= True airspeed
{title2=$V_{\rm TAS}$}
\b[True airspeed] is the magnitude of an <aircraft>'s <velocity> relative to the surrounding air,
$$
V_{\rm TAS}=\lVert\mathbf v_{\rm aircraft/ground}-\mathbf v_{\rm air/ground}\rVert.
$$
It determines the relative motion used in aerodynamic models, while <groundspeed> concerns horizontal travel over the ground. <Indicated airspeed> and <calibrated airspeed> describe stages in a pressure-instrument reduction, rather than another reference frame.<Glider Flying Handbook by Federal Aviation Administration>[Chapter 4, printed p. 4-5, True Airspeed]{ref}
For an aligned low-<Mach number> pressure measurement in the regime of the <Bernoulli equation>,
$$
q=\frac12\rho V_{\rm TAS}^2,\qquad
V_{\rm TAS}=\sqrt{\frac{2q}{\rho}}.
$$
An <equivalent airspeed> uses the same <dynamic pressure> with a standard reference <mass density>, $V_{\rm EAS}=\sqrt{2q/\rho_0}$. Hence
$$
V_{\rm TAS}=V_{\rm EAS}\sqrt{\frac{\rho_0}{\rho}}.
$$
Only where the low-speed pressure relations justify $V_{\rm CAS}\simeq V_{\rm EAS}$ may calibrated speed be substituted in this last expression without a separate compressibility correction.
For an original low-speed example, use $V_{\rm CAS}\simeq30\,\mathrm{m/s}$, $\rho_0=1.225\,\mathrm{kg/m^3}$ and ambient $\rho=0.800\,\mathrm{kg/m^3}$. The corrected difference is approximately $551.25\,\mathrm{Pa}$, giving \b[$V_{\rm TAS}\simeq37.12\,\mathrm{m/s}$]. At a fixed pressure difference, halving ambient <mass density> increases the inferred <true airspeed> by $\sqrt2$, rather than doubling it. This follows from the square-root dependence, not a wind correction.
Obtaining the ambient <mass density> can require independent <static pressure> and <thermodynamic temperature> measurements, with a suitable equation of state. For fixed $q$, a small relative density error changes the inferred speed by approximately $\delta V/V=-\delta\rho/(2\rho)$. Wind information is needed separately to predict the <ground track>. A single ground-travel speed cannot supply all of these quantities. The pressure inference also depends on clear passages and valid stopping-flow assumptions.<Pitot – Static Tube – Speedometer by NASA Glenn Research Center>[Solve for Velocity and Limitations]{ref}
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