In this section an analysis of the kick drum mallet movement is performed using a high speed camera, a tiny Qt application and some basic vector math.

Two types of analysis are performed:

• A single hard kick drum stroke.
• A series of strokes at high tempo.

These two types of strokes are the result of very different playing styles and should cover the most basic uses of the kick drum in metal music.

The experiment was performed on an Axis Longboard pedal only, but should for good measure be performed on other types of pedals too.

A movie was made with 200fps and the 10-20 frames containing each of the two stroke types were subtracted. A couple of examples can be seen here (click to enlarge):

Note the white dots on the center-of-axis as well on the mallet. These were added in order to be able to identify their exact position in the frame.

A plot of the angle velocities reveal a rather 'jaggy' picture:

The graph of these angle velocities show a picture rather more 'smooth' than the one rendered from the single stroke:

The maximum angle velocity was found in the single stroke and was 2061 degrees per second. That the maximum angle velocity should be found in the stroke type is not surprising since a single stroke is the result of the hardest foot impact on the pedal.

If we assume the target latency to be at most 1ms and we assume that the software is responding in the area of microseconds we can estimate the target ADC resolution.
Lets start by pointing out that since the video framerate was 200fps each frame represent a state in 5ms intervals; ie. we are looking for something around at least 5 times more accurate.

The single stroke took 11 frames in total which is 55ms and during this time the mallet moved 61.4 degrees, resulting in a minimum resolution of 1.12 samplings per millisecond.

However, if we look at the diff in the last two velocities before the impact it was 10.3 degrees in 5ms it is evident that the minimum resolution should be higher, namely 2.06 samplings per millisecond.

Ergo: A sampling of 2kHz should be sufficient.

However … the result of this mechanism is the playing of a sample at probably 44.1kHz or 48kHz and in order to avoid phasing problems when mixing with the analogue drumsound it should be considered to make the ADC samplerate 44.1kHz or 48kHz as well.

Lets again look at the highest angle velocity and extrapolate the number of sample values needed to describe each of the in between steps with a minimum step range of 1ms.

Between the last two frames (5ms) there are an angle diff of 10.3 degrees, ie. 2.06 degrees in the last millisecond before impact. If we divide the entire 84 degree (maximum angle span observed in the stroke sequence, not the single stroke) interval into 2.06 degree segments the result is a minimum of 40 steps.

Ergo: A bit precision of 6 should be sufficient.

However … since we cannot assume that we will work within the entirety of the bit span of the ADC it should be noted that the 6 bit precision is the used number of bits for the mallet swing and a substantial amount of headroom should be added in order to match different spring types and tensions. How much 'substantial' is in this case I am not able to evaluate in this article.

Since this experiment has not been performed by the fastest or hardest hitting drummer in the world, or the most latency sensitive one for that matter, we should increase both samplerate and bit precision in order to make sure all drummers are covered.

If say the drummer hits twice as hard (double the angle velocity) and cannot accept latency at more than 0.1ms the calculations from above will be:

Samplerate: 20.6 degrees in 5ms = 40kHz sampling (still considering 44.1kHz or 48kHz to avoid phasing problems)

Bit precision: 80 steps = 7 bit precision + headroom.