How do airplanes actually fly? - Raymond Adkins

1,857,710 views ใƒป 2023-02-09

TED-Ed


ืื ื ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ืœืžื˜ื” ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ.

ืชืจื’ื•ื: Or Sinai ืขืจื™ื›ื”: zeeva livshitz
00:07
By 1917, Albert Einstein had explained the relationship between space and time.
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ื‘ืฉื ืช 1917, ืืœื‘ืจื˜ ืื™ื ืฉื˜ื™ื™ืŸ ื”ืกื‘ื™ืจ ืืช ื”ืงืฉืจ ื‘ื™ืŸ ื—ืœืœ ื•ื–ืžืŸ.
00:13
But, that year, he designed a flawed airplane wing.
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ืื‘ืœ, ื‘ืื•ืชื” ืฉื ื”, ื”ื•ื ืขื™ืฆื‘ ื›ื ืฃ ืžื˜ื•ืก ืคื’ื•ืžื”.
00:17
His attempt was based on an incomplete theory of flight.
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ื”ื ืกื™ื•ืŸ ืฉืœื• ื”ื™ื” ืžื‘ื•ืกืก ืขืœ ืชืื•ืจื™ื” ื—ืœืงื™ืช ืฉืœ ื˜ื™ืกื”.
00:20
Indeed, insufficient and inaccurate explanations still circulate today.
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ืœืžืขืฉื”, ื”ืกื‘ืจื™ื ื‘ืœืชื™ ืžืกืคืงื™ื ื•ืœื ืžื“ื•ื™ืงื™ื ืขื“ื™ื™ืŸ ืžืกืชื•ื‘ื‘ื™ื ื”ื™ื•ื.
00:26
So, where did Einstein go wrong?
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ืื–, ืื™ืคื” ืื™ื ืฉื˜ื™ื™ืŸ ื˜ืขื”?
00:29
And how do planes fly?
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ื•ืื™ืš ืžื˜ื•ืกื™ื ืขืคื™ื?
00:32
Though we donโ€™t always think of it this way, air is a fluid mediumโ€”
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ืœืžืจื•ืช ืฉืื ื—ื ื• ืœื ืชืžื™ื“ ื—ื•ืฉื‘ื™ื ืขืœ ื–ื” ื‘ื“ืจืš ื”ื–ื•, ืื•ื•ื™ืจ ื”ื•ื ืืžืฆืขื™ ื ื•ื–ืœื™
00:36
itโ€™s just less dense than liquids like water.
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ื–ื” ืคืฉื•ื˜ ืคื—ื•ืช ืฆืคื•ืฃ ืžื ื•ื–ืœื™ื ื›ืžื• ืžื™ื.
00:39
Things that are lighter than air are buoyant within it,
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ื“ื‘ืจื™ื ืฉืงืœื™ื ื™ื•ืชืจ ืžืื•ื™ืจ ื™ื›ื•ืœื™ื ืœืฆื•ืฃ ื‘ืชื•ื›ื•,
00:42
while heavier objects require an upward force, called lift, to stay aloft.
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ื•ืœืขื•ืžืช ื–ืืช ื—ืคืฆื™ื ื›ื‘ื“ื™ื ื™ื•ืชืจ ื“ื•ืจืฉื™ื ืฆื™ืคื”, ื”ื ืงืจืืช ื›ื•ื— ืขื™ืœื•ื™ ื›ื“ื™ ืœื”ื™ืฉืืจ ืœืžืขืœื”.
00:48
For planes, this force is mostly generated by the wings.
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ืขื‘ื•ืจ ืžื˜ื•ืกื™ื, ื”ื›ื•ื— ื”ื–ื” ืœืจื•ื‘ ื ื•ืฆืจ ืขืœ ื™ื“ื™ ื›ื ืคื™ื™ื.
00:52
One especially pervasive false description of lift
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ืชื™ืื•ืจ ืฉื’ื•ื™ ื ืจื—ื‘ ื‘ืžื™ื•ื—ื“ ืฉืœ ื›ื•ื— ืขื™ืœื•ื™
00:55
is the โ€œLonger Pathโ€ or โ€œEqual Transit Timeโ€ explanation.
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ื”ื•ื ืดืžืกืœื•ืœ ืืจื•ืš ื™ื•ืชืจืด ืื• ืชืื•ืจื™ื™ืช ืดืขืงืจื•ืŸ ื–ืžืŸ ื”ืžืขื‘ืจ ื”ืฉื•ื•ื”ืด.
