strain-derived loads and parameters for use in the regression analysis presents little difficulty since all loads and parameters tend to approximate to zero in straight and level flight, as can be checked by comparison with the no-load ground condition, thus providing easily determinable datum levels from which to derive absolute loads. In the case of the wing the choice is not so obvious since
not only do the straight and level flight loads vary with flight conditions but the ground no-load condition is not readily producible because of the ever-present effects of gravity. Two choices present themselves; it may be possible to establish strain datum levels at zero load* by setting up a no-load condition on the ground - to achieve this the aircraft has to be supported at the fuselage and the wing weight counteracted by up-loads. absolute terms. Using these datum levels, loads can be derived in
The corresponding choice of true zero datum levels for the para-
meters is in most cases straightforward but care has to be taken in defining zero aileron angle on account of float**. normal acceleration datum level. In general, the constraint of parameters to zero values at zero load may result in the linearisation inherent in the regression analysis being less accurate than if this constraint were not imposed. The constraint can be removed very Care has also to be taken in the choice of
simply by allowing the regression to choose its own constant for inclusion in the parametric formula This allows more flexibility in llnearising non-linear aero-
dynamic and elastic effects. An alternative choice is to use an arbitrary steady flight condition to provide datum levels for all loads and parameters. This leads to the derivation
of incremental loads which can only be converted to absolute values if these are known at the arbitrary condition. This method is likely, however, to provide a Moreover, if
well matched set of datum levels for both strains and parameters.
the arbitrary steady flight condition is in the range where the manoeuvres, causing fatigue damage, commonly occu~ the need to introduce a constant into the regression because of non-linearities is not so great. In particular a realistic

wing loads were measured by means of strain gauges and at the same time measurements were made of parameters defining those motions of the aircraft and movements of the control surfaces thought relevant to the determination of the wing loads. Details of the strain gauge installation which was confined to the
measurement of bending moment in individual spars are given in Appendix B.
recording instrumentation is described in the earlier report ]. Measurements were made during general aerobatics and simulated combat manoeuvres~ they included aileron, barrel, slow and hesitation (8-polnt) rolls, loops, wing-overs, rolling pull-outs and vertical step runs. Only a few supersonic manoeuvres were performed Some measurements
because supersonic flying proved so expensive in flight time.
were also made during low and medium level atmospheric turbulence of light intensity. Table I. Maximum and minimumvalues of each strain gauge bridge output were extracted Cases selected for inclusion in the regression analysis are listed in
for the chosen flight cases, together with simultaneous values of the parameters A number of maxima and minima were usually extracted for each manoeuvre in order to cover fatigue load cycles of various magnitudes. The maxima and minima for
the different bridges did not necessarily occur simultaneously, major differences in timing occurring, as might be expected, between port and starboard wings. data relating to each station are listed in Tables 2a to g. 3.1 Interpretation of the strain gauge bridge outputs \ Because neither time nor funds were available for calibrating the strain The
gauges by the application of point loads as advocated in the Skopinski 4 method, the outputs from the strain gauge bridges could not be combined to give overall loads at the cross-sections gauged, as in the original concept of the parametric method. The only alternative appeared to be to treat the outputs of the strain
gauge bridges separately and to determine parametric formulae for each output. The question then arose as to whether the bridge output should be kept in the form of strain or converted to local load. For convenience in discussing the
parametric formulae it was considered preferable to express the bridge output in terms of local load. (Analytically the choice is trivial since it is only a
matter of scaling each par0metric formula by the appropriate conversion factor.) Generality is improved if the bridge output is expressed as a multiple of a local load which occurs in a simple flight condition related to a design case. The
effects of stress concentrations on the bridge output due to, ~g the proximity of rivets can then be partially eliminated, and the magnitude of the bridge output, particularly if expressed as a multiple of a | g load, rendered more meaningful. The output from each strain gauge bridge was accordingly converted to load expressed as a multiple of the corresponding local spar bending moment per g

normal acceleration at a position 355 am forward of the CG (8) , pitch acceleration aileron angle (E) ~ (~) , roll rate

($) , roll acceleration

Bitch and roll acceleration were determined by differentiPitch and roll rates were conditioned by multiplying
ating pitch and roll rates
them by dynamic pressure and by the inverse of true airspeed, and aileron angle by multiplying it by dynamic pressure The second set contained the additional Normal acceleraEs
parameters dynamic pressure~ Mach number and Math number squared tion Ks
was replaced by normal acceleration at the CG derived by combining
Either by applying Palmgren-MinerVs Law or by comparison with ground fatigue test results
with an appropriate proportion of
Two further independent variables were zCG by M and by M2o
then introduced by multiplying the parameter
The most notable omission in these lists of parameters is probably the angle of incidence. Sensors for measuring this parameter had not been fitted to the
Lightning during the original installation and time did not allow installation at a later date. Other parameters such as angle of sideslip and yaw acceleration,
which might otherwise have been included, could not be recorded owing to the shortage of channels on the main recorder. (Data for deriving additional slowly
varying parameters such as dynamic pressure and Mach number, could be accommodated on a supplementary photographic paper recorder but this recorder was unsuitable for the faster-varying parameters.) The loads and all parameters, other than dynamic pressure and Mach number, were subjected after digitising to a low-pass filter with a cut-off frequency of 5 Hz This was designed to retain as much of the high frequency content of the
loads as possible without running into structural oscillations (the fundamental wing frequency occurred at approximately 6 Hz). Even so it appeared that high
speed aileron movement and the resulting wing loads in certain aileron manoeuvres were being reduced by the digitising rate of 20 samples a second and the application of the above filter. The two hesitation rolls, in which this reduction
appeared particularly pronounced, were therefore re-digitised at 100 samples a second and subjected to a low-pass filter to remove information at frequencies greater than 20 Hz. A further 8-point hesitation roll included in a sequence of

