@trimtab
Can you explain this section

**"The power required for a given IAS rises with altitude (proportional to 1/sqrt of density differences) "**
I think it is related to something I have read multiple times years ago over on BT. That for piston planes, for a constant L/D ratio (e.g. constant IAS), the MPG stays the same regardless of altitude. Are these related, and does it make sense (and do I recall it correctly).

Tim

Lift is proportional to the density times v squared. So is drag. So the increase in velocity is proportional to the square root of the ratio at the densities.

Because power is force x velocity, if the velocity increases for the same drag force more power is involved proportional to the increase in velocity, given by the relationship above.

If you apply this reasoning to, for example, a P210, you will find the numbers for the brake horsepower available at 23000 feet when used for the 2,000 ft performance correspond closely to this approximation. In fact, the calculated airspeed will be several knots above the actual demonstrated indicated airspeed, again because the propeller loses efficiency as one gains altitude. You can use this to calculate the achievable true airspeed and you will arrive at the figures that look a lot like what are in the poh at 23000 feet. if you simply count on constant IAS the p210 will be a rocket ship compared to its actual performance.

Applying the same reasoning to the Otto airplane is pretty straightforward once a few assumptions are made about what was going on at fifteen thousand feet during the tests. if they were producing maximum horsepower at 15,000 ft to achieve roughly 250 knots, then it is clear that they would be expected to achieve somewhere between 350 and 400 knots TAS at 50,000 ft. The only way to project a 450 to 500 knot speed would be if they were only producing 50 or 60% of full rated horsepower during those tests to achieve those 250 knots.

But the bottom line is that as air density drops, the power required to achieve the same IAS rises. This is also the reasoning behind why Vx and Vy converge with altitude.

The only plausible explanation for the Celera 500 is that, during the testing, the engine power output was greatly reduced in achieving 250 knots, which is certainly possible, and would be an astounding achievement to be able to move that much airplane with only about 250 horsepower. But that makes more trouble for me for a couple of reasons. Firstly, I don't understand how laminar flow could provide anything like that performance increase, and secondly because the adjacent calculation of using the purported 22:1 lift drag ratio and a reasonable weight for the aircraft based on its stall speed and some other broad assumptions could yield that kind of ability with 250 hp.

And so, again, I remain interested in the kinds of calculations that make this possible, especially if they are obvious and I am simply missing it.