Drum hoops (also called rims) come in three basic flavors: flanged, die cast, and wood. Each have their own pros and cons. So read on to learn the differences and which style appeals to you.
-Flanged Hoops
The most common type of drum hoop used today is a flanged hoop. You'll find different types of metal with varying thickness used. How hard or soft the metal is will have an affect on tuning and ultimately the sound.
Flanged hoops are made by taking a strip of metal and folding it, creating approximate 90 degree bends called "flanges". Modern hoops have three bends and are called "triple-flanged". The folding is usually done by stamping the metal. The stamped metal is then made into a circle and welded. Evenly spaced holes are punched into the metal for the tension rods to pass through (which screw into the lugs!).
Regarding metal type and thickness, it's important to know that thinner metal is more flexible which makes good contact around the head and shell. This is great for cheaper shells since they may be more prone to be "out of round".
Thinner hoops are harder to tune though, but they are preferred on toms since they give a fatter sound. Thicker, stiffer metal is also used in flanged hoops. They behave more die cast hoops (discussed next).
BOTTOM LINE: Flanged hoops are cheaper than the others hoop types and event considered "flemsy", BUT they are great for specific tuning purposes.
-Die Cast Hoops
Die cast hoops are made by pouring molten metal into a mold (or die) that is the exact shape and size for the finished hoop. This results in a thicker and stronger rim than flanged hoops.
WHAT DOES THAT MATTER?
It means that the drum head can be tuned more evenly since it is more responsive through the tuning range with less varied overtones. However, limited flex of the hoop tends to show when the drum shell or head are not completely round, making it difficult to get the best sound out of the drum. Sounds like a two-edged sword eh?
The solid nature of die-cast hoops causes them to resonate along with the shell and head. This causes the drum to have a sharper sound with increased overtones and clarity.
Die cast hoops can be used on one or ALL of your drums. They are often used on the snare alone since the head tends to be harder, giving every strike a sharper sound. That is ideal for a snare, but most drummers don't want that kind of attack on their toms, which is why flanged hoops are popular for toms.
The fun part is trying die cast hoops on different types of drums on your kit to see how the head responds and tone changes.
-Wood Hoops
And now for those beautiful wood hoops. They are constructed in the same fashion as wood shells. The biggest difference is the number of plies (usually 10), and thickness (about 3/4"). You'll find that wood hoops are generally made out of maple wood.
Wood hoops can either be rigid or flexible depending on how they're made. As a result they can take on tuning features of die cast hoops (if rigid) or flanged hoops (if flexible).
An interesting feature of wood hoops is that they absorb much of the vibration and act like an extension of the shell which gives the drum a bright resonance.
FINAL COMMENTS: There are other drums parts not discussed here. These include snare strainer throw-offs, vent holes, screws, washers, and so on. For the purposes of buying or upgrading a drum kit, the two drum parts that you should pay the most attention to are lugs (remember- "low mass") and hoops (mix and match for an improved sound!).