Preheat the oven to 350°F / 180°C (160°C fan-assisted).
Whip the egg whites and cream of tartar together on low speed for 1-2 minute suntil they are white and frothy.
Gradually turn the speed up to medium-high speed. Don't start with high speed as this will create larger air bubbles which will be less stable and may cause your cake to collapse.
Add the sugar, one tablespoon at a time, letting it whip for about 15 seconds in between each addition to allow it to incorporate fully.
Once all the sugar is added, add the vanilla and whip until the meringue forms firm peaks. This means a peak that droops over on itself into a hook shape. See the post above for an example. Rub a little bit of the meringue between your fingers, it should be smooth - if it is gritty, continue to whip until the sugar dissolves.
Add the salt to the cake flour, then sift the mixture twice - the extra aeration will help give the cake a tender crumb.
Add the flour to the meringue in 3 batches - use the sieve to gently sprinkle the flour into the batter rather than dumping it on top. Gently fold in each lot of flour until it's almost completely incorporated before adding in the next. It's better to have a few streaks of flour than to knock too much air out of the batter.
Spoon the cake batter into an ungreased tube pan. Level it out, then run a skewer or toothpick through the batter a few times to release any big air bubbles.
Bake immediately for 35-40 minutes until the top of the angel food cake is golden brown all over and springs back when lightly pressed. A skewer should come out completely clean.
Remove from the oven and immediately turn the pan upside down. If your tube pan has little feet on the bottom, rest it on those. If it doesn't, place the pan upside down over a wire cooling rack. Let the cake cool completely in the pan.
Once the cake is completely cool, use a spatula or knife to run around the edge of the cake pan to help release it, then give the bottom a few taps and the cake should come out.
Egg Whites - It's best to use fresh egg whites as they will whip up better than carton egg whites. See my post on what to make with leftover egg yolks. Be careful not to get any egg yolk or fat in the whites at all as this will stop them from whipping up.
Cream of Tartar - This helps keep the whipped egg whites stable, which is important for baking. If you don't have cream of tartar, you can use 1 teaspoon of lemon juice instead, but the results won't be quite as good.
*Tube PanIt's very important that your tube pan is ungreased - if you grease it, then the cake won't rise properly, as it needs to cling to the sides of the pan to rise. It is also important to use a tube pan (with a hole in the middle) and not a bundt pan, as it needs the straight sides and bottom in order to rise properly.