Integrating Discrete Functions http://numericalmethods.eng.usf.edu

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Integrating Discrete Functions
http//numericalmethods.eng.usf.edu
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Integrating Discrete FunctionsSpline Method
http//numericalmethods.eng.usf.edu
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Problem Statement

• The upward velocity of a rocket is given as a
  function of time. Using quadratic splines, find
  the distance covered between t11 and t16
  seconds.

t v(t)
s m/s
0 0
10 227.04
15 362.78
20 517.35
22.5 602.97
30 901.67
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Data and Plot
t v(t)
s m/s
0 0
10 227.04
15 362.78
20 517.35
22.5 602.97
30 901.67
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Solution






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Distance from Velocity Profile
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Distance from Velocity Profile
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• END
• http//numericalmethods.eng.usf.edu

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Integrating Discrete FunctionsRegression
Method http//numericalmethods.eng.usf.ed
u
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Trunnion Shrink Fit into Hub
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Is the Contraction Enough?

• Magnitude of contraction needed in the trunnion
  was 0.015 or more.

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How do we find the contraction?
T(oF) a (µin/in/oF)
-340 2.45
-300 3.07
-220 4.08
-160 4.72
-80 5.43
0 6.00
40 6.24
80 6.47
Ta 80oF Tc -108oF D 12.363"
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Regression Model
T(oF) a (µin/in/oF)
-340 2.45
-300 3.07
-220 4.08
-160 4.72
-80 5.43
0 6.00
40 6.24
80 6.47
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Estimating the Contraction
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Calculating the contraction
Ta 80oF, Tc -108oF, D 12.363"
Magnitude of contraction needed in the trunnion
was 0.015 or more.
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• THE END
• http//numericalmethods.eng.usf.edu