Jerk limitation part 2

Concern about interpretation

It is relatively straight forward to define and apply limits on Jerk when we work with an idealised linear acceleration profile.However, as soon as we consider a non-linear acceleration profile, the interpretation becomes much more complex.

• In the graph above, the linear acceleration curve has a constant jerk of 650 g/s.
• For the non-linear acceleration curve, it is not possible to assign a single, meaningful jerk value: jerk varies continuously over time.
• This immediately leads to the idea of looking at jerk values over a time window, for example: “average jerk over 5 ms” or “peak jerk in a given interval.”

Discussing jerk over a duration essentially brings us back to a concept similar to acceleration: a rate of change measured over time. In short, “jerk during a time window” becomes another form of acceleration, raising the question of what additional insight it offers over time-acceleration analysis.

Additional concern: at which G level does jerk matter?

• Looking at these two curves, in both cases the maximum G is the same, and the pilot is exposed to the same jerk values , just the order is reverse.
• This raises a deeper question: should we consider the G level at which a given jerk is applied? In other words, does a jerk of 1000 g/s have the same effect at 10 g as it does at 40 g?

I do not know the answer to this question, and I suspect it is highly technical and depends on detailed biomechanical modelling of the spine and soft tissues. It is another example of how jerk is difficult to interpret in a clear and practical way for real-world impact protection.

Concern about mathematical complexity

Our acceleration signal is inherently noisy, and jerk is the time derivative of that signal. This means that when we compute jerk, the noise becomes much more prominent. I have already discussed this point int he previous document.

A common technical solution is to filter the signal before taking the derivative. In practice, the processing chain often looks like this:

Raw acceleration signal → Low-pass filter → Derivative (jerk)

Each step adds extra parameters and choices, which significantly increases the complexity of the evaluation.

Filtering choices

For example, when we decide to use this filter:

Butterworth low-pass, zero-phase (filtfilt), order = 1, cutoff = 150 Hz

we are already making several hidden choices:

• Filter family: we choose a Butterworth filter (it could have been Bessel, Chebyshev, FIR, etc.).
• Filter type: we choose a low-pass filter (it could have been high-pass, band-pass, or band-stop).
• Phase behaviour: we choose zero-phase filtering using filtfilt (it could have been a standard one-pass filter with phase distortion).
• Filter strength: we choose an order = 1 design (we could have chosen a stronger or weaker filter by changing the order).
• Cutoff frequency: we choose a cutoff at 150 Hz (a higher or lower cutoff would keep or remove more of the signal).

Derivative (jerk) computation

In the same way, when we decide to compute jerk with:

Savitzky–Golay derivative, polyOrder = 3, deriv = 1, window = 15 ms

we are also making several arbitrary choices:

• Method: we choose a Savitzky–Golay filter (we could have used a simple finite difference, spline derivative, or other numerical method).
• Polynomial order: we choose a 3rd-order polynomial (we could have used order 2, 4, etc., which changes how “smooth” or “wiggly” the curve becomes).
• Type of derivative: we choose the first derivative (deriv = 1), which gives us jerk in units of G/s.
• Time window: we choose a window of 15 ms (a shorter window is more sensitive to noise, a longer window smooths more but hides details).

Each of these choices affects the final jerk signal and can change the result in a non-negligible way.

In total, these choices add 5 to 10 parameters that directly affect the final jerk signal. Jerk becomes harder to interpret and very sensitive to the chosen processing chain, which is a poor basis for clear, comparable, and repeatable metrics.

If this arbitrary choice simply shifts all values in the same direction, it is not a big problem, because our comparisons are relative. But can we be sure there are no side effects? Can we be sure we can find a set of parameters that does not favour one type of protection over another without injuries reality? Will the same settings behave the same way on all test rigs, with different instruments and sampling frequencies?
We don't know if this given arbitrary choice of filter is going to result in a system that would classify pertinently shock absorbtion devices.

cutoff_list = [50.0, 100.0, 150.0, 200.0]   # Hz for Butter
order_list  = [1, 2, 3]                     # Butter order
window_list = [11, 21, 31]                  # samples, must be odd
poly_list   = [2, 3]                        # Savitzky–Golay polyorder

My view on jerk

Jerk does not directly cause bone fracture.
Bone injury is driven by mechanical stress from forces, those forces are given by F = m · a. Human tissues bring some damping this is why the duration as to be taken in consideration as well. Because this loading is time-dependent, the entire acceleration–time history matters; in a first-order description, the key variables for injury and protection assessment are therefore the acceleration G and the duration of high-g phases.

I agree that a lower jerk value is preferable only when the main loading parameters are the same: same peak acceleration (peak G) and same duration of the high-g phase. Once those are fixed, jerk becomes a secondary descriptor of how quickly the load is applied and removed, and can help distinguish between shocks with very similar acceleration–time histories. In paragliding, however, we are not yet at the point of routinely comparing such fine details; we first need robust, consistent descriptions of impacts in terms of G versus time.

My concerns about using jerk

• Jerk alone is almost useless for the pilot. It must be accompanied by other information, especially the maximum G and the duration spent at different G levels. This extra complexity makes it harder for users to understand and choose a protection.
• Computation relies on arbitrary choices. Even if jerk is mathematically computable, in practice it requires a lot of artificial or arbitrary decisions (filtering, sampling, windowing, etc.), and these choices have a significant impact on the result.
• It can be counter-productive. Pushing for a low jerk value tends to favor longer impacts. A longer impact at a given G level increase the risk of injury.

My preferred approach

I clearly favor a time-based approach instead of focusing on jerk. At the moment, two ideas look particularly promising:

• Dynamic Response Index (DRI): a dimensionless value that estimates the risk of spinal injury from a vertical shock load by calculating the maximum compression in a simplified spine model (mass–spring–damper), whose motion is governed by a second-order ordinary differential equation.
• Spine injury Criterion (SIC): the approach currently being developed by WG6. It integrates the acceleration over time with weighting coefficients and can be directly linked to the Eiband study.

In the current EN system the pilot need to look at 3 values ( max_g + 2 durations) to really assess the performance of his impact pad. Both prefered approaches have the advantage of producing one unique meaningful outcome value which makes them simpler for the pilot to compare the performance of different impact pads.

An analogy for a second-order model

To get an intuitive feel for what a second-order model means, here is a simple analogy. As usual, the analogy has its limits.

Imagine you are in a car and you only know the engine speed: the tachometer shows 2200 RPM. Can you guess the vehicle speed?

• We agree that, in general, higher RPM tends to mean higher speed.
• But without knowing the current gear, any speed estimate based on RPM alone is useless.
• knowing the current gear, my speed prediction will be better.
• then of course if you give me both the gear position and the RPM, I can estimate the speed much more precisely.