A comparison of high-speed photography and accelerometer data-reduction techniques

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  • A Comparison of High-speed Photography Accelerometer Data-reduction Techniques

    and

    A simple experimental test is discussed that can be characterized analytically. Experimental results of high-speed photography and accelerometers are then evaluated by comparison with theoretical predictions

    by Lee R. Calcote

    ABSTRACT--A simple experimental test is discussed by which the theoretical kinematic quantities of a moving target can be deter- mined. Experimental data are collected by means of high-speed photography and accelerometers, and the results of the two techniques are compared. It will be shown for the case of interest that the high-speed photography will yield results that are better than those obtained from the accelerometer data.

    Introduction Figure 1 i l lustrates a typical full-scale test sequence of an automobi le impact ing a h ighway guardrai l . In order to evaluate the guardrai l 's per formance, k inemat ic quan- tit ies sought inc luded the result ing vehic le trajector ies and the max imum 50-ms averages of the vehic le 's lateral and long i tud ina l accelerat ions. To obta in these data, t ransducers and signal condi t ioners were mounted on the test vehicle, and the signals were t ransmi t ted through a signal cable to the control station. F igure 2 summar izes the data=acquisit ion system.

    As shown in Fig. 3, the t ransducer data recorded from the on-board ins t rumentat ion were p layed back after the test th rough appropr iate filters (as specif ied by SAE Rec- ommended Procedure J211) to an osci l lograph for an im- mediate visual output. The data were then converted from analog to digital form and processed by computer to pro- v ide the desired output in e i ther tabu lar or graphic form.

    High-speed photography was used as an independent backup system for the tests. As shown in Fig. 1, two targets were mounted on the top of the test vehic le and reference range poles were set to obta in the test data. Typical camera coverages are shown in Fig. 4. Cameras 1 and 2 were the pr inc ipal cameras for data collection. F rom the h igh-speed-data film, readings of the two targets and

    Lee R, Calcotc i~ Se~illr ICe,earth l':n~meer, Southwest Real'atoll l~stitutc, S~tll A~ltlmio, TX 7~2bJ4.

    Paper i.~' sched~ded ~br pr~'~e~tatio~ at 1977 StiSA Spr i~ Mectil~ t, hc held in Dallas. TX on Mar./ 15~:20.

    reference range poles were taken by us ing a Vanguard mot ion analyzer.

    The desired vehic le trajectory, velocit ies and accelera- t ions were extracted f rom the film data through a pro- g rammed a lgor i thm which uses the s imple geometry of the test condit ions. The a lgor i thm curve-fits the cine read- ings of each of the vehic le targets, uses the results to calculate vehic le center-of-gravity locations, and finally curve-fits these c.g. locations. The curve-f i tt ing method used is a least-squares fit by or thogonal polynomials . 1 A f i fth-degree curve is the init ial trial, and the degree is increased unt i l no improvement in the index of determi- nat ion is noted or unt i l the degree reaches a specif ied max imum value k ...... Quantitat ively, the index of deter- minat ion is g iven by

    R - [n ~Y iY i - (ZYJ) (ZYi)] ~ [n 5.y~ - (Y.y~)~] In ZY~ - (ZY~) ~]

    where y~ are the measured ordinates of the curves, Y~ are the computed values, and n is the number of points. For a perfect curve fit, y~ - Y~ and the value of R becomes unity.

    At the t ime the f i lm-data program was written, some concern was felt about the d i f ferent iat ions of the curve- fitted vehicle d i sp lacements to obta in velocit ies and ac- celerations. The general consensus of op in ion was that better k inemat ic results could be obta ined by integrat ion of the acce lerometer data for velocit ies and displace- ments. F igure 5 shows th e typical results of both methods , but it was not possib le to ascerta in wh ich method actual ly produced the better results because of the complex i ty of the full-scale tests. Consequent ly , a s imple exper iment was conducted to evaluate the two methods.

    Experimental Program In the in teres t of ma inta in ing a commona l i ty of

    techn ique wi th the full-scale tests and the evaluat ion ex- per iment , the s imple two-target test apparatus shown in

    Experimental Mechanics I 167

  • Fig. 6 was devised. By rotat ing the apparatus at a constant angular speed 0, as shown in Figure. 7, the theoret ical non-zero k inemat ic quant i t ies of Target 1 could be easi ly estab l i shed by the re lat ionships

    x = r cos 0 y = r sin 0

    Vlat . : r a long . = r

    where r is the radius of rotat ion and 0 is the head ing angle. These quant i t ies could then be used to evaluate the ex- per imenta l values. In conduct ing the test, the procedures were ident ical to those used in the full-scale tests. For example, the init ial posi t ion and velocit ies obta ined f rom the high-speed-f i lm data were used as init ial condi t ions for in tegrat ion of the acce lerometer data. The instantane- ous head ing angles requi red in the acce lerometer data reduct ion were also taken f rom the film results.

