Wikipedia:Reference desk/Archives/Science/2023 December 14

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December 14

Hippo in the sky

Emblem of the Task Force Hippo

How fast would the pictured hippo have to flap its wings to become airborne? (Disclaimer: Not seeking advice.) ◅ Sebastian Helm 🗨 19:59, 14 December 2023 (UTC)

With wings that small it would never become airborne. Lift depends on the size of the wings much more than their speed. Shantavira|^{feed me} 20:01, 14 December 2023 (UTC)

Interesting opinion. I would expect the speed to be finite, since drag force (at least ideally) is proportional to
area · flow_speed². ◅ Sebastian Helm 🗨 20:25, 14 December 2023 (UTC)

Maybe it's part bumblebee. Especially if the illustration displayed here is life-size. ←Baseball Bugs ^{What's up, Doc?} carrots→ 21:46, 14 December 2023 (UTC)

You have a point, Bugs. I just had assumed the “hippo” referred to hippopotamus, but that might be wrong. The wings rather resemble those of millimeter-sized flying animals. ◅ Sebastian Helm 🗨 22:20, 14 December 2023 (UTC)

In theory, if the wings were to be flapped fast enough, they could generate enough downward force to lift a full-sized hippo off the ground, but I'm thinking they would have to move at extremely high, possibly even relativistic speeds in order to do so. Gyatt W Rizz (talk) 22:28, 14 December 2023 (UTC)

I find it hard to obtain quantitative date, but in this video we see a bald eagle lift off for a brief moment with a full wing flap from 0:51 to 0:59. The initial upward speed was almost certainly achieved by a jump, but let's take this as a lower bound. The video is recorded at 1000 fps. Assuming it is played at 24 fps, this means one wing beat in (24/1000) × 8 s = 192 ms, which means a frequency of about 5.2 Hz. Now an eagle weighs about 5 kg while a hippopotamus is more like 1400 kg. The wings on the hippo seem to be about the same size as those of an eagle. Going with the theory that lift is proportional to the square of the flow speed, so flow speed is proportional to the square root of the required lift, we get a back-of-the-envelope estimate for a lower bound of

√1400/5 × 5.2 Hz ≈ 87 Hz.

So we'd have a humminghippo. But intuitively this feels way to low to me, at least with this size of wing, so the theory may need some refinement. For comparison, a hippopotamus weighs more than the Airbus Helicopters H125.  --Lambiam 12:27, 15 December 2023 (UTC)

Excellent reply! And a beautiful video to boot. Yes, originally i would have agreed with your intuition, but i think your result is a good approximation and see no reason why it should be much higher, apart from some nonlinear effects that may not scale well.

That said, let's try another way: Since you mention a helicopter, and since this is the emblem of a helicopter task force, another way to compute this would be by comparison with a helicopter. For that, the H125 is a good choice, since, with a bit of cargo, it will weigh the same as a hippo. I don't know its rotation frequency, but if we assume (with [1])

$f_{helicopter}\approx 400\mathrm {RPM}$ ,

and if we treat the three blades as one rotating at 3 times the speed, we get:

$f_{helicopter}\approx (3\cdot 400/60)\mathrm {Hz} =20\mathrm {Hz}$ .

Now we know (from the specs in our article) that the rotor has a diameter of 10.7 m, with which we can estimate (from the picture) the area of one blade:

$A_{helicopter}\approx 4\mathrm {m^{2}}$.

For the depicted hippo i'd estimate the area of both wings together:

$A_{hippo}\approx 0.4\mathrm {m^{2}}$.

With this (and with $u=$ speed at the wing tip, $l=$ length of wing resp. blade) inserting the drag equation gives:

$u_{hippo}^{2}\cdot A_{hippo}=u_{helicopter}^{2}\cdot A_{helicopter}$

$u_{hippo}^{2}\approx 10\cdot u_{helicopter}^{2}$

$f_{hippo}^{2}\cdot l_{hippo}^{2}\approx 10\cdot f_{helicopter}^{2}\cdot l_{helicopter}^{2}$

Inserting

$l_{hippo}\approx 0.5\mathrm {m}$

$l_{helicopter}\approx 5\mathrm {m}$

gives

$f_{hippo}^{2}\approx 1000\cdot f_{helicopter}^{2}$

$f_{hippo}\approx {\sqrt {1000}}\cdot f_{helicopter}\approx 30\cdot f_{helicopter}=600\mathrm {Hz}$

