Hikerduane, Trailrunner is correct. For day hikes, the no-show permits are declared at 2 PM the day BEFORE. For overnight hikes, the no-shows are declared at 11 AM on THE day of entry.
Please visit the WhitneyZone site and click on the Wilderness Permit Options in the feature topics box. Box 6 of the Wilderness Permit Options
explains the Whitney Permit walk-in process.
But as some people come in the day before, even for the overnight permits, often times their party has fewer people than they have reservations, so those become available right away -- before the no-shows are declared.
Now for other trails
in Inyo National Forest, they all have walk-in quotas held back, and those become available at 11 AM the day before. I am not sure about no-shows, but I think those are maybe declared about 10 AM on the date of entry.
And a note about WhitneyZone.com -- We created the site because the info you find there was no longer welcome at the old site. We need YOUR participation to help it grow and become an actively used site. This year is especially important, so I hope you will join and help by posting questions/answers/etc. It will be greatly appreciated.