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


 When I printed out the enlarged picture of the plotter view
panel, I found the curve to cover 6.5 cm. Because of this, I
divided it into 12 rectangles with width .5 cm each (see
Figure 1). I then took
the height measurements of each rectangle and recorded them in a
spreadsheet (see Table
1).
 The program displays the plot from 0 to 1 square foot, so I
converted the Xaxis to (0 to 144) square inches. I then divided the
displayed 144 inches by the measured 6.5 cm to find an
Xscaling factor of
22.15. On the Yaxis, 1.0 psi was equivalent to 6.0 cm,
which gives the Yscaling factor of
.1666. On the spread sheet, I have multiplied by the
approtiate scaling factors.
 I then multiplied
the scaled values to find the total area under the curve. This
gave a value of 68.4
lbs which represented the lift force.
 I found the following functions to represent the curves (shown
in Figure
2):
f1(x) = 14.81
f2(x) = .0065 x + 13.87
 I finished by solving the following integral:
Integral (X=0 to X=144) [f1(x)  f2(x)] dx

135.3  66.3 = 69.0
lbs

 The value calculated by FoilSim is
66 lbs, so both
answers compare favorably.
Figure 1
Figure 2
Table 1

Measured


Scaled



Rectangle

Width (cm)

Height (cm)

Width (sq. in.)

Height (lbs/sq. in.)

Area (lbs)

1

0.50

4.2

11.07

.7

7.7

2

0.50

5.0

11.07

.83

9.2

3

0.50

4.6

11.07

.766

8.5

4

0.50

4.4

11.07

.733

8.1

5

0.50

4.1

11.07

.683

7.5

6

0.50

3.6

11.07

.6

6.6

7

0.50

3.1

11.07

.516

5.7

8

0.50

2.6

11.07

.433

4.8

9

0.50

2.1

11.07

.35

3.9

10

0.50

1.7

11.07

.283

3.1

11

0.50

1.1

11.07

.183

2.0

12

0.50

.7

11.07

.117

1.3











Total (in lbs)

68.4


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