Tree and rock method
In this method you run leftwards off the far end of the bridge from the lower deck or the bridge support, and bounce off the ledge then a tree and a rock. Suitable for PAL. Some possibility for NTSC?
Full description
There are two possible run-off points for this method but I'll concentrate on the primary one first. Go to the far end of the lower deck and run off the left corner. The angle isn't too critical but I suggest starting midway between the final pair of deck braces (each with a light at the bottom) and running towards a spot about a foot to the right of the deck's corner. That should set you up nicely for hitting the ledge in the right place. You need to hit just past where it bends around very slightly. There's a darkish patch there, handy for targeting.
As you near the ledge, try to be in contact with the cliff wall so you'll hit the ledge at the back, coming in completely vertically. I'd also recommend having your back to the wall by the time you hit, so you'll be facing the direction you're about to bounce off in. You can rotate gradually on the way down to the ledge, or more suddenly as you near it - whatever you prefer. Crouch as you hit, to slow you up a bit.
Bounce directly away from the cliff, out towards the right hand side of the tree which has a rock just to its right. Bounce off the branches and down off the side of the rock, crouching as you hit the rock.
There are five possible rocks (your rock was randomly determined at the last loading point) and some are friendlier than others for breaking your fall, but there's a way of making sure you get the best rock - in which case you can usually land with not even a flicker of your shield. For details of that, see my older separate article on this descent method.
An alternative run-off point is the nearby bridge support attached to the wall, which you can jump onto quite easily if you hold your nerve. The descent seems more awkward from there however. You'll probably find it harder to end up on the right trajectory towards the tree.
Incidentally, if you miss the tree it's actually possible to fluke survival just by grazing off the rock. That's happened to me a few times, skimming over and going beyond it. But surviving by intentionally using just the rock would be so fickle that I don't consider it worth calling a 'method' at all.
Checkpoint advice
To make things as easy as possible for repeat attempts, get a delayed checkpoint when ready to start your run off the bridge.
Difficulty and system differences
With PAL, if you've got one of the friendliest rocks this is an easy method. I managed 92% and 80% success rates for the best two rocks (measured over 50 consecutive tries), while the next best rock gave me a 50% success rate. The work with the controller is nothing tricky. You need little more than a bit of decent aiming and crouch timing. The descent has a rather elegant and relaxed feel, quite a contrast to most other methods.
Unfortunately, with NTSC or PC the game will probably kill you before you reach the ledge, even if you use the bridge support, the lowest run-off point. You might be able to manage it with NTSC though; in the HBO forum Captain Spark reported managing it twice, though it took him over twenty tries each time. However, I haven't heard any other NTSC users reporting success. From PC users I've heard only reports of failure (e.g. see UrsusArctos here), even when using the bridge support. cocopjojo helpfully illustrated his failure with two short movies: one using the lower deck for the run-off, and one using the support.
History and links
You can see me demonstrating the method in BCM7, eliminating covies as I go. It's also used in BCM8 (in which I first need to get into the entry passage, in connection with getting extra Marines). The movies were advertised in the HBO forum here, where quite a long thread developed.
One One Seven mentioned the general idea of this method to me on October 2nd 2004, and as far as he can recall, it was a method he found for himself. Initially I misunderstood the description and didn't get anywhere with it, but months later I realized out what I was supposed to be doing and posted the first version of my article on it on March 24th 2005, along with articles on how to use it to engineer some novel gameplay by rearranging things. I advertised the novel gameplay in the HBO forum and it got mentioned in the HBO news, but my ad didn't specifically mention the descent trick as it was really just a tool to me, not the main thing of interest. As such, it could easily have gone unnoticed by people who might have been interested.
I guess Juggertrout was one such, because the trick appeared in his June 17th 2005 video Things to do on the first AotCR bridge when you're bored, as one of two "new" descent methods. Juggertrout tells me that he'd read about it in a forum, and decided to film it. The video was advertised in the High Impact Halo forum and can now be found in his video archive there. He performs the trick around 1:59, though with some interesting variation in technique compared to mine. He leaves the bridge heading further right but drifts left and ends up hitting the ledge at about the same spot that I would. However, at this point he's actually facing along the cliff and thus bounces off sideways. He's also looking down, with reticle very close to the ledge impact spot. At the moment of impact he switches to his other weapon then back again, which mystified me. But later I came across someone suggesting that switching weapons while looking down reduces fall damage - which is news to me if true! - so I'm guessing that was the rationale.
It's quite possible that the method may have been described somewhere earlier though. In a High Impact Halo forum thread from late August 2004, Darkiller asks "How would one get to the bottom without a gun turret?", and grenadesticker replies "You have to hit the first ledge and than a tree or the warthog". The tree isn't identified, but is surely the one involved in this method.
While working on this guide in late January 2010, I realized you could also do the run-off from the bridge support, which I thought might be useful for people who've had a problem getting killed before they reach the ledge, i.e. NTSC and PC users. That doesn't seem to've been the case however. Nor was I the first to try the bridge support. Turns out that Juggertrout used it in his 2007 video Tribute to Assault on the Control Room (advertised here), which also features a standard run-off from the deck; all starting around 1:46.