    F igure 8 shows a compar i son of longi tudinal accelera- t ions, in wh ich the acce lerometers would be expected to g ive bet ter resu l t s . F igure 9 is a compar i son of x -coord inates , in wh ich the h igh-speed photography would be expected to be better. In the photography runs, the max imum degree of curve fit was specif ied at kmax = 20 deg, and film readings were taken at every frame. F i lm speeds were 196 and 168 f rames/second for Cameras 1 and 2, respectively.

    To check the sensit iv i ty of the max imum degree of Curve fit and the sampl ing rates w i th the h igh-speed photography, runs were made for every f rame with kmax = 10 deg and kmax = 20 deg, and for every 2nd, 4th and 8th f rame with k ..... = 20 deg. F igures 10 and 11 show plots of the results for long i tud ina lacce lerat ions and lateralveloc- ities, respect ively . Also shown on the f igures are the theoret ica l values and the 5 percent and 10 percent bands. Clearly indicated in both figures is the characterist ic tend- ency for the curve-f i tted quant i t ies to b low up near the ends of the data. In these runs, data sampl ing was started at 0.087 s before the first locat ion of interest and extended well past one revolut ion of the test apparatus. Results of the data reduct ions were computed at 0.01-s intervals f rom t ime t = 0 to t ime t = 1.00 s, the end of one revolut ion. This p roduced 101 pairs of data points for compar ison purposes.

    Discussion of Results Figure 8, where the acce lerometer data were expected to

    give better results, shows longi tudina l accelerat ion values for sl ightly more than hal f a revolut ion of the test ap- Fig. 1--Sequential photographs of full-scale test

    Fig. 2--On-board data-acquisition system

    TEST VEHICLE .j CHASE VEHICLE 9 I I z ~ 9 OR

    I c9 CONTROL BUILDING

    ~ SIGNAL CONDITIONING I I TRANSDUCER UNIT ATTENU TAPE RECORDER

    ' ~Accelerometers ~-Scoles Signol i i LRsd . . . . s,~.al~' Lp . . . . . . . t t--LOOd Cel l s ~-Amplifies Signal I I | Record

    I t t-Pressure Gages [--Ba, . . . . . Circuit I I / ~-Event J--Calibrates Circuit ~mJ ~-Rate Gyro L--Powers Circuit I MICROPHONE

    L--Other L ldent i f ies Test

    168 I May 1977

  • paratus. Of the total of 101 pairs of data points for the full revolut ion, 69 of the photography po ints and 32 of the acce lerometer points were closer to the theoret ica l value. F igure 9 shows that both techn iques are close for the x-coordinate. Of the 101 data-point pairs, the photography gave results closer to theoret ical in 62 cases, accelerome- ter data were closer in 37 cases, and, to two dec imal places, the results of the two methods were the same for 2 cases. F rom these and other figures, a pre l iminary conc lus ion can be drawn that the h igh-speed cine data are probab ly as accurate as the acce lerometer data for all of the k inemat ic quantit ies. As shown in Fig. 5, however, the cine data will not indicate the h igh- f requency peaks that are charac- teristic of acce lerometer data in the full-scale tests. Much of this f luctuat ion is caused by vehic le r inging and is of such h igh f requency that it is not l ikely to be felt by the vehic le occupant. A prev ious research project ~ revealed that accelerat ions wi th f requencies greater than 100 Hz have little, if any, inf luence on the occupant dynamic re- sponses and are therefore of only secondary interest.

    As expected, Figs. 10 and 11 show that the f luctuat ions of the results were of greater magn i tude as the sampl ing rate was decreased. Chang ing the max imum degree of curve from 10 deg to 20 deg did not appear to mater ia l ly

    affect the results. To be reasonab ly conf ident of results with 5-percent accuracy, the figures ind icate that at least every 4th frame should be read. With approx imate ly 200 f rames/second of film speeds in the evaluat ion experi - ment and 500 f rames/second in the full-scale tests, a corre- spond ing sampl ing rate for the full-scale tests would be 4 (500/200) or every 10th frame. Thus, it can be assumed that full-scale test runs wi th max imum 10-deg curve fits, data sampl ing at every 6th frame, and sampl ing that brackets the event by 0.10 s on each end will p roduce k inemat ic quant i t ies that are wi th in _* 5 percent of the actual values.

