The crane stance and its applications...?

What you call Crane stance with a single leg in contact with the ground actually has many applications besides kicking. BTW: As I understand it, doesn't bunkai mean "application"?

The single leg stance is also a mean to focus power from one rooted leg to your punch. The mechanics for a kick from the crane stance can also be used in a punch. It is actually the same. The force you exert from that single leg against the ground or your root-ness is transmitted through your body to the fist or even a block. Think about a situation where you are rapidly transferring your weight from one leg to the other such as when you are backpedaling or moving quickly and see an opening to strike. The power for that strike can still be generated by that one single leg in that instance when it is properly rooted. So rather than planting both legs first and then strike, you can do so with just that single leg that is already in place.

i havent explored too much into this stance
the stance it self works very well on uneven terrain such as stairwells or bleachers

as for bunkai, there are many application. the stance can be used as a leg lock or arm bar as well as a choke, it is also very useful on ground fighting for these types of trap.
you dont have t be standing to use a stance, your stances can be used on the ground
about 35 secs into the video, is a nice application
http://www.youtube.com/watch?v=quVc-P9uFzY

as i said these are just a few of the many applications,

stances are often misunderstood and few people realize the potention of the bunkai to them, people see them purely as a stance and not as a technique which is a mistake since it is both.

Great question. This is one of those "stances" that I believe can be more static in nature. I think this stance, as Kokoro points out, is a great example of a lying-on-the-floor technique without actually having to lie on the floor.

There are 3 kinds of crane stances, that I'me aware of:
1) the left foot is placed behind the right knee and the left foot's shin is perpendicular to the floor
2) the left foot is placed next to right knee and the left foot's shin is perpendicular to the floor
3) the left foot is placed next to right knee and the left foot's shin is ANGLED (sticks out to the left) to the floor

in method 1), the application can represent a bind, hook, or pull toward you, of opponet's knee/shin while standing or lying down.

in method 2), the there are a couple of applications:
2a) it is a on-the-floor position where you are mounted; your knee up represents keeping the distance open between you and opponent.
2b) it is a chamber of sorts to a jumping front snap kick (some call this a crane kick, which was a question that was asked about this a day or two ago) - and Shadam mentions this again in this question
2c) it is a check or block of a kick or weapon, as Liondancer mentions.

in method 3), the application represents that your opponent is kicked to the inside of the knee: either to disable or to sweep.

I use it for
evading/stepping away from an attack,
against a front leg sweep, you shift your weight to the other leg and pull up the front leg,
blocking/checking a kick,
striking with the knee,
breaking down a foundation on the downward motion,
hooking/trapping opponents leg on the upward motion especially if you hook your own foot around your leg you are standing on,
sweeping,....
just a few applications that come to mind off the tippy top of my head. So you see it is by no means just a defensive stance and can be quite offensive too.

Crane techniques tend to be more graceful and fluid than techniques such as tiger and dragon ones. Folks here have told you about how defensive and counterattacks can be applied from a crane stance.

I'll offer that most people in the west focus on more "hard" techniques such as those of the tiger and dragon as they're more "natural" to us. But if you look at the like you are and practice them, you'll find grace and beauty in your art. Plus done right they are very effective.

If you do Tomari No Rohai Kata (Okinawa prefecture classification in Shito Ryu it would be Matsumura no Rohai I think), I can give you three usages for that version

1. check a kick similar to how Weidman but adding more of a strike to it.
2. as someone tries to grab your front leg step back and drive the knee to his face while pressing down the shoulder blades.
3. side stepping an attack before rushing into the attacker.
good luck

There are a few single leg crane stances. Most are defensive in nature and posture. The one i particularly do (in Kuk Sool) is used as a block for kicks and is a defensive posture that sets up for crane techniques and strikes. You don't always need to kick from this posture. Crane is mostly tendon strength not muscle strength. It also elongates the body and makes you taller in appearance.

actually with my questions about the crane kick earlier ive been studying it and practing it all day in tang soo do/tkd we do it without stance and its called a jumping front kick and when we do we dont put the knee up first but it just comes up when you kick. but i dont think the stance does anything but mabey hurt the momentum of the kick a lil bit or i could be wrong because mabey its faster or something if you lift your knee first but it just looks flashy to me almost like a taunt and idk what bunkai is?

I think Tom had a great answer, if you look to the characteristics of the crane and the system you'll get an understanding of the stance, graceful and evasive etc,
next time you use the stance while training with a partner, take a look at the distancing or range in which you feel comfortable to execute a counter, I think you'll find it works best at distance utilising long range strikes and kicks but also quick on the defensive utilizing its circular movements.

“The spirit of the crane resides within the stillness.”
http://www.youtube.com/watch?v=TB2pKxwQqlg

In your search for a literal identification of the crane stance, or any physical move for that matter concerning
any martial arts is problematic. Although fighting techniques can be identified clearly and others obscure.
Instead, try looking at it for its most elementary purpose. That is to say not what can I do with it , but rather what it actually is.
By definition any stance is a method of travel to get form place to place, and to enhance your defense and offensive techniques. But not limited to only that. The possibilities then become whatever you discover! As a mater of fact, during any give day the amount of times you use a single leg stance
would surprise you.
I hope this helps.