one wing only and the accuracy of the conditioning data improved.
matters of concern in stage 2 were the choice of parameters for representing wing loads and the improvement effected by using parameters additional to CG normal acceleration.
The regression programme produced a series of parametric formulae for each of the four starboard stations 5-8, the accuracy of which, as indicated by the total correlation coefficient and standard deviation of the error, remained constant or even increased slightly as the first two or three of the ten parameters were discarded in turn. The accuracy then decreased ever more rapidly as the
remaining parameters were discarded.
Thus for all practical purposes the choice In general, better
for greatest accuracy fell on the 7-parameter formulae
accuracies were obtained for the rear than for the front spar stations and for the inboard than for the outboard stations (see Table 4) At best, ~e station 5,
the accuracy was comparable with that attained for the fin, the standard deviation of the error being 12.5%o The accuracy at the worst station, station 8,
where the standard deviation of the error was never less than 2].9%, was somewhat disappointing but still compared well with that obtained from normal acceleration alone which was as low as 58% Typical examples of the fit attained in the
regression between the strain derived and parametrically derived loads are given in Fig 2o It has to be emphasised that the accuracy of fit achieved in the
regression is not the final criterion of accuracy as regards the estimation of fatigue damage under operational conditions. Two further factors which have to
be borne in mind are the degree to which the sample represents the operational population of loading cases, and the tendency of positive and negative errors to cancel each other out in the final assessment of fatigue damage are discussed in more detail in the earlier report These matters
Because of misgivings with
regard to the first, a parametric formula is sought which gives a good fit in time history for a wide range of loading cases~ The second factor, on the other

methods attainable by the addition of a second parameter
multiplying it by dynamic pressure, is likely to be greater than indicated earlier since the previous comparisons were based on the assumption of an optimised empirical coefficient for 6 CONCLUSIONS A study has been made of the application to the wing loads in a Lightning of a parametric method in which load is not measured directly but is deduced from a statistical correlation with an appropriate combination of motion variables Because of the lack of opportunity to calibrate the zCG "
and control surface angles
strain gauges under applied ground loads, parametric formulae have had to be developed for local bending moments at a number of wing spar stations rather than for overall loads at a cross section. Since the former are, to a first approxi-
mation, combinations of the latter this restriction does not have too severe implications in the present context~ In order to attain a good match between strain-derived and parametricallyderived loads it is necessary to introduce into the parametric formulae certain parameters and possibly a constant to represent the steady state wing loads upon which the manoeuvre and other incremental loads are superimposed The need to
introduce a constant depends on the datum levels used in the flight test measurements on which the parametric formulae are based. The best results were obtained
with a quadratic in Mach number but better accuracy might have been achieved had the selection been from a wider range of parameters, and a regression on steady state loads performed separately from that on manoeuvre loads. A fair representation of local wing bending moment loads can be obtained with the parameters CG normal acceleration, multiplying it by dynamic pressure, (Sq), (zCG) , aileron angle conditioned by and Mach number squared although With the introduction of
representation is rather poor at high Mach number. further parameters, ~, MzCG , 0 and M,
the matching of time histories of
the parametrically and strain derived loads is improved, particularly in the case of rapid aileron usage, although the standard deviation of the error in matching the sample loads of the regression is only reduced from 21.9% to 18.2% (average errors for the starboard wing - which was studied in detail - expressed as a percentage of the rms loads). The parametric representation is some 5% less
accurate at the outboard section of the starboard wing than at the inboard The parameter, angle of incidence, was not considered since no sensor was fitted for its measurement. No conclusions can therefore be drawn as to its There were some indications that pitch
suitability for representing wing loads rate (8)
could play a small part in representing loads at the inboard section,

pressure, true air speed, Mach number and aircraft mass. (vi) Run special regression analysis programme on above data to select para-
meters and optimise their linear combination to give overall load6o (vii) Make final choice of parametric combination, re-running programme if
necessary to include subjectively chosen parameters. (viii) Check final choice to ensure close correlation between time histories of overall load and parametric combination outside matched points. A.2 Choice of parameters The choice under (vii) is guided by the following considerations: (i) The advantages of trading off accuracy for simplicity by reducing the

number of parameters.

