= Minimum-drag speed
{title2=$V_{\rm MD}$}
The \b[minimum-drag speed] $V_{\rm MD}$ minimizes the dimensional <drag> required for steady level flight at fixed <gravitational weight>, configuration and atmospheric conditions. It is not the speed at the smallest <drag coefficient>: changing speed changes the <dynamic pressure> and the <lift coefficient> needed to support the load.
For the <parabolic drag polar> $C_D=C_{D0}+kC_L^2$, assume $C_{D0}>0$, $k>0$ and constant <mass density> $\rho$. Substituting $L=W=qSC_L$ gives
$$
D(V)=aV^2+\frac b{V^2},\qquad
a=\frac12\rho S C_{D0},\qquad b=\frac{2kW^2}{\rho S}.
$$
The ideal finite-wing induced term motivates the quadratic dependence on lift coefficient; a measured whole-aircraft fit needs its own regime assessment.<Induced Drag Coefficient by NASA Glenn Research Center>[Drag Coefficient; total-drag decomposition and common reference area]{ref}
The <arithmetic-geometric mean inequality> proves a global bound for every $V>0$:
$$
D(V)\ge2\sqrt{ab},\qquad
\boxed{V_{\rm MD}=(b/a)^{1/4},\quad D_{\min}=2\sqrt{ab}.}
$$
Equality holds when $aV^2=b/V^2$, so the two modeled drag contributions are equal. Equivalently, the optimum lift coefficient is $C_L^{\rm MD}=\sqrt{C_{D0}/k}$.
An original model uses $a=0.20$ and $b=512{,}000$ when $V$ is in m/s and $D$ in newtons. It gives $V_{\rm MD}=40$ m/s and $D_{\min}=640$ N, with 320 N from each term. At 30 m/s, the terms are 180 and about 568.89 N, giving a larger total of 748.89 N. The slower state nevertheless requires less mechanical <power>, illustrating the distinct <minimum-power speed> objective.
At fixed weight, minimizing drag maximizes the <lift-to-drag ratio>. Under a shallow, steady-glide approximation this relates to best glide through the air, whereas <minimum sink speed> concerns altitude loss per time. The FAA polar explicitly distinguishes the corresponding operating points.<Glider Flying Handbook by Federal Aviation Administration>[Chapter 5, Glider Polars, Figure 5-11]{ref} Wind, variable coefficients or an unattainable lift coefficient can change the applicable optimum. These model results are not flight instructions or substitutes for measured aircraft performance.
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