I find it fascinating that something like cooking oil can be turned into fuel. I know it can't have that energy density off the bat. So what do they do to make fuel for cars? Do they have to add other ingredients, and if so, why?
Where you go wrong is in thinking that cooking oil has less energy density than biodiesel. The Wikipedia page for biofuel energy content list a number of different types of fuel. Along with a long list of other fuels, it lists the following:
Fuel Type Specific energy (MJ/kg) Energy Density (MJ/L) Methanol 19.9 – 22.7 15.9 Fat 37.656 31.68 Sunflwr oil 39.49 33.18 Olive oil 39.25 - 39.82 33 - 33.48 Biodiesel 37.8 33.3 – 35.7 Diesel 48.1 40.3
As you can see, both the specific energy (MJ/kg) and energy density (MJ/l) are about the same as biodiesel and close to those of ordinary diesel fuel. To convert the oil into biodiesel, some methanol is usually added, but that does not increase the energy density.
The OP is correct in the statement that cooking oil does not quite have the energy density of regular diesel fuel. On an energy per volume basis, vegetable oils have on the order of 3/4 of the energy available for combustion as does regular diesel fuel. But that's OK, particularly if it were not going to be reused or recycled in some other way.
There one problem with the physical characteristics of vegetable oils, namely that they are too viscous to use unmodified in most stock diesel engines. That leaves two possibilities: 1) modify the fuel or 2) modify the engine.
1) When the oil is modified so as to be used in a standard diesel engine it is called biodiesel fuel. According to this Wikipedia article:
Biodiesel refers to a vegetable oil - or animal fat-based diesel fuel consisting of long-chain alkyl (methyl, ethyl, or propyl) esters. Biodiesel is typically made by chemically reacting lipids (e.g., vegetable oil, soybean oil, animal fat (tallow)) with an alcohol producing fatty acid esters.
Biodiesel is meant to be used in standard diesel engines and is thus distinct from the vegetable and waste oils used to fuel converted diesel engines. Biodiesel can be used alone, or blended with petrodiesel in any proportions. Biodiesel blends can also be used as heating oil.
The National Biodiesel Board (USA) also has a technical definition of "biodiesel" as a mono-alkyl ester.
2) If the vegetable oil is not converted to biodiesel fuel, then it will be too viscous to form a fine enough mist in the engine to ignite. The simple solution here relies on the fact that viscosity is a function of temperature. So, the mechanical solution is to simply add a pre-heater to the fuel line to heat the unmodified oil such that it's viscosity will be low enough to form a fine enough mist to ignite, and no further modification is necessary.