Appendix A

preference

for parameters requiring little or no adjustment for
flight conditions. (iii) The preference for parameters which can be measured easily and with a Consistency of sensor performance, freedom from
high degree of reliability.
noise, and linearity of calibration are among the factors to be looked for here. (iv) The preference for parameters which provide data useful for other purposes

A~endix

STRAIN GAUGE INSTALLATION AND FLIGHT CALIBRATION B.] Strain 9aug9 ' installatio_n_n Micro-measurement EA350 gauges were attached with an epoxy adhesive to the (see Fig 1)o
exposed spar flanges of spars one and five at ribs six and fourteen
One longitudinal gauge and one cross gauge were fitted between rivets on the top and bottom spar booms at each station. The gauges were connected to form a
conventional bending moment bridge compensated for end load and temperature effects. The bridge outputs were conditioned using the fin load equipment and One bridge, namely that at station I)
were recorded as FM analogue signals.
became unserviceable at the beginning of the flight tests and remained so throughout. B.2 Calibration of strain gauges The flying was carried out in two main sections, namely calibration and manoeuvres The calibration flying consisted of steady turns and pull-ups at
different heights and speeds to cover the range used in the manoeuvres. The original intention was to evaluate the bridge response to applied normal acceleration at a variety of heights and speeds so that suitable calibration values in terms of ~-strain/g could be found, and zero strain datum levels g , dynamic pressure and Mach number With
established by extrapolation to zero a range of calibrations available) could be varied~ manoeuvre

