If air density remains constant, the relationship between IAS and TAS will remain constant. So if we double the IAS (in conditions of constant density) we will double the TAS.
It will be necessary to state EAS instead of IAS for this statement to be true without exception. The exception is not actually implicit so I should mention that it occurs, by design, only under the ICAO standard atmosphere at sea level. At any other pressure altitude TAS is not a linear function of CAS or, if the difference from CAS is neglected, IAS. On the other hand, if by "constant density" you don't mean constant freestream density but rather that the flow is not isentropic and that the density along a streamline does not vary with velocity, then the statement holds (but does not apply to air).
... calibrate the ASI so that if we double the TAS, this gives us four times as much dynamic pressure, but the ASI just indicates twice as much airspeed. This is all done by a system of levers in the ASI.
It's worth separating the ASI principle of operation from the convention defining dynamic pressure. Contemporary ASIs do not make use of dynamic pressure. The present FAA/EASA TSOs defer to SAE AS-8019 or AS-8019A for ASI minimum operational performance standards withcounterpart US DoD performance specifications in MIL-PRF-27197E (USAF). For the appropriate airspeed equations both standards refer to NASA Technical Note D822 which is based on the abovementioned NACA Report 837 (Aiken, William; 1946).
The NASA TN reiterates the appropriate solution to Euler's equation, presented in NACA Rep. 837, taking account of the isentropic change in state variables along a streamline as air is brought to rest at the head of the pitot probe. The total pressure at the head of the probe is certainly not given by summing the freestream pressure with the dynamic pressure but rather it is the sum of the freestream and
impact pressures; neglecting measurement problems.
While it is true that a four-fold increase in dynamic pressure is associated to a two-fold increase in TAS, it is necessary to impose standard atmosphere sea level conditions for the statement to be similarly true about the change in CAS (IAS).
gfunc,
... isn't coefficient of lift purely a function of angle of attack? You can't change the coefficient of lift, unless you change the shape of the wing (e.g with flaps), but you can change the angle of attack to that corresponding to the appropriate lower CL.
Not at all. As LM has hinted, the lift coefficient for the whole aircraft is simply
defined to be identically equal to L/(qS); L the lift, q the dynamic pressure and S any convenient reference area. The aerodynamic lift is a function of the freestream density & speed of sound & velocity & coefficient of viscosity, the aerofoil shape, the angle of attack, and the surface size. In the definition of the lift coefficient no new explanatory variables are introduced so this set is sufficient for a lift coefficient function. By incorporating some of these variables into the two similarity parameters, Mach and Reynolds numbers, the lift coefficient can be expressed simply as a function of alpha, Mach & Reynolds number.