In 2014, the qualifying exam for the US Physics Team
had this as question 19:
A helicopter is flying horizontally at constant speed.
A perfectly flexible uniform cable is suspended
beneath the helicopter.
Air friction on the cable is not negligible.
So, which of the following diagrams
best shows the shape of the cable
as the helicopter flies through the air to the right?
Is it A. hanging straight down.
B, hanging diagonally to the left?
C, this hook shape.
D, the inverted hook shape,
or E, a kind of S bend.
Now, apparently there's been a certain amount of controversy
about the correct answer to this question.
So, today we're gonna go up in this helicopter,
and put this question to rest once and for all.
Let's go.
(intense music) (helicopter blades whirring)
A portion of this video was sponsored by SimpliSafe,
which allowed us to rent this helicopter.
More about them at the end of the show.
I've got several thousand hours of carrying sling loads,
fire buckets, concrete buckets,
doing power line construction, actual power poles.
You name it, anything that needs to be moved
around the mountains, I've done.
Biggest concern that I have is
that the rope's gonna interact with the rotor wash
as its interaction with the ambient air around the aircraft.
And we'll get a whipping action that falls down the rope
and flips around on the end.
To a point that we worry if it will have a tendency
to work its way back up towards the aircraft.
Obviously, we don't want it getting in the rotors
or the tail rotor.
(helicopter blades whirring)
- [Derek] Alright, we're all set.
Movin' up.
(helicopter blades whirring)
(intense music)
Here I'm deploying a battle rope,
like you'd see at the gym.
This one is about 15 meters long and it weighs 20 kilograms.
- [Craig] See, the whipping action's begun.
- [Derek] I see it.
So, if we go really slow, will we avoid that?
- We'll see.
We'll see where the rotor wash
stops interacting with the rope
and the ambient wind.
Now the setup looks pretty simple,
but few people agree on what the right answer should be.
(peaceful music)
When I polled YouTube, the most common answer was C.
Well done on making that beautiful bell curve by the way.
We got in touch with the question's author,
professor Paul Stanley.
There was some creative students who actually constructed
their own homemade scenarios.
One had a fan to the side and another fan blowing downward
so that they could mimic the motion of the helicopter
and suspended a string and said, "Oh, it's this design."
And the faculty members looked at it and said,
"Oh, obviously I can prove that the answer is this answer."
They just didn't agree with each other.
- If we approximated as a chain of rigid links
- I don't think you can just do that.
- What do you think?
- I think you're more likely to be C.
- I think it is D.
- D.
- My guess is B.
- What do you think? - B.
- B?
- Imma go with A.
- Interestingly, no one chose E.
Have you locked in your prediction?
(helicopter blades whirring)
To make sure the rope doesn't come up
into the rotors of the helicopter,
pilot Craig wanted to keep the rope on our right side
so he could keep an eye on it.
Looks pretty good.
- I'm trying to make it look good.
I mean I'm really working on it.
- You're working hard.
So, we're not going straight forward.
We're actually going diagonally forward and to the left.
(upbeat music) (helicopter blades whirring)
But you can clearly see the rope is hanging straight,
diagonally to the left.
That's a pretty good diagonal, man.
So, the correct answer to the question is B.
You wanna pull it in?
- Up it comes.
- [Derek] We're going to try a few more experiments,
adding a weight to the end of the rope and then a parachute.
But first I want to discuss why the answer is B.
There are two external forces acting on the rope,
gravity pulling it down and air resistance to the left.
When flying along at constant speed,
these forces must be perfectly balanced
by the tension in the rope.
Now, when I set out to do this experiment,
I wondered if the rope would be affected
by the air pushed down by the helicopters rotor,
but judging by our results.
This was not the case.
- The rotor wash doesn't extend down below the helicopter,
all that far. It dissipates pretty quickly.
- So, you can consider the air resistance on the rope
as entirely due to its motion through still air.
Imagine dividing the rope up into many short sections.
Each section has the same weight
and experiences the same amount of air resistance
because it has the same cross-sectional area.
And it's moving at the same speed.
Now, the tension in any section of the rope
must balance the sum of the air resistance
and weight of all the sections beneath it.
So, the tension is zero at the bottom of the rope,
and it increases linearly up to a maximum at the top.
You can see the tension is small at the bottom of the rope,
and that's why it wiggles around
while the top is much steadier.
Now, although the magnitude of tension changes
throughout the rope, it's direction doesn't.
And that's because the ratio of air resistance
to weight is the same at every point along the rope.