1.489 23.958 $.359 3.240 51.649 0.200 3.846 29.028 -10.047 20,934.9.9?7 64.837 -&.E42 -73.065 -16.340 -0.998 -2.432 -16,194 -13.988 20.848 -1.332 3.931 1.056 -16.096 "23,918 "400,194 -61.239 473,486 - 3 1. 7 -447.380 31.808 418.064 2,650 50.810 -48.428 -64.991 5.758 24.674 -1.664 -6.333 -0,195 -9.698 -0.217 -7,917 0.417 -0.330 6.638 5.?40 -24.859 79,964 -31.441 -27.041 3,662 69,862 -7.404 -11.710 8.809 195,810 -6.382 18.359 6.112 39.386 1.064 23.159 9.262 48,128 -5,273 -2~.I89 -43.481 601.523 -17.752 -2?0.341 -36.508 2?3.459 5,973 17.062 7.376 41,521 -51.031 -31.503 11.602 -21.098 -48.961 8,304 1.215 37,915 -30.860 -14.706 2.34? -20.300 0.884 -9.839 1.054 -4.698 -0.049 -8.731 12.230 -70.856 -19,562 1,256 -02.807 45.144 -0.156 2.506 - 3 0. 0 -162.610 -40.199 208.820 34.79? 045.061 40,368 -330.592 -29.123 -285.363 "43.668 361,003 - 3 6. 4 -293.012 "2.034 24.350 65.131 -519.661 -39,693 -229.074 -6.300 ~6,299.979 4,705 -153.540 -11.114 -41.236 -102.303 86.017.23,865 65,425 -16.950 111,220 -05.688 -15.058 3.0?4 165.563 -7.086 -94.690 "10,801 34,520 27.804 8.218 -11.044 16,673 1.256 -~1.400 -16,?04 -16.909 6.073 73,031 -77.140 -7~.430 -54.-30,043 -175.599 -62.996 342.001 - , 0 -187.573 -72,511 264,104 -27,741 -191,487 -25.699 140,011 -26.~70 -106.095 -81,254 473,E09 - , 0 -185,656 -00,484 410.401 -43,168 -202.538 -?9.7?4 401.189 -51.691 593.E08 -60,306 413.168 -25,?54 -331.801 -$6,646 273.023 -35.380 -294.461 - 2 6. 8 -206.014 -86,083 396.149 - 3 ? , 4 -226.315 -86.380 470.874 -19.069 -200.802 -83.008 307.019 - , 6 -282.488 -52,001 3?6.549 -~3.605 -198.065 -02.926 483,654 1,090 376.432 51,005 -~25.607 1.203 340,698 53.53? -381.049 -24.293 344.398 41.883 -454.7?0 5.?24 367.241 60.226 -392,359 72.985 04,154 3?.323 -429.240 24.542 239.009 -3,383 86.E99 11,70~ "44.830 3.013 89.040
38,869 33.569 33.869 33.569 33.069 33,569 35,569 33,369 33.569 30.294 30.294 E0.294 30.294 30.094 30.294 30.294 30.204 30.294 30.294 30.294 20.6E1 28.671 22.691
24 Table 2d MAXI MU M AND MINIMUM BENDING MOMENT LOADS AT STATION 5 AND SIMULTANEOUS VALUES OF PARAMETERS
o H 0 NIILTtPtE ~F 16 10AP.n.~012 n.60~5 ~.1601 n.8551 1,8500 n,60?4 1.1794.n.7517 4.9339 t.0686 '~.6320 4.o906 n.8784.n.6115.8.6104 i~, 551~6 0.1,741. n , ~465 ~. 1367 - 1. R/~20.1.3000 ~.17o4 ?.8072.n.~664 A. 07r)4.11 Or,04.:',5470 X.60Q6 t,. 4,4760 X.0364 ~,7008 -n.43~0 ~.n~14 ~.1174 ?.0001 1.7131 -~.~573 t-1~43 ~. 54~;0 ~,/' 71~7 ~.~$92 VFRT, 8CEL. C~ 0 ~/LE~ON ANSLO 000 PITCH RATE nEG/$ 0,2169 - 0. 4298 -1.2740 O. 7861 -I,;055 -0,1920 -0,0413 0.5702 -4.6052 -3.4600 -4.5163 -8,7018 -0,6503 -0.0396 1.4107 -0,3521 0,9535 0.5591 - 5. 093t* 0~129~ -0,4422 -0,1700 -5.6101 1.839fl -1.1017 0.56?0 -4.8598 -9.2498 -0.104o -8,6048 -10.7550 -9.0638 1.8754 -9,35?? -10.071~ -8,6056 -0,0055 6.5452 -0.0080 -11.1552 "10,4000 -11. 760q -5,3008 -8.3261 -0.3750 0.991~ -6.2100 -0.1787 -6,3978 -I,591~ -5,5291 - 0. 499 ~. -7.5620 -1.7155 -7.1037 -3.2606 -6.259~ 0.8261 -0.885~, -11.~005 -7.9732 -6.2355 -16,4760 0,842H -0.11~9 -1,6299 -12.3341 -t,9903 "7,0031 0.4835 -11.2480 -12.3201 -0.1358 -16.1975 -11.9652 -6.9652 -4,4297 1.1216 -3.9750 -3.5020 -4.1205 -6.0558 4.467~ -5.5855 2.9581 -5.6320 -4.8/*65 -3.032? -3.0021 -1,9737 -3.476? -4.0687 -3.9?36 -2.048~ -1.3760 -/*.0787 - 3. 7601~ -5.0213 -6.8605 -6,4622 -5,0625 -3.6285 -5,3202 -2.9609 -3.09?4 -5.0716 -5.8683 - 6. k237 1.7196 -0.5436 -0.424? -3.6529 -5.1646 -B.1327 n.~11~ -1.6799 -1.0480 -1,5304 -2,0266 -3.0387 -5.0010 - 4. ~236 -5.9204 -5.9536 -4.8080 -6.6012 -5.7017 -4.5215 -5.4291 -5.3879 -1.4855 -3.2206 - 2. 4810 P|TOH ACCEL. 000/$2 0.4466 -2.1458 4.8305 -13.2441 -0.0932 -10.0A22 6.1191 -1.0864 1,0020 -5.0904 -0.5568 1.8453 7.9016 -5.5291 -13,8t27 -2.0489 4.5601 -4.0517 3,8094 -1.0014 -4.400t 0.8058 4.5818 - 0. 3097 4.0175 -0.5042 8.8721 -~5.4400 16.5662 -13.5504 -9,5360 -50.8086 3.0618 -24.0620 10.8677 ?,1832 -0,6154 -16.66~8 6.0~80 5.9713 14.9608 -0,6166 26,2~03 -7.0566.1.5226 -0.0352 1.4006 -4,1282 -16,9596 6.2231 -2.7426 -6,0030 2.6593 -6.5402 -0,3453 -10.9079 4,3585 -].0044 -0.0079 3.1359 1,6073 -5,3000 22,4795

