Tripod gaits Tripode gangarter

No one would have believed in the last years of the Nineteenth Century, that this World was being watched keenly by intelligences greater than mans.

Der var næppe nogen i slutningen af det nittende århundrede, der troede at vores verden blev nøje iagttaget af væsener der stod højere i intelligens end menneskene.

That as men busied themselves about their small chores, they were scrutinised and studied. In the same way that men themselves with microscopes scrutinise the transient creatures that swarm and multiply in a drop of water.

At menneskene, mens de var optaget af deres små gøremål, blev undersøgt og studeret. På samme måde som menneskene selv med mikroskoper undersøger de flygtige væsener som vimser omkring og formerer sig i en vanddråbe.

No one gave a thought to other Worlds as sources of danger.

Ikke én forestillede sig nogen fare fra andre verdener.

Yet across the gulf of space, minds that were to our minds as ours to those of the beasts; intellects vast and cool and unsympathetic, regarded this Earth with envious eyes, and slowly and surely drew their plans against us.

Men på tværs af rummets dybder, levede hjerner som i forhold til vores hjerner, var som vores i forhold til dyrenes; intellekter store og hårde og følelseskolde, betragtede misundeligt vores Jord, og lagde langsomt og sikkert deres planer imod os.

You know how it goes.

Du ved hvordan det går.

I read the story as a comic when I was a child, and I was deeply fascinated by it.

Jeg læste historien som tegneserie da jeg var barn, og jeg var dybt fascineret af den.

But one thing I was never entirely sure about: How did they walk with three legs?

Men én ting har jeg aldrig været helt sikker på: Hvordan gik de med tre ben?

Even though our intellects are no match for those of the aliens, that shouldnt stop us from guessing.

Selvom vores intellekter ikke er på højde med rumvæsenernes, kan vi jo godt gætte på det.

Gait 1

Gangart 1

Gait 1 is the one you normally see in films.

Gangart 1 er den man normalt ser i film.

The gait is defined by the "dance steps" and the triple that is written below them.

Gangarten er defineret af "dansetrinene" og det tripel der står under dem.

A gait is a repeated pattern of movements. The period it takes until the pattern repeats, is called a cycle. The triple lists when each leg takes the step that it does during the cycle. The length of the cycle is 1 for convenience sake. In real time it can vary greatly.

En gangart er et gentagent bevægelsesmønster. Perioden der går indtil mønsteret gentages, kaldes en cyklus. Triplet angiver hvornår hvert ben tager det skridt som det tager i løbet af cyklussen. Cyklussens længde er for nemheds skyld 1. I virkelig tid kan den være mange forskellige tidslængder.

The first number in the triplet is 0, so foot number one is put down when the cycle starts. The second number is 1/3, so foot number two is set down a third of the way into the cycle, and so on.

Første tal i triplet er 0, så fod nummer ét sættes i jorden når cyklussen starter. Andet tal er 1/3, så fod nummer to sættes i jorden en tredjedel inde i cyklussen, og så videre.

I think the notation comes from the mathematician Ian Stewart, who studied gaits among other things.

Notationen stammer vistnok fra matematikeren Ian Stewart, som blandt andet har studeret gangarter.

Gait 2

Gangart 2

You see gait 2 among quadrupeds that has lost a leg, and among humans that use crutches.

Gangart 2 ser man hos firbenede dyr der har mistet et ben, og hos mennesker der går med krykker.

What you see when you click the tripod images, is a programmatic animation of a virtual model. It is not a simulation that adheres to Newtonian mechanics. More like a puppet animation film. The gaits can be difficult to understand based on the "dance steps" and the triple, alone. So the animations hopefully help bring them to life.

Det man ser når man klikker på tripodebillederne, er en programmatisk animation af en virtuel model. Det er ikke en simulation der følger den newtonske mekanik. Mere noget i stil med en dukkefilm. Gangarterne kan være vanskelige at forstå alene ud fra "dansetrinene" og triplerne. Så animationerne hjælper forhåbentlig med at levendegøre dem.

Gait 3

Gangart 3

When I write #2 in the triple, it means that the third leg takes two steps in each cycle.

Når jeg skriver #2 i triplet, betyder det at tredje ben tager to skridt i hver cyklus.

