A solar sail doesn't work via aerodynamic lift. It works on conservation of momentum. Also, the biggest contributor to force on a solar sail is not solar wind, but radiation.
Right, radiation -- thank you. Nevertheless, you think that conservation of momentum is not the ultimate source of aerodynamic lift? It's not an electromagnetic phenomenon, obviously, neither gravitational -- so it has to be mechanical. Where that energy is otherwise coming from? Or are you claiming that aerodynamic lift is a fundamental force?
Energy can just as well be E = mgh (potential energy) or rotational energy E = 1/2Iw^2, or elastic energy E=1/2kx^2, chemical energy, nuclear energy etc. with momentum nowhere to be found in those formulas. When we talk about energy conservation we mean the conservation across all the forms of energy that the system can take on - that is what gets conserved.
It just happens that in one particular manifestation of the energy, the kinetic energy, can also be expressed with a squared momentum in the formula - but does not mean that momentum "is" energy by any interpretation.
As I said before momentum and energy are completely different concepts altogether - energy can be stored and transformed. Momentum cannot be stored nor can you transform a linear momentum into another kind of momentum.
If not convinced, consider for a moment (pun intended) that momentum is a vector and it conserves (in each dimension) as a vector! - whereas energy is a scalar and conserves as a scalar.
> does not mean that momentum "is" energy by any interpretation
I never said that. You literally said "momentum has nothing to do with energy", and I gave you one example where they are directly related.
> can you transform a linear momentum into another kind of momentum
Yes, you can. This is exactly why I mentioned yo-yo.
> momentum is a vector and ... energy is a scalar and conserves as a scalar.
That's a good point, it's 100% correct and I'm not arguing with that. But I insist that saying that they are unrelated is still wrong.
Let's go back for a second to where we started. My claim was (and still is) that the only source of aerodynamic lift is the kinetic energy of the air molecules acting on the airfoil. There is just nothing else, after all. This is not conceptually different from how [solar] sail works. Now, in this specific case, the energy of particles acting on the air/solar foil is directly related to their momenta.
Not sure what could be unclear there at all. Nuclear energy can be turned into any other energy and vice versa. As long as something has mass it has energy - whether or not we can readily transform that is beside the point.
Your recurring yo-yo example only demonstrates that you don't understand the physical phenomena in the first place. The linear momentum is conserved when the yo-yo pulls on your hand and through that your body, you are either pushing or pulling on Earth via gravitational force, the Earth wobbles opposite of the yo-yo (albeit infinitesimally, thankfully). That's the conservation of the momentum.
The rotational energy of the yo-yo has nothing to do with the linear momentum, that rotation comes from the chemical energy of your muscles that have first lifted, pulled or tossed the yo-yo. With that, you have transformed chemical energy stored in your muscles into the rotational energy of the yo-yo. Momentum has nothing to do with energy. Just because both exist and both get conserved. It is quite profound actually that they are not related at all.
As for this discussion we were talking about you conflating momentum with energy, a common misconception actually, your reticence of even remotely entertaining the idea that you did indeed misuse these concepts diverted into a lengthy discussion that slowly drifted away from the actual points to flawed analogies and yo-yos - also not surprising and a common predicament
Why am I still replying? Because it demonstrates why it is so hard to discuss flying (the very point of the original post) the majority of participants conflate and misuse scientific concepts - then go onto lengthy roundabouts to avoid owning up to these mistakes.