The Coriolis Effect
Thread - The Coriolanus Effect, Coriolis Effect etc.
On 26/12/2002, .Nisaba Merrieweather wrote:
Coriolanus effect? <moment
of rare self-doubt as my vocabulary and spelling suddenly seem shaky>
Y'know, the effect that has water spiralling down drains when uninfluenced
by other forces clockwise north of the equator and anti-clockwise south of
the equator?
I heard somewhere that it doesn't affect bodies of draining water smaller
than some large diameter (possibly fourteen metres?), and I suspect I heard
it here, possibly from the very lovely Ben Morphett. Or maybe at one of the
two meets I actually managed to attend.
Can anyone make my half-memory slightly more accurate?
John
Winckle replied:
I read a report
of work done at Sydney Uni where they got the minimum size for coriolanus
effect down a plug hole to a tub 6 feet across, but it was a major engineering
feat.
Zero
riposted:
You
mean thay got the whole cast and audience in a six foot tub? Did any
survive?
.Nisaba wrote:
Would that be a true coriolanus effect, or what that incorporate some other
form of energy into the water to make it spin in a desired direction? I can
do that in a bathroom sink with my fingers, get a spin going either way.
What kind of engineering was necessary, do you recall?
Do you know where I can find the literature?
Podargus
quipped:
The feat of getting a tub 6 feet across to show coriolanus probably depended
on how many feet were available and whether they were human or wether
feet and what the weather was like on the day.
I am sceptical that a tub of water so small would show coriolis even if
all the factors that normally effect the spiral are controlled.
John replied:
The whole point of the exercise was to eliminate all other effects but the
coriolanus.
They had to eliminate all movement of the water and irregularities within
the tub. and lots more I could not guess at.
The great Skeptic CD would have the report.
Paul
Williams added:
Try this
http://www.physics.ohio-state.edu/~dvandom/Edu/newcor.html
I recall
that we have discussed this subject previously on S/M.
The following
extracted from the above site is, I believe, demonstrably
true.
"Under
extremely controlled conditions, this (coriolis force) can cause water to
flow out of a container counter-clockwise in the northern hemisphere and clockwise
in the southern hemisphere, but your kitchen sink is not so controlled..."
"Water
in the sink doesn't go far enough to trigger a noticeable north/south deflection.
Most often, it simply spirals down the sink the way it went into the sink....
In any case, don't blame it on the Coriolis force unless your sink is the size of a
small ocean."
Toby Fiander responded:
> Packs vovo biscuit
> Exit
For anyone who hasn't a clue what happened, here is a site about Shakespeare's
play, Coriolanus:
http://www.sparknotes.com/shakespeare/coriolanus/
... which seems to have enough references to the text for most people.
And here is a translation of the account by Plutarch:
http://classics.mit.edu/Plutarch/coriolan.html
It seems unlikely at this point that the coriolis effect would need further
explanation, although as Paul, Podargus and a number of others have pointed
out, those with tubs the size of the small ocean may only now be catching
up:
http://zebu.uoregon.edu/~js/glossary/coriolis_effect.html
A classical thespian butcher I once knew used to say occasionally, "Ne fle."
Donald Lang added:
I think
Dr Karl had a go at this topic not too long ago. People do tend to talk around
in circles about it. There is a certain scatological charm in relating the
ring around the bathtub to the coriolis effect.
The swirling
bathwater is something that gets that "I've heard of that" look from people
if you mention it in a public place. But - elementary physics books don't
seem to mention it - or include the coriolis force in their index of topics.
There must definitely be some science content for the list in a bit of physics
that is avoided in elementary science and familiar in the market place.
I think
every time I see a discussion it is mentioned that you can make the circulation
go either way, in a bathtub, and it then persists. Once you have the water
in the bathtub circling and draining at the same time it carries angular momentum..
Pulling it closer to the centre with the same angular momentum increases
its speed. Once again, everyone watches ice skaters doing pretty rotations...
Viscosity then drags the layers that are a bit further away to circulate
the same way. They in turn are speeded up as they approach the centre and
you have a persistent effect.
