(16) shows the relation between Q-factors and velocity, nothing more. The relevant assumptions - those I've asked you to explain - are a bit higher up. To answer my own question, however, as you're possibily a wee bit out of your depths here.
You see the net power loss directly being transformed into kinetic energy (velocity), essentially making this device magical. There is, of course, a correction factor for his device (D
f), which is a bit concerning giving what he's trying to prove. All the complicated maths up and including this point are correct as far as I'm able to check them (I'm sure you did work through all of them on paper, too), and even some of his assumptions are reasonable.
There are some jarring mistakes, however, and anyone with some high school physics classes should've been able to spot them. To be fair, in his most recent version of the theory paper (9.4) they've been cut - not replaced or corrected, cut. So you might've missed the opportunity to reflect on them.
v9.3
[1] still has them.
So, all his fancy math proves that his EM waves push harder on the top than on the bottom if he uses the cone shaped apparatus. He, however, neglects a bit of the aforementioned high-school physics. Inelastic collisions always have a force component perpendicular to the resulting vectors. In other words, the EM waves do not just push on the top and bottom of the cavity, but also on the sides, resulting in a net downward push (do some vector analysis on a sketch to see it, it's really simple). You will see that this cancels the top/bottom difference out. He made the same mistake in his paper again, even in 9.4 p.4, when he imagines the system with a fluid instead of microwaves, discarding the push on the sides as a mere
mechanical strain.
If you would've used your own head instead of quoting Shawyer's own FAQ you might've spotted that.
It's impossible to do a proper survey of Shawyer's own measurements as there's no documentation and/or data published, which is not a good sign, as
a proper publication has the supporting information providing enough information to properly judge the procedures used in testing. The Eagleworks lab shared a bit more information, which is still not very good based on a few reasons I've already given. Let's rehash them.
1) They've measured 3.6mN on a scale with a single digit mN resolution.
2) They've measured the same net force on the active and 'inactive' device, which despite the flaws in the setup, strongly suggest that they might've gotten the same results if they put a potato in their test chamber.
3) They've measured at ambient pressure. Even a very small temperature gradient between the device and the atmosphere will lead to air convection exerting tiny pressures (mN!), too.
4) The devices are bulky and use active water cooling for their magnetrons, also a lot of cables. We're trying to talk about mN effects - the FTL experiment's error was a bad plug/connector, not a groundbreaking effect.
The 'ass in seat' example was an attempt to make an easy to understand example why conservation of momentum is violated. Real-life examples don't hold up well with quantum mechanical systems, however, just saying "quantum" and wave your hand doesn't help either (neither does saying 'relativistic' or 'Einstein'). Conservation of energy/momentum holds up in QM, which just shows how
passé Newtonian mechanics really are.