of capability in machines. At least, both the British and American services ended up using the equipment that the ARL originally developed for remote-controlled searchlights. These were the "oilgears"  although vacuum tubes were coming in well before the end of the war.

The thing about amplification is that we're misusing language again. The word is simple and descriptive, and hides the fact that there's no mysterious process here. There is a low power signal coming in, and we need to exactly imitate that signal with a great deal more power. It can be easy. There's a sense in which this is how levers work, and the American "oilgear"coinage is quite clever.

But that's only going so far. No amplification can be perfect. It will always introduce "noise" into the system. In practice, for this and other reasons, the process of firing AA guns with computers was never bloodlessly technocratic. The muzzle was always slewing about a bit, and in the kind of total failure that any computer gamer will recognise, the barrels would occasionally end up pointing at entirely the wrong sector of the sky and fighting any attempt to get them back onto target. Welcome to the wonderful world of debugging, gun crew!

That's one side of the story, the side with 1100 QF 3.7" AA in action in the summer of 1940. Back up to 22 January, 1937 to see how it got that way and the story has two sides. This very month, work began at the derelict site of the old National Ordnance Factory, Nottingham, where Cammell Laird had tried off and on for 17 years to make a go of the old shellmaking facilities originally thrown up by Lloyd George's Ministry of Munitions. The former shell factory would now be an "Engineering Factory" in the Royal Ordnance Factory's stable, making the 3.7"AA and, ultimately, the 40mm Bofors Light AA gun. Per the devoted research of some anonymous Wikipedian, the nation would invest £1.8 million in the plant this year and hiring 2200 people, with another 1500 joining the staff next year. ROF Dalmuir would follow Nottingham into 3.7"AA production, on a site vacated by  another industrial titan of old, Beardmore. Together, these firms (plus others if Wikipedia is not exhaustive) made the 3.7" guns of AA Command. Others made other guns for the army and the navy, and many other things as well.

And on 22 January specifically, the weekly number of Britain's oldest technical engineering paper, The Engineer published the first of a 14 part anonymous series entitled "Principles of Automatic Control." It's pretty obscure now. If you're really into the literature, you may know that authorship of this series has been claimed for Russian-American engineer Nicholas Minorsky, but I would like to see the evidence, as the author seems to be very closely plugged into the London official/consulting engineering sector. This allows him to note, however briefly, progress in everything from industrial thermostats to  torpedoes, albeit with a heavy emphasis on autopilots for ships and planes. The series ran to 23 April, when the paper finally published an Editorial discussing the series and introducing its general features (because, obviously, that goes at the end of the series). It is by far the longest and most exhaustive technical paper published in this journal in the period.

It's pretty challenging in places (not least when it criticises Minorsky, leading me to strongly suspect the attribution). But there's no getting around the fact that "automatic control" is becoming an ever more important problem in industry. There's also no question that technological development has been driven by the armed forces. It is the Admiralty and the Air Ministry that care about getting it right, as the series' stinging indictment of the Sperry autopilot demonstrates. And the implications are enormous. It is possible that the QF 3.7" AA is not the most ubiquitous application of computer calculation, automatic control, and amplification in the country at this moment, even leaving radios aside, because of progress with thermostats, which promise improved results and greater fuel economy in a vast range of industrial sectors. The equations, on the one hand, and the equipment, from oilgears to vacuum tubes, on the other, will have far-reaching consequences.

So this being said, I think that it is at least accidentally important that the entire Territorial Army has been given over to the care and operation of these beasts. They're young men, now, and at least for those who go on to work in industry --the ones that the Prime Minister is specifically worried about in withholding funding from the Army-- this is one of the first machine tools of which they will ever have had charge. The intimations bubbling up to the surface in the late 1930s suggest that it is far from a coincidence that they present these boys with the problems of automatic control. There is, after all, a particular reason that the War Office chose to order such a challenging piece of equipment. The alternative, the German 88 was after all right in front of them. It's far from clear just how much AA Command got from this increased accuracy: most people rate the deterrent effect of AA fire much higher than the number of kills achieved.

But still....

This will be far from their last experience of automatic control. It will be continue to get more important in industry in the years ahead. Ultimately, amplified, noise-free harmonics will make Britain a great many US dollars at a time when they are badly needed. Can there have been an odder British industrial export offensives against the United States than this?