The questions
are: Is there a preferred direction for a spontaneous circulation? How does
size make a difference? Is there a minimum size where the spontaneous spin
can be made to work? Is there a maximum size where a persistent spin can be
set up in the "wrong" direction?
Have to
admit I think the answer to each of the last two questions is "It all depends."
From what I read, the alternative is "Suck it and see."
Let me
have a go at the first question. If you fire a gun southward from anywhere
in Australia, the bullet has any velocity you happen to have, combined with
its velocity out of the gun. Someone watching from the moon would say
that your bit of the surface is moving steadily eastwards toward the rising
sun.. People to the south of you are also seen moving in that direction but
not so fast. So the bullet drifts to the east/left of the supposed straight
line path over the surface. If you fire a bullet north it is going more slowly
to the east than the terrain it is passing over. It drifts to the west/left
of its intended straight line path. In the southern hemisphere air that is
pushed by a pressure gradient to go in a given direction is also apparently
pushed to the left of that direction. Seen from the top of the atmosphere
a 'trough' of low pressure has winds going clockwise round it, in this hemisphere.
What stops
coriolis forces from ruling the roost is friction. Slosh some water onto a
level bit of concrete. It stops flowing in a few seconds. You can say, I
will say, that the deceleration is about a loss of two metres per second
in four seconds. Put that together it comes out at "half a metre per second
per second". Your slosh runs about four metres over the concrete.
Now it
the time to dig a bit deeper into some text book and ask about the size of
the coriolis acceleration. When you have gone back two pages twice or more
to find out which symbol means which thing, you find out that the important
bits are the speed of the water, and the rate at which the Earth rotates.
There are extras, but under the Pratchett "lies to children" rule we will
swear they don't exist.
We already
have the water speed claimed to be two metres per second.
We have
to put the Earth rotation into radians per second, remembering that on its
axis it turns 360 degrees in 24 hours. The number to play with is around 5
* 10^-5 radians per second. So while that water was slowing down it was pushed
about one tenth of a millimetre off course - as we would see that course.
Hands up all those who watched closely enough.
The wonder
is that coriolis forces can act on anything and be seen doing it.
So here
goes for the other extreme: a big chunk of air flowing towards somewhere of
low pressure. There is friction from the land or water underneath. You get
calmer air near wind breaks, but the influence does not extend much above
them. Away from wind breaks you seem to feel the full gale around head height.
The leaves are blown along right at ground level. Friction works only on the
lowest layers and not too effectively there. Kevin mentioned wind sheer, There
is very little influence of the stationary layers on the blob above.
Coriolis
acceleration however applies to the whole moving lump. So it does get pushed
as a lump and accelerated as a lump. The very simplest look at the total effect
says that the wind going to the centre is deflected and goes round it in
a time comparable with the rotation of the Earth. This is of course "lies
to children", but... A wind of fifty km/h, going around a low pressure trough
five hundred km away, would carry a raincloud right round it in about three
days.
So there
is a preferred direction. Existing turbulence and surface friction nobble
your demonstration on a small scale.
<soap
box> There is a moral somewhere. I think I am willing to assert that doing
the digging, and putting some numbers in, gives a better understanding, and
the triumph is worth it even if you went wrong at step one. </soap box>
OR <\soap box> --- whatever turns you off!
David Maddern
responded:
Interesting
Throw this into the mix
If an Artillery shell is destined to go over 15Km then the rotation of the
earth is taken into account.
So for a thing that is meant to cover an area anyway it must be deemed significant
for a projectile weighing 20kg with a time of flight around 20seconds
but not for smaller stuff
To which
Peter Macinnis replied:
On another
note, the German cruiser Emden used gunnery tables that included a Coriolis
correction, if I recall correctly -- I came across a reference to that while
researching its shelling of Sokehs Rock in 1911 on the island of Pohnpei.
Never mind why, it's a long story.
And Donald Lang added:
According to my calculation the weight of the projesctile is not important
unless you wish to complicate things a lot with [small] friction effects.
The trajectory has some influence. Thus something taking 20 seconds to go
15kms is in a relatively flat trajectory. If 15 kms lay at the end of the
range the time would be more like 39 seconds. For the same distance to the
target the faster the projectile, the less effect coriolis forces have.