00:59
It states that air molecules traveling over the top of a curved wing
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ื”ื™ื ืงื•ื‘ืขืช ืฉืžื•ืœืงื•ืœื•ืช ืื•ื•ื™ืจ ืฉื ืขื•ืช ืžืขืœ ื”ื›ื ืฃ ื”ืžืขื•ืงืœืช
01:03
cover a longer distance than those traveling underneath.
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ืžื›ืกื•ืช ืžืกืœื•ืœ ืืจื•ืš ื™ื•ืชืจ ืžืืฉืจ ืืœื• ืฉื ืขื•ืช ืžืชื—ืช.
01:07
For the air molecules above to reach the wingโ€™s trailing edge
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ื‘ืฉื‘ื™ืœ ืฉืžื•ืœืงื•ืœื•ืช ื”ืื•ื•ื™ืจ ืฉืžืขืœ ื™ื•ื›ืœื• ืœื”ื’ื™ืข ืœืงืฆื” ื”ืื—ื•ืจื™ ื‘ื›ื ืฃ ื”ืžื˜ื•ืก
01:11
in the same instance as those that split off and went below,
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ื‘ืื•ืชื” ื“ืจืš ืฉืœ ืืœื• ืฉื”ืชืคืฆืœื• ื•ืขื‘ืจื• ืžืชื—ืช,
01:14
air must travel faster above,
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ืื•ื•ื™ืจ ื—ื™ื™ื‘ ืœื ื•ืข ืžื”ืจ ื™ื•ืชืจ ืžืขืœ,
01:17
creating a pocket of lower pressure that lifts the plane.
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ื•ืœื™ืฆื•ืจ ื›ื™ืก ืฉืœ ืœื—ืฅ ื ืžื•ืš ื™ื•ืชืจ, ืฉืžืจื™ื ืืช ื”ืžื˜ื•ืก.
01:20
This explanation has been thoroughly debunked.
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ื”ื”ืกื‘ืจ ื”ื–ื” ื”ื•ืคืจืš ื‘ื™ืกื•ื“ื™ื•ืช.
01:24
Air molecules floating above and below the wing don't need to meet back up.
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ืžื•ืœืงื•ืœื•ืช ืื•ื•ื™ืจ ืฉืฆืคื•ืช ืžืขืœ ื•ืžืชื—ืช ืœื›ื ืฃ ืื™ื ืŸ ืฆืจื™ื›ื•ืช ืœื”ื™ืคื’ืฉ ื‘ื—ื–ืจื” ืœืžืขืœื”.
01:29
In reality, the air traveling above reaches the wingโ€™s trailing edge
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ืœืžืขืฉื”, ื”ืื•ื•ื™ืจ ืฉื ืข ืžืขืœ ืžื’ื™ืข ืœืงืฆื” ื”ืื—ื•ืจื™ ื‘ื›ื ืฃ
01:34
much faster than the air beneath.
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ื”ืจื‘ื” ื™ื•ืชืจ ืžื”ื™ืจ ืžื”ืื•ื™ืจ ืฉืžืชื—ืช.
01:37
To get a sense of how lift is actually generated,
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ื›ื“ื™ ืœื”ื‘ื™ืŸ ืื™ืš ื›ื•ื— ืขื™ืœื•ื™ ื‘ืขืฆื ื ื•ืฆืจ,
01:40
let's simulate an airplane wing in motion.
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ื‘ื•ืื• ื ื™ืฆื•ืจ ืกื™ืžื•ืœืฆื™ื” ืฉืœ ื›ื ืฃ ืžื˜ื•ืก ื‘ืชื ื•ืขื”.
01:43
As it moves forward, the wing affects the movement of the air around it.
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ื›ืฉื”ืžื˜ื•ืก ื–ื– ืงื“ื™ืžื”, ื”ื›ื ืฃ ืžืฉืคื™ืขื” ืขืœ ื”ืชื–ื•ื–ื” ืฉืœ ื”ืื•ื™ืจ ืกื‘ื™ื‘ื•.
01:47
As air meets the wingโ€™s solid surface, a thin layer sticks to the wing.