26 Table 2f M A X I M U M AND MINIMUM BENDING MOMENT LOADS AT STATION 7 AND SIMULTANEOUS VALUES OF PARAMETERS
;Lt6~ AHO RUN NO. 109.~ ~ '~ 7 MUITTaL3 nF In L ~ E -~.~1~Q 1.1676 ~.0~18 ~.3000 t.6n80 ~.E??7 1.3551 -n.6~? q.3460 ;.0~8 ~.03ol 1.0537 -n.6~So -n.6~16 n.o~? -n.5~1~ n.0~0S ~.Enq5 ~.8~65 -~.0~8 x.3317 -;.6~6fi ~.6~3 -?.0~0 ~.110 4.9n~4 ~.9~2 ~.~63 -n.~'?1 ~.6?40 ~.3~?~ ~.~35.1~,)1 &.7"~? x.71~5 ;. 1(,.~ -~,01~3 -n,1~9 &,?~13 ~.o~)~ ~.~5 ~.6'.~x 1.qA~ q.L,.Q~ ,,31~ ~.S'55 ).;70 ~.~]]1 ~.6~1 -n.~33~ -n.?*)6 -n.6.~1 1.4~6~ -~.~91 1,7n?5 ~.?np~ -~,3~A~ ~.477~.n,~? ~.01o? >.4~3 ~,~75 IOS.~ -,I.6 ;~9 3.~21 -~,S~;~ ~,0,,I? ,'.~',~A x.{'~&o L S ; 3 -'L3~I& ~,?~ -~.n.16 ~,~?S -1,~ ~ -,3.~ ,01 ~,I~?? ~.2~ 70 ).n.~ ~.~')4 -?.~%13 -~.3~73.~.?~o.~.lnQ? -~.~:11 -~.S:71 -~.o~3 "4.3"1R -1.&,? ~ -i,1~s~ -).4"~ n.6~5 -t;~36~ ~.0~6 -;.~6~ -~.4"~ -~.~'4 n -%.~'~% -I.O~z~ - ~ , I ~31 -1.?'60 -~.O~E ~.~150 *~.711 o ~.S'6E ->,0~o3 ~,o~)6 ?,1"47 2,~i~7 -.~ -nG~3.1.o)1o >.1~69 ~,2~ ?,0167 -~,336 ~ -~.~e64.n.?~9 -?.0S&? -~,2~t)8 -~.~350 -~.13~ o -;.6~03 n.q=66 -P,3~$ -~.3~1 n.q~8 -n.934~ 1.11~6 -n.6~x~ -~.~;~q ~,t~8~ -1.~&? VS~T. AO33L. CG n -0.~15' 0.6434 1.2311 -0300~ 0.9622 -~.0666 0.2230 3.116~ $.310~ 6.362~ ~.0o63 0.0387 0.082~ -0.267~ 0.6317 9.63~c 1.0685 0.666~ -~ 163~ -I.0016 3.193~ -0.253x 1.201 ~ 1.7340 ?.S?4p ~.639P -,3.1237 ~.t&2t ~,705~ ~.SSG% 4 016~ 4 013" 3.103~ -0.3oE~ ,1 1~01 4,147(, ~.166~ ~ 0.7100 -I ~65~ n.~7?~ & 703~ 3 8~7X 3,~I&? ~ ~o6 a -1.~626 -1.~43~ -~1)g~ 1,~064 -6.~62S G ~63P 1 ~07~ -1,189~ q.~3~ -3 ~13 c ~ ~59~ ' 766~ 0 201~ "~ ~1o7 1,~9~ -o 562= ? 19o; 1 13SR ~ 110& ? 7731 "~ '196~ ~ 1 ~6~ -3 J64~ ~Sq -=1.607~ 6,6)01 3,E 8x ~ 188, 0 J26~ -~.37~ -0.6207 -~ ?~6 o.) qo2~ -~ 1990 - l~gG -?.~C4~ "1.S "S~ -I.4006 -I.~76D -3.~06~ 3.1112 -,;.311~ *~ SEEs -0.4601 "~.$07t. -S, n817 -~ 5653 -~ 338~. i 606f "~.766 r - n. R78~ -~.S~9~ -n.17q~ -,~.018E -#.33~7 I 900c 2'260~ ~ 7237 -~.?08~ -3 &93~ -0.~7o~ ? 396~ -0.2653 - 0 o -.).66~ - t E~6~ - t 1 2? -I ESq2 -I09R - 78 -I.~00 n -0 6oS4 "~.7780 -~ 0390 c 0356 ~.~?96 -~ 2,?6 -~ 191~ -0.1222 -o 614 ~ AILER0~ Aff6LS OEG 1.717~ 1.1486 1.7699 1.0832 1.712& 1,~290 1.6612 $.6467 -Z.1103 0.39?2 o.3466 "0.308? 0.4672 -0.8~76 -0.6618 -0.6086 1.3~31 6.955? 1.1~10 6.8~03 -6.2315 5.$3~E -7.027? S.3379 -d.SA62 -0.2~02 0.1~31 O.OV06 0.0956 -0.31JS 0.03?0 6.?&&9.1.~766 1.1.)79 -1.64~3 -~.