My calculation says that a projectile taking 20 seconds to travel 15 km
[for most places in Australia] will land about 15 m from its aiming point.
I would not wish to come within 15 m of an explosion of a 20kg projectile.
If the area of devastation has a radius of say 20m, there would be a distinct
advantage in placing the centre with a margin of error less than 15m. For
some targets the radius of effectiveness and the desired accuracy would both
be measured as a smaller number of metres. The coriolis correction would
remain the same.
Adding more science content to the mix, the Foucalt pendulum demonstrates
the rotation of the Earth without leaving your building There is, or used
to be, one in the University of Adelaide. The mathematics of the coriolis
effect shows you how the pendulum works, or vice versa.
Steve
Berry wrote:
Most
gunnery tables from the 1890s to just after WW2 contained that correction.The
older guns often had a shell flight time at maximum range of 2-3 minutes.Big
Bertha the German rail gun used against Paris in WW1 had a flight time of
9 minutes at 85 kilometers.
Peter replied:
I am insufficiently familiar with the battlefield lines in France to know
whether Big Bertha was firing on a north-south or an east-west axis, but accuracy
was never a matter with those items, any mnore than with their direct descendant,
the V2. Which is how I came to be researching it earlier this year.
Here is a comment from the secretary of the Smithsonian, supporting a Goddard
rocket proposal in World war I. He suggested that a budget of $50,000
would allow Goddard to produce bombs that might travel 100 miles. With war
fever morality, he wrote:
"The lateral aim I should think would be good, but the under- or over-shooting
of the target quite probable. However if it were desired to destroy the Krupp
works at Essen a large number of trials with different probable ranges might
probably accomplish it from the French lines by means of Goddard's invention,
provided the Allies were as willing to disregard the rights of noncombatants
in Germany as are the Germans to murder noncombatants everywhere."
In other words, he was urging a course of action rather like that of the
German use of the V2 a generation later - except that the German were not
aiming the V2 for anything other than cities and ports, given their limited
accuracy. Of course, the Germans themselves had no such qualms, and on March
23, 1918, they brought in what they called either Lange Max or Wilhelm Geschutz
(William's Gun), but generally known as "the Paris Gun", or confusingly, as
"Big Bertha", a name that really belongs to a different gun.
The true "Paris Gun" 34 metres long, and had a range of about 130 kilometres
- big enough to fire from behind the German lines into Paris, though with
absolutely no accuracy. Not that this mattered, because like the later V2,
it was intended to destroy morale. Between March and August, 351 shells were
launched, killing 256 people and wounding 620, enough to make people angry,
but probably not enough to sap morale.
Like the guns on November 11, 1918, I am about to fall silent, as I have
an edited ms to work on -- the quote above has been flogged from it.
Like the guns, I'll be back.
John Winckle added:
Aeroplane navigation (inertial) has to take into account the rotation speed
of the earth at the take off point relative to the destination.
David Dixon replied:
A more interesting thought , rather than corrections for these large land
based guns, would be the corrections necessary for the large guns on battleships.
These could fire a projectile weighing up to 1 tonne a distance of 40km.(the
18inch guns on the Yamamoto) Whether they were firing North-South or East-
West was dependent on the disposition of the two combattants, which would
both be moving at a reasonable rate of knots at the time. They also had to
take other factors into consideration, such as wind speed at various levels
in the atmosphere, as the shells at the top of their trajectory could reach
over 25000ft.
In comparison, hitting a target like Paris, which doesn't move very much,
would be relatively simple.
Donald
Lang posted:
I must
be missing something.. A shell that travels 85 kms - neglecting friction - would be expected
to reach a maximum height of around 21 km. On a flat surface, more assumptions,
the up time and the time coming down would each be around 65 seconds.
With the assumptions I stated, maximum range is attained by aiming 45
deg above the horizontal. I have no simple rule to decide how to modify
things slightly for friction and curvature of the earth. Going to a nine
minute flight, 4and a half up and thse same coming down, sounds major. Is
there an easy way to understand what has been
modified,
and how?
Steve Berry replied
This was from a book about WW1 read many years ago and as Peter pointed
out containing some fundimental errors.
