Thanks! Clear and to the point.
Good staking technique is important. A few items that you didn't mention in regards to stake strenghth.
1) Angular displacement
Angular displacement is when a tarp uses low angles of incidence to the direction of the stress. We all know that angling a stake is stronger, this is not what I am refering to. Rather, the vector the stress is exerted from the tarp to the stake. A low pitched tarp, or "storm pitch" (Summit Lake pic with scouts 2011 in article)will exert a stress about 15 degrees to the ground. A taller pitch (Markus' Blue tarp in the article) pulls at ~40 degree angle. Given equivalent ground pressure, the stakes closer to a shear (0 degrees) will hold better. As you mention, though, the deflection is best described non-linearly. It applies to all staking points.
This is why adding a 1 "arm length" (about 3' or 1 meter) guyline to stake outs helps. The 8x8 tarp with a 42" center pole in front (Summit Lake pic, 2012) Adding a 3' tie out to the front corners decreases the angle from about 40 degrees to about 30 degrees.
Also, using longer tieouts on a narrow tarp is equivalent to using a full width tarp, in holding power. Ignoring wind catching, adding "arm length" guylines to the front corners will increase holding power to the tarp pictured at Summit Lake, 2012. Of course, you will also pick up more wind, a trade off.
2) Wind force
Wind force is something else that you don't mention. A nearly ideal shape would be a hemispherical shape or approching it. A good example is the pyramid, or, a shaped tarp from a tunnel tent. (Example: Exped Sirius allows only the tarp to be used.)This allows wind to be both deflected AND "sucked" back onto the tarp. (The wind force would actually create a tear drop bubble, but I am talking "ideal", here.)
This allows wind deflection from all sides, but is more expensive, in terms of weight, than the more usual 3 sided shelters UL'ers are fond of. Wind pressure will cause a vacume inside the tarp causing it to pull up, AND, push down. Often stronger stakes are needed where the "pulling up" force is greatest, usually the open, higer side. You can allow the wind through the tarp (after deflecting rain) to alleviate the air pressure differences by NOT pitching tightly to the ground. As you mention, stronger stakes are needed for higher areas("ridge lines") and areas that trap air pressure in high winds.
In more constant high winds, a "Diamond" pitch works better than a "Shed" pitch. The longer pitch angle of a diamond, along the diagonal, will hold better. The angle also reduces stake out patterns around the two sides allowing a higher density of stakes on the fully sheltered, upwind side. The trade off is reduced roof effectiveness by removing about the first 1/3 as a wind shelter (though this often stays much dryer than outside, it has less three dimensional protection.) The more enclosed 2/3 will be far better against winds/rain and have far less pressure against each stake. Since the wind is allowed to enter the shelter, from the sides, you gradually reduce the air pressure pulling up on the stake holding the peak.
Ground clutter has a lot to do with wind velocity, as Roger mentionesd in his articles. Indeed, weather staions often have higher towers for measuring wind speeds.
3) Multiple stake use (2 stakes in the same loop): You mention this but do not describe it. When using two stakes, I angle both away from each other creating a "ground claw" aginst the tarp.
4) Stretch vs Impact (Wind Hammer) One of the great weaknesses of cuben tarps is the lack of stretch. Like a hammer hitting a nail, simply resting a 10 pound sledge on a nail is not as effective as pounding it with a 1 pound hammer, both for driving and pulling a nail. This is an extream example regarding tarps, but the same principle applies. A "snap", nearly instantaneous, will pull a stake with light wind speeds. A stretchy elastic will distribute the same pressure over time. Example: Given a stake that takes 30 ft/pounds of force to pull it. A single snap of that pressure distributed over about .01 sec will pull it. If I distribute the same pressure over .5 sec, it is never in danger of pulling loose. A looser pitch means more snapping, but the danger of pulling a stake can be (largly) removed when tight pitches cannot be done due to ground variations, and/or, obstructions.
Silnylon can streatch a lot. Nylon absorbs water and stretches. Temperature softens it and it stretches. Pressure does the same. So, there is a built in "shock absorber." Cuben tarps do not have the same properties. I often recommend heavy duty hair ties, or, "shock cord" on cuben tieouts to supply the stretch needed for good stake holding for the above reason.
A nice, tightly pitched tarp can often do the same by gradually increasing pressure on a stake as wind speeds increase. But, this can be fiddly to set up requiring good ground. The elusive "perfect pitch" escapes everyone, sometimes.
Anyway, I would suggest many shaped tarps are designed incorrectly with the wider, taller living space closer to the door. Dynamics dictate a more "igloo" like design with the door open towards the smaller, narrower end (with the living space behind it.) As with the trailstar, this supplies good storm protection for the occupent and better overall wind stability by supplying a more storm resistant "tear drop" shape. Perhaps it could be placed into the wind? Hmmm... anyway...
I really liked the article! Thanks again, Ryan.