Over the years, I've found that many non-percussionist middle school and high school band directors feel like they just don't know enough about timpani. I know that in the whirlwind semester of percussion methods, a lot of details can be lost between triple paradiddles and which mallets to use on glockenspiel. This list isn't meant to be all-inclusive, but is a good start for those who want to know more!
The sizes of the drums are important to know, not just when ordering replacement heads (although this is important too!), but because individual timpani are often referred to by their size, of diameter in inches (i.e. "for the concert, we'll only need the 29 and 26," or "tune an 'A' on the 29").
Most middle school and high school band programs have 4 timpani, sized at 32", 29", 26", and 23" (less common sizes in school programs are 30", 28", 25", 22"). Advanced programs and colleges will typically have 5 timpani, adding a 20".
Band directors should know the ranges of the drums so they can help students with tuning schemes (knowing on which drum to tune each required pitch in a piece), and also so they can check to make sure that the drums stay in the correct ranges so that all necessary pitches can be reached. All of the ranges that I teach students span a perfect 5th of notes that you should always be able to count on sounding good on each timpano. Each drum should also reach a little higher and a little lower than the given range - maybe even up to an octave - but these are the pitches that you should always be able to tune on each drum.
32": D2 - A2
29": F2 - C3
26": B-flat2 - F3
23": D3 - A3
20": F3 - C4
*If you are a non-percussionist band director and you discover that one or more of your school's timpani are out of range, this is an example of a time I'd recommend calling a professional percussionist to work on the drums.
3. Grip and Stroke
Two of the most common timpani grips are French grip (thumbs facing up, palms facing in) and German grip (backs of hands facing up, palms facing down). As a performer, I use both, depending on the musical situation, but as a private teacher, I always start students on timpani with French grip. This is because one of the most important characteristics of a general timpani stroke is lift, or returning the mallet to the starting position immediately after attacking the head. The immediate lift results in a less "thwacky" sound and more pleasant and characteristic timpani tone. I introduce students to French grip on timpani first because I conceptualize that with less flesh on top of the stick (thumbs only), lifting comes more naturally. Ultimately, I find that developing and reinforcing good habits in grip and stroke is best achieved with consistent, mindful practice and the guidance of a private teacher.
4. Beating Spots
As a general rule for beating spots, I tell students to play in from the rim about 1/3 of the radius of the drum. This means that the beating spot is relative to the drum size. In practice, timpanists adjust their beating spots based on desired sound - moving a bit closer to the center will darken the tone, while moving closer to the rim will create a brighter tone. In the beginning, students tend to have inconsistent beating spots, and especially tend to play too far towards the center on the 23" drum, so it's important to correct and reinforce good beating spots in students' playing. Certain contemporary pieces do call for other beating spots, such as the center of the drum, as an effect.
5. Protecting the Timpani
Just like most of the rest of the percussion instruments in a band room, the timpani should always be covered by half or full drop covers when not in use. The covers can protect the instruments from accidental damage, but just as importantly, keeping the instruments covered shows that they are cared for and not to be played or touched by anyone walking by!
It's also best to attach a sign on top of the timpani covers that says nothing should be placed on top of the timpani, ever. Having others treat the instruments as a table is a pet peeve for many percussionists. It's just best, especially in an educational setting, to insist that nothing is placed on top of the timpani.
6. How to Move Timpani
First, the pedals should always be set in the highest position before moving the timpani. This increases the tension on the head, which decreases the chance of misaligning the head during moving.
Second, the drums should always be moved (pushed or pulled) by the struts, NOT the counterhoop. Again, this will keep the tuning and alignment of the head more intact. Many school timpani have only two wheels, with no wheel under the pedal. On these timpani, either an attachable wheel should be placed under the pedal if one is available, or the pedal must be lifted while rolling the drum. This is a bit awkward whether you walk forwards or backwards, and whichever way the timpani are tilted (sometimes I call this the "duck walk" with students), but lifting the pedal by the struts is necessary. Timpani should always be handled with care and lifted whenever possible over cracks, bumps, or door thresholds.
7. Protecting Timpani Mallets (and Bass Drum Beaters, too!)
Whether a school band program provides sticks and mallets, or requires students to purchase their own, it's important that students know how to care for felt mallets (in many programs, felt timpani and bass drum mallets are destroyed annually!). First, felt mallet heads should be touched as little as possible. I find that idle percussion students holding mallets during rehearsal tend to touch, rub, and pull at felt mallets to no end! This gets dirt and oil on the mallet and causes the mallet to wear out faster. Felt timpani mallet heads and bass drum beaters shouldn't be touched except when absolutely necessary. Mallets should also always be stored in a plastic bag, either in the original bag, or in a small sandwich bag that is twisted between the mallet heads.
I hope these timpani basics are helpful to my band director colleagues and music education majors! Questions and feedback are welcome.