Why do you keep repeating this? It was already explained to you that it is ALWAYS calculated. There is no instrument that can measure turn radius directly.
How did a front-line pilot determine turn radius without FTI, or was he quoting flight test results performed by some other entity? You again repeat this basic misunderstanding of how actual turn performance is determined. You can measure turn rate directly through timed turns, but you cannot measure turn radius directly without modern FTI. You have to calculate it from other parameters that can be measured directly, like turn rate (or load factor or bank angle in steady turns), airspeed, altitude and air temperature. This was explained earlier, yet you keep talking about "calculated" as if there was a more direct method available at the time to determine turn radius.
The aerodynamic forces are mostly proportional to air density, not pressure. The power and thrust generated are proportional to pressure, density and temperature as they contribute to different elements of thrust and power generation. There is nothing linear in these relationships. Nevertheless, for reference, on a "standard day" the relative values at the altitudes that you mentioned in your post are as follow:
Altitude / Temperature / Pressure Ratio (delta) / Density Ratio (sigma)
0 15 degC 1.0 1.0
8000 ft -1 degC 0.74 0.79
12000 ft -8.8 degC 0.64 0.69
15000 ft -14.7 degC 0.56 0.63
20000 ft -24.6 degC 0.46 0.53
In other words, at 20,000 ft the pressure is only 46% of what it is at sea level and density is 53%. Since no day is truly a "standard day", actual air temperature needs to be measured in order to calculate the true pressure and density ratios at the time of a test, but these values give you a very good idea of how they change with altitude. Comparing 12000 ft and 20000 ft, the pressure ratio drops from 64% to 46% and the density ratio from 69% to 53%. The difference in aircraft performance, especially its ability to maneuver (excess power to convert to climb rate or turn rate) between sea level and 20,000ft is huge and between 12,000 and 20,000ft it is still very large. Why do you think flight test reports are so pedantic about stating the altitude at which a test was done?
From the fundamental kinematic relationship for a steady turn or circle:
R = V/omega
As you go higher and because of the large atmospheric changes described earlier, the speed for minimum turn radius increases and the corresponding turn rate (omega) decreases. The two combine to cause dramatic increases in minimum turn radius with altitude. 280 feet is not as "gigantic" as you seem to think.
Unfortunately, this statement just shows a huge misunderstanding of basic flight mechanics, and not for the first time in this thread.