Peter
replied:
>In
comparison, hitting a target like Paris, which doesn't move very much,
>would
be relatively simple.
I thought the
whole idea was to make Paris move with the gun -- or at least to make the populace
move . . .
The V2
had an accuracy of about 1 km, the V1 was even worse, owing, I seem
to recall, to
some clever misreporting of strikes that fell short as spot-on -- one of the
advantages of having 'turned' the other side's networks.
David Maddern responded:
Could it be that Paris wasn't at maximum range for the charge they used.
In which case it would be a shallower trajectory
Another point of inaccuracy with (field) guns.
The barrel has to be calibrated every now and then. This determines
the elevation that that particular barrel must be laid at.
However laying the gun in the field is done on mechanisms on the gun, so
the relationship between the calibrated elevation and the theoretical elevation
the gun must be set at to correct for firings diverges.
Also the rifling in the barrel is inscribed on the shell in a brass or copper
band as it is forced out the barrel
And the ambient temperature, or if the gun has been fired lately, will make
the barrel a different diameter, supplying more or less 'choke'
The charge bags may have different humidity and will be filled within a
range and unlikely to be precise every time. And then there is the
age of the chordite.
Probably not finally the gunner responsible for getting the bubble between
the lines on the elevation of the barrel has to contend with the swing of
the barrel laterally as the bearing is applied by someone else, so has to
contend with his bubble moving after he has the right elevation set, so has
to centre the bubble. Depending on the urgency, nervousness, fatigue, sleeplessness
etc he might set it on a "running" bubble, assuming its end point in an oscillation.
And then there are elevation issues with the target.
So while the bearing is fairly easy to obtain (modified by the spin of the
shell, and the relative position of the gun to the local aiming from point
) range is far harder and when suprise isn't called for typically one gun
will bracket the target with ranging shots and a forward observer will call
back modifications to the target information to get within an area before
all the guns are brought into bear.
Of course, if one's target is as big as Paris.....
C'est la Guerre
Peter
commented:
>
The barrel has to be calibrated every now and then. This determines
the
> elevation that that particular barrel must be laid at.
Don't
blame me if I am wrong, but I seem to recall that the Paris gun actually
lost the inside of the barrel on each shot, so rounds of increasing calibre
were used. I certainly read that, but cannot guarantee which gun it
was -- and I can't give you a source. I suspect it was Peter Mason.
David Maddern replied:
Presumably they made such a big barrel as a laminate Casting it would
be a bit unsafe with catastrophic failure the price of an imperfection That
would explain the delaminating of the inside.
David
Dixon responded:
According to
my reference, ("Boys Own Annual, 1915) the barrels of these large guns, such
as large calibre naval guns etc were constructed in three parts.
The inner
part of the barrel was cast metal which was hammered, then shaped,bored
and rifled to the correct calibre on a large lathe/boring machine. This inner
blank was then wound with miles and miles of high tension steel wire, like
winding cotton onto a bobbin. Another cast, hammered blank was then bored
to the corrct dimensions and heated, causing it to expand. The previous cast
and wire wound inner barrel was then slid into the heated outer barrel which,
on cooling contracted around the inner.
Donald Lang wrote:
From: "David Dixon"
Picking up on just one point.
** Whether they were firing North-South or East- West **
This should not affect the coriolis corrections. It is easier to picture
a coriolis effect on a projectile heading directly north or directly south.
The effect is present however and of the same magnitude on the East-West flights.
(Best estimate - a couple of pages of kinematic calculations. It may be easier
if you learned spherical trig in your preschool! I didn't.)
Connecting up with Foucalt and his pendulum: Imagine sitting outside at
night a long way from a city and without cloud. (The last bit is easy. Clouds
are only certain to appear if there is a meteor shower predicted.) From
Australia the stars 'move in circles' about the direction corresponding to
the Earth's axis. Some dip below the horizon. Some do not. At the pole they
all go round at the same angle above the horizon all night. At the equator
all the circles dip below the horizon. If you are not claiming the stars are
moving, you have to say what the Earth is doing underneath you to produce
these patterns. At the pole, it is rotating under the sky. At the equator
it is moving from west to east under the sky. In between you can describe
what it is doing by combining a bit of each. It is the rotating bit that is
demonstrated by the Foucalt pendulum, and which requires the coriolis corrections
to aiming of guns. The west to east bit of motion underfoot does not complicate
matters.
and:
One more "just one point".
