How to explain why TAS increases with altitude?
Magnus,
I think I have a simpler explanation for you. The reason that TAS and
IAS differ with altitude is the air density. While you're probably
saying I already know that, it's probably a little more subtle than
you expect. Think of what the airspeed indicator does, it's a measure
of the dynamic pressure of the air entering the pitot tube. But how
does it compute airspeed? Well, the formula for dynamic pressure is
1/2*rho*V^2. Rho is the density of air and V is simply the airspeed.
So if the dynamic pressure can be measured and the density of air is a
given then V can be computed. If you rearrange the equation to solve
for V you would find that V varies with rho inversely. As rho
increases, V decreases for a given dynamic pressure and vice versa.
The airspeed indicator therefore must be calibrated for a certain air
density in order to provide the correct airspeed. The value of rho
used is the standard sea level air density.
You will notice that unlike the altimeter, which has a knob allowing
you to recalibrate the pressure setting, the airspeed indicator
doesn't have a knob that will allow you to adjust the density setting,
so you always use the same value which is sea level density. As you
climb the true value of density decreases, but the value that's used
to compute IAS, the sea level density, is always higher. Because the
higher sea level density is in the denominator and is higher than the
true value at altitude, the IAS will always be lower than the TAS.
This is the reason that takeoff and stall speeds are constant
indicated airspeeds. The IAS is a measure of the amount of air
molecules that the wings experience, and that's all they care about
when it comes to issues of performance such as takeoff or stall.
However, the TAS that is necessary for the wings to see that IAS will
depend on density. So while the stall speed may always be 45 knots
IAS, the TAS that corresponds to that given IAS will vary with
density, whether caused my altitude or temperature increases.
Dave
