Try to keep it simple. I am a simple person and get lost with big words. I will take 10, 50 or 100 words to get my point across, but they generally understand what I am saying.
Think of carpet as like at the beach the skim boards (the ones you toss out, run and jump on to skim over water. They slide over the top. Lay a piece of carpet on the sand add the power to the top of it and it slides along the top of the sand.
Now for a experiment; you probably done this or something like this already in your life. Dig a 12" hole in your yard however deep you want (6" should be enough). Put a piece of fabric over the hole (cheep piece of plastic tarp or what ever you have soft and flexible 24" X 36"). Now put some of the dirt over the hole where the hole was. The fabric will pull into hole with dirt.
Now that you got your hands dirty (do not wipe them on your clothed, this makes the laundry person upset) you are not through getting dirty.
Pull the fabric out of the hole, put dirt additional around the edges of the fabric. Now put the same amount of dirt over the hole again. You can even put more and the fabric and dirt will not sink into the hole.
Now that you have thought about working hard, and started sweating, you can wipe off your forehead and dry your hands on your clothes as you kept them out of the dirt.
Back to the carpet! Most people will toss the carpet on top of the sand, and try and drive over it. This kicks out and was a waste of time! If you had put some sand (couple of inches deep) on top of the carpet to anchor it down, you would have much less chance of it kicking out! A couple of inches of sand should not stop a vehicle but get it to hold the carpet down.
What makes the maxtrax and sand ladders work is the sinking into the sand with the rough surface allowing then not to slide out when the tire starts to spin on them. They also distribute the weight over a grater area.
Before you go - know! Read the Sand -
There are many types of sand and soundness to it.
Wet sand can be very firm, like hard dirt. Dry leeward dune sand can be almost like quicksand.
Learning to read the soundness of the sand will make the driving in it much easier. You will be able to adjust you driving to the conditions. Look and get a feel for indications of the consistency of the sand compaction. For dunes watch for the windward and leeward sides of the hills. The windward sides are generally more gradual slope, this can be identified ripples in the sand or a smooth surface. They generally are firmer surface and less chance of sinking in deep. The leeward side of hills are generally much softer and have a slip degree of about 31 degrees.
The mixed grain sized sand is generally firmer then all of one size. The smaller size grains of sand work down into the area between the larger size grains. This then will stabilize the larger grains of sand and make it firmer like a decomposed granite soil (dirt).
Sand of the same grain size will be softer what ever size that is. This can be all round 2 pound beach rock of the same size or grains as small as .005". This will be very unstable and you will sink in. The size dose not make the difference, just that they are the same size.
Sand Dunes will have a windward side (the direction the wind generally blows from), this is firmer then the other side. The other side is the leeward side (the side of the dune protected from the prevailing wind).
Windward side is a generally a gradual slope firmer packed sand. You can see ripples in this sand (similar to when the tide goes out on a beach) or it may be smooth. This is generally easy to drive on as the wind has helped to compact the sand together.
Leeward side is the softer side where the wind can no longer hold the grains of sand in the air and deposit them. As the winds blow up the dune hill the sand drops near the top. This in conjunction with the rolling sand get to the top of a hill and drop. The slope angle is close to 31 degrees, as that is all the sand can support on itself. At the top of the slop you drop a grain of sand and it can start a sand slide all of the way to the bottom.
Dunes are formed into ridges from a prevailing wind direction. They will generally be all in a direction do to the prevailing wind. As the seasons change and winds change the dune can change the windward and leeward sides switch. At the time right after a switch you can be fooled by the looks of the dunes. The ripples will be on top of the soft leeward sand, and the now leeward side may be firm. It may be only a thin crust that is firmer over the soft old leeward sand. The longer the winds stay in the new direction the sides of the dune will conform to the traditional firm and soft sides.
Driving in the dunes it is better to stay where the ripple are and off of existing tracks as they tend to be softer. Driving in existing tracks will steer your vehicle in the direction they are going. Crossing existing tracks will be bumpier for the vehicle and you.
If you are traversing a large set of dunes try and follow the valleys. The valleys are generally firmer and less chance to get stuck. You can ascend to the windward side of a dune to see where you are going as needed.
As the video shows they were in a mix of soft sand and rock outcrops. This limits lowering your tires as the side walls with the sharp rocks do not play well together.
The photo of the strap and vehicles pointing towards each other lets me feel less confident in what they did. With all of the room to turn around it looks as if they were going to hook up the vehicles and pull the stuck vehicle out in reverse. It is not best to put the strain on the reverse gear and the front axle.
JIMBO, "Heh Heh, the best sand/snow tires I ever had, was 35 years ago and they were "C" range Winston "Fun & Mud" 33" tires -in a 6000lb Dodge Ramcharger-those were the days-"
I had these tires also, as well as the Armstrong True-Trax 31X10.5 X 15 Bias ply tires. We had the big tires and we were the BIG DOGS back then. That was a few years ago.