Simpsons Rule - Unequal Stations

Discussion in 'Stability' started by Marbig, May 9, 2017.

  1. Marbig
    Joined: May 2017
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    Location: USA

    Marbig New Member

    Hi all - I am trying to use the simpsons rule but hit a road block with uneven spacing between stations/points. I have worked with half stations before, but this one has me stumped...

    Say I have 9 stations, each 1.0m apart - therefore a half station is 0.5m.
    8 (SM: 1)
    7 (SM: 4)
    6 (SM: 2)
    5 (SM: 4)
    4 (SM: 2)
    3 (SM: ?)
    2.5 (SM: ?)
    2 (SM: ?)
    1(SM: ?)
    0.5 (SM: ?)
    0(SM: ?)

    I am not sure what the Simpson multipliers are because I am not sure what to do between stations 0.5 and 2.5

    Just to show - I can work out the Simpons multipliers for the following unequal spacing...
    8 (SM: 1)
    7 (SM: 4)
    6 (SM: 2)
    5 (SM: 4)
    4 (SM: 2)
    3 (SM: 4)
    2 (SM: 1.5)
    1.5 (SM: 2)
    1 (SM: 1)
    0.5 (SM: 2)
    0 (SM: 0.5)

    Am I missing something very obvious?
     
  2. Heimfried
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    Heimfried Senior Member

  3. gonzo
    Joined: Aug 2002
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    gonzo Senior Member

  4. Heimfried
    Joined: Apr 2015
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    Location: Berlin, Germany

    Heimfried Senior Member

    With the folder mentioned above, you are also able to choose a different number of stations.
    E. g.:
    Given a sheerline with 9 unequal stations (values in mm, x = locus of station; y = height of sheerline from base plane):
    spl1.jpg

    The graph shows the spline and the station points in it (red):
    spl2.jpg

    The output sheet shows the respective numerical values:
    spl3.jpg

    You choose 10 Stations, which means 9 intervals. Divide the 5486 by 9 and add the result once, twice and so on in the 'living' area:
    spl4.jpg

    The results for 10 stations are given in the column y.
    So you are no longer depending on the original stations and their values and it should be easy to apply Simpson's rule to the new data.
     
    Last edited: May 10, 2017
  5. gonzo
    Joined: Aug 2002
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    Location: Milwaukee, WI

    gonzo Senior Member

    However, if you are using software it probably doesn't make sense to solve by hand using Simpson's rule. Might as well use integrating software.
     

  6. latestarter
    Joined: Jul 2010
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    Location: N.W. England

    latestarter Senior Member

    Regarding your first list of stations, is there a smooth transition between 0 and 1 also 2 and 3. If so are you gaining anything by using the .5 and 2.5 stations, much easier to ignore them.
    If you finished up with an uneven number of stations e.g. 9, you could use Simpson's rule for the first 8 stations then add ( station 8 + station 9 ) /2 times the spacing. Choose the end that has the least change between stations to minimise the error.
     
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