If the air suspension setting off road is selected and a proper supporting mechanism is installed such as a jack then the normal or entry setting is selected would the wheels on the supported side retract off the ground?
I suspect that the unsprung weight at the wheel / suspension linkage would be sufficient to keep the wheel on the ground. My thinking obviously is getting yourself unstuck by getting the tire off the ground so to install rocks or timber underneath the tire and or removing the tire.

 

No.

Just the opposite.Lr3 will feel, that it is grounded , with obstacle/jack underneath and when you lower the suspension it will actually go up a notch, two inches to be exact.you will get the wheels off when you put a bottle jack under a lower control arms, additionally to a jack stand that you already placed under the rear or front of the chassis, but this somehow not always works the same .why?
This is usually my way to change tire on LR3.Depending on the wheel, I usually raise that particular corner, just a bit,while being already in off road hight,just to take majority of the weight off the wheels, place jack stand under the chassis and then i pt a 6 ton bottle jack under the desire lower control arm , raise it and usually lr3 raises the wheel for me, but ,like I said , this not always works as sometimes, bottle jack will raise entire corner of the jack stand that is already there, but usually it works.

 

Jacking with the the air suspension is a tricky thing.

first off, 2x on thorgal. with or without the key in the ignition; in accessory or run; engine running or off; doors open or closed; placing a jack under the control arm makes jacking half the work. take weight with the jack, the air spring pulls tire up. works great if you do it right, pain in the *** if you do it wrong - see below.

To answer the original question - "how do I gain clearance when stuck off road?"

EXTENDED MODE:
if the vehicle is high centred (grounded) and traction control kicks in the air system will go into extended mode (see user's manual) page 174, 175

if more height is needed you can force it out of the system. while in extended mode apply the brakes and press the switch to "lower/access" and hold for 3 seconds. you are now in SUPER extended mode. lol

to exit extended mode press the raise or lower switch or drive more than 5km/3mph for 30 seconds

MAKE A RAMP:
jam stuff in front of or behind the wheels and drive onto it. only works if you can get enough traction to climb onto the ramp

LIFT AND BLOCK 1:
jack under the control arm to raise tire, add blocking, remove jack, repeat on other wheels

LIFT AND BLOCK 2:
use a hi-lift jack and lift mate wheel lift like this

to answer the second question/elaborate on thorgal's response:

CHANGING/REMOVING A TIRE
IF you make a bottle jack tight by screwing out the top FIRST and then jacking, you are making life harder. the tire goes up because the air spring went up, but when you let the jack down the tire has gone up with the air spring so now when your tire touches the ground the jack is stuck. easiest way to avoid this is to raise the wheel high enough to put something like a two inch board under the wheel. other ways to avoid this: 1) jack up with out screwing out the top. 2) don't use a bottle jack, use a floor jack instead. 3) pull the fuse for the air system in the engine bay fuse box (26) or disconnect the battery (no movement of air springs) 4) only use the proper technique in the owners manual. 5) use a lift mate and a hi-lift - requires blocking before you can remove a wheel.

ALWAYS follow safe lifting techniques *use wheel chocks *use jack stands or blocks *only on firm level ground *no one inside the vehicle if only on a jack (changing a flat with screw jack) and so on.
Air suspension safety *disconnecting an air line could cause movement *adding or removing weight to the vehicle could cause movement*OPENING A DOOR IS NOT A GUARANTEE that there will be no movement *the only guarantee is to pull the fuse in the engine bay (#26 EAS CPU) or disconnect the battery

Play around with the system a bit. I learned about the stuck jack the hard way. also, check the spare tire winch from time to time. it won't do you any good if it is seized and you can't get your spare

 

Ok that makes sense and I guess I knew that already but didn't if you know what I mean.
I do have a Hi-lift jack and wheel mate as well as wheel chocks in my extraction kit bag.

 

Over the weekend I had some firsthand experience with this. Was installing the rock sliders on the Landy and one of the bolts wouldn't start in the back so I got the floor jack out and put some upwards pressure on the bottom of the sill plate. Engine off, doors shut, keys out of the ignition tail gate open. I jacked it up maybe an inch past contact maybe a bit more and after stopping the jack for maybe 30 seconds of a full minute the air suspension extended maybe an inch. My buddy helping me was like "Woh! What just happened?" Once I expanded he was all "make it do it again!!", he's a Jeep guy they are easily entertained....

 

I like that comment! I think with the Jeep guys, it has to be simple; their solution to getting thru a rough spot seems always to be the same - spin the wheels faster.

At the same time, for the life of me, I cannot figure out why taking a wheel off a 3 is such a production, but it is.

I carry three jacks with me, a 2 ton and 6 ton bottle and a small trolley plus lengths of 2 x 6 - what a production! O yeah, there is the LR scissor jack as well but .... About the only excuse I have is that there is so much wheel articulation that the rubber just never seems to lift off the ground.

No wonder at the dealer, they use a frame hoist for everything and the wheels hang - droop actually.

I also carry a small air compressor so that I perhaps do not have to change a flat tire - and once a year I drop my under the rear spare tyre down just to make certain it still drops - and yes, I am on my second spare tyre winch. Maybe Jeeps do have some merit.