= Area rule
The \b[area rule] is an aerodynamic design principle relating transonic <wave drag> to the longitudinal distribution of the total cross-sectional area of an <aircraft>, including its <fuselage> and <aircraft wings>. A wing-body combination can create a rapid area increase even when each part appears streamlined in isolation. Redistributing the <fuselage> area near the wing can smooth the combined distribution. This does not say that any reduction in frontal area guarantees lower total <drag>.<Richard T. Whitcomb by NASA>[Area-rule account, combined cross-sectional-area distribution and wing-body model test]{ref}
An original geometric model makes the redistribution explicit. Let $x$ increase along the <fuselage>, and let $A_b(x)$ and $A_w(x)$ denote body and added-wing areas, counting their overlap only once. Over a stipulated interval of length $\ell$, take
$$
A_w(x)=a\sin^2(\pi x/\ell),\qquad 0\le x\le\ell.
$$
If the desired combined distribution on that interval is $A_0$, the bookkeeping choice $A_b(x)=A_0-A_w(x)$ gives $A_b+A_w=A_0$. For $A_0=3.0\,\mathrm{m^2}$, $a=0.6\,\mathrm{m^2}$ and $\ell=4\,\mathrm m$, the body's area is $2.4\,\mathrm{m^2}$ at the midpoint. Relative to a constant-area body, the removed volume is
$$
\int_0^\ell A_w(x)\,dx=\frac{a\ell}{2}=1.2\,\mathrm{m^3}.
$$
This invented example exposes a design tradeoff: smoothing an area distribution can consume internal volume. It is not a calculation of <wave drag>, and the rest of the vehicle still needs smooth transitions.
<Richard T. Whitcomb>'s motivating test used a specially built wing-body model in a <wind tunnel>, before applying the shape change to a fighter configuration. Comparing measured <drag> through the transonic range tests the proposed area-distribution effect; appearance alone does not. <Viscous stress>, <lift-induced drag>, loading and off-design conditions still matter to the complete <aircraft>.<Richard T. Whitcomb by NASA>[Prioritized Langley model experiment and subsequent F-102 modification]{ref}
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