%~1 ~,0~13 1,6753 ~,4~$6 U.41~2 -~,21~ -11.8330 ~,46Z4.11.3522 1.26~1 1,056~ 1.S~01 1,6~ -0.1~24 u,l?al o.o~o O.l,qO '~.0600 -0,4331 -0.6SO& n,6,105 -4.7373 6,9~16 -2.9092 -E,9"~6 -o,IV06 - J.6(.19 ~,0~S4 -v.?,-~ -5,6~31 -~.~2 u.0 ~ 9 -J.363 ?.66? 0 Z,2733 /.6~1~ ~.17;13 -J,??~? -0,0756 2.~30 -1,6~E3 3.0r.28 -~,3167 ~.~?~ -~.E~O9 3.9&~1 ~.7R~$ -?.06~5 I,~It~ -r.3~6 ~.9~63 -?,7~36 4,13oi 4.0036 -8,201~ 3.10?3 -9.0~3 3.?q75 "1.3~12 -8,30~3 3.b?~2 -8.1~)41 ].6o~I "6.0?69 3.00d5 =?,6~EZ 2.1838 -?.9O3S 3.0936 1,1~55 1,1371 1,3109 E.3642 1,6%10 1,200~ 1,E60O 1,41~S.J.3163 Z,10~0 16.1063 9.7660 S.79O7 mS.1066 ~.Z~E~ -0.2660 6.9530 -8.3177 4.E197 ~.27~I -O.1306 3.?029 "I.?~32 -0.0310 -0.3030 -~.6236 -~.1~06 ~1T0~ RATE DESIS -0.0147 0.320~ -0.8380 0.7861 -0.~593 0.6197 Pl~=~ ACSEL, DEal62 -6.~007 8.1366 8.7310.13.2641 3.0193 -1;.1600 E.7309 0.~690 S,3611 -10.5736 11.3o92 2.1960 -3.k900 -20.3031 3.6938.12.??39 -2.1217 2.9767 ~.~150 -~.900~ ).800~ "~.~01~ 10.7492 -6.6001 1).3&?S U.8958 -0.9179 -1.8677 -2.6077 Z.~721 =1.6106.10.8112 1,.$887 4. 0390 -IS.~60E ~ , 6,)02 3.2615 0,9931 "5,0106 IU.8O77 16.9000 1,~566 -0.61)~ -O.02~7 ~.~ESS -9.8735 02,2925 -2,6166 ROLL RATE OEO/S -?.103 1.67~ -3.625 -4.180 -1.260 "S.33~ 2.926 20.067 "16.308 "3.317 -0.8~7 " "1~.$35 -3.963 -~0.026.9.573 -0676 5.580 0.538 2.266 -114.216 121.~S0 -122.606 10)?00 16.~11 4.68~ 3.310 "o.300 2.36~ -7.004 -7,~40 ~.438.2~.~65 -~.~75 -~).29~ -3. ? -6.762 O,328 6,110 -30.019 8.84& ~.36~ -&o.117.6A,971 -48813 0.690 ?.376 -,.601 RDLL ACCEL, DEE/S? -6.030 13.987 -12.13? -18.929 =?.076 3.&36 1~,86~ 67~035 -1~.107 -2~.470 -a.897 "60.766 36.83~ 66.149 -23~9~9 0.81~ 8.537 13.$83 22.793 -10.025 20.972 ~S.162 ?.655 ~$,701 -169.93~ 6.568 49.$47 -1.107 -5.1~ 18.209 -~6.$61 -12.898 66.038 -1.206 12.106 -3S,943 -10.0~ 0,8g0 ~9.)86 -E080839 -182.671 -60.03~ -S~1.919 315,~06 -&06,14? -9.460 ~,561 "~,066 -3~.9~7 -13.667 "0.160 -5,03? 1,E6~ 1.668 29,037 36.130 -7.611 134.170 Z9,209 "0.~0U -110.368 49.754 -51.10~ "~2.603 "=0.~37 ?~.639 3~,066 -216.006 -7~.190 66.50~ "I~9.068 ~96.579 -13.~88 57,5S9 0,769 76.460 I~,270 -~4.037 "014* ~;86 ~13.905 ),$4~ 3~2,201 ld2.420 -~.?~9 377.~9& -06.057 &69,960 -~I,276 410,401 )$9.0~ -199,935 396.967 -S?~,~70 E07.067 111.763 -126,992 5ul.601 -69,878 53?,]69 -94.S~4 $40. ~?~ -1~o.s~ 438,9S] "198,6e~ ~06.301 ?,139 -88.606 -3~,02~ -10.702 -~,01~ 7.?30 30,901 S,171 -08.$65 -~,10~ -5,329 2,403 ?A.606 =~25.~$7 31.S79 "63?.?39 34~.395 "S00.826 E09,930 241.668 "339.~91 02.899 3,&93 60.173 -]1.$87 -~0.869 106.780 TRUE

