centre and radius equal to the maximum radius of the polar curve, a semi-circle is OR LRM drawn. A convenient number of points on this semi-circle (say 10° points) are projected onto any vertical plane as shown. For example, points etc. are projected to and so on. From a,b,c d,e,f point the horizontal line is drawn equal to the intercept of the polar diagram on the d, dg OA radius Similarly, = = and so on. The points etc., define the oa. eh OB, fk OC g, h, k Fig 3.25 Rousseau figure. The average width of this figure represents the M.S.C.P. to the same scale w as that of the candle powers in the polar curve. The average width is obtained by dividing the Rousseau area by the base of the Rousseau figure length lm which is the projection of the i.e. semi-circle on the vertical axis. The area may be determined by rule or by LM Simpson‘s using a plani meter
centre and radius OR equal to the maximum radius of the polar curve, a semi-circle LRM is drawn. A convenient number of points on this semi-circle (say 10° points) are projected onto any vertical plane as shown. For example, points a,b,c etc. are projected to d,e,f and so on. From point d, the horizontal line dg is drawn equal to the intercept OA of the polar diagram on the radius oa. Similarly, eh = OB, fk = OC and so on. The points g, h, k etc., define the Fig 3.25 Rousseau figure. The average width w of this figure represents the M.S.C.P. to the same scale as that of the candle powers in the polar curve. The average width is obtained by dividing the Rousseau area by the base of the Rousseau figure i.e. length lm which is the projection of the semi-circle LM on the vertical axis. The area may be determined by Simpson‘s rule or by using a plani meter
43-Uses-of-Polar-Curves.docx