I did a little research and found this article by Shirley Corriher. I think next time I bake the cake which called for self-rising flour, I will substitute AP flour and baking powder based on her formula:
For Great Cakes, Get the Ratios Right
by Shirley Corriher
Have you ever wondered how a baker can create a cake recipe from scratch and know that it will work? Unlike a savory chef, who can often use intuition to design a successful dish, a baker must work within defined parameters to produce a cake that will rise, set, and taste the way she wants. Experienced cake bakers would never dream of trying to bake a cake without first “doing the math” to make sure that the ingredients are in balance. Having the right proportions of flour, eggs, sugar, and fat makes all the difference.
Flour and eggs for structure, fat and sugar for tenderness
In cakes, the protein ingredients, which are the flour and eggs, are the major structure-builders. They’re essentially what holds the cake together. Fat and sugar do the opposite; they actually wreck or soften the cake’s structure, providing tenderness and moisture.
If you have too much of the structure-building flour and eggs, the cake will be tough and dry. If you have too much of the moistening, softening fats and sugars, the cake might not set. It could be a soupy mess or so tender that it falls apart.
Bakers have formulas that balance these ingredients so their cakes have the strength to hold together but are still tender and moist. These formulas don’t have to be followed dead on, but if you stray by more than about 20 percent, you may have problems.
There are two sets of formulas: pound-cake (or lean-cake) formulas, which have less sugar than flour; and “high-ratio” formulas, which contain more sugar. The general rule is that high-ratio cakes require shortening, whose added emulsifiers help hold the cake together. You can, however, make successful high-ratio cakes with butter if you aerate the butter by creaming it and if you add emulsifiers in the form of egg yolks. Some bakers even make cakes with olive oil, which contains natural emulsifiers (mono- and diglycerides).
Here are the three formulas for the more popular, sweeter, high-ratio cakes:
Sugar = Flour
The sugar should weigh the same as, or slightly more than, the flour. Remember that this is weight, not volume. A cup of sugar weighs about 7 ounces, and a cup of all-purpose flour weighs about 4-1/2 ounces. So, if we’re building a recipe with 1 cup sugar, we’ll need about 1-1/2 cups flour (about 6-3/4 ounces).
The eggs should weigh about the same as, or slightly more than, the fat. One large egg (out of its shell) weighs about 1-3/4 ounces. If our developing recipe contains 4 ounces butter (or shortening), we could use two whole eggs (3-1/2 ounces). This is a little under, but remember that these rules are flexible, and we’re still within 20%.
Eggs = Butter
But eggs have two parts: whites, which dry out baked goods, and yolks, which make textures smooth and velvety. A yolk from a large egg weighs about 2/3 ounce. One way to balance the eggs with the fat and to get a smoother cake is to add extra yolks. You could use one egg plus three yolks for a total of about 3-3/4 ounces.
The liquid (including the eggs) should weigh the same as, or more than, the sugar. Our recipe now has 7 ounces sugar and 3-1/2 or 3-3/4 ounces eggs. To get the total amount of liquid to weigh more than the sugar, we could add 4 ounces (1/2 cup) of a liquid, like milk or buttermilk.
Eggs + Liquid = Sugar
Proper leavening is also critical. If a recipe is overleavened, the bubbles will get too big, float to the top, and?pop! There goes your leavening, and here comes a heavy, dense cake. One teaspoon of baking powder for one cup of flour is the perfect amount of leavening for most cake recipes. For baking soda (which is used if the recipe has a considerable amount of acidic ingredients), use 1/4 teaspoon soda for each cup of flour. Finally, don’t forget a little salt, about 1/2 teaspoon for a small cake like this. It’s a major flavor enhancer.
Once you have a working recipe, you can test it and start making adjustments to taste. I like baked goods very moist, so I would have started with one egg and three yolks. If I decided I wanted a moister cake, I could bump up the sugar, or I could replace some or all of the butter with oil. Oil coats flour proteins better than other fats and will make a more tender, moister product.
From Fine Cooking 42 , pp. 78