## What is the appropriate rotating vehicle % drag factor?

Topics related to collision & Trajectory analysis formerly on our 'Registrants only' area however which we get asked about frequently so believe shoud be in the open forum too
MSI
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### What is the appropriate rotating vehicle % drag factor?

To approximate the drag factor for a rotating vehicle, we caution against attempting to use any arbitrary % drag factors like: "50% to 80% of the standard drag factor" or "70-75% of the full drag".
In our paper "CRASH-97 - Refinement of the Trajectory Solution Procedure" SAE Paper 97-0949, there is a discussion of approximations for drag factors.
• As we point out in the paper, with the astounding power and performance of common PC computers the use of a simulation to approximate the spinout of a vehicle to rest is a relatively easy task. Any user of the CRASH3/EDCRASH or other CRASH based program has the trajectory solution procedure from SMAC included. The CRASH3 trajectory simulation procedure is basically the SMAC trajectory solution procedure.
The following is from an Appendix of SAE 97-0949 which contains a discussion of rotating vehicle drag factors, etc.
APPENDIX 1: DISCUSSION OF SPIN2
• The SPIN2 procedure of the original CRASH program uses as a starting point the relationships developed by Marquard [1].
The Marquard procedure takes into account the fact that the linear and angular (i.e., yaw rotation) displacements of a four wheeled vehicle subsequent to a collision each occur under conditions of intermittent deceleration when the wheels are free to rotate. By approximating the linear and angular deceleration rates of a vehicle with either
• (1) all wheels freely rotating or
(2) all wheels locked during different phases of spinout motion,
Marquard developed approximate relationships between the total linear and angular displacements during the travel from separation to rest and the corresponding linear and angular velocities of a vehicle at separation from its collision partner, for the two cited cases of rotational resistance.
In the CRASH program [2], the SPIN2 routine was developed to extend the relatively simple Marquard relationships to include the cases of partial braking and/or damage-locked individual wheels.
• Evaluations of the resulting, modified relationships by means of trial applications to spinout trajectories generated with SMAC [3] revealed several shortcomings of the initial SPIN2 relationships. First, a residual linear velocity frequently exists at the end of the rotational (i.e., yawing) motion. Next, the general shapes of plots of linear and angular velocity vs. time changed substantially as functions of the ratio of linear and angular velocity at separation from the collision. Finally, the transitions between the different deceleration rates of linear and angular motions were found to occur gradually rather than abruptly. Slope changes in the plots of linear and angular velocity vs. time were found to generally occur in the form of rounded "corners" in the curves.
To improve the accuracy of approximations of separation velocities, provisions for the introduction of a residual linear velocity at the end of the rotational motion and the development of empirical coefficients, in the form of polynomial functions of the ratio of linear to angular velocity at separation, were incorporated in the SPIN2 analytical relationships of the CRASH program. Since the separation velocity ratio is initially unknown, a solution procedure was developed whereby several trial values of the ratio, based on an approximate equation, were used to test multiple solutions.
The cited analytical developments, reported in [2], involved only limited efforts which were aimed primarily at demonstrating the feasibility of the CRASH concept.
• Polynomial functions to generate empirical coefficients were developed, on the basis of 18 single-vehicle SMAC runs with relatively high linear and angular velocities for starting (i.e., separation) conditions. In the more common, real-life accident case, a relatively small rotation (i.e., yawing) velocity may exist at separation. In such a case the initial direction of the velocity vector with respect to the longitudinal axis of the vehicle will obviously affect the sequence and the duration of the linear and angular deceleration rates of the vehicle.
In consideration of known shortcomings of the SPIN2 aspect of the CRASH program, a subcontract to refine SPIN2 was undertaken in 1979 [4].
• A representative sample of actual accident cases was selected from the NCSS [5] files for use in the study. A total of 50 cases were selected and then reconstructed with the SMAC computer program. For each of the SMAC reconstructions, separation information was used to formulate a basis for a refinement of the SPIN2 empirical coefficients.
A careful examination of the time-history plots of linear and angular velocities for all of the cases in the sample revealed a significant number of cases in which the SMAC-predicted behaviour deviated from the analytical assumptions upon which the SPIN2 routine is based. Attempts were undertaken within the research project to discriminate characteristics of separation conditions. Unfortunately, only partial success was achieved in the attempts to accommodate deviations by means of the use of logic and discriminators.
As a result, a realistic appraisal of residual scatter in the empirical fits led to the conclusion in [4]:
• "To achieve a general improvement in the reliability and accuracy of approximations of the angular and linear velocities at separation, a step-by-step time history form of trajectory solution should be implemented."
Subsequent work which has been performed on investigation and refinement of the SPIN empirical coefficients [6,7] and the corresponding modifications to CRASH is subject to the effects of ‘scatter’.
• Any proposed refinements of the SPIN empirical coefficients and any reconstruction techniques which are based on the refinements of the SPIN empirical approach will ultimately fail in some applications to individual case reconstructions due to the possibililty that the particular case being investigated may be characteristic of a "scatter" point.
The research cited in this paper strongly supports the conclusion from 1981 that implementation of a trajectory solution procedure should utilize an iterative time-history simulation.
References
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MSI
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### Re: What is the appropriate rotating vehicle % drag factor?

