Monday, 20 July 2015


When the girls Dau.I and Dau.II were small, we acquired a copy [I may even have bought it!] of Stronghold, a logistics and warfare game which they loaded into a an old Dell "laptop" the size of a briefcase. The idea was to acquire and manage resources - wood, stone, beer, wheat, peasants, spears - to build a castle and develop a position of power with [dis]respect to other local magnates. They played each in her own distinctive style: one more amused to maintain a happy people dancing round maypoles, talking in rustic British accents and making bread; the other more keen to "take it to Baron Corpulent" who lived on the other side of the hill.  One of the acquirable resources was  a pack of savage war-wolves which could be unleashed with deadly effect on lightly armed troops from the other side. Both of the girls are working in the catering trade but only one of them eats meat.

But I'm not here to have a nostalgia attack about how the girls learned their maths and engineering by counting arrows and mustering the materiel for making things rather than going to school.  No, today we are back to 20 July 1304 and the end of the Siege of Stirling, a telling episode in the interminable wars that were fought between England and Scotland until they were united under a single "nosmo" king in 1603, and finally achieved full political union in 1707. One of the persistent problems in Scotland's history was the early death of successive monarchs, leaving infants as the oldest direct descendants. Edward I "Longshanks" of England (b.1239; r.1272-1307) was known as Malleus Scotorum, Hammer of the Scots. But he preferred to go through the rule of law as conceived in medieval times and in the early 1290s arranged for John Balliol to be appointed King of Scotland while acknowledging that Edward was his liege. Balliol's father was the founder of Oxford's Balliol College.  That showed how intertwined were the land-holding of the magnates of those days: everyone who was anyone had land on both sides of the border and this conflict of interest made for trouble. King John lasted but four years before the impossibility of his situation, between English hammer and intransigently independent Scots anvil, became impossible.

After invading Scotland in force to bring these unwilling vassals to heel and prevent them getting too chummy with the French, Edward had cleared all resistance except the strategic castle of Stirling overlooking the then most down-stream bridge over the Forth.  The Scots garrison held out from April 1304 until Edward built the largest trebuchet [L diagrammatically] known to have been constructed in medieval times.  The diagram shows the theoretical features which hinge on mechanical advantage.  A huge (5 tons was possible) counterweight on the short side of the arm falls a short distance under gravity and shifts a smaller weight at the end of the longer arm. That smaller weight travels faster and further than the counter-weight.  The Scots in Stirling castle didn't weren't allowed to surrender until the English had actually used their new toy to knock down a section of the curtain wall. The English accounts, kept in Latin and itemising payments to carpenters and other effectives, called it Lupus Guerre which was translated as Loup-de-Guerre, Ludgar or Warwolf.

Don't imagine that the physics and engineering implied by the cartoon above is, in reality, straight-forward.  One of the issues is how to bring the counterweight back up to height after release and this was apparently solved by teams of men in two circular treadmills. 8 fit-soldiers weighing 500kg have to walk 30m in a suitably geared mill-wheel; actually it's more efficient to make t'buggers run further with better gearing ratios.  With smaller trebuchets you can achieve the mechanical advantage with a  series of pulleys but the long lengths of rope involved require constant attention to prevent kinks and tangles.

The other issue is getting your payload furthest with the mostest and this is largely about tricking about with the release mechanism [L]. A key element of the trebuchet is the sling which extends the length of the delivery arm in the same way as a pelota basket extends the arm of Basque Jai Alai players.  Extended arm means faster travel and speeds of 100km/h can be achieved. A lot of the early-modern mathematicians were employed in the field of ballistics because medieval princes wanted to get the biggest bangs for the bucks. It was soon calculated that a 45o launch would give you the furthest trajectory, but sometimes furthest is not the most desirable. Lobbing a missile beyond the far wall of the besieged town was less useful than landing a plague-dead corpse in the market square. The sling for the payload has a fixed and a ringed loose end, which is held in place by a pin [L]. The angle of the pin dictates the moment of release, and the Master Armourer would be responsible for the fine adjustments.  And of course the whole machine has to be shifted left and right to get on target.

These things were lost in the mists of time as gunpowder-based siege technology swept the world.  They have been lovingly reconstructed by the sort of chaps who dress up in cardboard armour and whack at each other with rubber swords on the anniversary of great battles of the past.  There's one which is set off regularly each Summer in Warwick Castle in central England, and another in North Wales.  But why piffle about with beams made of ash Fraxinus excelsior which you can weld a trebuchet out of scrap steel and launch a few cars into the air . . . why stop there when you can launch a car with a boat and it's trailer?  That's an interesting vid because it shows a work in progress, the missiles are flying every which way until the boys master their kit.  That's what real science is about - finding how the material world works by controlled experiments. On the all-good-fun-front, check out the annual Punkin Chunkin event in Delaware. Real engineers of course make their stuff from raw stock; bricoleurs make it from old bicycle wheels and repurposed washing-machines; wannabees go to Amazon to buy a trebuchet kit.  But a warning: don't do this at home: it could all go horribly wrong.

Punkin chunkin could qualify as an extreme example of yesterday's list of weird sports.  [Weird. adj. More interesting than baseball or soccer].  I forgot a couple of others:
Extreme ironing. "Mixes the thrill of outdoor activity with the satisfaction of a well-pressed shirt."
Mountain unicycling. Bonkers.  I wouldn't even be carried down those slopes on my sofa.

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