Preheat the oven to 350 degrees.
With a fine sieve, sift together flour and 3/4 cup of the sugar four times.
In the bowl of a stand mixer on medium speed, beat together egg whites and water until foamy. Add salt, cream of tartar, and vanilla; beat until soft peaks form. Increase speed to medium-high and sprinkle in remaining sugar, 1 tablespoon at a time. Beat until stiff but not dry.
Transfer to a large bowl. In six additions, sift dry ingredients over meringue, folding in quickly but gently.
Pour batter into an ungreased 10-inch tube pan with removable bottom. Smooth top with an offset spatula. Run a knife through batter to release air bubbles. Bake for 35 to 40 minutes, until golden brown and springy to touch.
Invert pan on its legs or over the neck of a glass bottle, and let cool completely, about 1 hour. Carefully run a long offset spatula or knife around the inner and outer perimeter of the pan to release cake. Place on a plate, bottom side up; cover with plastic wrap until ready to use.
Just before serving, poke the top of the angel food cake all over with a skewer. Pour glaze over cake and garnish with lime zest.