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A stellar wind removes mass and carries energy and angular momentum from a star into its surroundings. Hot gas can escape through thermal pressure; radiation transfers momentum through continuum or spectral-line absorption, and radiation acting on dust can drive surrounding gas. Magnetic stresses can extract rotational energy and angular momentum. These mechanisms have different dependencies on heating, opacity, stellar luminosity and field geometry.

For a steady spherical isothermal pressure-driven model, mass conservation gives $\dot{M}=4\pi r^2\rho u$. With $p=a^2\rho$ and constant isothermal sound speed $a$, the radial Euler equation becomes the Parker wind equationA smooth transonic flow solution crosses $u=a$ at $r_s=GM/(2a^2)$. Its inner subsonic atmosphere connects to a supersonic outflow; continuing heat input is needed to keep that expanding wind isothermal. Other boundary pressures can select a breeze rather than this escaping branch, and the mass-loss rate needs boundary/heating information. A polytropic outflow instead converts finite enthalpy into escape energy and has a different terminal budget.

The solar wind supplies a nearby plasma example. Spectral-line Doppler shifts and profiles diagnose more distant winds; blueshifted absorption against stellar light indicates material moving toward the observer. Inference of a mass-loss rate additionally needs density, ionization, geometry and velocity information, rather than a line shift alone.

Wave drag is the component of aerodynamic pressure drag associated with the compressible wave field produced by a moving body, including the effects of shock waves. It becomes important in transonic flow and supersonic flow. A freestream Mach number below one does not exclude locally supersonic regions and shocks around an accelerating flow over an airfoil.^[ref]

Wave drag can occur at zero lift, because a body of finite thickness displaces the flow. Its identification therefore differs from that of lift-induced drag, which depends on the finite wing's loading and wake. A measured high-speed increase in total drag can also include changed flow separation and other losses; attributing the entire increment to one mechanism requires an explicit decomposition.

Richard T. Whitcomb's report compared wing/body combinations with bodies of revolution having the same axial area distribution. Compensating for the wing's area by indenting the body substantially reduced the zero-lift drag-rise increment near sonic speed.^[ref] The related NASA account describes testing the proposed area rule using a specially prepared wing/body model in the Langley transonic tunnel.^[ref] The observations support a design principle for the tested regime rather than proving that a shape's area distribution determines all of its drag.

For a stated decomposition, the wave-drag coefficient is $C_{D,w}=D_w/(qS)$, using common dynamic pressure $q$ and aerodynamic reference area $S$. An original illustrative estimate with $q=20,000$ Pa, $S=0.30$ m${}^2$ and stipulated $C_{D,w}=0.012$ givesAt a speed of 250 m/s, overcoming that component alone requires mechanical power $D_{w}U=18$ kW. These are constructed values, not measurements from Whitcomb's report.

A useful apparatus comparison retains force-balance data, surface pressure measurements and flow visualization while recording Mach number, Reynolds number and lift. Observing a shock locates part of the wave field; it does not, by itself, measure the integrated wave-drag force.