CHANOINE WICKET DAMS. 235 



Then, taking moments about C, the moment of P = sum of moments of P'+P", or 



sec a 





Whence & = 



sec 2 a 



P"X seca 

 3 



sec 



a. I , H 

 (c?+ 

 \ 3 



2 P 



I x 



Ibs. 



sec 



+ ad) 



To find Q, take moments about C, whence 



wH 2 



n wH 2 sec 2 al H\ 

 .l = P.k,or Q = - - t - ld + ~\X fo\ Ibs. 



Then from the proportion between the sides and sines of a triangle, 



Q X sin (90 + a - /?) _ Q . cos ( - /?) 

 sin (90 a r+P)~ sin (90 - a - 7- + /?) 



and 



Q sin 7- 



sin (90 a f + 



FIG. 18. 



The pressure of the wicket against the sill at D=>P Q, and the upward pull on 

 the anchorage at D = T cos /?. 



In the preceding calculations we have neglected any water pressure below the 

 wicket, in order to obtain the maximum strains which can occur. f 



With the axis of rotation placed at the height dictated by experi- j 

 ence and mentioned a little farther on, it has been found that / 

 wickets do not trip themselves under any ordinary conditions of /' 

 practice, and that they will support without derangement a pool-level 

 1 2 to 1 8 inches above their tops. The latter condition is one which 

 sometimes proves of much benefit, not only when an unexpected 

 rise comes, but also where an extra channel depth is required for a short while to float 

 too heavily loaded craft. 



At the mouth of a stream, however, tributary to a large river which may cause 

 backwater during a flood, the tributary itself being at an ordinary stage, it will be 

 necessary to adjust the height of the prop so that the wicket will not trip before the 

 backwater is level with the pool above. Unless this be provided against the wickets 

 will begin to swing themselves too soon, thus reducing the upper pool-level and the 

 depth of the water at the lock above and on the shoals. Such cases have occurred and 

 have caused trouble to craft. 



To find the height at which the prop should be placed in order to avoid this self- 

 operation, let P, H, d, etc., represent the same quantities as before, and let h represent 

 the depth of the water below, and R its pressure (Fig. 19). 



Then R = wh sec X 62$ Ibs. x - = secaX 62$ Ibs. 



Its moment about C 



h sec a wh 3 sec 2 a X 62^ Ibs. 

 K X - - = ~ 



