What is the Static Stability Factor?

[MSI]

A simplistic viewpoint is frequently encountered in which the so-called "static stability factor", or T/2H, is cited as the ultimate measure of the rollover resistance of a given vehicle design configuration.

• The static stability factor is, of course, derived on the basis of a rigid body, such as a block of wood or a brick.
• The analytical derivation of the factor assumes a purely lateral motion, without any rotation about a vertical axis (i.e., yawing), on a uniform high-friction surface.

The total static weight is assumed to be supported by the leading edge of the rigid block at the point of incipient rollover.

rollover model.jpg (21.32 KiB) Viewed 11865 times

• Note: Figure from Rollover Analysis: minimum speeds and roll velocity approximation
  includes additional related discussion on rollovers

In an actual highway vehicle which is somehow made to operate at a large sideslip angle on a high-friction surface, the lateral acceleration achieved at the point of incipient rollover ranges (in G units) from approximately 70% to 90% of the calculated value of the static stability factor, depending on design details of the vehicle.
Thus, individual vehicles with T/2H values of 1.20 and 0.94 respectively could have identical lateral acceleration values at incipient rollover, for the cited operating condition, if their design details produced the indicated extremes of performance:
(0.70)(1.20) = 0.84 (0.90)(0.94) = 0.84

The following is an excerpt from 1987 "Safety Issues Related to Mini-Cars from a Roadway Perspective",(11 megs!) Council, F.M., Reinfurt, D.W., McHenry, B.G. Pages 53-56, and Appendix E Details of the HVOSM runs

Vehicle parameters associated with rollover.
While other accident and HVOSM related efforts have examined issues related to roadway parameters, this specific HVOSM effort was designed to further examine vehicle parameters which might be related to increased rollover propensity.

• Past theory has suggested that a critical indicator of rollover propensity is the ratio of the half track width to the height of the center of gravity (T/2H).

The goal of this effort was to further examine this hypothesis and to search for other parameters which might be related to rollover propensity.

• This HVOSM effort involved repeated runs involving eight vehicles ranging in weight from 1699 to 4450 lb (0.77 to 2.02 Mg).
  • While the initial goal was to input a steering maneuver which would put the vehicle in a near-rollover position and to then modify various parameters to determine which were critical, the method had to be modified due to the difficulty of obtaining such a state on a flat area with a normal coefficient of friction.
  • As a substitute, the vehicles were run from the roadway onto a flat, high friction surface and placed in a yawed (nontracking) attitude. The nominal friction value for the test surface was then increased until a rollover occurred. The vehicle parameters were then studied as they changed with this change in critical rollover friction.
  The results indicated that while both vehicle weight and T/2H are related to rollover, there are clearly some other vehicle parameters involved.
  This is most clearly shown by figures 3 and 4 below.

  

  hsrcfig3.jpg (17.23 KiB) Viewed 11865 times

  Figure 3

  

  hsrcfig4.jpg (16.28 KiB) Viewed 11865 times

  Figure 4
  Here, vehicle weight and then T/2H values are plotted against the critical friction value resulting in rollover. If either weight or T/2H was a perfect indicator of rollover, then one would expect a fairly straight-line relationship with very little variability. However, as can be seen from the figures, there is some variability, with both vehicle weight and T/2H deviating from an increasing slope. More pertinent to this effort, the maximum variability is at the lower weight and T/2H values, values pertinent to smaller vehicles.
  
  In a related set of runs, the center of gravity heights were changed in order to give all vehicles the same basic T/2H value. Simulation runs were then made to see if the critical friction factor remained constant.
  • Results here also indicated that for the higher T/2H values (approximately 1.3) the critical friction coefficient for rollover was a constant function of the static stability factor (T/2h). However, for lower T/2H values of approximately 1.1, there was a great deal of deviation in the friction factors, again denoting the fact that T/2H is certainly not the only predictor of rollover potential.
  Additional runs were made involving other vehicle parameters related to roll stiffness, radii of gyration about various axes, and suspension travel.
  • Whereas these analyses indicated a general trend that would explain larger cars having greater resistance to rollover, there does not appear to be any single variable in itself that would indicate why certain vehicles roll at a friction coefficients which are 65 to 70 percent of their static stability factors while others roll at 90 percent of their static stability factors.