Total correlation coefficient x 10-3~ + 0.9900 0.9859 0.9458 J
Standard deviation of error % of rms

10-3~q - 6.784

x I0-3~
+ 1.9579M~ - 3. M + 2.5649M 2 + 1. 10-3Eq + 0. M 2 + 0. 9 6

13.9 16.3 31.4

1.0202~CG - 3.9083 !.0242~CG + 0.14209 1.060~CG - 8. 2.1796
x 10-3~q - 10.02 10-3~ - 4.2985M + 0. 5 M 2 + 1. 0.9862 0.9777 0.8099 x 10-3~ - 0.9801 0.9724 0.9258

., _.,

x - + 2.1248M~ 10.045

16.6 20.8 57.6

1.3434~CG EM6 BM7
x lO=3~q + 1.0749M 2 _ 8. 8
1.30611~CG + 0,026132 0.94947~CG 1.6748 - 3.5'92 x 10-3Eq ' ' - 9. 5 6
- 3 ~ + 0.3435ME - 3,962M + 2.7473M 2 + 1. l O - 3 ~ q + 0.9548M 2 - 0. 1 6

20.3 23.5

BM7 ]~M7 HM 8
1.2148~CG - 4.7098 1.2126~CG - 0.2746 0.5964~CG - 7.7496 2.69537

x 10-3~q - 13.664

10-3~ + 0.9763 0.9605 0.8052 (SEE APPENDIX C) 21.9

x 10-35 + 0.90148I~

0. 7 M + 3.3289M 2 + 1. 7 3
1. ~ C G - 0 - 3 ~ q + 1.17137M 2 - 0. 1.2937~CG - 0.17554 7-PARAMETER FORMULA FOR STATION 5 CHOSEN BY REGRESSION
0.8256~CG - 4.2164 0.07646

10-3~q - 0.gill

10-3~ V-~t 0.9919 12.5
x - ~-t - 4.0503M + 2.724M 2 + 0. 6 ] M 2 ~ + 1. 2

",.O

30 "~Table 5
CALIBRATION FLIGHT GAUGE RESPONSE

Flight

Portstatlons Height (ft) 10000
Starboard stations Case SG4 93.9

(kn) 350

SG2 146.0

SG3 111.5

SG5 184.3
SG6 122.5 !!8.5 117.9 !17.4 175.3 120.6 ' 100.4 108.2

SG7 97.0

SG8 70.7
3g turn - port 3g pull out
138.3 134.9 135.2 ]34.I136.5 123.6 163

I131.7

104.8 102.5 105.8 105.3 101.7 93.5

87.8 84.2 87.6 85.6 -

181,2 174.3 174.6 ]79.2 147.3 167.9
90.9 90.0 91.3 94.2 68.1 76.2
i68.4 i67o4 66.5 69.3 49.4 54.0
Tul-n Turn Turn Turn Turn port Turn

148.!128.3 ]18.133.8

113.9 111.1 90.8 105.7

100.2 107.1

168.0 162.2 158.5

182.8 180.9 173.0

114.5 113.2 99.7 127.2

127.5 125,8

80.26 57.8 83.8 69.9 89.8

85.3 87.3

60.4 51.5 66.2

65.7 64.8

Turn port Turn starboard Turn port Turn starboard Turn Turn
134o8 ]67 ]136.4 124.4 168

]143.7

103.5 105.1 95.0

100.5 97.1 97.0

87.4 71.9 82.4

164.8 162.9 164.3

154.3 176.3 154.8

117.3 114.3 114.8

107.0 |39.8 108.5

80.6 81.2 77.1

BM8 multiple of lg load

a. Flight 159 run 1. High Mach number longitudinal manoeuvring, 36000 ft, M = 1.2 to 1.6. 7-parameter formulae
Time histories of parametrically derived and strain derived bending moment loads for formulae containing 7, 3 and 1 parameters
. BM5 multiple of lg load 40 ~

100 Time, s

BM 6 multiple of lg load

BM 7 multiple of lg load

,.L. [. ~.. Jl
2 BM 8 multiple of lg load
a. Flight 159 run 1. 3-parameter formulae

Strain derived

ILH~uWmOl~m~llmm ~ d ~ ~ u~ ul~

Parametrically derived

BM 5 multiple of lg load

2"0

Time, s
2 BM 7 multiple of lg load 0
2 BM 8 multiple of lg load 0
a. Flight 159 run 1. 1-parameter formulae
Fig 3 Strain derived tr~i~ BM5 multiple of lg load. Parametrically derived ~i '
~"""V" 0 ~ ' ~ 20

/~"~

-BM6 multiple of lg load

. [.. i. J. Jl

-BM7 multiple of lg load 0
--BM8 multiple of lg load
-5 b. Flight 163 run 1. Supersonic manoeuvres, 25000 ft, M = 1.0 to 1.2. 7-parameter formula Fig 3 contd
5 BM5 multiple of lg load #~_ ZJ ''h~. Strain derived 'Parametrically derived.~pe~l%~#~ ,##

--,'~,~,---. ,

lit, __
\]~ 7~', "<#' ~<.,-.<., ,,.~.,~.~.~-hl/

w"~r%:,~, q' __ _.

"' 20

BM6 multiple of lg load

L.]:L_L..

BM8 multiple of lg

.. L. LC. L L._L~$ I I L. _.J
b. Flight 163 run 1. 3-parameter formula

.lI~llll~l~.,

~ ~ "
Strain derived Parametrically derived -,.~. j.~l

.ij,,,l~ll~@Ill

~I~ j.~

..~ ~ ~ E ~

''"

~. ~.~.

-BM 6 multiple of lg load

tbJ~%t=,d

. JL. i..

