[NBLUG/talk] OT: physic puzzle reviewed.

Mitch Patenaude mrp at sonic.net
Fri Jan 9 17:20:04 PST 2004


As someone with a physics degree, i can say this is not a 
straightforward physics problem, nor even a straightforward engineering 
problem.  Anybody who tried to give you "numbers" should be treated 
very skeptically.  I can try to do some back-of-the-envelope 
calculations, but it's hard to say what they mean.

I don't remember the poster exactly, but I think the wave is on the 
order of 100 meters (m) tall.  A wave that large would only 
realistically be created by something like a large meteor impact.  At 
the kinds of speeds that would involve, water can be thought of as 
solid.   You could try to calculate the momentum/impulse of the water 
by using the density of water (1e3 kg m^-3) multiplied by the surface 
area of the bridge seen side-on (just a guess, but it's probably on the 
order of 1e4 m^2) times the thickness of the wave (figure an average of 
10 m) times the velocity of the wave (use 30 m/s, or around 65 mph).  
That gives a momentum of 3e9 kg m/s, with a kinetic energy of 4.5e10 J 
(45 Gigajoules). Compare that with 1 kiloton, which is 4.2e12 J, so it 
may seem like that the energy is only 0.01 kiloton, but keep in mind 
that this represents the kinetic energy of the water that hits the 
bridge directly.  The whole wave has about 1.4e12 J of kinetic energy, 
or roughly 1/3 kiloton.  All these numbers are very rough, and based on 
vague assumptions, but should give an order-of-magnitude feel for 
what's involved.)

But you can't just calculate the momentum/impulse/energy, that's not a 
sophisticated enough take.  The Tacoma narrows bridge was brought down 
by nothing but wind[*].  The forces on the bridge would be immense, and 
in a direction that wasn't engineered to take much force. As mechanical 
engineers are fond of saying: "Any fool can build a bridge that will 
stand up, but a good engineer can build one that just barely stands 
up."  They wouldn't have engineered it to withstand something like 
this.. and I doubt it would.

[*] contrary to popular opinion, it wasn't a simple resonance problem 
either.  Classical simple harmonics wouldn't account for the large 
twisting motions observed, and the cables supporting the roadway going 
in and out of tension added a large non-linear component that simple 
harmonic models aren't sophisticated enough to deal with.  This is a 
classic chaos theory problem.

-- Mitch

On Friday, Jan 9, 2004, at 16:26 US/Pacific, <sms at sonic.net> wrote:

