Preheat oven to 325°F. Beat egg whites in a large bowl with an electric mixer fitted with a whisk attachment on high speed until foamy, about 1 minute. Add water, cream of tartar, and salt; beat until soft peaks form, about 2 minutes. Add sugar 2 tablespoons at a time, beating until stiff peaks form, about 2 minutes. Sprinkle and gently fold flour into egg white mixture 1/4 cup at a time. Fold in vanilla and almond extracts.

Pour batter into an ungreased 10-inch tube pan, spreading evenly with a spatula. Bake in preheated oven until cake springs back when lightly touched, about 45 minutes. Remove from oven, and turn pan upside down. Let cake cool, upside down in pan, 40 minutes. Remove cake from pan.