That is why a uniform flexible cable hangs
in a straight diagonal line when pulled at constant speed
by a helicopter.
If the helicopter flies faster,
the angle of the rope changes,
but it still makes a diagonal straight line
because the ratio of air resistance to weight
is still constant along the entire length of the rope.
But this got me wondering,
"What would happen if we added a weight
to the end of the rope?"
Here, I have a 20 pound,
that's an eight or nine kilos kettlebell.
And I want to ask you to make a prediction.
What shape do you think the rope will make now?
Will it still be that diagonal,
or will it be one of the other five options?
One more question for you.
If we chucked a weight at the bottom,
which shape would it be?
- Oh. - Probably D.
- B, or possibly C.
- [Derek] Does that change it?
- Then I think it would be B.
(whimsical music)
- Easy to do on the ground.
(helicopter blades whirring)
Alright, we're dropping the rope over the side.
This one has 20 pound kettlebell off the end of it.
How's that feel when it's dangling?
- No lateral displacement at all.
- Alright.
- How's your forearms doing?
- I'm feeling good, you know.
I feel like this is the easy way, obviously.
Gonna feel different when I gotta pull it up.
- Okay, is it down? - Yup.
Okay, let's give it a shot.
(whimsical music) (helicopter blades whirring)
Here the helicopter is flying
at nearly a hundred kilometers per hour,
and the rope makes a different shape.
You can clearly see,
it looks like an inverted J.
This is option D.
In fact, this is how the question
on the qualifying exam originated.
- So, I taught for a semester in Hong Kong,
and we'd go hiking in the new territories.
One of the times I was hiking,
I saw a helicopter fly with a cable beneath it.
It was carrying something to one of the remote parts
of the Hong Kong new territories.
And I saw the shape of the cable and thought to myself,
"That looks a little counter intuitive and very neat.
This might make a good multiple choice question
for the selection exam for the students."
The cable that I saw had a weight hanging on the end,
which gave it a certain curved shape.
When I shared this with the other coaches, another coach,
Andrew Linn, looked at it and said,
"I think the question might even be more fun
if there is no weight on the cable
because that is even harder to imagine."
- [Derek] To understand why the rope makes this shape,
we can use the same analysis as before.
But now we need to add a large weight
to the end of the rope.
And this means at the bottom,
the tension needs to be almost vertical
to support the weight of the kettlebell,
which has a lot of weight but not much air resistance.
As you go up the rope, the ratio of total air resistance
to weight for everything beneath increases.
So, the rope turns more horizontal in order for the tension
to balance out that increasing air resistance.
- You're more than halfway. You got it.
(woman laughing)
- [Derek] For the final test,
I wanted to add something to the bottom of the rope
that added almost no weight, but significant air resistance.
So, I picked a Veritasium flag, of course.
So, what do you think about hanging this
at the end of the rope?
- Well, it's all science experiment for me
'cause these are all the things you'd never do
with a helicopter in a row.
- What would it be the real risks,
like tail rotor or this rotor, or both?
- Either.
Any kind of this getting into the inner tail rotor
would be destruction to the aircraft.
(helicopter blades whirring) (intense music)
And we'll start, here we go.
- [Derek] Now the rope still seems to be pretty straight.
I think it's because the flag
isn't actually adding much drag.
Still looks pretty crazy, interestingly.
So, we decided to add a small parachute
to the end of the rope.
All right, let's try it.
The concern here was that the parachute
could get flipped up into the rotors during deployment.
So, we bundled the shoot up into a backpack.
- [Craig] Very nicely done.
- [Derek] Does it deploy more than that?
- [Craig] No, but once we start moving,
its gonna grab a lot of air.
- [Derek] Now, with the parachute at the end of the rope,
it makes a J shape, which is answer C.
With extra air resistance at the end of the rope,
but not much weight,
the tension has to be virtually horizontal.
And then as you go up the rope,
the ratio of total air resistance to weight
for everything beneath decreases.
So, the rope becomes more vertical
to balance out the increasing weight.
So, depending on what's on the end of the rope,
you could get answers B, C or D.
Now, if you enjoyed this video,
I bet you would also like my bullet block experiment series.
So, check it out.
(retro beeping sound effect)
Now, hanging out the side of a helicopter
was not my safest moment,
but I do always feel safe here at home.
Thanks to SimpliSafe, the sponsor of this portion
of the video.
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You know, I started thinking seriously about home security
when there was a police helicopter circling overhead
one day, and it was not dangling any ropes.
It turned out the house across the street
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I want to thank SimpliSafe for sponsoring this portion
of the video.
And I want to thank you for watching.