    Conc lus ions

    It has been shown by means of a s imple test how the data-acquis i t ion techn iques of h igh-speed photography and acce lerometer readings compare wi th theoret ica l val- ues. It had been assumed that the d i f ferent iat ion of c ine data wou ld not be as accurate as in tegrat ion of ac- ce lerometer data for the desired k inemat ic quant i t ies. However, this was not the case, and it can be conc luded from this s tudy that the cine data will yield results that are just as accurate, and probab ly more accurate, than the acce lerometer data. Of course, cons iderab ly more in-

    _~ANALOG TO DIGITALL~[ CONVERTER [ [

    TAPE L~

    RECORDERI t ELECTRONIC ]

    ,,TERS I "1

    COMPUTER

    OSCILLOGRAPH~

    Fig. 3~Data-processing system

    125 ft (38.1 m) 25Oft (76.2 rn)

    CAMERA 7 T (24 fps)

    EXPERIMENTAL ~IMPACT POINT BARRIER~ /

    9 ~ ] CAMERA, %PACT i -> ~" (600 f p s ~

    TEST VEHICLE

    REFERE~E ~R,O AND OVERHEAD I CAMERAS 4 (600 / fps) ANO 5 (600fps~

    CAMERA 2 (600 fps) 9 _ ___

    CAMERA 3 (750 fps)

    150 ft 45.7 m)

    4

    CAMEl 6 (64 fps)

    (38.1 in)

    fps = f rames per second

    .7m)

    Fig. 4--Typical camera positions for crash test

    Experimental Mechanics I 169

  • s t rumentat ion is necessary for retr ieval of the accelerome- ter data and can present undes i rab le sources of instru- ment error. Further , init ial condit ions must be known in the integrat ion process, and the ins tantaneous direct ion must be determined if the mot ion is curvi l inear. The h igh-speed cine retr ieval has the advantages of greater s impl ic i ty and the self -start ing character ist ic , but care must be exercised in the di f ferent iat ion of the data. The errors caused by di f ferent iat ion of curve-fits near the ends of the sampled data can be made less s ignif icant if the per iod of interest can be bracketed on both ends by the data sampl ing.

    Acknowledgments

    The author wishes to express his apprec iat ion to the Internal Research Pane l of Southwest Research Inst i tute for sponsor ing the project in which this work was per- formed.

    References

    I. Rank, P. H., Jr., "'FORTRAN II Subroutine fi~r Least-Squares Polynomial Fitting by Orthogonal Polynomials." Clearinghouse Document AD 620802 (April 1965).

    2. Calcote, L. R., -Investigation of optimum Crusb/Breakaway Characteristics af Roadside Structures," Final Report, Southwest Research Institute Internal Research Pr~ject 03-9122 (Jan. 1975).

    Fig. 6--Experimental-test apparatus

    Fig. 5~Typical computer plots

    /

    (~~.a.CCELEROMETER

    ~TARGET ~ .......... 2 Fig. 7--Plan of test apparatus

    170 J May 1977

  • Fig. 8--Comparison of longitudinal accelerations

    3.0

    ~ ~5 ~-<

    o,~ o

    2.C

    THEORETICAL ~HIGH-SPEEO PHOTOGRAPHY DATA

    "~ACCELEROMETER DATA == a ee~eaaeeo e

    / 9 point c;oser to fheoret lco l

    0 .05 O.lO O.iG 0 .20 0.25 0 .50 035 0 .40 0 .45 0 .50 O~G

    T IME (seconds}

    Fig. 9--Comparison of X-coordinates

    f t

    0 .5 - -

    - I @

    < - THEORETICAL

    0- -

    _ oHIGH-SPEEO PHOTOGRAPHY DATA

    aACCELEROMETER DATA -0 .5

    --2 ~ l l , *n~l 0 0 .05 0.10 0.15 0 .20 0.25 0~0 0 .~ 0 .40 O. 5 0 .50 O.D5

    T iME [seconds}

    Fig. l O--Longitudinal accelerations for various sampling rates

    3.0 oEVERY 4th FRAME aEVERY 8th FRAME a EVERY 2rid FRAME

    * 9 EVERY FRAME WITH km= x 9 I0 I e 9 EVERY FRAME WLTH kmo x 9 20"

    ~ w

    ou l - - ' - ~ ~ - - : -~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . < , - -u 5~ ;~;; - . . . . . . . . . . . . . . . . . . . . . . . . . .

    = = = I0% BAN{)

    2.D 0 .05 0.10

    T iME (second=}

    Fig. 11--Lateral velocities for various sampling rates

    m/s f/g

    4.2

    13.5 4.1

    <

    ~: 130 w . "

    J

    5,e 12.~

    "THSORETICAL +~o% eEVERY 4th FRAME A EVERY e~h FRAME o EVERY 2nd FRAME

    e o o 9 EVERY FRAME WITH kmaN r iO" 9 EVERY FRAME WITH kmoxe20 e

    o= o

    R~: :o

    9 , " '4 t :

    ~~ :~, , , I ;2 ' .~ so ,e"

    & = ~ ~ = o ~*~THEORETFCAL

    " 'o'o;'' . . . . 'o',;' ' ~o!,~'' %;" 'o!~'' 'o.i;'' 'o'~;'' 'o!,~'' 'o!,~'' 'o!~'' 'o~ T IME [seconds)

    Experimental Mechanics I 171