How to calculate displacement with simpson's rule

Discussion in 'Stability' started by Adeyele, Aug 1, 2012.

  1. Adeyele
    Joined: Jun 2012
    Posts: 48
    Likes: 0, Points: 0, Legacy Rep: 10
    Location: Lagos

    Adeyele Junior Member

    Dear all, am a student and i was given an assignmnt to find displacemnt with simpsons rule without common interval. the draught are 0.762M Forwd and 1.905M Aft.

    The segments are 0, 3.04, 4.9, 5.02, 4.62, 4.21, 3.8, 3.38, 2.93, 1.79 and 0 metre-sqs

    pls can any1 hlp me on how to find d displacemnt.

    Looking forward to a reply.

    Regards
    Mike
     
  2. DCockey
    Joined: Oct 2009
    Posts: 4,371
    Likes: 201, Points: 63, Legacy Rep: 1485
    Location: Midcoast Maine

    DCockey Senior Member

  3. Ad Hoc
    Joined: Oct 2008
    Posts: 6,126
    Likes: 361, Points: 83, Legacy Rep: 2488
    Location: Japan

    Ad Hoc Naval Architect

    You still need a common interval for the 5 8 -1 rule. Which the OP says he doesn't have.
     
  4. DCockey
    Joined: Oct 2009
    Posts: 4,371
    Likes: 201, Points: 63, Legacy Rep: 1485
    Location: Midcoast Maine

    DCockey Senior Member

    Any suggestions for what he could use?
     
  5. DCockey
    Joined: Oct 2009
    Posts: 4,371
    Likes: 201, Points: 63, Legacy Rep: 1485
    Location: Midcoast Maine

    DCockey Senior Member

    What are the distances between the stations?
     
  6. Ad Hoc
    Joined: Oct 2008
    Posts: 6,126
    Likes: 361, Points: 83, Legacy Rep: 2488
    Location: Japan

    Ad Hoc Naval Architect

    There is Tchebycheff's rule, failing that, just treat each as a trapezoid and work each individually.
     
  7. TeddyDiver
    Joined: Dec 2007
    Posts: 2,553
    Likes: 112, Points: 73, Legacy Rep: 1650
    Location: Finland/Norway

    TeddyDiver Gollywobbler

    OP's numbers look like something isn't right or is missing..
     
  8. PAR
    Joined: Nov 2003
    Posts: 19,133
    Likes: 471, Points: 93, Legacy Rep: 3967
    Location: Eustis, FL

    PAR Yacht Designer/Builder

    Durand's rule still requires uniform spacing doesn't it? I'd agree he'll have to treat each section with the trapezoidal rule.
     
  9. Ad Hoc
    Joined: Oct 2008
    Posts: 6,126
    Likes: 361, Points: 83, Legacy Rep: 2488
    Location: Japan

    Ad Hoc Naval Architect

    Yes:
    http://mathworld.wolfram.com/DurandsRule.html

    He could use Guass' Rules, but that is very long and tedious. I think trapezoidal rule for each segment is quicker and easier.
     
  10. gonzo
    Joined: Aug 2002
    Posts: 13,613
    Likes: 383, Points: 93, Legacy Rep: 2031
    Location: Milwaukee, WI

    gonzo Senior Member

    Simpson's rule is based on equal intervals. I agree that the trapezoidal rule is easier.
     
  11. ldigas
    Joined: Feb 2011
    Posts: 187
    Likes: 4, Points: 18, Legacy Rep: 60
    Location: Zagreb, Croatia

    ldigas Senior Member

    Mike, please, it would be very useful if you could tell what were your exact input data, for (I at least) cannot make sense of what is the above you've been given. What are the 0, 3.04, 4.9 ... values? Metre-sqs is meters squared I presume?

    Anyway, as others have already noted for Simpson's rule (either the most popular one using a quadratic curve) or some of the less popular variants, you need to have equidistant spacing of points. That means the distance between the points can change, but you need AT LEAST three equidistant points.

    For example, this series could work
    0 1.5 3 6 9 10 11
    Because the distance in the first few points is 1.5, then 3 then 1. But you need to have at least three points to put the quadratic curve through.

    That being said, Simpson's rule is merely a way to integrate an area beneath the curve. You could fit a curve through your points, interpolate a new set of equidistant points and then use Simpson's rule to calculate the area beneath it.

    All of this, however, is rather moot since we would need to first determine what is the given set of data.
     
  12. Adeyele
    Joined: Jun 2012
    Posts: 48
    Likes: 0, Points: 0, Legacy Rep: 10
    Location: Lagos

    Adeyele Junior Member

    Dear all, sorry for late reply; I av a problm wit my connection.

    Actly i saw an example in d ship stability for masters and mates txtbk. Dey use first rule SM to multiply d areas, and divide d sum of area by Product sum. dis givs displacemnt.

    Many thanks.
    Mike
     
  13. ldigas
    Joined: Feb 2011
    Posts: 187
    Likes: 4, Points: 18, Legacy Rep: 60
    Location: Zagreb, Croatia

    ldigas Senior Member

    Still, please, if you could present the assignment as it was given. It would help to clarify the problem at hand. And not everyone has the copy of the book in question.

    Willing to help, by all means, but the given explanation doesn't make much sense (could be a language issue).

    Displacement is usually calculated in one of three ways, which are analogous ... either by integrating the areas below the design waterline of the buttocks, or the sections, or by integration of waterline areas up to the design waterline.
     