Gait 3 is slightly limping maybe, but who knows, maybe it was one of the tripod gaits.

Gangart 3 virker lidt haltende, men hvem ved, måske var det en af tripode-gangarterne.

It is obvious that gait 3 can be varied by letting leg three take even more steps during the cycle. That results in a series of gaits ( 0 , 1/2 , (2·n)^-1 # n ) where n is a positive integer. All seen from a theoretical point of view. In practice it would quickly become inefficient. But that does not change that there are an infinity of tripod gaits.

Det er klart at gangart 3 kan varieres ved at lade tredje ben tage endnu flere skridt i cyklussen. Det giver en serie af gangarter ( 0 , 1/2 , (2·n)^-1 # n ) hvor n er et positivt heltal. Altså set ud fra en teoretisk betragtning. I praksis vil det ret hurtigt blive ineffektivt. Men det ændrer ikke ved at der findes uendeligt mange tripode gangarter.

Stotting

This gait is wellknown among gazelles and Looney Tunes roadrunners. It is not particularly efficient, and is, as far as we know, used mostly to signal "Im in good shape" and "it is futile to chase me".

Denne gangart er kendt blandt gazeller og Looney Tunes hjulben. Den er ikke særligt effektiv, og bruges så vidt man ved, mest for at signalere "jeg er i god form" og "det er nytteløst at jagte mig".

Stotting works best for creatures that are not too heavy, and while tripods will be able to stot, the signal they would be sending would be... perplexing. If you sit in the tripod while it stots, you are also probably not having the most comfortable time.

Stotting fungerer bedst for væsener der ikke er for tunge, og mens tripoder godt vil kunne stotte, ville det signal de ville sende være... forvirrende. Sidder man i tripoden mens den stotter, er det nok heller ikke den mest behagelige tur man har.

Faster

Hurtigere

Back in 1887 Eadward Muybridge succeeded in photographing a horse galloping, so that for the first time ever you could follow its legs and hooves throughout a cycle. His photographs were a huge sensation.

Tilbage i 1887 lykkedes det Eadweard Muybridge at fotografere en hest i galop, så man for første gang nogensinde kunne følge dens ben og hove gennem en cyklus. Hans fotografier blev en sensation.

The tripods can easily do that too...

Tripoderne kan sagtens være med...

Gallop

Galop

This is equivalent to gallop if you only have three legs. It is really just a variation of gait 1, but I didnt want you to miss out on it.

Dette svarer til galop hvis man kun har tre ben. Det er egentlig bare en variation af gangart 1, men jeg syntes ikke du skulle snydes for den.

Otherworldly

Uvirkelige

Remember that the tripods are constructed by intellects that are superior to ours. They might use technology that is far advanced to ours. So they might be able to move their legs in ways that nothing on Earth is able to. For example like this:

Vi skal huske på at tripoderne er konstruerede af intellekter der overgår vores. De kan anvende teknologi som er langt forud for vores egen. Så det kan være at de kan bevæge benene på måder som intet på Jorden er i stand til. For eksempel sådan her:

Spin

It is conceivable that human engineers could, with some effort, be able to imitate the spin gait. But the waddling gait would pose more of a challenge to them...

Spin gangarten kunne man godt forestille sig at menneskelige ingeniører, med noget besvær, ville være i stand til at efterligne. Men vralte gangarten ville de få det en hel del sværere med...

Waddling

Vralten

Unexpected

Uventede

The tripods were "invented" by H. G. Wells, who used them in his classic story "War of the Worlds". It was published in magazines in 1897 and as a book in 1898.

Tripoderne blev "opfundet" af H. G. Wells, der brugte dem i sin klassiske historie "Klodernes Kamp". Den udkom i magasiner i 1897 og som bog i 1898. Historien udkom første gang på dansk i 1912, som føljeton i Politiken.

In the story the aliens only land in England, and even though they mow down everything around them, there is a quiet relief that they after all are trapped in Great Britain, so the rest of the world might get off free. That lasts until the point in the story where some people are fleeing Great Britain on an overcrowded ferry. As they are sailing out, they see the tripods appear on the shore. The ferry is sailing at full speed, the distance to the shore increases, and it appears that they will succeed. But then a tripod steps into the water and sails off at lightning speed, standing on its feet in the water...

