Re: True Airspeed Riddle? air is half as dense at around 22,
Unfortunately I still haven’t got an answer. Doing these equation just confirms what I have be saying: If you are moving through air that is half as dense, you have half the dynamic pressure, which one would think is half an airspeed reading.
Has anyone read "Understanding Flight" -Anderson,Everhardt ?
Adrock, you are correct that 1/2 the density equates to 1/2 the dynamic pressure. The answer to your question lies in thinking about how the ASI converts dynamic pressure to an airspeed.
Ok, so dynamic pressure is 1/2*density*velocity^2, right? By the way, dynamic pressure is frequently represented as q and density as "rho" so I will use those from here out: q=1/2rhoV^2.
But we don't care about dynamic pressure (at least, not when we are trying to look at the ASI to find airspeed, we don't). We want airspeed! So let's re-arrange the equation to solve for velocity:
V=Square root of (2q/rho). Now based on this equation if you increase altitude, AND keep true airspeed the same (remember all of the V's in these equations are TRUE, not indicated), then rho decreases by 1/2, and q decreases by 1/2 as well.
But look at the equation V=SQRT(2q/rho). If q and rho BOTH decrease by 1/2, then V should stay the same, shouldn't it? Based on this knowledge only, we might be led to believe that the airspeed indicator would indicate very close to the true airspeed regardless of altitude. Obviously, this still doesn't explain how the ASI works, because we know that at the same true airspeed but different density (a different altitude), indicated airspeed DOESN'T stay the same. Or put it another way, if you keep indicated airspeed the same but increase altitude true airspeed increases. So what happened?
Back to the equation: V=SQRT(2q/rho).
Well, the diaphragm moves based on the difference between total and static pressure, as you've already mentioned. Basically, it measures q, and ONLY q. As you've already noted, the static pressure, which is affected by altitude, is on both measured on both sides of the diaphragm, and therefore, it is kind of irrelevant. It is not, I repeat NOT, an altitude calibration. Instead your airspeed indicator is calibrated to be most accurate at sea-level.
The instrument can only measure q, dynamic pressure, and convert that to V, velocity. It is calibrated for sea level density (.002377 slugs/ft^3). So instead of solving the equation V=SQRT(2q/rho), the ASI actually solves the equation V=SQRT(2q / rho at sea level).
Basically, the ASI takes the square root of the dynamic pressure and multiplies it by a calibration constant to get the velocity. This is the most important sentence in my whole post, so make sure you understand that.
So now, what happens when we fly at 200 knots true at sea level? The ASI measures 200 knots indicated (more or less... you still have installation error and compressibility errors... but both of these are very small, especially at low altitude and airspeed). What happens when we fly 200 knots true at 22,000'? Well, the ASI measures half the dynamic pressure that it normally senses at 200 knots, but in converting to velocity remember it uses the square root? Well the square root of 1/2 is .7071 (approximately). So instead of reading the 200 knots true that you are actually flying, it reads about 70.71% of that... or about 141.4 knots.
Suppose we were to fly 200 knots true, but so high that density was only 1/4th of the sea-level value (40-some odd thousand feet or so)? Well, the indicated airspeed would be the square root of 1/4th as much... The square root of 1/4th is 1/2, so 200 knots true would be 100 knots indicated.
And yes if you blow across paper it will rise because of the lower pressure. but what caused the lower pressure. Have you ever tried to hold paper straight down while blowing across it? the paper won’t be deflected to the side of the airstream. The bernoulli strip experiment is always done with a curved shape. I am telling you guys that I had an epiphany the other day while reading Understanding Flight. The static port on a plane is subjected to fast moving air running parallel to it and yet have you ever heard of any problems associated with false altimeter readings as the speed of the airplane increases? The fact is that TOTAL PRESSURE is not a constant if say, a propeller adds kinetic energy to it. Therefore, the speed of the air can increase and the static pressure port can still read the original value! Who has a vacuum gauge and shop air?
