27
$\begingroup$

If I go for a walk at, say 4 km/hour, unless there is a breeze blowing, I probably won't notice the air around me at all. If I go for a swim though, I will immediately notice the viscosity of the water and the effort needed to move through it.

On that sort of scale, I wonder is it possible to estimate how normal still air applies in terms of viscosity, to a mosquito or other similar sized insect, utilising standard fluid dynamics techniques?

I don't wish to ask a biology based question, or how any insect actually flies, which can be found at Insect Flight. This article implies that insect flight is still a subject of active investigation.

The range of Reynolds number in insect flight is about 10 to $10^4$, which lies in between the two limits that are convenient for theories: inviscid steady flows around an airfoil and Stokes flow experienced by a swimming bacterium. For this reason, this intermediate range is not well understood.

Instead I wonder do we know, compared to the human experience with respect to the fluid viscosity difference between still air and water, what air "feels" like to move through for an insect, such as a mosquito?

In other words, is it possible to scale up the insect flying "experience" to the human level, and get an idea of what the human equivalent of the viscosity involved is? I appreciate it may be impossible to answer this question without referring back to the flight dynamics of insects, in which case my apologies as there may be no current answer.

$\endgroup$
  • 2
    $\begingroup$ It's not really about aerodynamic techniques -- jet planes are a feat of engineering unmatched by nature. It's about scale. Flying only really gets easier as you get smaller. Remember a speck of dust can easily fly across entire oceans, and it's not powered at all. $\endgroup$ – user10851 Sep 10 '15 at 15:59
  • 3
    $\begingroup$ @ChrisWhite: The mosquito flies at around 0.5m/s, which is many (approx. 50?) times its body length per second. Wouldn't that mean that we would have to calculate the viscosity to get to that Reynolds number for a human flying at e.g. 100m/s? $\endgroup$ – CuriousOne Sep 10 '15 at 15:59
  • 1
    $\begingroup$ One way to compare their experience to ours is to imagine a wind which they can't fly against. Maybe a wind of 1m/s. For a person the wind speed we can't move against is probably an order of magnitude higher. So when they feel a light breeze its like a hurricane! $\endgroup$ – Alex Sep 10 '15 at 16:23
  • 1
    $\begingroup$ @AcidJazz mosquitoes live on sugars, mostly from plant nectar. The females feed on blood because they need proteins to make eggs, so the energy comes from plant sugars. (source: wikipedia on Mosquito) $\endgroup$ – Mindwin Sep 10 '15 at 21:41
  • 2
    $\begingroup$ @MichaelT I had to do some searching around to make sure that one wasn't a hoax. Mindblowing stuff. $\endgroup$ – WetSavannaAnimal Sep 11 '15 at 6:16
23
$\begingroup$

What you need to compare when looking at bodies of different sizes and asking how the forces relate, is in general, the Reynolds Number as you included in your question. This is defined as:

$$ Re = \frac{u L}{\nu} $$

where $u$ is the fluid velocity, $L$ is a representative length scale and $\nu$ is the kinematic viscosity of the fluid. This can also be thought of as the ratio of the inertial forces to the viscous forces. So, when this number is small, the viscous forces dominate and when it is large, the inertial forces dominate.

The hardest part is picking an $L$. In this case though, it's not so bad. Let's assume that a mosquito is approximately a sphere. Adults rarely exceed 16mm in length, so let's just approximate and say they are 10mm long, so as a sphere they would have a radius of 5mm. Let's then take a normal day at standard temperature and pressure (STP) so that the kinematic viscosity of air is $\nu = 15.11e-6$. And let's assume a light breeze, say 5 m/s. This gives us a Reynolds number of (which hey, also matches the range you posted -- good start!):

$$ Re = \frac{u L}{\nu} = \frac{5 \times 0.005}{15.11e-6} \approx 1655 $$

Okay, so now if we want a human to feel the same inertial-to-viscous force ratio, we want to keep the Reynolds number the same. We can pretend a human is a cylinder. And we can further say that an average human is, roughly, 0.4 meters wide which would give a radius of 0.2 meters. We'll assume the Reynolds number is the same and the air viscosity is the same and solve for a wind velocity to give a similar feel:

$$ u = \frac{\nu Re}{L} = \frac{15.11e-6 \times 1655}{0.2} \approx 0.12 m/s$$

Counter-intuitive maybe, but what we're considering here is what velocities are required to feel the same ratio of inertial to viscous forces.

In this case, we altered the wind speed but we could also alter the viscosity. If we wanted to do that, let's say we held the speed the same, we would get:

$$ \nu = \frac{u L}{Re} = \frac{5 \times 0.2}{1655} \approx 0.0006 m^2/s$$

This number is almost 40 times larger than the viscosity of air. This means that for a human to feel an equivalent set of forces, they would have to be in a 5 m/s flow of something like hot asphalt, SAE 150 gear oil or diesel fuel. None of which sounds very pleasant, but honestly neither does flying around as a mosquito.

