the difference between rim shots and regular strokes doesn't have as much to do with the torque as you might think.
rim shots have to do with physics of sound, i.e. sound waves. the sound waves are a combination of sine and cosine functions. The resonation of the head and the rim are opposite functions. The louder sound is caused by the two waves intersecting.
basically the head resonates as a sine function and the rim resonates as a cosine function.
now that was all an example. I’m not sure if a snare drum head resonates in a sine function or a cosine function. I'm a history major. I got a c in physics so you have to understand I’m in no way a leading expert. From what I understand about the subject this sounds right.

the type of wave should be null.
they both have the same shape, a cosine wave simply leads a sine way by 1/4 of it's cycle (or technically, a 90 degree phase shift).

OH my god so many people are saying so many wrong things.

First of, I don't know exactly why rimshots sound different, but I think it has to do with the slight additional tension produced around the part of the rim where your stick hits, and the way in which that tension propagates throughout the drum-head, intersecting with the waves produced from the bead of the stick.

Anyway the main thing I wanted to point out is that TenorTones' post didn't make any sense, because if I'm reading it right, the stick would have to have a sort of "hinge" right where it strikes the rim in order for angular momentum to be recalculated...

Also, I kinda dig the idea of the rim producing a sine wave, and the head producing a cosine wave, but of course any wave can be represented as a unique sum of sin and cos waves, so it doesn't really make much sense to say that. I think you might have meant that they have different frequencies or something?

It does make sense to talk about the difference between sine and cosine when we're talking about the interference between them...For example, a pure sine wave transmitted through the same medium at the same time as a pure cosine wave, will appear as nothing at all, because their troughs and peaks will exactly cancel. However, a sine wave and a sine wave being transmitted simultaneously, will seem like one big sine wave, with twice the amplitude.

Anyway, hypothesize on y'all, but I do think I remember UNCGQ requesting "don't be stupid." (to paraphrase)

You are right. There is no real difference between a sine and cosine wave other then their orientation. What i was trying to illustrate was that each wave has a different progression that when combined create the distinct noise of the rim shot.
It all comes down to how the frequencies of each vibration(the head and the rim) play off each other.
I’ve done the best I can with out any real education in physics of sound.
If you want to learn about drum harmonics and such check out:
http://www.tabla.com/tablaph1.html
http://www.biowaves.com/Physics/Drums/DrumVibrationalModes.cfm
http://hep.physics.indiana.edu/~rickv/Standing_Sound_Waves.html

One slight error correction to my previous post is in order:
Sin and Cos don't cancel each other out when added--they actually create a new wave with the equation: y=sqr(2)*sin(x + pi/4).
Sorry for the misunderstanding, but I was just trying to point out that a "sine" wave and a "cosine" wave could cancel each other out if they were shifted properly...e.g.
consider the addition:
cos(x) + sin(x - pi/2)

Anyway, these points are neither here nor there, and my errors should be attributed from posting late at night and from an "elevated" or "lofty" position, if you catch my drift.

Cool links Bismark! You aint as dumb as you look! (just kidding)

I hate physics....

Tbone, yeah, thats kinda what I was trying to get at. The rim sort of whips the tip of the stick around due to all the stuff I just explained, and there is an increase in the force producted through contact. Drumsticks (as do all objects) have the ability to bend or shift slightly without breaking. So, I dont quite see why you believe my entire hypothesis to be completely incorrect. If you look, his question was "why is a shot louder then a regular stroke," and my hypothesis seems to fit and work...however, I may be wrong. I just want to know WHY I am so wrong and why I make no sense.

The recalculation of torque/moment at the rim has little to do with the loudness of a rimshot. If that was the only thing necessary, a drum without a shell (like a remo legato top section, or an HTS/ffx with the shell removed) would sound just as loud as a normal drum. This is not the case.


The actual loudness comes from several aspects working together, but here's the main things:

#1 -- People hit rimshots harder. This is the biggest reason, actually. Hit a rimshot at a normal velocity/height, and it's not really significantly louder. You just hit louder most of the time.

#2 -- Emphasis / deformation of primary drumhead mode. The primary mode of vibration for a drumhead is a full-membrane concentric ring. In other words, the entire head moving up and down as one. This is where almost all energy is exhausted. The much higher energy of this mode compared to the higher order modes is why most drums don't produce a discernable pitch (the drums that have this mode at least partially muted -- i.e., a tabla by the paste in the middle of the head, or a timpani by the shape of the bowl -- can produce real pitches). When you hit a rimshot, you partially deform the head, as the rim moves down slightly under your stick. This deformity causes what used to be a relatively simple movement (head moves up and down like a trampoline) to a complex movement (different parts of the head moving at different rates). This makes the tone more complex, which we perceive as a "fuller" sound. This explains two other phenomen exhibited by rimshots:

a- the difference in sound between die-cast, triple flanged, single-flanged, wood, etc. hoops. The more deformity allowed by the hoop (the less stiff the hoop), the "richer" the rimshot will sound

b- This is part of the reason why a ping sounds thinner -- the point of deformity is farther away from the impetus of force on the stick, which causes less deformity to the rim/head

#3 -- The shell resonance. This generally is negligible at tensions used by marching drums, but you can definitely hear a difference on drumset drums between a rimshot hit on a steel shell versus a wood shell. I would imagine that the woodshell of a marching snare imparts some degree of richness to the sound, even if most of it is several octaves below the perceived "pitch" of the drum. This gives the "woody" sound to the rimshot.


The effect of constructive interference is most likely negligible, due to the large difference in relative tensions / vibration speeds of the different materials. Even if they were close enough to create interference, the extremely complex waveform of a vibrating membrane would be just as likely to create destructive interference, which would reduce the total sound output.


Phew.

Okay, I think that's all the ideas I have floating around in my head. It's been a while, but I had a fair degree of training in musical acoustics, and TA'ed a class on it in college.


bp

Cool post project, seems to make sense to me...How did you figure this out?

I agree with tbone. That's an interesting explanation (with many things I never even thought about).