Naval Architecture Homework #3: Calculating Waterplane Area and Coefficients, Study notes of Aerospace Engineering

Download Naval Architecture Homework #3: Calculating Waterplane Area and Coefficients and more Study notes Aerospace Engineering in PDF only on Docsity!                 Homework  #3                         LTJG  Zachary  B.  Robertson,  USCG   Mechanical  Engineering  M.S.  Student   DUINS,  USCG  Marine  Engineering,  Virginia  Tech                         Naval  Architecture,  AOE  3204   Professor  P.  Kumar,  Virginia  Tech   LTJG  ZACHARY  B.  ROBERTSON,  USCG   NAVAL  ARCHITECTURE  (3204)   PROFESSOR  P.  KUMAR,  VIRGINIA  TECH   HOMEWORK  #3     #1     DEFINE     GIVEN:         FIND:     a) Using  the  trapezoidal  rule,  calculate  the  waterplane  area  of  the  vessel.   b) Using  Simpson’s  First  Rule,  calculate  the  waterplane  area  of  the  vessel.   c) Discuss  which  calculation,  either  that  of  part  a  or  part  b,  you  believe  is  more   accurate.   d) Calculate  the  waterplane  coefficient  using  your  most  accurate  estimate  of   waterplane  area.     CRITICAL  FORMULAS:     Trapezoidal  Rule:   ! ! !" = !! ! !! !!(!!) ! !! !"!′′(!) ! !       Simpson’s  Rule:   ! ! !" = !! ! !! !!!(!!)!!(!!) ! !! !"! !(!)!!!!     CW = AW L*B     REFERENCES:     [1]   Zubaly.  “Applied  Naval  Architecture”.  Cornell  Maritime.  Centreville,  1996.   [2]   Burden,  R.  L.,  and  Faires,  J.  D.,  2005,  “Numerical  Analysis:  8th  Edition,”  Thomson   Brooks/Cole,  Belmont,  pp.  188-­‐192.         LTJG  ZACHARY  B.  ROBERTSON,  USCG   NAVAL  ARCHITECTURE  (3204)   PROFESSOR  P.  KUMAR,  VIRGINIA  TECH     VERIFY     Units  are  accurate  and  reasonable.    Significant  digits  taken  to  2,  due  to  accuracy  of  the   values  at  Station  10.    Answer  is  appropriate  –  and  both  parts  a  and  b  were  found  to  be   similar.     ENCLOSURES     None.   LTJG  ZACHARY  B.  ROBERTSON,  USCG   NAVAL  ARCHITECTURE  (3204)   PROFESSOR  P.  KUMAR,  VIRGINIA  TECH   HOMEWORK  #3     #2     DEFINE     GIVEN:       Figure  2:  Design  waterline  for  simplified  hull  form.         Figure  3:  Immersed  midship  section  for  simplified  hull  form.     LTJG  ZACHARY  B.  ROBERTSON,  USCG   NAVAL  ARCHITECTURE  (3204)   PROFESSOR  P.  KUMAR,  VIRGINIA  TECH   FIND:     a) AW   b) M∞   c) LCF  (Relative  to  miships)   d) I∞   e) IL   f) IT   g) AS   h) CM   i) CIT     j) CIL     CRITICAL  FORMULAS:     AW = ydx!L 2 L 2" M# = 2 x* y( )dx!L 2 L 2" LCF = x = M# AW I# = 2 x 2y( )dx!L 2 L 2" IL = I# ! AW (LCF) 2 IT = 2 3 y3 dx !L 2 L 2" AS = 2 ydz0 T " CM = AM B*T CIT = 12* IT B3 *L CIL = 12* IL B*L3     REFERENCES:     [1]   Zubaly.  “Applied  Naval  Architecture”.  Cornell  Maritime.  Centreville,  1996.   [2]   AOE  3204:  Naval  Architecture:  Class  Slides  –  20JAN11.     [3]   AOE  3204:  Naval  Architecture:  Class  Slides  –  25JAN11.   [4]   AOE  3204:  Naval  Architecture:  Class  Slides  –  27JAN11.         LTJG  ZACHARY  B.  