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ื›ืฉื”ืื•ื•ื™ืจ ืคื•ื’ืฉ ืืช ื”ืžืฉื˜ื— ื”ืงืฉื™ื— ืฉืœ ื”ื›ื ืฃ, ืฉื›ื‘ื” ื“ืงื” ื ืฆืžื“ืช ืœื›ื ืฃ.
01:53
This layer pulls the surrounding air with it.
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ืฉื›ื‘ื” ื–ื• ืžื•ืฉื›ืช ืืช ืฉืืจ ื”ืื•ื•ื™ืจ ืื™ืชื”.
01:56
The air splits into pathways above and below the wing,
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ื”ืื•ื•ื™ืจ ืžืชืคืฆืœ ืœืžืกืœื•ืœื™ื ืžืขืœ ื•ืžืชื—ืช ืœื›ื ืฃ,
01:59
following the wingโ€™s contour.
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ืขื•ืงื‘ ืื—ืจ ืงื• ื”ืžืชืืจ ืฉืœ ื”ื›ื ืฃ.
02:01
As the air thatโ€™s routed above makes its way around the nose of the wing,
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ื›ืฉื”ืื•ื•ื™ืจ ืฉืžื ื•ืชื‘ ืžืขืœ ืขื•ืฉื” ืืช ื“ืจื›ื• ืœืืฃ ืฉืœ ื”ื›ื ืฃ,
02:06
it experiences centripetal acceleration,
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ื”ื•ื ื—ื•ื•ื” ื”ืืฆื” ืฆื ื˜ืจื™ืคื˜ืœื™ืช,
02:09
the force you also feel in a sharply turning car.
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ื›ืžื• ื”ื›ื•ื— ืฉื ื™ืชืŸ ืœื”ืจื’ื™ืฉ ื‘ืžื›ื•ื ื™ืช ืฉืคื•ื ื” ื‘ื—ื“ื•ืช.
02:12
The air above therefore gathers more speed than the air traveling below.
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ื”ืื•ื•ื™ืจ ืฉืžืขืœ ืฆื•ื‘ืจ ื™ื•ืชืจ ืžื”ื™ืจื•ืช ืžื”ืื•ื™ืจ ืฉื ืข ืžืชื—ืช.
02:17
This increased speed is coupled with a decrease in pressure above the wing,
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ื”ืžื”ื™ืจื•ืช ื”ื’ื•ื‘ืจืช ื”ื–ื• ืžืฉื•ืœื‘ืช ืขื ื™ืจื™ื“ื” ื‘ืœื—ืฅ ืžืขืœ ื”ื›ื ืฃ,
02:22
which pulls even more air across the wingโ€™s upper surface.
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ืืฉืจ ืžื•ืฉืš ืืคื™ืœื• ื™ื•ืชืจ ืื•ื•ื™ืจ ืžืขื‘ืจ ืœืžืฉื˜ื— ื”ืขืœื™ื•ืŸ ืฉืœ ื”ื›ื ืฃ.
02:27
The air flowing across the lower surface, meanwhile,
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ื”ืื•ื•ื™ืจ ืฉืžืจื—ืฃ ืขืœ ืคื ื™ ื”ืžืฉื˜ื— ื”ืชื—ืชื•ืŸ, ื‘ื™ื ืชื™ื™ื
02:30
experiences less of a change in direction and speed.
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ื—ื•ื•ื” ืคื—ื•ืช ืฉื™ื ื•ื™ ื‘ื›ื™ื•ื•ืŸ ื•ืžื”ื™ืจื•ืช.
02:34
The pressure across the wingโ€™s lower surface is thus higher
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ื”ืœื—ืฅ ืžืขื‘ืจ ืœืžืฉื˜ื— ื”ืชื—ืชื•ืŸ ื™ื•ืชืจ ืฉืœ ื”ื›ื ืฃ ื”ื•ื ื’ื‘ื•ื” ื™ื•ืชืจ
02:37
than that above the upper surface.
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ืžืืฉืจ ื–ื” ืฉื ืžืฆื ื‘ืžืฉื˜ื— ื”ืขืœื™ื•ืŸ.
02:40
This pressure difference results in the upwards force of lift.
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ื”ืชื•ืฆืื” ืฉืœ ื”ื”ื‘ื“ืœ ื”ื–ื” ื”ื•ื ืฆื™ืคื” ืฉืœ ื›ื•ื— ืขื™ืœื•ื™.