Over and above the coriolis effects that change the direction in which you
should aim, there is an east-west effect on the range of a projectile. Obviously
if you fire east, the surface is dropping away below the projectile. Midway
on a flight it is further above the surface than it would be without the earth
rotating. It is going to travel further. Similarly if you fire west the ground
comes up to meet the projectile and the range is shortened..
In a limit to consider a kick to the east that will put a satellite into
orbit needs not to be as big as the one required to send a satellite into
an orbit going westward.
Kevin Phyland added:
>Y'know, the effect
that has water spiralling down drains when uninfluenced
>by other forces clockwise
north of the equator and anti-clockwise south of
>the equator?
Coriolis effect would only normally
manifest itself (at a considerable distance from the equator) on meso-scale
systems...(i.e. > 1000 [kilo?]metres) ...
having said that...I do recall an experiment that sh(e)wed that water could
go down the plughole in a ten-metre vat if it was left for a couple of weeks
and allowed to drain VERY slowly...
apropos of that...it is the major influence on tropical disturbances such
as eventual tropical cyclones (such as "Zoe" I'm told!) as it allows low shear
convective systems (on the order of hundreds of kilometres mind you) to organize...
Finally,...since I don't know Peter very well I have to say that *perhaps*
he didn't know how when quoting "ex cathedra" that it could only have come
from a bloke like him...my Catholic upbringing still recalls the quote "...ex
cathedra...From the chair of Peter"!
I hope his hubris doesn't extend to bunging that on his letterheads!
<BIG GRIN>
and three days later posted a
"last word" on the subject"
So on Wednesday January 9th, 2003, quoting from
a much earlier SMH "Good
Weekend"
Mythconceptions
On the downward spiral
Dr Karl S. Kruszelnicki tackles life's myths, curiosities and absurdities.
It's often said that in the Southern Hemisphere, all cyclones, whirlpools
and spiralling garden vines turn clockwise, as does water the minute it hits
the sides of toilet bowls, bathtubs or handbasins. This might be easily observed
with cyclones (whose northern counterparts go anticlockwise), but it's much
less obvious on the domestic front. The supposed force behind these phenomena
is the Coriolis Force, named after Gustave-Gaspard Coriolis, who first described
it in 1835. The force, generated by the spinning of the Earth, is zero at
the equator, strongest at the North and South Poles and affects anything
that moves across the surface of the earth, from hurricanes to golf balls
to bullets.(Even Tiger Woods might have to allow for it when teeing off on
an Australian golf course.)
But a toilet or handbasin is, of course, much smaller than a hurricane. The
Coriolis Force on such a small body of water is about 10 million times smaller
than the pull of gravity. The rotation effect is so small that it appears
to be vastly overruled by the direction at which the water enters. However,
under the right conditions - and with patience - it is possible to determine
the hemispheral spin, as did Ascher H. Shapiro in 1962 at MIT in Massachusetts,
an experiment repeated in 1965 by Lloyd Trefethen at the University of Sydney.
Shapiro had a very shallow dish about 2 metres across and 150 millimetres
deep. The outlet hole was about 9 millimetres across. He added the
water through a hose, deliberately swirling it clockwise. He then covered
it with a plastic sheet, and let the water stand for 24 hours, to reduce
the initial rotation of the water. He placed a small floating cork on the
water, and then
released the stopper plug.
The water took 20 minutes to drain out, with no visible rotation for the
first 12-15 minutes. Then he could see the cork begin to spin anticlockwise
- slowly at first, then gradually increasing to one rotation every four seconds
by the end. Shapiro wrote in Nature magazine: "When all the precautions described
were taken, the vortex was invariably in the counterclockwise direction".
The University of Sydney team used very similar apparatus, but, being in
the Southern Hemisphere, got consistent clockwise rotations.
As for those vines, as any gardener will tell you: every which way but loose.
