162 



of h 



tval 



UN m^Oin \ \\II( s 1\ sllll' Dl'SICN 



Wove LcnijtM Lyv 



Srr. -IS.-I 



Direction 



Wove Trovol j ^. ^ 



- « I St«epnwa Rotio -^ of the Wove Drown a -j- 



RiM of Crest 



Wove Veloclt^^ 

 " or Celerity c T Mommurtu- 



J^ '^Qve Slope 

 Orbitoi Velocity "P^b^^ _^ ^ _'t- ..^h^ 



Cirtulor Orbit Fhth 



Depth h An(]ular Velocitu In Orbit u 



WoveLenqth Lw " "T^ V^fave Celentij c -^^^ Orbital Veloci ty at S urfoce- cjRs" u)(-/)- 1Tc(x^j 



Wove Period T^y -"y a * ' ~C~ " o^ *°'e Frequencu- y- - ^ 



Fig. 48.B Definition Dr.\wing for a Trociioidal Wave 



(0 The depth of the liciuid body is uiiliinitcd 

 (g) The Uquid is ideal, without viscosity'. 



The results of iiriniipal interest are, based upon 

 a wave length L „• , a wave celerity (velocity) c, a 

 wave period r«- , a wave height hw , b, surface- 

 particle orbit radius 72.9 , and an acceleration of 

 gravity g for sea level at 45 deg latitude of 

 32.174 ft per sec' or 9.80G65 m per sec": 



(1) Lir = 2-kRrc , where R,ic is the radius of 

 the rolling circle for the graphic trochoidal con- 

 struction 



(2) 



c = V gL „./2Tr 

 = 2.2G3\/L^, in fpswhen L„- is in ft 

 = 1 .249 V L ir , in mps wlien L »■ is in m 

 = IMOVT^-, in k( wlioii /.„ i.s in ft 

 = 2A27VT^-, in kt when /,„• is in m. 



"- 2r^ " 

 = 5.1217',,. in fps 

 = 3.0327',, in kt 

 = 1.5G17',, in ini)ersec. 



(3) 



T„ = \/2rLJg 



= 0.4419\//y„-, in sec wh en /vn- is in ft 

 = O.SOOSvLic, insecwlien //„ i.s in m. 



i IT — — 



(4) 



I'rr'(|Ufnry = rn— 

 i w 



(5) L„- = 2-KC'/g 



= 0.1953c", in ft when c is in fps 

 = 0.5571c", in ft when c is in kt 

 = 0.<il07c", in in wiien c i.s in mps 

 = 0.1G97c', in m when c is in kt. 

 /.,.. = ff2l,-/(2,r) 



= 5.r217'H-, in ft wlicn 7'„- is in .sec 

 = 1.5(il7';',-. in in wlicn Y',,- is in sec. 



(6) /i„- = 2U, and Rs = h„-/2 



(7) Till' (irliital vcldrily, as derived in See. 4.'^.7, 

 is 



f/o,b = 7r/i„/(0.4419 VZ^) = 7.109/i„-/V^ 



= irc(/i„-/L„), 



wiiere r,,,!, is in fps when /i „ and L^ are in ft 

 and c is in fjis. 



(8) The angular orbital velocity ui is, from (3) 

 and (4) preceding, 27r/7'i,. , or 



2ir 



l2wL,r 





(9) Tlie line of orbit centers of the surface 

 particles is at the distance 5r(/i„)V(-l^'ii) = 

 tt/i" .?//>„. = 0.7854(/i„)V/.„. above the still-water 

 level. At any depth h, where the orbit radius is R, 

 tli(! con^'spniiding distiineo is 



2ir 





2ye«, 



