Flight-Velocity, Etc; 1899-1910 (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1906 Excerpt: ...prove this, I must go on a little more mathematically than was originally intended with this lecture. Steering and other effects of the stroke. The centre of air-pressure in each wing, while the flyer is gliding, can be exactly determined by the principle that in every strip of the supporting area, parallel to the direction of flight, the centre lies at V3 of its length from the front border. But this point is not decisive for the propelling force, because the latter is in proportion to the square of the stroke-velocity, which is again proportional to the square of the distance from the centre of oscillation. Therefore some other point of the wing must be the propelling centre. We shall now refer to Fig. 23. The variable velocity u, at which the centre of propelling moves in its down-stroke, produces the reacting air-pressure, the latter always existing at the same instant; and one of its components, viz. that one, which is parallel to the direction of flight, causes the propulsion. The stroke begins in the highest position of the propelling centre; from this point in time and space, the point zero, begins the observation. The duration of time may be measured on the axis of abscissas from 0 signifying zero, to Z, in such a way that the length OZ is equal to the whole duration T of the stroke; but when the time t, growing from zero to T and measured from O, is passed, the stroke velocity is u. While now the time t increases by the differential dt, the space s traversed by the point, measured from zero, may increase by ds. The velo ds city which took place in this element of time is: u =-gr, that is the differential of the traversed space divided by the constant differential of time. The velocity u belonging to every value of time, measured from zero may be d...