  14. Adeyele
    Joined: Jun 2012
    Posts: 48
    Likes: 0, Points: 0, Legacy Rep: 10
    Location: Lagos

    Adeyele Junior Member

    My Assignment

    Dear all,

    Please kindly checK the information below; for the assignment i was talking about.

    Type of vessel is Single Screw Dry Cargo Coaster
    Length Overall 31.85 Metres
    Load Line Length 30.00 Metres
    Breadth Moulded 6.71 Metres
    Moulded Depth Amidships 2.87 Metres
    Full Load Draught (Amidships to underside of keel) 2.53 Metres
    Displacement to Full Load Draught (Amidships to underside of keel) 423.5 Tonnes
    Maximum Deadweight 294.5 Tonnes

    QUESTION 1
    When an inclining experiment was performed on the vessel the draught forward was noted as 0.762 Metres (frame 53) and aft 1.905 Metres (frame 3).
    The waterline length is 29.50 Metres and for the purposes of this assignment has been divided into ten equal segments with the half-area at each section, from aft, being as follows: -
    0 0.00 M2
    1 3.04 M2
    2 4.90 M2
    3 5.02 M2
    4 4.62 M2
    5 4.21 M2
    6 3.80 M2
    7 3.38 M2
    8 2.93 M2
    9 1.79 M2
    10 0.00 M2
    Using Simpson’s rules calculate the displacement in salt water including the position of the longitudinal centre of buoyancy.
    The total weight used for the inclining experiment was 3.60 Tonnes, positioned on the side decks port and starboard, (half each side), 18.22 Metres forward of the transom and 3.25 Metres above the keel, the shift was 5.200 Metres transversely. The forward pendulum length was 3.040 Metres and the aft pendulum 2.545 Metres. What effect does the removal of the weights have on both the vertical and longitudinal centre of gravity?

    Question 2

    Below are the pendulum deflections from the inclining experiment: -
    Experiment
    Weight Moved
    Forward Pendulum Deflection
    Aft Pendulum Deflection
    1
    0.400 Tonnes starboard to port
    35.00 mm
    23.00 mm
    2
    1.200 Tonnes starboard to port
    75.00 mm
    65.00 mm
    3
    0.800 Tonnes port to starboard
    55.00 mm
    45.00 mm
    4
    0.400 Tonnes port to starboard
    22.00 mm
    20.00 mm
    5
    0.400 Tonnes port to starboard
    29.00 mm
    21.00 mm
    6
    0.800 Tonnes port to starboard
    51.00 mm
    45.00 mm
    7
    0.800 Tonnes starboard to port
    51.00 mm
    43.00 mm
    8
    0.800 Tonnes starboard to port
    53.00 mm
    44.00 mm
    9
    0.800 Tonnes starboard to port
    50.00 mm
    43.00 mm

    Using the answers to Question 1, the pendulum deflections and the hydrostatic data below calculate the GM and VCG of the vessel in the inclined condition.
    Draught Amidships (Metres)
    0.914
    1.067
    1.219
    1.372
    1.524
    1.676
    1.829
    Displacement (Tonnes)
    128.2
    153.0
    178.2
    204.0
    230.2
    257.0
    284.3
    Block Coefficient
    0.504
    0.535
    0.562
    0.580
    0.592
    0.602
    0.610
    LCB from Transom (Metres)
    14.833
    15.048
    15.198
    15.302
    15.370
    15.411
    15.430
    LCF from Transom (Metres)
    16.178
    16.143
    16.070
    15.962
    15.831
    15.691
    15.539
    KB above Base (Metres)
    0.501
    0.579
    0.658
    0.737
    0.8183
    0.900
    0.983
    BMt (Metres)
    3.905
    3.382
    2.982
    2.669
    2.418
    2.213
    2.042
    KMt above Base (Metres)
    4.355
    3.908
    3.590
    3.362
    3.196
    3.076
    2.991
    BML (Metres)
    64.033
    56.545
    51.169
    47.253
    44.282
    41.874
    39.959
    KML above Base (Metres)
    64.535
    57.124
    51.827
    47.991
    45.100
    42.775
    40.941
    TPc (Tonnes/cm)
    1.607
    1.641
    1.673
    1.707
    1.742
    1.775
    1.810
    MTc (Tonne. Metres)
    2.609
    2.755
    2.912
    3.087
    3.274
    3.467
    3.671
    In the full load condition the vessel can carry 280 Tonnes of homogeneous cargo having an LCG of 16.55 Metres from the transom and 1.94 Metres above the keel. Calculate the draught, trim, position of the longitudinal and vertical centres of gravity for the loaded vessel? Using the KN data below prepare a GZ curve for the loaded vessel?

    I will really appreciate any help on how to solve this questions.

    Looking forwarda to a reply
    Regards
    Mike
     

  15. Leo Lazauskas
    Joined: Jan 2002
    Posts: 2,696
    Likes: 146, Points: 63, Legacy Rep: 2229
    Location: Adelaide, South Australia

    Leo Lazauskas Senior Member

    Maybe it would be better if you showed us your attempts at the answers first,
    including any working out, and we can then make comments.
    It is not in our interest to help naval architecture students pass exams without
    any effort. Imagine the type of bozos we would end up with in the profession! :)
     
Loading...
Forum posts represent the experience, opinion, and view of individual users. Boat Design Net does not necessarily endorse nor share the view of each individual post.
When making potentially dangerous or financial decisions, always employ and consult appropriate professionals. Your circumstances or experience may be different.