English: Defining image, Flippin-Lodge angle, ${\displaystyle \alpha _{FL}}$ (blue arc), a nucleophile approach trajectory, after Heathcock (1990). The boxed image is a three-dimensional (3D) representation of the approach of a nucleophile, Nu, with lone pair electrons (red ":"), to an en electrophile, here a carbonyl functional group of an organic compound (an aldehyde, ketone, or carboxylic acid derivative, though the following concepts also extend to carbon-carbon double bond reactions). The Flippin-Lodge angle (${\displaystyle \alpha _{FL}}$; Heathcock, 1990) describes the displacement of the attacking Nu, at its elevation, toward one or the other substituent of the carbonyl group. (The angle describing the elevation of the attacking Nu above the plane of the organic compound, the Bürgi–Dunitz angle (${\displaystyle \alpha _{BD}}$), is described in its own article, and with its own images, at the English Wikipedia. Analogy is made between these two angles and the azimuth and altitude parameters in a celestial/horizontal coordinate system, see BurgiDunitzFlippinLodgeCelestCoordAnalogyBoxed.jpg here at Wikimedia Commons.) The inset at upper left represents the carbonyl-containing electrophile, shown in the plane of the page. It is an aldehyde when one substituent is a hydrogen (e.g., R' = H), a ketone when neither is a hydrogen or non-carbon atom, or a carboxylic acid derivative (e.g., ester or amide, with one substituent being an O- or N-substituent, respectively). The inset structure is a line-angle representation, so the attached substituent groups R and R' attach via an atom in each substituent to the carbon atom of the carbonyl group; the carbon atom is implied at the vertex of these bonds. This inset structure serves as the basis for the following Newman projection, and rest of this description. The remaining central part of this image is a two-dimensional representation of the 3D approach of the Nu to the carbonyl-containing compound. The compound of the inset lies in horizontal plane I (gray segment), which projects toward the viewer from the plane of the page (and behind it). Hence, the view of the compound is "edge-on" this plane, so this is a Newman projection of the compound and its carbonyl group (as indicated by the black circle). Specifically, the view of the carbonyl group is from the carbon atom, down the C=O bond. The attached groups R and R' project toward the viewer from plane III, the plane of the page. (Plane III contains only the carbon atom of the carbonyl group, which is implied at the vertex of the two bond wedges to substituents R and R'.) The carbonyl oxygen, behind the carbon—behind the plane of the page—is not shown. Finally, another plane is implied, plane II (maroon segment), a vertical plane, also viewed edge-on, that contains the carbonyl C=O bond, and bisects the R-C-R' bond angle. The long solid black arrow connecting the lone pair of the electronegative atom of the Nu (red ":") to the carbonyl carbon atom represents the approach vector (trajectory) of this relevant electronegative Nu atom, from above plane I, to the carbonyl, projected from its 3D location onto the plane of the page, plane III; the short solid arrow below it indicates that the Nu could just as well approach from "below" plane I. ${\displaystyle \alpha _{FL}}$ can be estimated crystallographically, based on positions of atom electron densities (with its value determined by vector algebra). Graphically, its value can be see as the angle between plane II and the projected approach vector of the nucleophile, from its position in 3D, onto plane III, as is shown here. Alternatively, the nucleophile position in 3D can be projected onto Plane I, as suggested by the dashed line, and the angle between the approach vector and plane II is equivalent to ${\displaystyle \alpha _{FL}}$. A stated convention for ${\displaystyle \alpha _{FL}}$ is that it is positive when deviating in the direction away from the larger substituent (or away from the more electron-rich substituent, which is similarly repulsive). Hence, if R'=H, R=alkyl (i.e., the electrophile is an aldehyde, positioned with H substituent to the right), the Nu would be expected to approach as it is presented here, and give a positive value of ${\displaystyle \alpha _{FL}}$. The important concepts and the utility associated with these angles (and further formal mathematical ways of determining or measuring them) are expected to appear in the relevant Wikipedia articles. Note: Drawing created for "Flippin-Lodge angle" article at English Wikipedia by delta0349 in 2014. REFERENCE: C.H. Heathcock (1990) Understanding and controlling diastereofacial selectivity in carbon-carbon bond-forming reactions, Aldrichimica Acta 23(4):94-111, esp. p. 101, and references to Flippin et al. and Lodge et al. articles therein; see [1], accessed 30 November 2014. [Le Prof]