Creating graphs of rocket exhaust blowing lunar soil. This is "parameter space" so it doesn't look much like lunar soil in this view🤨. All I can say (for now) is this explains why measurements from Apollo videos gave a different result than our experiments, so I'm very happy🤓/1 
2/ Prior work is here, ascelibrary.org/doi/abs/10.106…, where I proved that erosion of soil under a rocket gets faster than expected, when we are landing on a planet with a very thin atmosphere or no atmosphere like the Moon. (Knudsen Number, Kn, is bigger when the air is thinner.)
3/ We couldn't explain that fact, but we couldn't explain another thing: in experiments, we measured the erosion of soil is proportional to the forces in the gas. That makes sense. But on the Moon, the erosion is proportional to those same forces raised to the 2.5 power. WHY?🤯🤷♂️
4/ This was especially confusing because, as a rocket is higher & higher above the Moon, the value of Kn goes up, so the 1st result says erosion should increase. But the forces get less, and the 2nd result says erosion decreases much faster than expected (to the 2.5 power).WHY?🤯
5/ Over the past few days I finally had time to focus on the math, merging the theories. What I found is that the surface has an inflection so in one region the erosion rate goes up, while in another region it goes down. I don't have the physics totally explained yet, but...
6/...I'm pretty sure this inflection is a result of the boundary layer of the gas flow over the lunar soil. Boundary layers were first studied in 1904. Gas flowing across a surface goes slower and has different turbulence close to the surface than the gas far from the surface.
7/ This has been studied by many researchers since 1904, but there hasn't been much research into the boundary layer when the gas is very thin, like in rocket exhaust on the Moon. (Picture of an Apollo landing blowing lunar soil, from my paper here: agupubs.onlinelibrary.wiley.com/doi/abs/10.102…)
8/ I'm pretty sure that, when the gas is thin enough, faster gas molecules get thru the boundary layer. Even though the forces may be constant, the faster gas lifts the sand grains easier, creating more saltation and more erosion. (Image:Balme et al.2018, research.ncl.ac.uk/abrade/science…)
9/ Regardless what is going on in the physics, what I discovered these past couple days is this inflection on the surface in parameter space. When I mapped the conditions of the Apollo lunar landings onto this surface (the blue points) none of them cross that inflection. So...
10/ this explains why measurements in the Apollo landings were different than experiments on Earth. Experiments on Earth were on the flatter left side (gas force to the 1.0 power), but Apollo landing conditions were on the steeper right side (gas force to the 2.5 power).
11/11 We have a lot of work left to do to solve all this. I've actually got 8 different contracts & grants right now, each studying a different piece of this puzzle. A good article on this topic came out a couple days ago, here. To the Moon! space.com/nasa-moon-land…
And here it is: a 40 ton lunar lander. Unlike a 5 ton Apollo lunar module, in this case the blue dots DO cross over the inflection. This means the erosion of soil during final touchdown will be less than the equations say from the Apollo landings. This is great news!
