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Getting a Little "Lift" out of Calculus Part II: Answers

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Calculus Problem 1

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Calculus Problem 2

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Calculus Problem 3

Problem 1:

This was solved using the geometry method described in the first part of the lab. The answer to the actual problem is shown using Figure 1 and Table 1.

Figure 1
Graph of pressure versus chord for problem 1 with small boxes superimposed to determine 
      area under the curve
Table 1

Measured

Scaled

Rectangle

Width (cm)

Height (cm)

Width (sq. in.)

Height (lbs/sq. in.)

Area (lbs)

1

0.54

4.90

8.45

16.61

140.40

2

0.54

2.90

8.45

9.83

83.09

3

0.54

2.32

8.45

7.86

66.47

4

0.54

2.05

8.45

6.95

58.74

5

0.54

1.80

8.45

6.10

51.57

6

0.54

1.70

8.45

5.76

48.71

7

0.54

1.45

8.45

4.92

41.55

8

0.54

1.38

8.45

4.68

39.54

9

0.54

1.25

8.45

4.24

35.82

10

0.54

1.15

8.45

3.90

32.95

11

0.54

1.10

8.45

3.73

31.52

12

0.54

0.98

8.45

3.32

28.088

13

0.54

0.85

8.45

2.88

24.35

14

0.54

0.70

8.45

2.37

20.06

15

0.54

0.64

8.45

2.17

18.34

16

0.54

0.50

8.45

1.70

14.33

17

0.54

0.34

8.45

1.15

9.74

Total (in lbs)

721.18

 

Problem 2:

This was solved using the geometry method described in the first part of the lab. The answer to the actual problem is shown using Figure 2 and Table 2.

Figure 2

Graph of pressure versus chord for problem 2 with small boxes superimposed to determine
        area under the curve

Table 2

Measured

Scaled

Rectangle

Width (cm)

Height (cm)

Width (sq.in)

Height (lbs/sq.in)

Area (lbs)

1

0.30

2.03

4.64

6.41

29.79

2

0.30

1.10

4.64

3.48

16.14

3

0.30

1.11

4.64

3.51

16.29

4

0.30

1.27

4.64

4.01

18.64

5

0.30

1.54

4.64

4.87

22.60

6

0.30

1.88

4.64

5.94

27.59

7

0.30

2.13

4.64

6.73

31.26

8

0.30

2.44

4.64

7.71

35.81

9

0.30

2.70

4.64

8.53

39.62

10

0.30

3.00

4.64

9.48

44.03

11

0.30

3.15

4.64

9.95

46.23

12

0.30

3.35

4.64

10.59

49.16

13

0.30

3.44

4.64

10.87

50.48

14

0.30

3.56

4.64

11.25

52.24

15

0.30

3.56

4.64

11.25

52.24

16

0.30

3.58

4.64

11.31

52.54

17

0.30

3.55

4.64

11.22

52.10

18

0.30

3.57

4.64

11.28

52.39

19

0.30

3.50

4.64

11.06

51.36

20

0.30

3.46

4.64

10.93

50.78

21

0.30

3.34

4.64

10.55

49.01

22

0.30

3.28

4.64

10.36

48.13

23

0.30

3.17

4.64

10.02

46.52

24

0.30

2.90

4.64

9.16

42.56

25

0.30

2.65

4.64

8.37

38.89

26

0.30

2.40

4.64

7.58

35.22

27

0.30

2.18

4.64

6.89

31.99

28

0.30

1.93

4.64

6.10

28.32

29

0.30

1.60

4.64

5.06

23.48

30

0.30

1.10

4.64

3.48

16.14

31

0.30

0.75

4.64

2.37

11.01

Total (in lbs)

1162.56

Problem 3:

This was solved using the integration method described in the second part of the lab. The answer to the actual problem is shown using Figure 3 and the functions shown below.
Figure 3

Graph of pressure versus chord for problem 3 with two functions defined, one for the upper curve
       and one for the lower curve

Function for upper curve defined in previous graph, f1(x) = sin(x) + 9.64
Function for lower curve, f2(x) = 1.05X
Integral solution to previous functions: integral of f1 - f2 = 183.77 lbs

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Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Jun 12 2014

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