## Sunday, 20 December 2009

### Analog Computers

In her excellent book, Longitude.  Dava Sobel told how a clock behaving in a deterministic way is a crucial component of successful navigation. The first accurate clock which could maintain synchronisation with the time at zero degrees longitude was the beginnings of an analogue navigation computer, albeit one that needed a little manual assistance to complete its task.

What makes an analogue? An old style vinyl album records a representation of the sound waves that took place when the original piece was recorded. A frozen graph of the sound that’s been curved into a spiral from the outside to the centre of the record. The volume level of the sound is represented by the depth of the peaks and troughs of the graph, and the pitch by the interval between the peeks and troughs. Low volume sounds tend to be hard to distinguish from imperfections in the manufacture of the disk - noise. The primary characteristic of analogue systems, and their main limitations: the magnitude of all values is represented by the magnitude of a signal somewhere.

The schematic above shows the Moniac analogue computer. (currently on display in the Science Museum in London.) It was used as a teaching aid to model the national economy. Moniac used the flow of water through the system to 'model' an economy. It featured valves to create the effect of changes in taxation and other policy decisions. See Monica technical description for a complete article.

Analogue computers used in gunnery and navigation need to be built like the proverbial brick outhouse. They generally used gears and motors. Again physical values are used with, for example, the distance turned by a wheel representing values such as speed or distance.

A number of mathematical functions must be performed and over the years engineers have dreamt up different ways of performing them. A classic problem in air navigation is distance travelled over ground when all we know is airspeed and direction. Before we get very far we need to do a little Polar to Cartesian conversion. If airspeed is known, and heading, how can we get distance travelled north and south, east and west?

One answer was the ball resolver, see below. Essentially it is an infinitely variable gear. (This is actually from an early 20th century computer in the Science Museum for predicting tides but the same mechanism in somewhat miniaturised form featured in many navigation computers.)

An electric motor turns the disc at a speed that represents airspeed. The disc turns the brass ball and the ball turns the roller. If the ball is positioned at the outside of the disc the roller will turn quickly, if the ball is moved towards the middle of the disc it will turn the roller progressively slower.

The system has another motor, this driven when the aircraft heading changes. This motor moves the ball from side to side. When the plane is flying due north the ball is positioned at the outside of the disc. The roller is turning at it’s highest possible speed for the speed of the disc. If the aircraft turns to the right and flies more east, as in the diagram below, the system will move the roller towards the centre of the disc. Even with the airspeed the same the velocity north will reduce.

A second resolver is used to calculate velocity east. Identical to the north one except that the ball is set up to move differently. With this one the ball is at the outside of the disc when we are flying east and at the inside when we are flying north.

With the two revolvers we can convert the polar parameter airspeed and heading to the cartesian velocity north and velocity east. And velocity north goes negative when the aircraft is flying south and velocity east goes negative it is going west.  (and, BTW those same resolvers can work the trick backwards and convert Cartesian back to Polar.)

With the velocities it’s pretty easy to calculate distance travelled. Those mechanical counters on bikes and speedometers integrate speed and get distance. It’s just a matter of gearing. If we’ve decided that 60 miles an hour is represented by 60 revolutions per minute we just have to arrange the gearing so that one mile will pop up after 60 revolutions of the velocity rollers.

We can even turn distance in miles into degrees of Latitude and Longitude. 60 nautical mile is one degree of Latitude, but Longitude is a little more tricky. Those pesky lines of Longitude get closer together as we move away from the equator so a third disc resolver needs to be added to correct the velocity East/Longitude, for changes in Latitude.

Of course, these calculations assume no wind conditions, unlikely. But supposing we have a system that can measure groundspeed and drift. Moving on a few years from the Norden bombsight etc (which needed ground observation to get drift) we had aircraft like the Vulcan with downwards looking doppler radar that could directly measure groundspeed and drift. So, instead of feeding the computer airspeed we feed it groundspeed derived from radar, Green Satin.

Green Satin  also supplies the drift angle, the effect of wind on the aircrafts track across the ground. In order to complete our analogue computer we have to find a means of adding two angles together, the original heading angle and the drift angle. For such an apparently simple problem the mechanical analogue computer  uses a differential. Two input values, one for heading angle, one for drift angle are (algabraically) added to produce track. Track is the angle of the aircrafts path over the ground.

All the above techniques are only a sample of what was done with electromechanical analogue computers. The mechanical systems have their shortcomings and there are numerous other analogue techniques, many of them purely electronic. Vacuum tubes amplifiers were used, and as soon as they became available, transistors. And I’ve not even mentioned a now totally obsolete lost world ‘solid state’ technology called magnetic amplifiers.

Now the analogue computer has had its day, although it arguably reached it technical best, (with integrated circuit operational amplifiers) just as it was being made obsolete by the digital computer. As Robert Heinlein observed, that tends to be the case, by the time a technique is finally perfected, it’s generally obsolete. And so it is with the analogue computer.