The Principles of Aeroplane Construction; With Calculations, Formulae, and 51 Diagrams (Paperback)

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: CHAPTER II PRINCIPLES OF INCLINED PLANES Let Fig. 3 be an inclined plane in which Ab is the plane, Ac the base, and Bc the perpendicular; the three sides form what may be called the triangle of the plane. Let P represent the pull, or push, moving a body F up the plane, the direction of the force P being parallel to the base of the triangle. The vertical arrow represents w the weight of the body. And R normal to the plane is the resultant of the two forces P and w. From c draw a line parallel to R, cutting Ab in c, and from c draw a line parallel to the base, cutting Ec at b. Then it can be shown that - = ? = ? = w oc Ac height of perpendicular The weight raised = w. If w = 6 and P is found to be = 1, then? p 1 Bc 1 w = 6 - - Ac 6- The ratio of Bc to Ac is the ratio of the force P to the weight w. If there were no friction on the inclined plane when P is proportional to Bo and w to Ac, the forces P and w would be in equilibrium, and the body would be balanced between the two. When motion occurs work is done. If the body F moves horizontally from A to o while rising from c to B B b Fig. 3. ? Inclined plane. in 60 seconds, and Ac = 60 ft. and Cb = 10 ft., v, the horizontal velocity, is 60 ft. per second, while vl, the vertical velocity, is 10 ft. per second. If w = 1 Ib. the work done to raise 1 Ib. 10 ft. per second = 10 ft. Ib. The pull P travels in the same time 60 ft., and as the ft. Ib. in the pull must equal the ft. Ib. in the lift, per sec. = 60 ft. per sec. The inclined plane in this case is fixed and the body F movable under the force P. But the plane may be moving, that is to say pushed under the body F, like a wedge, in which case the body will be raised while the plane moves. The same effects occur if ? = -, t...