= Compact rotating two-blade loading source
{title2=$\rho'\propto R^{-1}\sin^2\theta\sin(2\Omega\tau_0)$}
Two diametrically opposite rotating blades with equal tangential loads have zero total rotating <force>. Their leading compact <acoustic dipoles> cancel, but their retarded positions and <moving-surface retarded Jacobians> leave an <acoustic quadrupole>. For line load $2Fr/a^2$ and angular speed $\Omega$, the first radiating density is $2F\Omega^2a\sin^2\theta\sin(2\Omega\tau_0)/(3\pi c_0^4R)$. The twofold geometry gives frequency $2\Omega$, while projection into the rotor plane gives the amplitude directivity $\sin^2\theta$.
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