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So let's have another look at that little whirly diagram and relate it to how Goliath is moving. Here we go with him moving in a straight line:

The plan view on the left there is Dagu's own drawing of the Rover 5 chassis and as you can see I've superimposed the last diagram from the last page over it showing the motor pair running in opposite directions relative to each other but in the same direction along an imaginary line running through the centre of their output shafts and parallel to the short faces of the rectangle comprising the main body of the chassis and therefore perpendicular to the tracks.


If you are new to this that last bit up there is going to have you scratching your head, chewing your pencil and saying "is he writing in Dutch or something here?" but fear not because I'm now going to spend a number of paragraphs banging on about absolute and relative references. If you don't know the difference between absolute and relative references don't worry. By the time you've read this you will. Whether you like it or not. Ready?

Here we go with a bit of good old British Jingoery and if you've never seen the film Zulu you won't have a clue what I'm rambling on about but bear with the outpourings because it does have a point at the end. Plus, if you have never seen the film Zulu, and you are not a girl, what's wrong with you??


It's a peaceful Sunday afternoon, you've had your roast beef with potatoes, two veg and a heap of Yorkshire puddings, done the washing up and the relatives have gone out for a walk round the park. Perfect, because you know that Zulu is on the telly, and you're sitting there with your big cup of tea and your feet up on the pouffe getting a good eyeful:

telly eyeball

And there on the bottom to the right is the scientific symbol for an eye looking in whatever direction the curved bits are pointing, in this case the fictional recreation of the moment when a handful of South Wales Borderers mount a spirited defence of the lonely little outpost that is Rourke's Drift. Stanley Baker and Michael Caine have looked all heroic, everybody's got their red jackets a bit dirty and thousands of Zulus are running down the hill waving their pointy spears.


You know you've got a rousing chorus of  "Men of Harlech", The exciting bit with all the cows, and the bit at the end where Michael and Stanley get all noble and prepare for death until the Swiss bloke laughs at them and says "they're saluting you!" and then comes the lump in the throat bit as the Colour Sergeant calls the muster and shows the tiniest possible bit of emotion as he ticks off the names of the dead, and then Stanley gets all noble again and the film ends. All in all, a very decent way to pass a Sunday afternoon.

Look, if you don't fancy Zulu, you can substitute it for some other film. Me. I'm having no truck with Mary Poppins, and the least said about Bridget-bloody-Jones, Notting-bloody-Hill, Four Weddings and a Funeral or Love Actually (what is that film about??????) the better. Nor am I having Wimbledon, or anythying at all with Colin-bloody-Firth in it unless it's Tinker, Tailor, Soldier, Spy where he gets shot at the end. If "The Great Escape" or "The Eagle Has Landed" is on the other side I might consider it, but if it's Keira Knightly in a period drama that remote control is steering the telly in the direction of Zulu every time. I hope that's all clear.


What was the point before I began that tirade?  Oh, yes, all the best bits of the film are about to come before your eyes when dimly you hear the front door open. Oh dear. Because here's what's going to happen now:

telly eyeball DGB

Yes, some Dreadful Gooey Brat (DGB) is going to position himself between you and the Battle of Rourke's Drift and start blathering on about a squirrel he saw in the park. The DGB will batter on at length about this amazing and miraculous vision in which the squirrel was seen  to eat a nut  and completely and utterly astoundingly, proceed to climb a tree. Then a bit further on another squirrel was seen. Or it might have been the same squirrel, nobody's quite sure. The stupendous news is that the second squirrel (which may or may not have been a reappearance of the original squirrel) did not climb a tree. What it did do was climb over a park bench and disappear under a bush.


It will now dawn on the DGB that you are watching Zulu and he will turn round to look at the screen. He will not move out of your field of view and so now instead of watching a clash of military cultures you're looking at the back of the DGB's head. You now have three options to recommence looking at the conflict between the soldiers of Her Majesty Queen Victoria and those of His Excellency King Cetewayo.


Option 1 is to smack the DGB round the back of his head and shout "Move!"   Not a realistic prospect as not only will the DGB howl through the rest of the film, the subsequent argument with the DGB's mother will ensure you don't notice even the bit with the cows happening on telly.

Options two and three are illustrated below:

telly eyeball DGB telly eyeball DGB

It does of course mean moving your head to see round the DGB thus altering your field of view. Now, after all that rambling about Zulu and why it's better than anything with Colin Firth in it, comes the point of this narrative. Because look at the DGB. He has not moved. He has maintained a fixed position in front of the telly. But in the drawing on the left, according to the field of view, he is to the right of the soldier in the foreground. In the drawing on the right the DGB is to to the left of the same soldier.

What's happening here is that if you give the DGB a map reference he will remain constantly at that reference. He has an absolute value. But because you move your head, the reference value of the DGB in relation to the telly changes. To you and your eyeball, he has a relative value. Try it. Put your hand in front of the computer screen and focus on one of the pictures of the DGB above. Now keep your hand still and move your head so that the DGB appears to go under your hand and re-emerge at the other side. Do the same the other way. The DGB will be either next to your little finger or your thumb depending on which way you are going and which hand and picture you use. The computer screen has not moved though. Your field of vision has, and created from the absolute value of the position of the DGB a relative value between the position of the DGB and your eyes.


In physics this is called co-variance and what it means is the same thing looks different depending on how you are looking at it. if you aren't careful it can cause error in your experiments and it's the reason that lots of people every year claim to have seen a UFO over Lincolnshire, when what they've actually seen is an aircraft coming in low and at a funny angle because the pilot is having a range practice at Donna Nook and is either going in or coming out again. The same is true of other places; lots of UFO reports come from places off the flight-paths of the airlines because the observers on the ground are seeing brightly-lit Lufthansa vessels on the way to Frankfurt or somewhere at shallow angles at night and the shape does not look like an aircraft far away but a UFO quite near. I've done it myself until I realised what I was seeing by putting binoculars on it.

So what's this got to do with Goliath?  Let's look at those diagrams from over the page again.

Motorsidebyside motor90 motor180

One of these motors does not move at all. It has a fixed absolute position. The other moves twice, in increments of ninety degrees. Therefore, in the beginning, the motor that does not move is in relation to the motor that does, parallel, and of course the relationship is mutual. Because they spin in opposite directions, the forces cancel each other. Consider now the red lines crossing the centre of each motor.  When the moving motor moves the first time through the ninety degree turn, they are mutually perpendicular, and when it moves the second time they form a straight line (180 degrees). If you looked at the motors in parallel, they would indeed move in opposite directions. If you looked at them in the 180 degree formation above, even though both motors are still spinning in opposite directions to each other, because of the disparity of the displacement they are in fact spinning in the same direction to the eye and will produce force in the same direction too. This is co-variance at work and it fools even experienced people into wiring covariant motors up to spin in the same direction if they aren't concentrating. If you do that, you'll get forces acting in opposite directions, and in the case of Goliath it will cause a turn rather than a progression in a straight line.


It's one of those weird things that physics often throws up just to confound common sense. The best thing to remember is: two motors at 180, wire up red from one to black from the other (or whatever colour your wires happen to be, wire them in opposites).

Ian Lang, September 2013

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