02:44
The faster the plane travels,
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ื›ื›ืœ ืฉื”ืžื˜ื•ืก ื ืข ืžื”ืจ ื™ื•ืชืจ,
02:46
the greater the pressure difference, and the greater that force.
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ื›ืš ื”ื”ื‘ื“ืœ ื‘ืœื—ืฅ ื’ื“ื•ืœ ื™ื•ืชืจ, ื•ื›ืš ื’ื“ื•ืœ ื™ื•ืชืจ ื”ื›ื•ื— ื”ื–ื”.
02:49
Once it overcomes the downward force of gravity,
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ื›ืฉื”ื•ื ืžืชื’ื‘ืจ ืขืœ ื›ื•ื— ื”ื›ื‘ื™ื“ื” ื›ืœืคื™ ืžื˜ื”,
02:52
the plane takes off.
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ื”ืžื˜ื•ืก ืžืžืจื™ื.
02:54
Air flows smoothly around curved wings.
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ืื•ืŸื™ืจ ื–ื•ืจื ื‘ืื•ืคืŸ ื—ืœืง ืกื‘ื™ื‘ ื”ื›ื ืคื™ื™ื ื”ืžืขื•ืงืœื•ืช.
02:57
But a wingโ€™s curvature is not the cause of lift.
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ืื‘ืœ ื”ืขื™ืงื•ืœ ืฉืœ ื”ื›ื ืฃ ืื™ื ื• ื”ืกื™ื‘ื” ืฉืœ ื›ื•ื— ื”ืขื™ืœื•ื™.
03:01
In fact, a flat wing thatโ€™s tilted upwards can also create liftโ€”
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ืœืžืขืฉื”, ื›ื ืฃ ืฉื˜ื•ื—ื” ืฉื ื•ื˜ื” ื›ืœืคื™ ืžืขืœื” ื’ื ื™ื›ื•ืœื” ืœื™ืฆื•ืจ ื›ื•ื— ืขื™ืœื•ื™
03:05
as long as the air bends around it,
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ื›ืœ ืขื•ื“ ื”ืื•ื•ื™ืจ ืžืชืขืงืœ ืกื‘ื™ื‘ื”,
03:08
contributing to and reinforcing the pressure difference.
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ืชื•ืจื ื•ืžื—ื–ืง ืืช ื”ื”ื‘ื“ืœ ื‘ืœื—ืฅ.
03:12
Meanwhile, having a wing thatโ€™s too curved or steeply angled
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ื‘ื™ื ืชื™ื™ื, ื›ืืฉืจ ื™ืฉ ื›ื ืฃ ืฉื”ื™ื ื™ื•ืชืจ ืžื“ื™ ืžืขื•ืงืœืช ืื• ื‘ืฉื™ืคื•ืข
03:16
can be disastrous:
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ื–ื” ื™ื›ื•ืœ ืœื”ื™ื•ืช ื”ืจืกื ื™:
03:17
the airflow above may detach from the wing and become turbulent.
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ื–ืจื™ืžืช ื”ืื•ื•ื™ืจ ืฉืžืขืœ ืขืœื•ืœื” ืœื”ืชื ืชืง ืžื”ื›ื ืฃ ื•ืœื”ืคื•ืš ืกื•ืขืจืช.
03:22
This is probably what happened with Einsteinโ€™s wing design,
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ื–ื” ื›ื ืจืื” ืžื” ืฉืงืจื” ืขื ื”ื›ื ืฃ ืฉืื™ื ืฉื˜ื™ื™ืŸ ืชื›ื ืŸ,
03:25
nicknamed โ€œthe catโ€™s back.โ€
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ืฉื›ื ื•ื™ื” ื”ื™ื” ืดื”ื’ื‘ ืฉืœ ื”ื—ืชื•ืœ.ืด
03:28
By increasing the wingโ€™s curvature,
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ืขืœ ื™ื“ื™ ื”ืจื—ื‘ืช ื”ืขืงืžื•ืžื™ื•ืช ืฉืœ ื”ื›ื ืฃ,
03:30
Einstein thought it would generate more lift.
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ืื™ื ืฉื˜ื™ื™ืŸ ื—ืฉื‘ ืฉื–ื” ื™ื™ืฆื•ืจ ื™ื•ืชืจ ื›ื•ื— ืขื™ืœื•ื™.
