The Traffic Accident Reconstruction Origin -ARnews-

Re: Rotating Vehicles Drag Factor

Brian McHenry (mchenry@interpath.com)
Sat, 15 Mar 1997 11:54:59 -0500 (EST)

To approximate the drag factor for a rotating vehicle. I caution against attempting to use the arbitrary % drag factors mentioned in this thread: "50% to 80% of the standard drag factor" or "70-75% of the full drag".
Our recent paper "CRASH-97 - Refinement of the Trajectory Solution Procedure" SAE Paper 97-0949
includes a discussion of approximations for drag factors and the use of a "Runge-Kutta form of differential eqaution for the numerical integration" (also mentioned in this thread).
As we point out in the paper, with the astounding power and performance of common PC computers (Pentiums, etc.) 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 vhicle drag factors, etc.
(The paper is (c) SAE, please visit SAE at
http://www.sae.org
to obtain a copy of the full paper).

APPENDIX 1: DISCUSSION OF SPIN2 from SAE 97-0949

The SPIN2 procedure of the original CRASH program uses as a starting point the relationships developed by Marquard [38]. 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 [1], 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
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    where
    • adf = acceleration/deceleration factor
    • d = distance in feet
    • t = time in seconds
    • t^2 = t squared- (4^2) = 16

    Compute Acceleration Factor

    : Vi, Vf, and Time Known: Computes an acceleration factor when the initial velocity, final velocity, and time are known.
    a = (vf - vo) / (32.2t)
    where
    • a = acceleration factor
    • vf = initial velocity in feet-per-second
    • vo = final velocity in feet-per-second
    • t = time in seconds

    Compute Deceleration Factor

    : Vi, Vf, and Time Known: Computes a deceleration factor when the initial velocity, final velocity, and time are known.
    a = (vo - vf) / (32.2t)
    where
    • a = deceleration factor
    • vf = initial velocity in feet-per-second
    • vo = final velocity in feet-per-second
    • t = time in seconds

    Compute AD Rate

    : AD Factor Known: Once the factor is known, the rate is computed by multiplying the factor time the gravity (32.2 feet per second per second).

    DOS Operations

    iCAR provides the user with two important DOS-related operations. Both are important and necessary. Being able to escape into the DOS shell without leaving a program provides significant flexibility and a result recording operation which runs in the background allows the user to concentrate on the difficult task at hand without having to worry about the details of file manipulation.

    Exit to DOS

    : Temporarily suspends iCAR, clears the screen, and displays the DOS prompt, from which you can run other programs or DOS commands. You must remember, however, that iCAR is still resident, so your computer will not have as much memory as it would normally. To return from the shell, simply type EXIT at the DOS prompt.

    Create an ASCII Session Record

    : Creates an ASCII text file using a name of your choosing, activates an internal boolean variable, and will faithfully record calculations results for the duration of the session. Please remember that the file name chosen must follow normal DOS protocol, and that any identical file name will be overwritten. Choose a file name that means something to you (i.e., case0914.jp).

    Appendix A - Vehicle Parameters

    The appropriateness of the set of eight frontal stiffness coefficients used by the CRASH3 program were examined in an SAE paper entitled "A Comparison Between NHTSA Crash Test Data and CRASH3 Frontal Stiffness Coefficients". The authors (Messrs. Strother, Woolley, and James) generated a new set of stiffness categories which are shown in the following table.

    Vehicle Type A(lbf/in) B(lbf/in^2) A(lbf/in) B(lbf/in^2)
    Stiffness CatagoryCRASH3
    Users Guide    		CRASH 3
    Users Guide    		Strother,
    et al    		Strother,
    et al
    1) Subcompact302.047.0 237.958.9
    2) Compact259.043.0240.060.0
    3) Intermediate317.056.0247.558.95
    4) Full-size356.034.0236.751.5
    5&6 Largest325.037.0247.257.9
    7) Vans383.0126.0349.799.8
    MPV's383.0126.0350.9100.5
    8) Pickups 480.050.0425.6 72.5
    9) Front Wheel Drive373.038.0240.458.2

    Appendix B - Vehicle Size Categories

              SIZE