I came across an old post (8/31/98) with some additional information in response to a question on 'MU for rotation':
Aug 1998: This is prepared in response to a question on the tire model in SMAC and equations to use in a spreadsheet program.
As Monday mornings normally go, the stuff is hitting the fan so my response at this point will be brief. In addition to normal consulting and software business, we are in the process of preparation for our seminar in October and this very topic may be added to the hand calculations portion of the seminar (OK, sorry for the blatant sales plug, but at least I'm admitting it!)I have loaded on our web site some information from our m-smac manual on the tire cornering stiffness
You will find that we reference the Radt/Milliken paper rather than Fiala paper (as EDSMAC apparently does posted to this thread). The Fiala paper assumes that traction and braking are zero (the title is "Lateral Forces on a Rolling Pneumatic Tires"). Radt/Milliken paper included consideration of braking and traction. The mathematical relationships presented in the paper, including the introduction of the friction circle concept, have been used in the original development of the SMAC/m-smac computer programs (and therefore it's clones like EDSMAC and WinSMAC).
So what does all this have to do with MU for a rotating vehicle?
The mathematics presented in the paper point to some important facts:
• 1) A rolling tire produces a side force perpendicular to the wheel plane when travelling in a direction other than straight ahead.
2) A tire saturates (generates maximum available friction force) somewhere between 15 and 25 degrees of sideslip
3) Braking forces occur in the plane of the wheel. However at the maximum condition (locked wheel) the braking force opposes the motions of the wheel.
4) Friction circle concept - the maximum force possible is independent of the direction in which the tire is moving.
Side Force Max = Sqrt(Mu**2 * Weight**2 - Braking**2)
Braking Max = Mu*Weight*Cos(Slip Angle)
5) Also presented in the paper is the Fiala cubic. That is simply a parabolic variation of the side force with the slip angle up to the maximum side force where the tire saturates (generates maximum friction). You will find PC-CRASH has taken what appears to be a step backwards in their tire model and assume a linear variation of the side force with slip angle up to saturation.
So with a simple spreadsheet program or calculator how can you use these items?
Given an initial heading angle, speed, sideslip and braking:
• Determine the braking force in the plane of the wheel.
• Next, from the current sideslip angle, apply a side force perpendicular to the wheel plane, limiting the maximum available by the friction circle concept. Use a linear variation of side force with slip angle for starters.
• Apply the force in the X & Y direction and take a step forward (You can manually integrate the model by applying a constant force for a period of time).
• Determine the new speed, then the new forces, apply and continue until the vehicle comes to rest
You can then with a spreadsheet vary the time step to determine the effects.
I hope this brief discussion helps to introduce some concepts that you should be thinking about when trying to determine the Mu for a rotating vehicle. The use of a % can give you a ballpark figure, but these relationships will give you an insight into the actual phenomena which occur.
Brian McHenry
References
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(c) McHenry Software, Inc ALL Rights Reserved.