The Eclipse, the Eclipse!!

[Anomalocaris]

The bailey beads happen when the limb of the sun stick out from behind the edge of the moon by an amount less than the the height of the topographic variations on the limb of the moon.   Let's say the average topographic variation on the edge of the visible lunar disk is 2kms.   The moon sweeps around the earth at an average speed of 1.02km/s.   The bailey beads phenomenon at the leading and trailing edges of the lunar will last around 2 seconds each, max.

However, on the top and bottom edges of the lunar disk, the motion of the moon is orthogonal to the height of lunar topography.   So bailey beads can last much longer.   The closer you are to the edge of the totality track, the more bailey beads will manifest themselves closer to the top and bottom of the lunar disk rather than the leading and trailing edges of the lunar disk.

Also, keep in mind that although the moon is tidally locked and more or less keep the same face to the earth, the orbit of the moon around the earth has not yet been circularized.  That is why sometimes there is annular eclipse, sometimes total eclipse.   But it also means the rate of lunar rotation is not exactly the same as the rate of lunar revolution at every part of the lunar orbit.   When viewed from the earth, the moon does not keep exactly the same face to the earth during the entire month.   Instead the moon disk appears to be shaking its head and nodding with each revolution abouthe earth.   So during each eclipse, we are not seeing exactly the same topographic features on the limb of the lunar disk.   This means during some eclipse, the edge of the lunar disk might be more jagged, and thus more conducive to making bailey beads, than others.

First, good explanation.

Second, I understand why Bailey's Beads happen, my question is that even if you assume perfect conditions to see the maximum amount of Bailey's Beads it's possible to see at once the maximum would still only last a few seconds because you're on the edge of totality and the further from the centerline of totality the shorter the eclipse experience is.  Right?

For example: In Oregon, McMinnville was just a handful of miles inside the path of totality and they got something like 40 seconds of totality, while 20 miles south toward Salem totality lasted just over two minutes.  If you're on the very "top" or "bottom" edge of totality you'd get seconds of totality and if you're going for maximizing Bailey's Beads around the rim of the moon you'd be on the very very top or bottom edges of totality, so you'd get a handful of seconds of them.

Or am I misunderstanding something?

Is there a circumstance where you could get, let's say, 30 seconds of Bailey's Beads?

Well, assuming the same 2km roughness to the edge of lunar disk.   lunar curvature is about 2 Kms for every 70 Kms.  So the moon needs to move 70kms in its orbit about the earth for the top and bottom of the lunar disk to move up and down by 2 Kms.    So in theory, if you are right on the edge of totality track, the bailey bead phenomenon on the very top or bottom of the lunar disk can last up to around 70 seconds.

The problem is as you pointed out, totality doesn't last that long at the edge of the track   In principle, you can have bailey beads on the top and bottom of the lunar disk even when the eclipse is not quite in totality, because the limb of the sun at top and bottom may only shine through gaps in lunar terrain at the top or bottom of the disk, but other parts may already emerges from behind the lunar disk at the leading or trailing edge of the lunar disk.  But in reality in such circumstances the bailey beads will be lost in the glare of the part of the sun not in eclipse.

So the longest visible bailey bead phenomenon is limited by the length of totality.   So during a total eclipse, the length of bailey bead phenomenon will get shorter as one approaches the center of totality track, while the length of totality will get shorter as one approach the edge of the totality track.   The longest bailey bead phoenomeon will be where the two duration curves intersects.