NASA Logo - Web Link to NASA.gov Vertical Line

+ Text Only Site
+ Non-Flash Version
+ Contact Glenn

Go
ABOUT NASA NEWS AND EVENTS MULTIMEDIA MISSIONS MyNASA WORK FOR NASA

NASA Logo

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

Aeronautics Logo

 

Pointer

Calculus Problem 1

Pointer

Calculus Problem 2

Pointer

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

Related Pages:
Standards
Activity
Worksheet
Lesson Index
Aerodynamics Index

 

     First Gov Image


+ Inspector General Hotline
+ Equal Employment Opportunity Data Posted Pursuant to the No Fear Act
+ Budgets, Strategic Plans and Accountability Reports
+ Freedom of Information Act
+ The President's Management Agenda
+ NASA Privacy Statement, Disclaimer,
and Accessibility Certification

 

NASA Logo   
Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: May 13 2021

+ Contact Glenn