$\endgroup$
  • 1
    $\begingroup$ Thanks very much for your time and the details involved in answering. The question occurred to me because I threw a spider out of an upstairs windows, and a concerned niece asked me would it survive? I said yes. $\endgroup$ – user81619 Sep 11 '15 at 9:46
  • $\begingroup$ @AcidJazz Based on the math, that would likely be comparable (although once you include gravity and buoyancy, other non-dimensional numbers become important like the Froude number -- as does terminal velocity, likely to be much higher for a human than a spider) to a human jumping into a tar pit. The fall would likely be just fine. Although jumping into a tar pit has other issues... $\endgroup$ – tpg2114 Sep 11 '15 at 10:17
  • $\begingroup$ I'm uncertain what those numbers mean. Here is a guess: $0.12 m/s$ is the amount of wind that an insect would feel similar to a $5 m/s$ wind on a human? And SAE 150 gear oil at $5 m/s$ is the viscosity required to get the same feel on a human as $5 m/s$ wind on the insect? $\endgroup$ – Yakk Sep 11 '15 at 13:28
  • $\begingroup$ @Yakk The velocity result is counter-intuitive for sure. What it says is that $0.12 m/s$ on a human generates the same ratio of inertial to viscous forces as $5 m/s$ does on the bug. Your understanding of the second case is correct though -- it will take a flow of $5 m/s$ SAE 150 gear oil to feel the same on a human as a $5 m/s$ flow of air does on a bug. The reason the first is counter-intuitive is because we're looking at the ratio of forces and the viscous forces on a human would be way bigger than those on a bug, just due to the change in surface area. $\endgroup$ – tpg2114 Sep 11 '15 at 13:47
  • $\begingroup$ Hmm. What is an inertial force force in this context? The force required to accelerate your limb to a certain speed in a certain amount of time in a vacuum? Then "the ratio of inertial to viscous forces" ratio would be ratio with the force required to do the same with that wind? Seems like there would be uneliminated degrees of freedom there. ... basically, I cannot connect your ratios to something concrete, and without that I don't see how to determine if they are plausible, or if I should expect a hidden math error. $\endgroup$ – Yakk Sep 11 '15 at 13:51
6
$\begingroup$

Viscosity of air will be same for both fly and human. In the case of flies, from the point of view of the fly, it would seem to it that the viscous force is very high as it keeps the fly afloat. In case of humans, such viscous forces are negligible. So we don't notice it. If you want to scale up the insect flying "experience" to the human level, think about a situation in which a force of wind is able to pull you up in the sky (or rather just keep you afloat in air). What happens is that the air's resistive force acting against the downward motion of the body, equals the body weight and keeps you afloat with net force on body = zero.

That's why if you let a little insect fall from a height you will notice that it does not accelerate in the downward direction. The air drag(or resistance) cancels the little weight of the insect and it falls down with a constant velocity.

That kind of experience for a human is only possible when the air drag is able to produce a force of 60 kgf(or whatever your weight is). That's impossible on Earth. So you get a similar (but not exact same) experience with a wind pulling you up.

For the best experience you may put yourself in some kind of a fluid medium of quite a high density than air but less than your body density(not water as its density is higher than your body).

$\endgroup$
  • 2
    $\begingroup$ So you're saying a comparable experience is a very strong wind? I'm not sure I understand what you're trying to say here. What about a case where there is no breeze, and the air is completely still? $\endgroup$ – Ajedi32 Sep 10 '15 at 18:54
  • $\begingroup$ @Ajedi32 What do you mean "Air is completely still" - that's not how gases work, though. $\endgroup$ – corsiKa Sep 10 '15 at 19:50
  • 1
    $\begingroup$ @corsiKa By "completely still" I mean no wind. Obviously I'm not saying it doesn't move in response to the movements of the insect itself, or that it's not moving at all on a molecular level. Shubham mentioned a situation where "force of wind is able to pull you up in the sky", so I'm asking what happens when there is no wind at all. $\endgroup$ – Ajedi32 Sep 10 '15 at 20:02
  • $\begingroup$ @Ajedi32 what corsiKa is trying to say that to a mosquito, the air is never completely still. There are currents here and there that to the mosquito can be considered wind. A truck or bus moving down the street, a door opening or closing inside the house, the AC blowing, all those minute things move air around in an amount that affects the mosquito, but for a human seem like still air. P.S: there are also convection currents between hot and cool air pockets everywhere. $\endgroup$ – Mindwin Sep 10 '15 at 21:22
  • $\begingroup$ @Ajedi32 Check out the extension of my answer. Hope it clears all your doubts. $\endgroup$ – Shubham Sep 11 '15 at 12:33
1
$\begingroup$

Your thought about feeling the water viscosity seems along the right lines, with the small modification that flight is easier to insects than swimming is to humans.

One consideration, though, is an entity's limbs and their capacity to influence personal position: Insect legs and antenna may feel less rheological resistance and drag in air than ours would in water, but their wings would cause intense personal-position changes similarly to our legs against the ground. Insects would feel 'torque-ier' or zippier because they have so much less mass.

$\endgroup$
0
$\begingroup$

Just imagine yourself shrunk down to the size of an insect. The air would "feel" the same but because of your mass and because you have no special organs to grip surfaces, you would feel constantly thrown around by tornado level winds caused by the swing of a regular sized human's hand. Insects are specially designed to handle these frequent gusts of wind so it feels "OK" to them but for a human it would feel like a constant barrage of hurricanes.

$\endgroup$
-1
$\begingroup$

Air viscosity is not enough to be noticed by moving mosquito. But for it's wings air viscosity is important thing, not because their size, but speed.

$\endgroup$