Eagle 1,
For the sake of simplicity, the explanation below ignores the finer distinctions between IAS, RAS, CAS and EAS. They don't change the sense of the overall effect, but simply adjust the magnitude of the changes a little.
An airspeed indicator produces an indication (IAS) that is proportional to dynamic pressure. For any given dynamic pressure, the IAS will be constant regardless of altitude. So climbing at constant IAS means climbing at constant dynamic pressure.
Dynamic pressure is equal to the TAS squared, multiplied by half the air density. But density decreases with increasing altitude. So for a given IAS, the TAS must increase, such that the rate of increase in TAS squared, just balances the rate of decrease in density, thereby maintaining a constant value of dynamic pressure. At 40000 feet ISA for example, the density is about a quarter its sea level value. So the TAS squared must be 4 times the IAS. This means that the TAS at 40000 ft is approximately twice the IAS.
The ASI cannot detect dynamic pressure directly, so it takes total pressure (dynamic plus static) and feeds this to one side of a capsule. By feeding static pressure to the other side, the instrument subtracts static from total, to leave dynamic. As altitude increases, the static pressure decreases, but this decrease is felt on both sides of the capsule. So the overall effect of reducing static pressure is nil.
So the overall effects are:
a. At any given IAS the dynamic pressure is constant at all altitudes.. .b. As altitude increases at any given IAS the TAS increases.. .c. Although static pressure decreases with increasing altitude, this does not affect the relationship between IAS, dynamic pressure.
[ 07 February 2002: Message edited by: Keith Williams. ]</p>