8/13/2019 ENGAGE E3S Dynamics Mosquito

1/2

Funded by a grant from the National Science Foundation. Opinions expressed are those of thauthors and not necessarily those of the funders.

Using Everyday Examples in Engineering (E3)

Mosquitoes: Surviving raindrop impacts by virtue of their low mass

Andrew Dickerson, David Hu

Georgia Institute of Technology

Mosquitoes can be found in almost every climate, but thrive in particularly moist

environments. Familiar pests to most, their status as a disease vector makes themabundantly available for research, and a suitable model organism for flight studies.

Now, imagine walking across a busy, multi-lane highway. There is a risk a car travelingat high speed, many times your mass, will collide with you. Even if you see it coming atthe last moment, your avoidance efforts are futile. There is no chance of walking away

unscathed. If we now replace thecars with raindrops and people with

insects, we begin to understand aninsects reality while flying in a

rainstorm.Raindrops are found to have a range

of sizes, but generally share the samelength-scale as a mosquito. Due to

their density however, raindropshave a mass m1 up to 50 times

greater than that of a mosquito witha mass m2 = 1-2 mg. Additionally,

raindrops fall with a terminal verticalvelocity u1of up to 9 m/s.

There are two types of collisions amosquito may experience in rain.The first, a glancing blow, is when

the raindrop hits a mosquitos wing, legs, rear, or proboscis (snout), as shown in thepicture above. Glancing blows act to quickly rotate a mosquito, leaving it momentarily

disrupted. The second type of collision is a direct impact, the most perilous type ofcollision. A direct impact occurs when the raindrop impacts a mosquito very near its

center of mass. This causes the mosquito to accelerate downward, momentarilyconnected to the raindrop. Conversation of momentum for inelastic impacts can be easily

expressed asu1m

1+ u

2m

2= u'(m

1+m

2) (1)

where u is the post-collision speed of the two masses. If we assume the initial verticalvelocity of a mosquito u2= 0, we may rewrite Eq. 1 as

www.EngageEngineering.org

8/13/2019 ENGAGE E3S Dynamics Mosquito

2/2

u'

u1

= 1+m

2

m1

"

#$

%

&'

(1

. (2)

Evaluate: using equation (2), calculate the percent decrease in falling speed a raindrop

would experience if it impacted a lighter (1 g) hovering insect. Assume the raindrop has a2 mm diameter and is falling at 8 m/s. Also assume the impact is inelastic and the drop

remains intact.

Through high-speed video, it has been shown that mosquitoes experience more than 300Gs of acceleration upon impact by a raindrop. This staggering figure is far above human

tolerance. Newtons second law is an expression of the time rate of change ofmomentum. It can be written to calculate the forceFimparted on a mosquito by a falling

raindrop as

F =u'm

2

"

(3)

where !is the duration of impact, on the order of 2 ms. Though uis on the order of 9 m/sand ! is very short, Fmust remain sufficiently small for a mosquito to survive impact.

Mosquitoes are able to survive raindrop impacts by virtue of their low mass m2.Considering the magnitude of a mosquitos mass, it might not be surprising the impact

force F was calculated to be approximately 0.6 grams-force, or the weight of a smallfeather. A mosquitos exoskeleton allows it to withstand a force more than one thousand

times its own body weight, so 0.6 grams-force is easily survivable.

Experience: try to kill a mosquito-sized insect by swatting out of the air with you hand.Can you do it? An air-filled balloon can demonstrate the same idea. Compare the force

you can impart on a balloon, versus the force you can impart on a baseball.

Newtons third law tells us that for every action, there is an equal and opposite reaction.

A mosquito does not impart much force on raindrops either, allowing them to stay intact.When flying objects approach the size of birds, drops loose practically all of their

downward momentum and break apart, thereby imparting

a larger force than if they stayed intact and continuedfalling.

Elaborate: the interested student will calculate the force

a raindrop imparts on a solid, unyielding surface.

Engineering Application:Think about how we canapply what we now know about mosquitoes to micro-

aerial vehicles (MAVs). What design characteristicsmight we incorporate to ensure a MAV is robust to

rainfall?

For high-speed shaking videos and more information visit:

dickerson.gatech.edu

All images: Tim Nowack and Andrew Dickerson, Georgia Institute

of Technology