I historien lander rumvæsenerne kun i England, og selvom de mejer alt ned omkring sig, er der en skjult lettelse over at de trods alt er fanget i Storbritanien, så resten af verden måske kan gå fri. Dette varer lige indtil det sted i historien hvor nogle folk flygter fra Storbritanien på en overfyldt færge. Mens de sejler ud ser de tripoderne dukke frem inde på kysten. Færgen har fuld kraft på, afstanden til kysten øges og flugten synes at lykkes. Men så træder en tripode ud i vandet og sejler lynhurtigt afsted, stående på sine fødder...

Fin-slapping

Finneslag

Yes, it is actually possible that the tripods would be able to sail or swim, or whatever the right terminology is.

Ja, det er faktisk muligt at tripoderne ville være i stand til at sejle eller svømme, eller hvad den rigtige terminologi nu er.

Two of the feet can function as hydrofoils, providing lift, while one foot can function as a fin, providing propulsion. The two feet that are hydrofoils are static. They dont take part in the cycle of the "gait". That is why they are #0 in the triple.

To af fødderne kan fungere som hydrofoiler, som giver opdrift, mens én fod kan fungere som finne, som giver fremdrift. De fødder der er hydrofoiler er statiske. De tager ikke del i "gangartens" cyklus. Derfor står der #0 ved dem i triplet.

Hydrofoils only work at speed. But it wouldnt be a problem for the tripods to keep in the same spot, because they can also tread water.

Hydrofoiler fungerer kun i fart. Men det ville ikke være noget problem for tripoderne at blive på samme sted, for de ville osse kunne træde vande.

Water-treading

Vandtrædning

Here the feet are used in sculling motions.

Her bruges fødderne i skoddebevægelser.

Phew... six and a half gaits, and two kinds of swimming. There is more, because the topic is inexhaustible, but that must be enough for now.

Pyha... seks en halv gangart, og to slags svømning. Der er mere, for emnet er uudtømmeligt, men det må være nok for nu.

Three legs

Tre ben

After all this, there is one question that begs to be asked: What advantages are there to walking with three legs?

Efter alt dette, er der ét spørgsmål som trænger sig på: Hvilke fordele giver det at gå med tre ben?

It could be that H. G. Wells chose three legs to make it feel alien. He gave another of the alien machines five legs, maybe for the same reason.

Det kan være H. G. Wells valgte tre ben for at det skulle virke fremmedartet. En anden af rumvæsenernes maskiner fik fem ben, det kunne være af samme grund.

The theory of evolution can help us answer that. Which three-legged animals do we have here on Earth? None! Even though evolution has tried out all sorts of legged locomotion for hundreds of millions of years, for an immeasurable number of species. Three legs must surely have been tried over and over, as it doesnt take much for a quadruped to give up on one legs (turn it into a vestigial body part). Nature does not shy away from the number three otherwise. There are lots of plants with that number of petals.

Det kan evolutionsteorien hjælpe os med at svare på. Hvilke trebenede dyrearter har vi her på Jorden? Ingen! Det selvom evolutionen har afprøvet alle mulige benkonfigurationer i hundreder af millioner af år, for et uoverskueligt antal arter. Tre ben må helt sikkert have været prøvet igen og igen, for det er ikke noget stort spring for en firbenet dyreart at opgive et enkelt ben (lade det blive en rudimentær legemsdel). Naturen har ellers ikke noget grundlæggende mod tallet tre. Der findes masser af plantearter med det antal kronblade.

From that observation it appears that it is probably not very good to be three-legged.

Ud fra den iagttagelse ser det ud til at det nok ikke er særlig godt at være trebenet.

But that answer makes it even more of a mystery why the aliens were using tripods... It could come down to that they simply think three legs look cool. Maybe it is more fun to walk with three legs. Who knows?

Men det svar gør det bare endnu mere mystisk hvorfor rumvæsenerne brugte tripoder... Det kunne være at det i bund og grund er fordi de synes at tre ben ser sejt ud. Måske er det sjovere at gå når man har tre ben. Hvem ved?