.. ] 1

-BM 7 multiple of lg load 0
~=,=~,~=~,II~=,~,~,~Li. -li.~-~l.~ = =.fL.k J.1.1~ k. 11
-BM 8 multiple of lg load
-5 b. Flight 163 run 1. 1-parameter formulae (Zcg) Fig 3 contd
... Strain derived BM 5 multiple of lg load Parametrically derived

50 Time, s

i BM 6 multiple of lg load
-BM 7 multiple of lg load

. L I l

BM 8 multiple of lg load

--1. J. L.

c Flight 164 run 6 Hesitation roll and g manoeuvre with aileron, 9000 ft (approx), 450 kn IAS (approx) 7-parameter formulae Fig 3 contd
..Strain derived BM 5 multiple of lg I o ad "===~="~=~" Parametrically derived

L_____J

5O Time, s
--BM 6 multiple of lg load 0

,____I. J.. L ~ O

BM 8 multiple of lg load. L. ~ J I 1
c. Flight 164 run 6. 3-parameter formulae Fig 3 contd
. BM 5 multiple of lg load

.__I___I. I____

._L~_J.

. L _ _ I _ _. L _ _

C. Flight 164 run 6. 1-parameter formulae (Zcg)

20 Time, s

III aft ik
BM 8 multiple of lg load -2
d. Flight 167 run 2. Hesitation roll, 10000 ft, 400 kn IAS. 7-parameter formulae
Fig Strain derived BM5 multiple of lg load Parametrically derived

16 2O Time, s

-BM7 multiple of lg load

JL. J.

BM8 multiple of lg load -2
d. Flight 167 run 2. 3-parameter formulae Fig 3 contd
.. BM 5 multiple of lg load.
--BM 7 multiple of lg load

II l :I

d. Flight i67 run 2. 1-parameter formulae (Zcg)

BM8 multiple of lg I oad

e. FligWc 163 run 0. 3.5g turns port and starboard, 10000 ~, 350 kn IAS. 7-parameter formulae Fig 3 contd
Fig 3 ~ m. Strain derived Parametrically derived
BM5 multiple of lg load 40

multiple of lg load BM

VltI~JFI~

I,iill!l

e. Right 163 run O. 3-parameter formulae Fig 3 contd

concld

Strain derived Parametrically derived 2 BM 5 multiple of lg load

multiple of lg load

e. Flight 163 run O. 1-parameter formulae (Zcg)

concOd

. ~---------~-,.-~.=---~ Strain derived Parametrically derived
BM 5 multiple of l g load

$"

L. J. M,.

L. ]. ~.. !

~-rn e0

Constant

a. Flight 159 run 1. High Mach number longitudinal manoeuvring, 36000 ft, M = 1.2 to 1.6 F i g 4. Separate parametric components in 7 - p a r a r n e t e r formuHae

Mz"

Strain derived BM 5 multiple of lg load ~==~===w===~ Parametrically derived

. ~'~"20

m.~ E"a
b. Flight 163 run 1. Supersonic manoeuvres, 25000 ft, M = 1.0 to 1.2

10 BM 8 multiple of l g load 0 10

.. ~ = ~.

=-=~ Parametrically derived

.III.Ii.

rlll~,~

. ~. o , - 2

_.~-0.
,,, ~I~,II,~~,II,~,IIWI" ,I"~
=.. ~,,,I,.,.~.~.,.~,.~,.,.o~====--.~,.=,~.==-.=,,,,,.=.,.

'"='"' 1

~i I ~l

~' Ir/

0 ~t~ ,2.~. t- O

0. o 0 o ~o

iW=~=-l~======l~w-~

-10 Mz" 0

~,,m.mm~,~=~=.=~.

,,.,.. ,,

c. Flight 164 run 6. Hesitation roll and g manoeuvre w i t h aileron, 9000 f t (approx), 450 kn IAS (approx)
.. BM 7 multiple of lg load 0.

Ill,If ~ ~'

--x,,N

~)"

V"

V "

,. L. 1.

I ~ _ I ~ L _ _ _ J

Flight 167
run 2. Hesitation roll, I0000 ft. 400 kn
Strain derived ~ - ~ ~ Parametrically derived
o IIn,,#=~,~,~,,d:;.l~h,,~=n,,~:~uI~-. ~-~-~,,,t,~ --~L-. L-~5--;~I~"~=~L---~.---:-~'~@~, I;~.~.:~==%~,~.=~. I~

. ,.. ,..

.. I.. L. L ~. ~. I. =====7. ~. ~.

. ,. L. T.

~. II.

~ T = ~ 3

80 Time, s

. I. 1__.

L__=---[

I ~ _ 1

L , ~ L _ _ _ _ _ J
e. Flight 163 run 0. 3.5g turns port and starboard,.10000 ft, 350 kn IAS

Fig4 concid

Strain derived Formula with z', ~q, ~)',~, M, Mz, M2 (parameters standardised to conform with those of stations 6, 7 and 8)
BM5 multiple 2 of lg load

BM5 multiple of lg load

10 ~ Strain derived

Formula with z, ~q, ~ T

' ~ V--T' M, M2, M2z" q Flight 165 run 4. Vertical step runs and rolling manoeuvres, 8500 ft, 330 kn IAS
(parameters originally selected by regression programme) ~-~ Fig 5
Time histories for alternative 7-parameter formulae for BM 5 compared with strain-derived bending moment
Crown copyright 1979 First published 1979
HER MAJESTY'S STATIONERY OFFICE
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R &M No.3836 ISBN 471169 0