1. Integrating Discrete Functions http://numericalmethods.eng.usf.edu1

2. Integrating Discrete Functions Spline Method http://numericalmethods2

3. Problem Statement
The upward velocity of a rocket is given as a function of time. Using quadratic splines, find the distance covered between t=11 and t=16 seconds. t
v(t) s
m/s 10
227.04 15
362.78 20
517.35
22.5
602.97 30
901.67 3

4. Data and Plot t v(t) s m/s 10 227.04 15 362.78 20 517.35 22.5 602.9710
227.04 15
362.78 20
517.35
22.5
602.97 30
901.67 4

5. Solution 5

6. Distance from Velocity Profile6

7. Distance from Velocity Profile7

8. END

9. Integrating Discrete Functions Regression Method http://numericalmethods.eng.usf.edu

10. Trunnion Shrink Fit into Hub

11. Is the Contraction Enough?
Magnitude of contraction needed in the trunnion was 0.015” or more.

12. How do we find the contraction?
T(oF)
α (μin/in/oF)
-340
2.45
-300
3.07
-220
4.08
-160
4.72
-80
5.43
6.00 40
6.24 80
6.47
Ta = 80oF
Tc = -108oF
D = "

13. Regression Model -340 2.45 -300 3.07 -220 4.08 -160 4.72 -80 5.43 6.00
T(oF)
α (μin/in/oF)
-340
2.45
-300
3.07
-220
4.08
-160
4.72
-80
5.43
6.00 40
6.24 80
6.47

14. Estimating the Contraction

15. Calculating the contraction
Ta = 80oF, Tc = -108oF, D = "
Magnitude of contraction needed in the trunnion was 0.015” or more.

16. THE END