# Technical Explanation – Jerk

#### Theoretical description

What is it?

The contraction speed of muscles, and therefore the speed at which they generate force, depends on their length: shorter muscles, other factors being equal, contract faster. However, shorter muscles often tend to be smaller in cross-section and so generate smaller peak forces than the large locomotion and lifting muscles in the body. Even these large muscles, when contracting at their highest speeds produce lower forces: fast-changing forces tend to be smaller. As acceleration is just mass-specific force (from F=mA), every muscle contraction, in principle, generates a signal that can be sensed by a body-mounted accelerometer. However, in practice the accelerometer output is dominated by (i) gravity acceleration, and (ii) the large accelerations generated by the contraction of large muscles. This means that it can be hard to detect events that involve more rapid muscle movements in the accelerometer data stream. Such rapid muscle movements could be associated with strikes at prey, ingestion, predator detection and avoidance, sound production, breathing, heart-beat and many other important activities that we would like to detect reliably. Calculating the jerk is a great way to emphasise these smaller-but-sharper components in the accelerometer data (Johnson et al., 2004).

In physics, jerk is the differential (i.e., the rate of change) of acceleration and has units m/s3. Taking the differential emphasises the fast-changing parts of a signal and de-emphasises the slow-changing parts. Applying this to the accelerometer data, computing the jerk suppresses orientation changes and steady movements such as locomotion while boosting faster transient movements of typically smaller muscles. The jerk is computed on each axis of the accelerometer separately, giving separate jerk signals in the longitudinal, transverse, and dorso-ventral directions. These can be useful for some analyses but it is often simpler to combine these into a single signal, the norm-jerk, which represents the magnitude (or norm) of the jerk in any direction.

How is it measured?

We can’t directly compute the differential of a sampled signal such as the accelerometer data, but we can approximate it with a first-order difference, i.e.:

Jt = (At – At-1)fs

where At is the accelerometer vector at time t, At-1 is the vector at the previous sampling moment, and fs is the sampling rate in Hertz. If At is in m/s2, then Jt is the jerk vector at time t with units m/s3.

The norm-jerk is just the vector magnitude of Jt, i.e., the square-root of the sum of each axis squared:

jt = ||Jt|| = √(Jt,x2+Jt,y2+Jt,z2)

The units of jt are also m/s3. The sampling rates of Jt and jt are the same as the sampling rate of At.

What is it good for?

Jerk is good for emphasizing transient events prior to event detection. Such events include attacks at prey, respiration, flinches and startles, and fast activities such as scratching or sprinting. For example, combining njerk() with `peak_finder()` or `detect_peaks()` can be an effective way to locate prey capture attempts in large data sets. By highlighting these often brief but important activities, jerk can help in behavioral sequencing.

The norm-jerk is independent of the orientation of the tag on the animal, but may be affected strongly by the position of the tag on the body. Stronger jerks are likely to come from muscles that are closer to the tag, and that are not separated from the tag by joints. Therefore comparisons of jerk intensity between animals must be made with care if the tag placement varies.

#### Caveats

Jerk is not generally a good measure of activity because it de-emphasises steady powerful movements such as locomotion. ODBA, VeDBA and MSA are more appropriate as activity measures.

There are no adjustable parameters for jerk but the sampling rate of the acceleration data has a strong impact on jerk (Ydesen et al., 2014). The higher the sampling rate, the greater the emphasis on small-but-rapid changes in acceleration. Sampling rates of 100 Hz or higher can produce excellent clear jerk signals for sharp transient behaviors such as strikes at prey or respirations. However, if there is a frequency above which the acceleration signal is dominated by sensor noise or turbulent flow buffeting the tag (Cade et al., 2018), the sampling rate should be decimated (e.g., using decdc()) prior to computing jerk. The decimation factor is chosen so that the new sampling rate is close to twice the highest frequency at which there is useful data in the accelerometer signal.

#### References

Cade DE, Barr KR, Calambokidis J, Friedlaender AS, and Goldbogen JA. (2018). Determining forward speed from accelerometer jiggle in aquatic environments. Journal of Experimental Biology, January 2018; 221 (2): jeb170449. doi: 10.1242/jeb.170449.

Johnson, M. P., Madsen, P. T., Zimmer, W. M. X., Aguilar de Soto, N., and Tyack, P. L. (2004). Beaked whales echolocate on prey. Proceedings of the Royal Society of London. B, 271, S383–S386.https://doi.org/10.1098/rsbl.2004.0208

Ydesen KS, Wisniewska DM, Hansen JD, Beedholm K, Johnson MP, and Madsen PT. (2014). What a jerk: prey engulfment revealed by high-rate, super-cranial accelerometry on a harbour seal (Phoca vitulina). Journal of Experimental Biology, 217, 2239–2243. https://doi.org/10.1242/jeb.100016