 Minimum sink speed

The minimum sink speed is the airspeed at which a glider has its smallest steady downward speed relative to the air, for a specified configuration, loading and flight condition. It maximizes time aloft from a given height in still air. It does not generally maximize horizontal range, which defines best glide speed.^[ref]

For a differentiable glider sink polar $w(V)>0$, an interior minimum satisfies $w^{\prime }(V)=0$, with a positive second derivative sufficient for a strict local minimum. For the original shallow-glide model developed in best glide speed,With $A,B>0$, this givesIndeed $w^{\prime \prime }=(6AV+2B/V^3)/W>0$ for $V>0$. The speed ratio is about $0.7598$, within this stipulated parabolic drag polar approximation. A real polar need not follow that numerical ratio, especially near aerodynamic stall.

Using the same original $W=3000\mathrm{N}$, $A=0.12$ and $B=67500$ gives $V_{\mathrm{MS}}\simeq 20.81m/s$ and $w_{\min }\simeq 1.442m/s$. From a stipulated $1000\mathrm{m}$ height, the model's times are about $693.6\mathrm{s}$ at minimum sink and $608.6\mathrm{s}$ at best glide. Yet the approximate range ratios are $14.43$ and $16.67$, respectively. The slower optimum buys time rather than maximum distance.

A horizontal wind changes range without changing air-relative sink at a fixed condition. Vertical air motion changes ground-relative height loss as well: descending at $w$ through air rising at $u_z$ gives ground-relative descent $w-u_z$. Observing constant height therefore does not establish zero air-relative sink. A bank angle also changes the required lift and hence the appropriate polar; the straight-glide optimum cannot simply be reused for a tight turn.