Thus, the test runs have indicated that while T/2H is certainly related to rollover propensity, it is not the sole indicator of the vehicle's propensity to roll.
There exists an inherent resistance of vehicles to roll which must be a function of certain other vehicle parameters which are yet to be defined.
The results of these HVOSM analyses were then utilized in the development of research plans.

[MSI]

June 2021:
On the NAPARS Facebook page Wade presented some tips for easy measurement of track width.

Please see the NAPARS facebook page topic: Track Width Discussion

Track width.png (147.53 KiB) Viewed 1759 times

And it included a link to this McHenry Forum topic (Thanks Wade!)

In reviewing the topic we wanted to add that there are obvious limitations to a simulation study particularly as related to design.

• For this 1987 study we simply changed the CG height dimension and other items of interest without actually having to see what's involved in the vehicle design to actually accomplish the design change in the specific vehicle.
  • The HVOSM simulation program (now msmac3D) includes simplifying assumptions and is not a vehicle design program.
    It is an excellent and accurate tool for investigating and reconstructing vehicle crashes and rollovers, etc
    However
    Any 'design changes' made with ANY simulation program do not always include consideration for what actual design changes to the vehicle would be required to raise or lower the center of gravity of the vehicle or make other change to vehicle properties.
  We have seen some "experts" in litigation cases make simple numeric changes to inputs without any consideration of the requirements to actually achieve the change in the vehicle design.
  • I am reminded particularly of 'experts' using occupant simulation program. They do a simplistic 'reconstruction' (which with all the input assumptions and differences in humans it makes for a sketchy 'reconstruction') and then they claim simple 'padding would have avoided the injury? To add padding they simply change the force/deflection "stiffness" of the pillar without any consideration of any required dimensional changes? and/or whether any material available might provide such 'padding' while also functioning as an A-pillar.
  Just a word of caution when using ANY simulation program related to vehicle design changes.

[MSI]

Another post on Static Stability and a shoutout to us from the NAPARS Facebook page:

• • Today's Terminology Moment:
    Static Stability Factor.
    Imagine we're looking at the back of a car taking a right turn. There are competing forces at work.
    IMPORTANT FORCE #1:
    • Laterally, there is a centripetal acceleration (mv² / r) acting at the Center of Gravity (CG) towards the left trying to roll the car CCW about a point near the outer edge of the left wheels. The car's pivot point is really somewhere between the edge and midline of the tire, but for now bear with me and assume the car is going to roll about center of the tire contact patches. The torque acting to turn the car CCW, or the "overturning moment" in engineerese, is the product of that centripetal acceleration and the mass involved and the height of the CG.
    IMPORTANT FORCE #2:
    • The weight of the car is acting at the CG to keep it on its wheels. In other words, it creates a stabilizing CW torque (moment) about that same point.
    When these moments are equal, our idealized car will begin to tip up, so it's an important relationship.
    • The quantity of half the track width (t/2) divided by the CG height (h), or t/2h, is called the Static Stability Factor, or SSF. It doesn't fully capture all the nuance of dynamic events (hence the name STATIC), but it goes a long way towards explaining which cars, SUV, or trucks are at the greatest risk to tip over.
    Typical values:
    • Passenger cars: 1.4
      Pickups, Minivans, SUVs: 1.2
      Fullsize vans: 1.1
    Because the seats are above the car's CG, adding occupants decreases the SSF. Turns out each occupant typically reduces the SSF by about 0.01
    • (based on SAE 920583, The Variation of Static Rollover Metrics With Vehicle Loading and Between Similar Vehicles, by Riley Garrot, where he also showed that there's a standard deviation of about .01 when measuring different "similar/identical" vehicles, and a range of about 0.05.)
    Some further reading:
    • NAPARS member Brian McHenry has discussed SSF on his website: What is Static Stability Factor
    • NAPARS member Ron Huston coauthored a 2014 paper showing how SSF is still a good predictor of vehicle dynamics. Another look at the static stability factor (SSF) in predicting vehicle rollover
    • Sean Kane provides some history of the regulatory environment here: Rollover / Stability
    • 2005 NHTSA paper has a bunch of raw numbers, Trends in the Static Stability Factor of Passenger Cars, Light Trucks, and Vans

also see Rollover Analysis: minimum speeds and roll velocity approximation