Coreolis Effect

[arobie]

What is the Coreolis Effect?

 

[mrmorris]

Well -- I'd like to say that it's what causes toilets to flush clockwise in the northern hemisphere and counterclockwise in the southern hemisphere... except that's a myth. The Coriolis Effect is so small that it's only true if the toilets in question were perfectly circular. The shape of the toilet/sink/bathtub determines the direction of the swirl.<br /><br />However -- I doubt that's what you were looking for. In terms of spacecraft, and in particular space stations rotating to create 'artificial gravity' the Coriolis Effect is basically the curving path that items take in flight. If you are standing on Earth, hold a ball centered on your bellybutton and were to drop it -- the ball would hit the ground right between your feet (i.e. straight down). If you were on a space station rotating to create 'gravity' and were to perform the same action -- the ball would trace what would 'appear' to be a curving path (actually it's straight and everything <b>else</b> rotates) and hit the floor of the space station some distance 'anti-spinward'.<br /><br />My favorite anecdote about this is in a book by Joe Haldeman 'Buying Time'. In it, the protagonist is on a spinning space station. He goes into the bathroom and there's a 'bullseye' to the left of the toilet with a note reading 'Aim here, stupid'. <img src="/images/icons/smile.gif" />

 

[arobie]

Thank you mrmorris. <img src="/images/icons/smile.gif" /><br /><br /><font color="yellow">He goes into the bathroom and there's a 'bullseye' to the left of the toilet with a note reading 'Aim here, stupid'.</font><br /><br />LoL! <img src="/images/icons/laugh.gif" /> <br /><br />A question:<br /><br />The further away one is from the center of rotation, is the coreolis effect greater or less?

 

[henryhallam]

The Earth is spinning about the axis which joins the North and South poles. Obviously the angular velocity is the same for all latitudes, viz. 360 degrees per day. (note that this is not the case on Jupiter or the Sun).<br /><br />Now although the angular velocity is the same for all latitudes, the tangential velocity varies. Standing "still" on the equator, in one day you travel a distance equal to 2 * pi * (radius of earth), while at the north pole you travel no distance at all in the same period of time. <br /><br />Therefore, tangential velocity is greatest at the equator and decreases as you go further north. In fact it is proportional to the cosine of your latitude.<br /><br />Now, imagine that you are standing on the equator and you fire a cannonball northwards. Disregard the atmosphere, and we are not interested in the vertical velocity of the cannonball i.e. its altitude.<br />When the ball leaves the cannon it carries a full 460m/s of tangential velocity, going eastwards since the earth rotates from west to east. This is in addition to the northwards velocity which we have given it from the cannon.<br /><br />Time passes, and the ball impacts some distance to the north. During the flight it had a constant 460m/s eastward velocity so in absolute terms (if the Earth had not been spinning) it has moved a considerable distance to the east. But of course the Earth is spinning, so the land on the impact site has been moving eastwards too. HOWEVER, because the impact site is north of the equator, it does not have such a great eastwards velocity as was explained earlier. For example if the impact site is at 20 degree latitude, the eastwards velocity of the surface there is 460 * cos(20) = 432 m/s. So the land hasn't moved so far east as the ball. Therefore, the ball appears to land somewhere to the EAST of the direction it was fired in. For someone in the rotating reference frame of the Earth, there appears to be a mysterious force pushing it eastwards.<br />

 

[arobie]

Thank you henryhallam.<br /><br />Both you and mrmorris are a great help. <img src="/images/icons/smile.gif" />

 

[nacnud]

<font color="yellow">anti-spinward</font>widdershins <img src="/images/icons/laugh.gif" />

 

[nacnud]

<font color="yellow">The further away one is from the center of rotation, is the coreolis effect greater or less? </font><br /><br />I would have thought less. <br /><br />

 

[spacester]

Arobie, when I've referred to coreolis effect, I've been less than precise - using it the refer in general to the weird dynamic effects spin-g will have on folks. Take a look at those 3 links to space.ref articles by Ted Hall in the summary thread. <br /><br />I've used the term 'coreolis effect' to refer to 'cross-coupling'. I wanted to lift a quote from one of those links to illustrate, but couldn't find one that didn't have a lot of math in it.<br /><br />Basically, if you're standing on the floor facing in the same direction as the axis of rotation and you turn to the left, you experience the sensation of pitching forward. Motion sickness ensues. This is the primary reason why the RPM of the spinning habitat needs to be kept below 3 rpm or so.<br /><br /> <div class="Discussion_UserSignature"> </div>

 

[steve82]

When you start getting into mechanics ourses as part of your physics training you will inevitably run into the anecdotal story about the British Naval guns that were missing during some engagements around the Falklands in WWI. Supposedly the British aiming equipment and artillery tables had assumed that all naval battles took place in the northern hemisphere so their Coriolis acceleration correction was in the wrong direction. The German guns took this into consideration. I haven't been able to find any confirmation of this, however, in the historical record. <br />There is another story about the Paris guns in WWI that were dropping shells into Paris and could not be located until a mathematician took the Coriolis acceleration into consideration along with trajectory data extrapolated from a dud that went down through several floors of a building. I suspect in that case uncertainty in their atmosphere models led to more inaccuracy than the Coriolis acceleration.