is evident that if the velocity of translation be zero, and that of rotation finite, the position of the centre of pressure will coincide with the centre of gravity. If, on the other hand, the velocity of rotation be small in comparison with that of translation, there will on the whole be but little lateral displacement of the centre of pressure, and in the limit, if we suppose the rotation to be extinguished, although the centre of pressure will be displaced forward, as in the simple aeroplane, there will be no lateral displacement, and the torque that produces the precession about the transverse axis will vanish.
Let us represent the boomerang by a straight narrow aeroplane as in Fig. 200, and let us suppose that the instantaneous
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Fig. 200.
centre be moved from the geometric centre away to infinity, so that in the first instance the motion is pure rotation and in the latter the motion is of pure translation. It is evident that, as above stated, for these extremes there is no displacement of the centre of pressure; on the basis of equal increments of K (comp. § 107), the pressure curve in the two cases is as represented respectively in Figs. 201 and 202. Now, for intermediate positions of the instantaneous centre of motion there will be displacement of the centre of pressure, as indicated in Fig. 200, in which the displacement of the centre of pressure is represented by the ordinates of a curve where abscissae give the position of the instantaneous centre. As plotted, this curve is based on the V squared law and on the assumption of a uniform value of K per unit length. If the aeroplane is other than flat,
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