Chain drive efficiency has been studied to understand energy loss mechanisms in bicycle drive trains, primarily for derailleur-type systems. An analytical study of frictional energy loss mechanisms for chain drives is given along with a series of experimental measurements of chain drive efficiency under a range of power, speed and lubrication conditions. Measurements of mechanical efficiency are compared to infrared measurements indicating that frictional losses cannot account for the observed variations in efficiency. The results of this study indicate that chain tension and sprocket size primarily affect efficiency and that non-thermal loss mechanisms dominate overall chain drive efficiency.
The primary problem i n the design of antenna. zrrays is the satisfaction of the requirements of side-lobe level and beamwidth. An additional major consideration which has only recently received an analytical treatment1 is the problem of the deterioration of the beamwidth and side-lobe level arising from the variations in the excitation of "each element. These variations are due primarily t o the inaccuracies inherent i n t h e manufacturing processes used t o produce the array.The first problem has been discussed i n great d e t a i l by many authors,*and it will be the purpose of t h i s paper t o analyze the seuond problem. The a n a l p i s is formulated in general f o r a symmetrically excited broadside array and then, as a specific & a m l e , is applied t o a linear shunt slot array which uses a Dolph-Tchebyscheff 3 distribution for the element excitations. This distribution optimizes the relationship between beam width and side-lobe level.However, the method of analysis is general and may be applied t o any linear array of radiators with arbitrary excitation, if the t o t a l mutual coupling between individual radiators may be neglected and no cross correlation exists between the inaccuracies of m y two sourceso Consideration w i l l be given t o these fundamental assumpt i o n s t o show that the general metho& w i l l yield useful results for slot a r r a y s .It i s also notewortm that the statistical'method shown here may be applied t o q radiative devicepvhose t o t a l effect is obtained by suxning the effects from a large number of smaller radiators. If the amplitude and phase of the excitation from each radiator are independent functions of the physical dimensions of the structure, size and spacing, then the technique developed in this paper may be modified t o give useful results concerning the effect of manufacturing inaccuracies.The general method t o be used in the analysis may be applied t o q distribution of n independent radiators, The instantaneous field strength a t a point P fram' such an array can be given as where Ai r e l a t i v e is the relative amplitude phase O f the contribution and Gi a function of t o the f i e l d pattern P, which is t h e from the i-th source.
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