# The Physics Behind the Mantis ShrimpBy: Andrew Poteres

The Mantis Shrimp is a well-known deep sea creature. It may look like a friendly creature out of a Disney film, but it is far from. In fact, the Mantis shrimp is one of the fiercest predators of the sea. They typically reach about 30 cm in length once full grown, and get about 10-12 cm tall. They live alone and are fighters. They're extremely aggressive and use 2 hammer-like appendages to strike prey. These deadly appendages move about 13-23 m/s in water, and aren't weak either....

In a study published by The Journal of Experimental Biology, they concluded that these strikes can get up to 1500 N of force! One oddity that they noticed in this study, was that there were two force peaks showing when only one appendage was striking the sensor. Close inspection of the strike, through the use of a high speed camera, revealed a  small cavitation bubble being created by the strike. A cavitation is a phenomenon engineers deal with in plumbing. Rapid changes in fluid pressure causes cavitations to occur and create small vapor bubbles. Inertial Cavitation, the type in this case, is a destructive phenomenon; when these vapor bubbles collapse, they essentially cause a small implosion in the water which produces a shock wave sending out heat, light and sound. The study later indicated the average limb strike to be about 327 N and the average cavitation force to be about 278 N.

Peak 1 is from the appendage striking the force sensor, and peak 2 is the explosion of the cavitation bubble. Data from smaller shrimp

(Note: above video was originally filmed in 5000 FPS then later slowed down to 15 FPS to better visualize cavitation bubble) I did a video analysis of the video above to come up with my own appendage and cavitation force observations.

Velocity vs Time and Position vs Time Graphs (seconds are not converted in above images)
Data table and Position vs Time graph (seconds are not converted in above figures)

Calculations for Force of appendage strike:

x = ½ a t^2 + v(initial) t + x(initial)= -.0394 t^2 +21.42 t - 24.78

½ a t^2 = -.0394 t^2

a= 2(-.0394 m)

a=-.0788 m/s/s

5000 FPS /15 FPS = 333.33

333.33 * a = a(adjusted for fps change)

a= 26.26 m/s/s (adjusted for fps change)

F=m(appendage)* a(appendage)

F=~13 g (26.26 m/s/s)

F= 341.125 N

Now the Calculations for the Force of the Cavitation bubble:

F(collapse of one bubble)= 2π * p * r min * ( (√h^2 + r^2) -h)

where p is the pressure of the fluid, r min is the minimum radius of the bubble, h is the distance from the middle of the bubble to the wall, r is the radius of the bubble

F= 2π * (P(initial) + pgh) * (.001 m) * ((√(1.6e-5 m^2 + .44444m^2)) - .004 m)

F= 2π * (1e5 Pa + 1000 kg/m^3 * 9.8 m/s/s * .2 m) * .001 m * (.662678666 m)

F= 2π * (101960 kg/s^2) * 6.6267 e-4 m^2

F= 2π * 67.566 N

F= 424.528 N

Now we have to account for negative Force occurring during implosion/explosion:

F/s= F(negative)

s= (Pr - Pv) / (1/2 ρ v^2)

s= (1e5 Pa - 23.8 Pa) / (.5 1000 kg/m^3 * (8.7 m/s)^2)

s= 2.64

F-F/s=F(negative)

F(negative)= 160.806 N

F-F(negative)= F(positive)

F(positive)= 263.722 N

where s = cavitation number, Pr is the reference pressure, Pv is the vapor pressure, p is the density, and v is the speed of the fluid during explosion (speed of appendage right before contact). The negative force was found to be inversely proportional to the cavitation number of the bubble.

Indicated in the box is the negative force of a cavitation

Negative force does not mean physically negative force. It just means that it was in the opposite direction. I wanted the force in only one direction so i had to account for the force in the opposite direction and subtract it. After all my calculations I got:

Force of appendage strike = 341.125 N

Force of cavitation explosion = 263.722 N

Combined force = 604.847 N

Ratio of strike to bubble = 1.293

I calculated the ratio because I wanted to weigh the accuracy of my calculations to the accuracy of the force sensors in the actual studies. The studies said that their ratio for strike to bubble was 1.17. Mine was 1.29 so I think i was pretty close to the actual sensors. I feel I was only off a bit because I rounded a couple numbers. The appendage strike was only ~341 N which would be on the low end for the study I looked at but still pretty high for a crustaceans appendage in water.

# How is this possible?

After analyzing, and figuring out how hard these things actually hit, I became curious as to how this was possible at all. Upon further research, I was led to the mechanism that dictates the appendages movement. The Mantis Shrimp have a saddle shaped spring -like above the appendages that is responsible for the strengths of the strikes.

Drawing of 'click' and 'latch' mechanism

This sort of mechanism is called a 'click' mechanism. These types of mechanisms take awhile to store up energy. The muscles contract, like a spring, and are held in place by a latch. Once the shrimp wants to strike, it releases the latch, and all the stored up potential energy becomes kinetic. Kind of like a catapult. This explains why the shrimp strike significantly harder than a usual crustacean. Instead of relying on the potential energy stored in a small amount of time to strike, like humans and other animals, the mantis shrimp stores it up over time and waits for the opportunity to unleash it. It uses potential energy stored up over a time period instead of drawing up energy in the moment to strike like a human would do in a punch thrown.

Saddle shape above appendage responsible for energy build up

This dynamically flexible structure is responsible for the energy buildup and release in the mantis shrimp strikes. Though it may not look like it, it is actually a type of spring. A spring is the only way the shrimp could achieve the high levels of force that it came to. During a normal strike, the saddle structure was observed as contracted at the beginning. Then as the strike was carried out the saddle extends and even goes as far to hyper extend. This type of mechanism is known as a hyperbolic-paraboloid, and is the key to paralyzing strikes that mantis shrimp is known for.

This was used to bridge a gap between engineering and biology. Many engineers used this design for structures that needed to be very strong while utilizing a small amount of material. This type of structure can be seen a lot in architecture. I just found it amazing that we utilized the biology of a shrimp and applied its years of evolutionary knowledge to  our modern day engineering in order to better our usage of resources.

building utilizing hyperbolic-paraboloid