>
> Thanks to all who've commented!
>
> Sadly, all the arguments to date have been "merely" common-sense; I 
> won't
> win this argument (nor be defeated!) without hard numbers.  I'll "come
> clean" and admit that I'm in the "bridge goes down" camp (I try to hide
> my side of any argument, when I pitch it to a 3rd party); BUT, I'm not 
> at
> 9 9's of certainty  ;-)   Frankly, I think any of us lay scientists who
> DO claim incredibly-high confidence are speaking either from ignorance
> (there are a LOT of factors involved, and I know *I* am not competent 
> to
> evaluate them!), or from modesty (i.e. they aren't ignorant of the 
> forces,
> but are "modestly" claiming less awareness than possessed).
>
> I'm really hoping for someone with the civil engineering / 
> hydrodynamics
> skills to make a educated guess, instead of my own ignorant guess.  
> From
> my (admittedly ignorant) perspective, I don't see any replies from 
> anyone
> whose got the specialized training.  :(
>
> Specifically replying to folks:  Gandalf -- yes, I'm taking an out-of-
> county class.  Others -- Sorry if I misattribute.
>
>
> Cal -
> Yes, water has inertia; BUT, enough mass can resist the inertia and 
> will
> redirect _ANY_ amount of water.  I *THINK* the wave will utterly 
> overwhelm
> the bridge.  But, I don't know it for absolutely certain; I'm not sure 
> to
> what extent my "gut feel" for this problem is led astray by the scales
> involved.
>
> Your wall, for example:
>    rigid (likely old) concrete,
>    a solid surface designed to catch/stop everything
>    not designed to accept any flexion.
>
> The GG Bridge:
>    Steel & cement, well-maintained
>    with NARROW components (i.e. mass of the wavedoesn't have to divert 
> very
>      far to "flow around").
>    it's designed to flex/stretch
>
> It's not entirely clear what degree of lesson can be learned from your 
> wall.
>
>
>
> Troy -
> Never surfed, but I've played in the surf; yes, I've planted face on 
> the
> bottom because a wave nailed me.
>
> But...
> I weigh ALMOST the same as water; when the water rises, so do I.  Then,
> I go where the water sends me.  I *DO* know from experience that if I'm
> in SHALLOW water and can brace myself, I can hold firm in one place
> against a MUCH larger wave.
>
> MY question is, what would happen if I borrowed concrete overshoes from
> the mafia, and a steel exoskeleton from the military/university 
> robotics
> teams... (yah I know:  I'd drown; but would I drown _in_one_place_?)
>
>
>
> Eric -
>> Things required to analyze this:
>> 1) force (weight) rating of the bridge for straight downward force
>> 2) same rating for lateral forces
>> 3) some kind of measurement of how high the wave is
>> 4) some kind of measurement of how much water is there (gallons, feet
> thick,
>> etc.)
>
> Also:
>
> We need coefficients of friction (if the bridge survives the initial
> impact):  how much stress will the water exert as it flows by, & for 
> how
> long?
>
> I'm sure we'd need to know how much torque the GG can take, too:  the 
> water
> is gonna exert different forces on the bridge at different places 
> along the
> length, different front/back, different top/bottom.  That bridge is 
> gonna
> TWIST...
>
> There's probably other factors we've both missed.
>
>> there's no "just water and will flow freely".  Really.  Try diving in 
>> a
>> pool wrong.
>
> Yah.  The question is, will the _bridge_ dive in _right_?  Or at least,
> well _enough_.  OK, an Ohio-class boomer it isn't, but it *MAY* be 
> strong
> enough & shed ENOUGH water...
>
>
>> I suspect that as much water as depicted in that poster, any water 
>> that
>> missed the bridge would sweep away enough earth from under the bay
>
> Actually, I tend to doubt that.  The gate has been opened for c. 10K 
> years,
> with continuous net flow out (from rivers), & intermittent 
> bidirectional
> scrubbing (from the tides).  Ain't much stuff LEFT to get swept away; 
> AFAIK,
> the brige sits on bedrock (I *THINK* it's actually embedded, concrete 
> poured
> into holes blasted into the bedrock).
>
>> that not only would the bridge be smashed, but all its parts washed 
>> away.
>
> Agreed; if the wave took down the bridge, we'd find parts of the 
> bridge all
> through the East Bay, the Sacto Valley, and likely on to the Sierra
> foothills.
>
>> (the infamously damaging "tidal wave" tends to be about an inch or so
>> high; water has a lot of mass)
>
> Out in  the open ocean:  yes tidal waves are very small; most 
> open-ocean
> craft won't even notice a tsunami pass them.  But these waves DO rise 
> (a
> LOT) as they come to shore.  Most seriously-damaging tidal waves are 
> feet
> high by the time they come onshore.
>
>
>
> Meg-
>> I also don't have enough physic skills to show exactly what would
>> happen, and agree that there is not enough information given, as Eric
>> pointed out,
>
> ALL the info available is what's in the picture (in the end, this is a
> beer-N-pretzels question, not "hard" physics); sadly, I haven't found 
> the
> pic online or I'd offer a link.  It's obviously been diddled (darkroom 
> or
> photoshop).  Shows the GG bridge from inside the gate, Marin side.  We
> see a beautiful "pipeline" breaker, the kind a skilled surfer likes to
> crouch inside and race through... but the scale is wrong:
>  - The "froth" atop the wave hides the exact top, but it appears that 
> the
>    wave is continuous to about the same height as the towers of the GG.
>  - The front face of the wave is reaching into the bay; the bottom edge
>    extends forward between the towers, & the hollow "pipeline" actually
>    wraps around the road-bed where traffic drives.
>
>> Also consider that a wave of that size would most likely originate
>> outside the Bay, and most likely wider than the entrance to the bay.
>> When it comes to the coast, the much of the water is going to take the
>> path of least resistance, ie into the bay, instead of hitting land.
>> This means that the wave will be hitting the bridge with much more 
>> force
>> than it originally had outside, due to this tunneling effect it will
>> experience.
>
> Yes; as per my reply to Eric, above, the wave will follow the lay of 
> the
> land.  Presuming it's a tsunami, with a 'quake epicenter out near the
> Farallons, it'll hit everything from Pt. Reyes in Marin, to Moss Beach 
> in
> San Mateo, within a few seconds.  There will be a fair bit of "funnel"
> effect, but less than in many places because the 'Gate is relatively
> recent & is more sheer (less sloping/gentle) than many "bay" entrances;
> so, the water won't have as much TIME to funnel together, and much of 
> it
> will head straight inland (I gotta grin imagining the "WTFO??!?" of 
> folks
> on the bay side of the peninsula, a a huge wall of saltwater comes down
> from the hills above 'em!).
>
> Thanks to everyone who has been playing the game!
>
> If I come up with a more-satisfying solution or relevant info, I'll 
> post
> it...
>
>
>
> - Steve S.
>
>
>
>
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