03:32
But one test pilot reported that the plane wobbled
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ืื‘ืœ ื˜ื™ื™ืก ืžื‘ื—ืŸ ื“ื™ื•ื•ื— ืฉื”ืžื˜ื•ืก ื”ืชื ื“ื ื“
03:36
like โ€œa pregnant duckโ€ in flight.
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ื›ืžื• ืดื‘ืจื•ื•ื–ื” ื‘ื”ืจื™ื•ืŸืด ื‘ื˜ื™ืกื”.
03:39
Our explanation is still a simplified description
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ื”ื”ืกื‘ืจ ืฉืœื ื• ื”ื•ื ืขื“ื™ื™ืŸ ื”ืกื‘ืจ ืคืฉื•ื˜.
03:42
of this nuanced, complex process.
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ืฉืœ ื”ืชื”ืœื™ืš ื”ืžืกื•ื‘ืš ื”ื–ื”.
03:44
Other factors, like the air thatโ€™s flowing meters beyond the wingโ€™s surfaceโ€”
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ื’ื•ืจืžื™ื ืื—ืจื™ื, ื›ืžื• ื”ืื•ื•ื™ืจ ืฉืžืจื—ืฃ ืžื˜ืจื™ื ืžืชื—ืช ืœื‘ืกื™ืก ื”ื›ื ืฃ
03:48
being swept up, then downโ€”
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ื–ื–ื™ื ืžืขืœื”, ื•ืื– ืžื˜ื”
03:50
as well as air vortices formed at the wingโ€™s tips,
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ื’ื ื›ืฉืžืขืจื‘ื•ืœื•ืช ืื•ื•ื™ืจ ื ื•ืฆืจื• ื‘ืงืฆื•ื•ืช ื”ื›ื ืคื™ื™ื,
03:54
all influence lift.
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ื”ื›ืœ ืžืฉืคื™ืข ืขืœ ื›ื•ื— ื”ืขื™ืœื•ื™.
03:56
And, while experts agree that the pressure difference generates lift,
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ื•ื›ืฉืžื•ืžื—ื™ื ืžืกื›ื™ืžื™ื ืขืœ ื›ืš ืฉื”ื”ื‘ื“ืœ ื‘ืœื—ืฅ ื™ื•ืฆืจ ื›ื•ื— ืขื™ืœื•ื™,
03:59
their explanations for how can vary.
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ื”ื”ืกื‘ืจื™ื ืฉืœื”ื ืขืœ ืื™ืš ืฉื•ื ื™ื ื–ื” ืžื–ื”.
04:02
Some might emphasize the airโ€™s behavior at the wingโ€™s surface,
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ืื—ื“ื™ื ื™ื“ื’ื™ืฉื• ืืช ื”ืชื ื”ื’ื•ืช ื”ืื•ื•ื™ืจ ื‘ืžืฉื˜ื— ื”ื›ื ืฃ,
04:06
others the upward force created as the air is deflected downwards.
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ื•ืื—ืจื™ื ืืช ื›ื•ื— ื”ืขื™ืœื•ื™ ืฉื ื•ืฆืจ ื›ืฉื”ืื•ื™ืจ ืžื•ื˜ื” ืœืžื˜ื”.
04:10
However, there's no controversy when it comes to the math.
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ืื•ืœื, ืื™ืŸ ืžื—ืœื•ืงืช ื›ืฉืžื“ื•ื‘ืจ ื‘ืžืชืžื˜ื™ืงื”.
04:14
Engineers use a set of formulas called the Navier-Stokes equations
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ืžื”ื ื“ืกื™ื ืžืฉืชืžืฉื™ื ื‘ื ื•ืกื—ืื•ืช ื‘ืฉื ืžืฉื•ื•ืื•ืช ื ืื•ื•ื™ื”-ืกื˜ื•ืงืก
04:18
to precisely model airโ€™s flow around a wing
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ื›ื“ื™ ืœื™ืฆื•ืจ ื‘ืžื“ื•ื™ืง ืžื•ื“ืœ ื–ืจื™ืžืช ื”ืื•ื•ื™ืจ ืกื‘ื™ื‘ ื”ื›ื ืฃ
04:21
and detail how lift is generated.
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ื•ืœืคืจื˜ ื›ื™ืฆื“ ื›ื•ื— ืขื™ืœื•ื™ ื ื•ืฆืจ.