ROBERTSON,  USCG   NAVAL  ARCHITECTURE  (3204)   PROFESSOR  P.  KUMAR,  VIRGINIA  TECH   f)   Calculate  the  transverse  moment  of  inertia.     IT = 2 3 y3 dx !L 2 L 2" IT = 2 3 5x ! x 2 50 ! x3 625 # $ % & ' ( 3 dx !L 2 L 2" IT = 2 3 5x ! x 2 50 ! x3 625 # $ % & ' ( 3 dx !50 50 " IT = 2 3 46520 7 ) *+ , -. IT = 93040 21 IT = 4430m 4     g)   Calculate  the  immersed  station  area  at  midships.     AS = 2 ydz0 T ! AS = 40" 2 4 625 z4 dz 0 5 ! AS = 40"8 AS = 32m 2     h)   Calculate  the  midship  section  coefficient.     CM = AM B*T CM = 12m4( ) 10m( )* 4m( ) CM = 12m4( ) 40m4( ) CM = 12 40 CM = 3 10 CM = 0.333         LTJG  ZACHARY  B.  ROBERTSON,  USCG   NAVAL  ARCHITECTURE  (3204)   PROFESSOR  P.  KUMAR,  VIRGINIA  TECH   i)   Calculate  the  waterplane  inertia  coefficient  CIT.     CIT = 12* IT B3 *L CIT = 12* 4430m4( ) 10m( )3 * 100m( ) CIT = 53165.7m4( ) 100000m4( ) CIT = 0.532     j)   Calculate  the  waterplane  inertia  coefficient  CIL.     CIL = 12* IL B*L3 CIL = 12* 418184m4( ) 10m( )* 100m( )3 CIL = 5,018, 214m4( ) 10,000, 000m4( ) CIL = 0.502     VERIFY     Units  are  accurate  and  reasonable.    Significant  digits  taken  to  2  and  3,  dependent  on   accuracy  of  given  data  for  each  specific  problem.    Answer  is  appropriate  and  of  proportion   of  those  found  in  the  25JAN11  and  27JAN11  class  note  examples.     ENCLOSURES     N/A.   LTJG  ZACHARY  B.  ROBERTSON,  USCG   NAVAL  ARCHITECTURE  (3204)   PROFESSOR  P.  KUMAR,  VIRGINIA  TECH   HOMEWORK  #3     #3     DEFINE     GIVEN:     DD-­‐692  Class  Length:  383  ft   TF  =  12’9”   TA  =  13’3”   KG  =  16’     FIND:     a) TM   b) ΔSW   c) CB  @  Level  Trim   d) CM   e) CW   f) LCF  (Relative  to  Midship)   g) GM   h) KML   i) TPI  *  1”     CRITICAL  FORMULAS:     TM = TF +TA 2 CB = Displacement _Volume L*B*T Displacement _Volume = ! !g CM = AM B*T CW = AW L*B GM = KM "KG KML = KB+BML     REFERENCES:     [1]   Zubaly.  “Applied  Naval  Architecture”.  Cornell  Maritime.  Centreville,  1996.   [2]   AOE  3204:  Naval  Architecture:  Class  Slides  –  27JAN11  –  Slides  6-­‐16   LTJG  ZACHARY  B.  ROBERTSON,  USCG   NAVAL  ARCHITECTURE  (3204)   PROFESSOR  P.  KUMAR,  VIRGINIA  TECH   BML = 478* 200 100 = 956 ft KB = 783* 1 100 = 7.83 ft KML = KB+BML KML = (7.83 ft)+ (956 ft) KML = 963.83 ft KML ~ 963 ft     i)   After  a  period  of  time,  the  mean  draft  decreases  by  1  inch  with  the  same  trim.    How   many  tons  of  fuel  and  stores  have  been  consumed?     TPI =1402* 2 100 = 28.04 tons in !! =1inx28.04 tons in !! = 28.04tons     VERIFY     Units  are  accurate  and  reasonable.    Significant  digits  taken  to  3  and  4,  dependent  on   accuracy  of  given  data  for  each  specific  problem.    Answer  is  appropriate  and  of  proportion   of  those  found  in  25JAN11  class  note  examples.     ENCLOSURES     • USS  Gearing  DD  710  (692  Class)  Curves  of  Form  -­‐  Annotated   ° °° c So z Oo = c ce F i i § i i ‘i my j | a