This is an order of magnitude more than your estimate, but given how crude some of my assumptions are, i think the true value will lie closer to your result. Besides, i prefer the idea of a humminghippo over a soprano hippo. ◅ Sebastian Helm 🗨 19:38, 15 December 2023 (UTC)

Yes, at that frequency it would be more of a mosquippo. {The poster formerly known as 87.81.230.195} 90.199.215.44 (talk) 03:29, 16 December 2023 (UTC)

Maybe your hippo can run really, really fast to get airborne? There are quite a few papers and sites on aerodynamics of flapping wings for ornithopters such as "How Ornithopters Fly" with different models, but they all seem to be applicable for large heavy birds with high aspect ratios, large forward velocity, and low flapping frequency. Michael Dickinson says for insect flight wing sweeping is a bit like a partial spin of a "somewhat crappy" helicopter propeller which seems to validate your approach. Maybe something like "Wing Rotation and the Aerodynamic Basis of Insect Flight" could help? fiveby(zero) 16:18, 16 December 2023 (UTC)

Niagara Falls through a straw

This question may have been answered by someone on the internet at some point in time, but I'm still going to ask it. What would happen if you tried to funnel Niagara Falls through a straw? What would be the result of taking a straw, raising it up to the Falls, and somehow getting all the water coming down to enter the straw? Gyatt W Rizz (talk) 22:21, 14 December 2023 (UTC)

Water moving through a more constricted pipe or channel tends to speed up. So the physics question would seem to be, how fast could the water move through a straw (of what size?) such that it wouldn't back up and spill over. ←Baseball Bugs ^{What's up, Doc?} carrots→ 23:09, 14 December 2023 (UTC)

I've thought about that before, about how it can back up. Wouldn't the water coming from upstream push the water that's closer to the edge of the Falls forwards, preventing it from backing up? Think of it as a sort of vertical compression-like thing, where there's a small opening at the end for water to go through. It'll only go through it at a certain speed, but if you compress the water behind it, it pushes that water forwards, resulting in an increase of speed. Using this information, what would the implications be of water going into that straw? Gyatt W Rizz (talk) 23:18, 14 December 2023 (UTC)

See the article Choked flow.  --Lambiam 11:09, 15 December 2023 (UTC)

When a river backs up, the waterflow can get wider and deeper. It isn't confined in a straw to prevent that. This happens often. For example, what would happen if you took the Colorado River and forced it to flow through a few tubes (very large metal straws) that happen to be connected to some hydroelectric generators? You end up forming a lake (Lake Mead). What happens when you take the Columbia river and force it through a large metal straw in a hydroelectric generator? You form the Franklin D. Roosevelt Lake. What happens when you force the Osage river to go through a metal straw? You form the Lake of the Ozarks. Do you see a trend here? 97.82.165.112 (talk) 11:26, 15 December 2023 (UTC)

• Answered by Randall Munroe, here: You would get in trouble with the International Niagara Committee, the International Niagara Board of Control, the International Joint Commission, the International Niagara Board Working Committee, and probably the Great Lakes–St. Lawrence River Adaptive Management Committee. Also, the Earth would be destroyed. --142.112.220.136 (talk) 23:41, 14 December 2023 (UTC)
  • Forgetting the legal issues, I think it could be done - with a really, really big straw. ←Baseball Bugs ^{What's up, Doc?} carrots→ 02:18, 15 December 2023 (UTC)

    Is it a straw, then, if it's big enough? Is, the Large Hadron Collider (or any other tube) just a really fancy straw? Where's the line between "straw" and "tube", assuming there is any? And if the straw is big enough for that, I'd imagine it would need to be town-sized or something ridiculously large like that.

    Also I am astonished the first reply wasn't "yes, see Randall Munroe, because that's the answer to the question you were asking, and also he's really funny". 71.112.180.130 (talk) 17:12, 16 December 2023 (UTC)

• Sorry, I didn't see it soon enough to answer first! --142.112.220.136 (talk) 20:00, 16 December 2023 (UTC)

• I don't see anything in Drinking straw that defines its size, though implicitly it would need to be narrow enough to fit in one's mouth. ←Baseball Bugs ^{What's up, Doc?} carrots→ 18:19, 16 December 2023 (UTC)

• In the Summer my daughters go for the fancy and weird drink of Bubble tea that comes with straws that can be 10-12 mm in diameter, and it's still a straw but that's not what comes to mind when one says 'straw' in geneal. Anything larger wouldn't be a straw any more I guess; I wouldn't call fax paper roll cores 'straws' for the life of me even if they're plastic and can have an internal diameter of 20 mm. --Ouro (blah blah) 07:28, 19 December 2023 (UTC)