= Glider sink polar
A \b[glider sink polar] relates a <glider (aircraft)>'s steady downward <speed> relative to the air to its <true airspeed>, for specified loading, configuration and atmospheric conditions. Write it as $w(V)>0$ with downward motion positive. Some plots instead put descent below the horizontal axis; the sign convention must accompany the curve. The <minimum sink speed> and <best glide speed> select different points on this same performance relation.<Glider Flying Handbook by Federal Aviation Administration>[Chapter 5, printed pp. 5-10–5-11, Glider Polars and Figure 5-11]{ref}
The curve is a measurement or model of performance, rather than a drawing of the flight path. At steady speed, its horizontal air-relative component is $u=\sqrt{V^2-w^2}$. Thus time per height lost is $1/w$, while horizontal distance per height lost is $u/w$. The <best glide speed> article derives the tangent construction and an original <parabolic drag polar> example; those results need not be recomputed to interpret a measured polar.
A useful extension is <glider ballast scaling>. Suppose the <gravitational weight> changes from $W$ to $\alpha W$ at unchanged air <mass density> and geometry, and suppose the same <lift coefficient> and <drag coefficient> remain applicable. At corresponding steady glide conditions, the <lift-to-drag ratio> and <glide angle> are unchanged. Since $L=\rho V^2SC_L/2=W\cos\gamma$,
$$
V_2=\sqrt\alpha V_1,\qquad w_2=\sqrt\alpha w_1,
\qquad w_2(V)=\sqrt\alpha\,w_1(V/\sqrt\alpha).
$$
For an original stipulated point $V_1=25\,\mathrm{m/s}$ and $w_1=0.80\,\mathrm{m/s}$, increasing <gravitational weight> by $25\%$ gives \b[$V_2\simeq27.95\,\mathrm{m/s}$ and $w_2\simeq0.8944\,\mathrm{m/s}$]. The corresponding distance-to-height ratio is unchanged, but the same height is lost sooner. This scaling assumes the aerodynamic coefficients transfer; changes of <Reynolds number>, surface condition or trim can invalidate it. The FAA illustrates the loading-dependent displacement of glider polars.<Glider Flying Handbook by Federal Aviation Administration>[Chapter 5, Effects of Weight and Figures 5-9 and 5-14]{ref}
To measure a polar, record steady <true airspeed> and height change at several operating points while documenting configuration and loading. Ground-relative descent $s$ includes vertical motion of the air: with upward air <velocity> $u_z$, $s=w-u_z$. For example, an air-relative sink of $1.5\,\mathrm{m/s}$ in air rising at $0.5\,\mathrm{m/s}$ appears as $1.0\,\mathrm{m/s}$ ground-relative descent. Repetition can reveal variability, but one trajectory cannot separate these two contributions without additional information. A measured <groundspeed> is likewise not automatically the horizontal component of the air-relative polar.
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