= Winglet cant angle
The \b[winglet cant angle] specifies the inclination of a <winglet> away from a stated reference direction. Here $\phi=0$ means an upright winglet, with positive $\phi$ tilting outward from vertical in the transverse plane. A convention measured upward from the main wing plane would instead give $90\,{}^\circ-\phi$ for this ideal geometry. A quoted angle therefore needs its reference plane. <Winglet toe angle> concerns a different orientation, involving the chord and incoming flow.
For a straight unswept winglet of length $\ell$, the purely geometric projections are
$$
h=\ell\cos\phi,\qquad \Delta y=\ell\sin\phi.
$$
If symmetric winglets attach at the tips of a main <wingspan> $b$, their outer-tip projected separation is $b+2\ell\sin\phi$. With stipulated $b=10\,\mathrm m$, $\ell=0.60\,\mathrm m$ and $\phi=20\,{}^\circ$, the vertical height is \b[$0.5638\,\mathrm m$], each tip moves outward $0.2052\,\mathrm m$, and the total projected separation is about $10.4104\,\mathrm m$. None of these projections alone supplies a new <span efficiency factor> or a prediction of <lift-induced drag>.
Cant also changes how loads act on the supporting wing. In a right-handed frame with $y$ outward, $z$ upward and $x$ completing the triad, the rolling-moment contribution of an applied <force> is $M_x=yF_z-zF_y$. For a stipulated $200\,\mathrm N$ vertical force applied at the outer tip, the moment about the vehicle centreline is $1000\,\mathrm{N\,m}$ when the winglet is upright and about $1041.0\,\mathrm{N\,m}$ at the stated outward cant. This isolates the changed <moment arm>; an actual aerodynamic load need not stay vertical or keep the same magnitude when cant changes.
<Richard T. Whitcomb>'s primary design discussion explicitly balances <lift-induced drag>, skin friction and wing bending moments, and discusses outward cant separately from incidence and twist. It also identifies interference at the upper-winglet root as part of the design problem.<A Design Approach and Selected Wind-Tunnel Results at High Subsonic Speeds for Wing-Tip Mounted Winglets by Richard T. Whitcomb>[Printed pp. 7–8, Incidence and twist and Cant or dihedral]{ref} A controlled <wind tunnel> comparison must therefore record <forces> and moments at matched conditions, rather than infer an optimum cant solely from the projected span.
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