Viscous Criterion (VC)

Description

The Viscous Criterion combines thorax compression and compression velocity to represent soft-tissue injury loading. WebSAT provides five calculation methods because test procedures differ in how compression velocity is obtained [1] [2] [3] [5].

When this feature is available

VC becomes available when either the current curve selection or any loaded test contains a thorax measurement set that meets the requirements for the selected method. Only channels with a usable data status count.

The required measurement set includes:

• The occupant must not be a Hybrid III 10-year-old dummy.
• The group must contain at least one deflection channel in millimeters attached at the chest, sternum, or an upper/middle/lower rib location.
• If the selected method is SAE J1727 1 or Directive 96/27/EC, the deflection channel is sufficient.
• If the selected method is SAE J1727 2, SID 2S, or SID Method 2, the same occupant group must also contain two acceleration channels with units G'S:
  • For a rib deflection: the acceleration of the same rib, and an acceleration at SPINE - UPPER or SPINE - LOWER.
  • For a chest or sternum deflection: the acceleration at STERNUM, and the spine box acceleration at CHEST. If the test has no CHEST acceleration, WebSAT uses SPINE - UPPER or SPINE - LOWER.

On a Hybrid III dummy, the CHEST acceleration is the spine box accelerometer. So WebSAT uses it only as the spine acceleration, never as the sternum acceleration. A rib acceleration never pairs with the deflection of a different rib.

WebSAT gives one VC result for each rib or sternum deflection of an occupant. For example, a EuroSID with upper, middle, and lower rib deflections gives three results. For the methods that use acceleration, a deflection without its paired accelerations gives no result. WebSAT enables VC if any deflection meets the requirements of the selected method.

Settings

The button's dropdown selects the method. The default is Directive 96/27/EC.

WebSAT option	Method
SAE J1727 1	Differentiate filtered deflection
SAE J1727 2	Integrate chest and spine acceleration separately, then subtract velocity
Directive 96/27/EC	EC deflection/differentiation method
SID 2S	Subtract chest and spine acceleration, then filter and integrate
SID Method 2	Integrate the rib-minus-spine acceleration from onset to peak deflection, with a drift correction

How WebSAT processes the data

1. Validate the thorax channels required by the selected VC method.
2. Convert deflection and acceleration inputs to consistent units.
3. Process compression velocity according to the selected method:
   • SAE J1727 1: filter deflection at CFC 600 and differentiate it.
   • SAE J1727 2: filter deflection and accelerations at CFC 600, integrate chest and spine acceleration separately, and subtract the velocities.
   • Directive 96/27/EC: filter deflection at CFC 180 and use a 0.140 m normalization.
   • SID 2S: subtract chest and spine acceleration, filter the difference at CFC 600, and integrate it.
   • SID Method 2: integrate the difference between rib (or sternum) and spine acceleration from T0 to TmaxD, as described in SID Method 2.
4. Select the method-specific scale factor and chest-depth normalization.
5. Calculate VC at every time sample:

$VC=SF\times\frac{dD}{dt}\times\frac{D}{D_0}$

Here, $D$ is chest compression, $dD/dt$ is compression velocity, $SF$ is the ATD scale factor, and $D_0$ is chest depth or half-width.

6. Find the peak VC and its time.
7. Report the selected method, peak VC, and supporting deflection and deflection-rate histories.

SID Method 2

SID Method 2 follows Appendix B of the side airbag procedure [5]. It calculates compression rate by integrating the difference between rib (or sternum) acceleration and spine acceleration, instead of differentiating the deflection.

1. Filter the accelerations at CFC 1000 and the deflection at CFC 600. Convert the accelerations to m/s².
2. Find T5%, the first time when the magnitude of the rib or sternum acceleration reaches 5% of its peak magnitude.
3. Find T0 by examining the rib or sternum acceleration backward from T5% to the point where the slope of the curve changes sign.
4. Find TmaxD, the time of the largest-magnitude peak in the deflection.
5. Subtract the spine acceleration from the coaxial rib or sternum acceleration. Set the difference to zero at and before T0.
6. Integrate the difference from T0 to TmaxD with the trapezoidal rule to get the compression rate, $CR(t)$, with $CR(T_0)=0$.
7. Check the accuracy. If $|CR(T_{maxD})|$ is 0.1 m/s or less, use the result.
8. Otherwise, calculate the correction $C = CR(T_{maxD}) / (T_{maxD} - T_0)$. Subtract $C$ from the filtered rib or sternum acceleration from T0 to TmaxD, then repeat steps 5 to 7 one time.

The compression rate is defined only from T0 to TmaxD, so the reported deflection-rate history is zero outside that interval. WebSAT stops with an error in these cases:

• TmaxD is at or before T0. This usually means that the deflection and acceleration channels are not from the same rib or sternum, or that the deflection contains a spike.
• $|CR(T_{maxD})|$ is still greater than 0.1 m/s after the correction.

Appendix B defines T0 as the first contact of the airbag with the dummy. In a full vehicle test, T0 is the first contact that loads the instrumented rib.

Reference values and injury risk

ATD	Scale factor	Normalization (mm)
Hybrid III 95th male	1.3	254
Hybrid III 50th male	1.3	229
Hybrid III 5th female	1.3	187
Hybrid III 6-year-old	1.3	143
Hybrid III 3-year-old	1.3	122
SID-IIs	1.0	138
ES-2re	1.0	140
EuroSID	1.0	140

Not every row applies to every method. SAE J1727 supplies ATD scaling, and SID Method 2 uses the same scaling; the EC and SID 2S methods use the normalization defined by the European side-impact requirements [4]. A commonly used VC assessment reference is 1.0 m/s; the cited IIHS rating boundaries are 0.8, 1.0, and 1.2 m/s for good/acceptable, acceptable/marginal, and marginal/poor transitions [3]. WebSAT reports VC but does not report an AIS probability for this function.

Results

The results identify the occupant, calculation method, input attachment, and peak VC. Each rib or sternum deflection has its own row. In a batch summary, the row name includes the attachment, for example VC (RIB - LEFT UPPER). WebSAT also displays the processed VC, chest-deflection, and chest-deflection-rate histories used to calculate that peak.

VC summary table with the reported result and selected method.

Viscous Criterion history and peak response.

Processed chest-deflection history.

Chest-deflection-rate history used with deflection to calculate VC.

References

[1] SAE International. Calculation Guidelines for Impact Testing. SAE Recommended Practice J1727.

[2] Lau, I. V. and Viano, D. C. “The Viscous Criterion—Bases and Applications of an Injury Severity Index for Soft Tissues.” SAE Transactions, 1986, pp. 672–691.

[3] Insurance Institute for Highway Safety. Frontal Offset Crashworthiness Evaluation—Guidelines for Rating Injury Measures, 2009.

[4] European Parliament and Council. Directive 96/27/EC on the Protection of Occupants of Motor Vehicles in the Event of a Side Impact, 1996.

[5] Side Airbag Out-of-Position Injury Technical Working Group. Recommended Procedures for Evaluating Occupant Injury Risk From Deploying Side Airbags, Appendix B: Chest Deflection (Compression) Rate: Calculation by Integration of Acceleration Differences.