Mark do us a favor and run both motors on the same way on the same plane. After that see how much do you put back in the pack. Just make sure you run the same RPM. Doing stunts is irrelevant, flying level should be sufficient. Also if you can check temperatures on the motor battery and ESC.
Thanks Traian
You mean, in essence, exactly what I did. I ran both motors using the same ESC, timer and battery at the same RPM with a load meter in line. In case one the propeller was a 9 x 4.7 and both configurations ran basically the same 200 watts at 10,000 RPM. In case two the 10x5 the smaller motor drew 30 more watts at the same 9400 RPM. The load (RPM) had to be reduced because the smaller motor was beyond it's efficiency rage and it consume more power for the same output power. Therefor I reduced the RPM into a zone the motor wouldn't melt and took a power comparison 236 Watts for the larger motor and 263 Watts for the smaller motor. I could have run at 10k RPM but the smaller motor was pushed up above 300 Watts which is above it 280 Watts continuous rating and I didn't want to hurt it. This fact along begins to tell a story.
I could have gone back and reduced the first test to 9400 RPM and taken readings again but the result would very similar again. Both motors would be pulling roughly the same wattage from the battery at a lower wattage than the original test point which would result in a greater power difference between case 1 and case 2. I don't see value added in taking the time to do that. I don't think that has much benefit. If it does to you, then I would suggest going out and doing the test. I personally have a solid understanding of the physics involved and I just did this testing because it was convenient timing.
Putting both on the same airplane wouldn't change the results much either. Agreed that the unloading when airborne might cause, in this case, the 10x5 prop power consumption to drop more than the 9x4.7 but what you would find is that the total power consumed over the flight for the smaller motor would still be greater which I think is the point of the first question, would switching to a larger motor help. The answer is maybe, if the smaller motor is being taxed and is running beyond it's efficiency zone then yes, otherwise no. The performance of the airplane is a different question. Yes, the airplane would work better in this case with the 10x5 but it works the way this category airplane should with either.
Here's the take away. If the motor being flown is operating within it's performance range, switching to a larger motor isn't going to make much of an impact. If on the other hand the first motor is operating in a range where it is demanded, as in being loaded above it's efficiency range, moving to a larger motor would be beneficial. Again, if on the other hand the motor is already "oversized" for its task, then switching up isn't going to make a big difference. The corollary to that is that going with the next size up in diameter isn't going to hurt and will benefit from bragging rights which, all told are very important.
End of the day the propeller requires X amount of power which comes from the motor. The battery has to provide that much power plus whatever is lost along the way. As Igor pointed out in many constants and much physics interpretation required, as the torque required increases the resulting current demand increases differently for each motor. The smaller motor increases at a higher rate than the larger motor. At the propeller that power is torque times RPM = current times voltage. Between the battery and the motor output a crap ton of power is lost to heat where the power lost is current squared times the resistance along the current path. So the little motor looses because torque is a function of current which drives the power loss by a square function of that current. The battery has to provide the power for the propeller I*V plus the power lost I^2*R. Think of the power loss as that heat gun you use to shrink moneycote. It uses 1500 ish watts. That's 6 times the power of the 10x5 propeller running at 950 RPM.