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The Aspect Ratio of Wings
| Review: |
As air flows over and under a wing, we know from our study of lift
that the air flowing over the top flows faster than the air that flows
under the wing. We also know from BernoulliÕs Principle that the air
that flows faster applies less pressure to the surface it is flowing
over. Therefore, since the air flowing over the top of a wing has
less pressure (because it is flowing faster), the air pressure on
top is less than on the bottom of the wing. The higher air pressure
on the bottom "lifts" the wing.
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| Background: |
When engineers design a new airplane, the size and shape of the
wings are a very important issue. Wings provide the majority of the
lift for the airplane, but they also cause drag. Remember that drag
is a force that opposes the thrust force. Engineers are always trying
to find ways to increase lift and reduce drag caused by the wings.
In addition to flowing faster, the air that flows over the top
of the wing also tends to flow inward, toward the fuselage. The
air that flows over the bottom is flowing more slowly and tends
to flow outward. As these two airflows meet along the trailing edge
of the wing, they form a rotating column of air that extends from
the wing tip. This is called a wing-tip vortex.
If they are lucky, passengers riding behind the wing of an airplane
can sometimes see a wing-tip vortex - particularly if they are flying
in the morning or on a slightly humid day. It looks like a long,
slim whirlwind that extends from the tip of the wing.
Unfortunately, while they are fun to watch, the same characteristics
of the airflow that create wing-tip vortices (the plural of vortex
is vortices) also create drag.
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Teacher - Led Exercise
| Directions: |
In their efforts to increase lift and reduce drag, engineers use
a mathematical formula called the "aspect ratio". The "aspect ratio"
is simply a comparison between the length and width of the wing:
length of the wing = aspect ratio
width of the wing
Experiments have shown that a wing built with a higher aspect
ratio tends to create less drag than a wing built with a smaller
aspect ratio -even when their area remains the same!
Examine the three wings drawn below, calculate the area and aspect
ratio of each wing, and fill in the following table. Then, rank
the wings according to the drag that each will create, given their
aspect ratios. Rank the wing with the least drag number 1, and rank
the wing with the greatest amount of drag, number 3.
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Exercise 1
| Step 1: |
Create and draw your own wings below. Shape them like airfoils and
give each the same area of 200 square units.
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| Step 2: |
Label the length and width of each wing. |
| Step 3: |
Calculate the aspect ratio for each wing and fill in the table below.
DonÕt forget to include the units! |
| Step 4: |
Rank the wings according to the drag that each will create, given
their aspect ratios. Rank the wing with the least drag number 1, and
rank the wing with the greatest amount of drag number 2. |
The Aspect Ratio of Wings
Teacher - Led Exercise Key
| Wing "A": length: 20 units |
width: 5 units |
| Wing "B": length: 25 units |
width: 4 units |
| Wing "C": length: 50 units |
width: 2 units |
Even though each wing has the same area, 100 square units, Wing "C"
has the greatest aspect ratio, and Wing "A" has the smallest aspect ratio.
This implies that Wing "A" creates more drag than Wing "C".
Maybe you've wondered why sailplanes and gliders have long, slim wings.
Since they don't have engines to provide thrust, their wing shape helps
to provide the greatest amount of lift with the least amount of drag.
Exercise 1 Key
Step 1:Possible wing dimensions and aspect ratios:
| length = 100 |
width = 2 |
aspect ratio = 50 |
| length = 50 |
width = 4 |
aspect ratio = 12 R2 |
| length = 20 |
width = 10 |
aspect ratio = 2 |
| length = 25 |
width = 8 |
aspect ratio = 3 R1 |
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