mws_civ_inp_txt_spline_examples

# mws_civ_inp_txt_spline_examples - 05.05.1 Chapter 05.05...

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Unformatted text preview: 05.05.1 Chapter 05.05 Spline Method of Interpolation – More Examples Civil Engineering Example 1 To maximize a catch of bass in a lake, it is suggested to throw the line to the depth of the thermocline. The characteristic feature of this area is the sudden change in temperature. We are given the temperature vs. depth data for a lake in Table 1. Table 1 Temperature vs. depth for a lake. Temperature, C T Depth, m z 19.1 0 19.1 –1 19 –2 18.8 –3 18.7 –4 18.3 –5 18.2 –6 17.6 –7 11.7 –8 9.9 –9 9.1 –10 05.05.2 Chapter 05.05 Figure 1 Temperature vs. depth of a lake. Using the given data, we see the largest change in temperature is between m 8 z and m 7 z . Determine the value of the temperature at m 5 . 7 z using linear splines. Solution Since we want to find the temperature at 5 . 7 z and we are using linear splines, we need to choose the two data points that are closest to 5 . 7 z that also bracket 5 . 7 z to evaluate it. The two points are 8 z and 7 1 z . Then , 8 z 7 . 11 ) ( z T , 7 1 z 6 . 17 ) ( 1 z T gives ) ( ) ( ) ( ) ( ) ( 1 1 z z z z z T z T z T z T ) 8 ( 8 7 7 . 11 6 . 17 7 . 11 z Hence 7 8 ), 8 ( 9 . 5 7 . 11 ) ( z z z T At , 5 . 7 z ) 8 5 . 7 ( 9 . 5 7 . 11 ) 5 . 7 ( T C 65 . 14 Spline Method of Interpolation-More Examples: Civil Engineering 05.05.3 Linear spline interpolation is no different from linear polynomial interpolation. Linear splines still use data only from the two consecutive data points. Also at the interior points of the data, the slope changes abruptly. This means that the first derivative is not continuous at these points. So how do we improve on this? We can do so by using quadratic splines. Example 2 To maximize a catch of bass in a lake, it is suggested to throw the line to the depth of the thermocline. The characteristic feature of this area is the sudden change in temperature. We are given the temperature vs. depth data for a lake in Table 2....
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mws_civ_inp_txt_spline_examples - 05.05.1 Chapter 05.05...

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