(1.23 kg/m^3)*(1.00*(6"/2)^2)*((3.7*3*2230/minute*3"))^2/(9.8 m/s^2) = 720 grams
(1.23 kg/m^3)*(3.14*(6"/2)^2)*((3.7*3*2230/minute*3"))^2/(9.8 m/s^2) = 2.26 kg
NOTE: I assume in the following analysis that the propeller's pitch speed is equal to its efflux velocity. This is most accurate in the static case but does not apply once the velocity of the incoming airstream is no longer zero.
I used your figure of 72mph in post #43 as the efflux velocity. I was wrong, I realize now that I calculated the mass flow rate (0.719 kg/sec), not the thrust. Multiplying by the efflux velocity results in a thrust force of 23.1N (which, when divided by g = 9.81 m/s^2 yields more or less your 2.26kg of thrust (within rounding error, at least). However,
this does not account for pressure drag due to the lower pressure of the faster moving air on the backside of the prop.
The dynamic pressure of a 72mph (32.2) efflux is 635 Pa. Assume the air velocity in front of the prop is 0 (this is true at infinite distance and in ideal circumstances). Since total pressure remains constant in isentropic flow, the static pressure behind the prop is 635 Pa lower than in the front. Multiplying this figure by the x-sectional area of the prop disk (0.0183 m^2) yields a force of 11.6N.
Subtracting this from the prior figure yields 11.5N (or, if you'd like, around 1.17kg) of thrust.
Of course, this is a simplification of things. It
does not take into consideration the RPM drop under load that the motor experiences, which changes the efflux velocity, mass flow rate, and pressure difference. It is also general in that it represents the aggregate and average case - the efflux velocity will most certainly not be constant along the radius (in part due to aerodynamics and the lift distribution across the prop radius, but more obvious in that no air flows through the motor itself). A more accurate definition of thrust would be something along the lines of "The integral of mass flow rate times efflux velocity along the radius minus the integral of pressure times area along the radius".
I redid the calculations from some data on the
1806 datasheet, which lists a 6x4 prop pulling 460g at 15160 rpm (pitch speed = 25.7 m/s). This yielded a theoretical thrust from mass flow of 14.8N and a thrust loss due to pressure of 7.4N, resulting in a net thrust of 7.4N or ~750g.
Just for giggles we can calculate the efficiency of the 6x4 setup and apply that to your setup to get a rough idea of real-world thrust. The efficiency looks to be (460g / 750g =) 61%, which puts your theoretical thrust figure (WITHOUT accounting for the RPM drop under load!) at 0.71 kg. If we assume thrust scales linearly with RPM (which, it doesn't, I know, but with things being locally linear and all) and adjust from the unloaded 12.6v * 2280kv = 28730 rpm to something more reasonable like 17000 rpm (the motor spec sheet lists a 5x3 prop at 18510 rpm and a 6x4 at 15160, this seems reasonable), we get (17000 / 28730 * 0.71kg = ) 420g of thrust, which is much more in line with the existing data and what I would expect.
Regardless of the math, I can speak from experience and common sense when you claim to get over 2kg of thrust out of an 1806 on 3s and a 6" prop. And to get over 300 watts out of an 1806 requires putting more than that in. I have a little 3D plane with an 1806 and a 12A ESC that runs on 2S and pulls 300g. At most, I'm running 8.4v * 15A = 125W, and that's nearly enough to melt the firewall off the airframe with the help of some Florida summer sun. I can't imagine managing 300W of heat in such a small motor and the proppage it would take to load it to such a state.
It's a good exercise to extrapolate performance data from existing data and equations. With that said, it is imperative to cross-check the numbers you get with existing data and verify those numbers via more direct means. I believe you when you give a calculated efflux velocity, thrust figure, and power output. But unless those numbers can be verified through more direct means (you appear to have a load cell suited to that very purpose), we must keep in mind that most equations are useful generalizations.