04:24
More than a century after Einsteinโ€™s foray into aeronautics,
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ื™ื•ืชืจ ืžืžืื” ืœืื—ืจ ื”ื’ื™ื—ื” ืฉืœ ืื™ื ืฉื˜ื™ื™ืŸ ืœืื•ื•ื™ืจื•ื ืื•ื˜ื™ืงื”,
04:28
lift retains its reputation as a confounding concept.
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ื›ื•ื— ืขื™ืœื•ื™ ืฉื•ืžืจ ืขืœ ื”ืžื•ื ื™ื˜ื™ืŸ ืฉืœื• ื›ืžื•ืฉื’ ืžื‘ืœื‘ืœ.
04:33
But when it feels like itโ€™s all going to come crashing down, remember:
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ืื‘ืœ ื›ืฉื–ื” ืžืจื’ื™ืฉ ื›ืื™ืœื• ื›ืœ ื–ื” ื”ื•ืœืš ืœื”ืชืจืกืง, ื–ื›ืจื•:
04:36
itโ€™s just the physics of fluid in motion.
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ื–ื” ืจืง ื”ืคื™ื–ื™ืงื” ืฉืœ ื”ื ื•ื–ืœ ื‘ืชื ื•ืขื”.
04:42
This video was made possible with support from Marriott Hotels.
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ื™ืฆื™ืจืช ื•ื™ื“ืื• ื–ื” ื”ื™ื™ืชื” ืืคืฉืจื™ืช ื‘ืขื–ืจืช ืชืžื™ื›ืชื ืฉืœ ืžืœื•ื ื•ืช ืžืจื™ื•ื˜.
04:46
With over 590 hotels and resorts across the globe,
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ืขื ื™ื•ืชืจ ืž- 590 ืžืœื•ื ื•ืช ื•ืืชืจื™ ื ื•ืคืฉ ื‘ืจื—ื‘ื™ ื”ืขื•ืœื,
04:50
Marriott Hotels celebrates the curiosity that propels us to travel.
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ืžืœื•ื ื•ืช ืžืจื™ื•ื˜ ื—ื•ื’ื’ื™ื ืืช ื”ื™ืฆื™ืจืชื™ื•ืช ืฉืžื ื™ืขื” ืื•ืชื ื• ืœื˜ื™ื™ืœ.
04:54
Check out some of the exciting ways TED-Ed and Marriott are working together,
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ืชื‘ื“ืงื• ืืช ื›ืžื” ืžื”ื“ืจื›ื™ื ื”ืžืœื”ื™ื‘ื•ืช ื‘ื”ืŸ ืฉื˜ื“-ืื“ ื•ืžืจื™ื•ื˜ ืขื•ื‘ื“ื™ื ื™ื—ื“,
04:58
and book your next journey at Marriott Hotels.
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ื•ื”ื–ืžื™ื ื• ืืช ื”ื˜ื™ื•ืœ ื”ื‘ื ืฉืœื›ื ื‘ืžืœื•ืŸ ืžืจื™ื•ื˜.
ืขืœ ืืชืจ ื–ื”

ืืชืจ ื–ื” ื™ืฆื™ื’ ื‘ืคื ื™ื›ื ืกืจื˜ื•ื ื™ YouTube ื”ืžื•ืขื™ืœื™ื ืœืœื™ืžื•ื“ ืื ื’ืœื™ืช. ืชื•ื›ืœื• ืœืจืื•ืช ืฉื™ืขื•ืจื™ ืื ื’ืœื™ืช ื”ืžื•ืขื‘ืจื™ื ืขืœ ื™ื“ื™ ืžื•ืจื™ื ืžื”ืฉื•ืจื” ื”ืจืืฉื•ื ื” ืžืจื—ื‘ื™ ื”ืขื•ืœื. ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ื”ืžื•ืฆื’ื•ืช ื‘ื›ืœ ื“ืฃ ื•ื™ื“ืื• ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ ืžืฉื. ื”ื›ืชื•ื‘ื™ื•ืช ื’ื•ืœืœื•ืช ื‘ืกื ื›ืจื•ืŸ ืขื ื”ืคืขืœืช ื”ื•ื•ื™ื“ืื•. ืื ื™ืฉ ืœืš ื”ืขืจื•ืช ืื• ื‘ืงืฉื•ืช, ืื ื ืฆื•ืจ ืื™ืชื ื• ืงืฉืจ ื‘ืืžืฆืขื•ืช ื˜ื•ืคืก ื™ืฆื™ืจืช ืงืฉืจ ื–ื”.

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