Flying Squid And Velocity Vs. Acceleration
    By Danna Staaf | February 22nd 2012 04:26 PM | 9 comments | Print | E-mail | Track Comments
    About Danna

    Cephalopods have been rocking my world since I was in grade school. I pursued them through a BA in marine biology at the University of California...

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    If you haven't heard the kerfuffle about flying squid by now, you've been under a rock. A cephalopod-free rock. 

    Jessica Marshall wrote a story for Nature which also ran in Scientific American. Then Discover, the LA Times, and Discovery News jumped on the bandwagon. They're all great articles, but Discover's got the cutest summary:
    To propel itself out of the water and into the air, the squid fills its mantle with water and then quickly shoots it out. This is the same thing it does underwater, but air is less dense, so it produces more scoot for the squirt.

    "Scoot for the squirt." For the squid! Hee.

    I am particularly excited because it's my grad school pal Julie Stewart who's getting all this press. She's second author on the squid flight poster, after awesome squid dude Ron O'Dor, and she was the one to present it at this week's Ocean Sciences meeting* in Salt Lake City.

    (Not to be outdone by all the other news outlets, the BBC ran a squid piece too. But instead of focusing on the poster, Jonathan Amos reported on the talk Julie gave the next day, which was about deep diving rather than high flying. Always gotta be different, don't you, BBC?)

    I've written about squid flight before, and as I said, the spate of recent articles is lovely. But one bit of science seems to have gotten confused: the difference between acceleration and velocity. 

    Marshall wrote in Nature,
    They found that the velocity in air while the squid were propelling themselves with the water jet was five times faster than than any measurements O’Dor had made for comparable squid species in water.
    But Deborah Netburn got this quote from O'Dor for the LA Times:
    "The acceleration rate in air is five times faster than any acceleration I've measured in a squid in water," he said. 
    (Emphasis in both quotes is mine.) Now, velocity is a measure of speed--miles per hour, or meters per second. Acceleration, though, is a measure of how fast your speed is changing--miles per hour per hour or meters per second per second

    Acceleration is what people are talking about when they say the Mazda RX-8 can go from zero to sixty in under six seconds. Velocity is all right--it's nice that the car can go sixty--but acceleration is hot. So which does the five-times-faster squid statistic refer to?

    I didn't go to Ocean Sciences (boo!) but Julie very kindly sent me a copy of the poster, so I checked the data. They had to compare different squid species, because the same species haven't been tested in both air and water. In order to make the numbers more comparable, they focused on units of body length, rather than absolute distance. 

    Here's a simplified table I made from their data. In each case, several species of squid were measured, so I just took the fastest. (We're looking at extremes here, okay?) Velocity is in BL/s and acceleration is in BL/s2.

     water  air   so air is how many times faster? 
     average velocity 7263.7
     maximum** velocity 11373.4
     average acceleration 43179 4.2
     maximum acceleration 882653.0

    As it turns out, the journalistic confusion actually didn't matter that much. Flying through the air increases both velocity and acceleration by a factor of 3 to 4. But I'm guessing it's that 4.2 number--for average acceleration--that O'Dor was thinking about when he talked to reporters.

    Incidentally, can I get a WOW on that maximum acceleration? It's incredible! I may have to work this into my squid racing novel . . . 

    * This page actually contains two errors: the spelling of Julie's last name and the fact that she isn't a student. Whoops.

    ** One of the members of my thesis committee struck out "maximum" everywhere in my thesis that it occurred as an adjective, and replaced it with "maximal." I see his point, but my inner descriptivist finds "maximal" unnecessary and pretentious, and apparently she won the coin toss for editor today. Sorry George.


    I would not expect the acceleration and velocity ratios should to differ much. If the time spent accelerating is the same, the ratio (5:1 or whatever) should be the same, too. The terminal velocity at thrust cutoff is given by the logarithm of the mass ratio of a full and empty squid times the exhaust speed at the siphon nozzle, so measuring that should give a convenient approximation for the squid speed.
    In order to get into outer space, one would probably need a multistage squid (imagine an Architeuthis with a D. gigas on his back, then some Loligo and an reentry-Idiosepius on top of that). It seems the squids noticed that their deuterostomian rocketmakers (May 2011 here) failed badly and they are doing the work now themselves.
    And then there is Laura Dekker who had a research vessel (without the research) totally for herself, "caught" many flying squid and all she did was to clean them away (

    Danna Staaf
    HAH! Thanks for pointing out the obvious with regard to relative ratios (which I should have realized) and for the fantastic concept of a multistage squid rocket. I totally want to draw that now! Especially the reentry-idiosepius, that's just too cute for words.
    In the meantime I came up with an even simpler solution for an upper bound of the terminal speed that requires no dynamic measurement at all. The exhaust velocity is determined by the pressure (corrected by a little friction in the siphon which can be assumed to be a cylindrical tube), and the maximal pressure is given by the amount of muscle in the mantle wall.
    So all what we need is the mantle geometry (both maximal cavity volume and wall strength (which in reality is a (preserved) volume as well)) and some numbers about how strong squid muscles are per cross-sectional area (I believe sports scientists have such data for humans); and the payload (i.e. mass of the empty squid).

    Danna Staaf
    Well . . . gosh! It's like you knew I was writing a paper about this. =) One of my thesis chapters was on "The littlest squid: low Reynolds numbers and funnel aperture modification" and I'm working it up into a paper now (it probably won't be ready to submit for a few months, since my recent academic publishing efforts have been siphoned (see what I did there?) into getting one of the other chapters out the door).
    Annnyway, point is, I worked with Mark Denny to make a mathematical model of squid jetting, and parameterized it by looking up all that stuff: max pressure, mantle dimensions, etc. and how they scale with size. Max pressure turns out to be about 2.5 x 105 N/m2. The model does require some dynamic parameters--e.g. how long the squid spends in contraction vs. refilling phase--but happily, folks have measured most of that stuff, or it can be estimated.
    2.5 bar corresponds (ideally) to 22.3 m/s speed at the nozzle. Using Tsiolkovski's equation, we'd need a mass ratio of 7*10^153 just to get into orbit (7.9 km/s). Since squid spaceships are known to perform interstellar flights (see (Maxim Kammerer flying to Sarraksh)), we either need better fuel or multistage squid. 10^153 is just too much - we'd need more water than the mass of the whole universe just in order to get a single neutrino into low earth orbit.

    Danna Staaf
    Ah well, it was a splendid idea . . . 
    On the language issue:

    I’m something of a fossil myself.  For example, I still distinguish in pronunciation between ‘whales’
    and ‘Wales’, which most people in the UK no longer do.

    But I have never in my whole scientific career used the adjective ‘maximal’.  However, people often use ‘minimal’ in speech, but for emphasis, as if to say “you’re being mean!”  I would, however, say things like ‘the minimum required amount’.

    This is the effect of importing Latin words into what is basically a Germanic language.  There will always be a tendency to relax them into a native form of usage.
    Robert H. Olley / Quondam Physics Department / University of Reading / England
    Danna Staaf
    I always enjoy talking with someone who pronounces "whales" and "Wales" or "where" and "wear" differently, since in my dialect the post-w "h" is completely silent! It's interesting to hear that may be on the way out, though.
    Totally agree on the inevitability of English modding Latinate words.
    ‘the minimum required amount’
    Ugh!  :)

    Since "minimum" is next to "required" the implication is that there is some sort of choice of required amounts and we are focussing on the smallest of them. "Required minimum amount" would, of course, be even worse as it implies that there are other minimum amounts that are not needed at all. It also conveys an ominous sense of foreboding: what will happen if I fail to produce said amount? Will I get a visit from the Minimization Police?  However,  "minimum amount required" is unambiguous and flows easily. It has the added advantage that it leaves the way open to enlarge upon what the amount is required to achieve if that is not already obvious. For example: "the minimum amount required to neutralize the excess acid".  That, admittedly, is a different construction, and some people may not be happy with "amount required" on the grounds that, in English, adjectives usually precede nouns. Anything else carries a serious risk of our turning French.