I 6 i
Cranfield
College of Aeronautics Report No. 8509 June 1985
Kiuyverweg l - OELFT
The Experimental Determination of the Subsonic Aerodynamic Characteristics of an Ogive-Cylinder Body
Including a Comparison with Theoretical Estimates Volume 1
D.I.T.P. Llewelyn-Davies
College of Aeronautics Cranfield Institute of Technology
Cranfield
College of Aeronautics Report No. 8509 June 1985
The Experimental Determination of the Subsonic Aerodynamic Characteristics of an Ogive-CyUnder Body
Including a Comparison with Theoretical Estimates Volume 1
D.I.T.P. Llewelyn-Davies
CoUege of Aeronautics Cranfield Institute of Technology
Cranfield, Bedford, UK
ISBN 0 9477 67 24 X £7.50
'The views expressed herein are those of the authors alone and do not necessarily represent those of the Institute. "
This report presents the results obtained from two series of wind tunnel
tests made on an ogive cylinder body of 6:1 fineness ratio in the CoA 8ft x 6ft
Low Speed Wind Tunnel.
The distribution of pressure on the body was measured over an incidence
range of -1 to 10 degrees. The local loading distributions were then obtained
by integration of the pressure coefficients; further integration yielded the
overall normal force and pitching moment coefficients and hence the centre of
pressure position.
The results showed that the aerodynamic characteristics were very
sensitive to conditions in the base region and that unexpectedly large
loadings were present over the last 10% of the body length. There are
indications that the bluff asymmetric model support system may be the source
of some additional interference effects at the higher incidences, even though
it is some 3.7 body diameters downstream of the base.
The experimental results have been compared with theoretical estimates
obtained by an inviscid ring-source method of estimation for axisymmetrical
bodies. The theory overestimated the loadings of the ogival nose and under
estimated the loadings over the parallel afterbody; in particular the large
loadings over the rear of the afterbody were not predicted. The agreement
between theory and experiment does not worsen appreciably at the higher
incidences as would be expected because of the presence of flow separations.
The theoretical results are very sensitive to the base closure assumed,
thus it may be possible to achieve closer agreement by suitably altering the
closure.
Section Page 1 INTRODUCTION 1
2 EXPERIMENTAL DETAILS 2 2.1 The Model and Support
2.2 Transition Fixing 2.3 Instrumentation
3. FIRST SERIES OF TESTS .5 3.1 Test Programme
3.2 Analysis and Discussion of Results 3.2.1 Incidence flow determination
3.2.2 Loadings and pressure distributions
4. SECOND SERIES OF TESTS 10 4.1 Yawmetsr and Incident Flow Determination
4.2 Circumferential Pressure Distributions Around the Body in the Neighbourhood of the Base
4.3 Local Load Distributions and General Aerodynamic Characteristics
4.4 Overall Normal-Force, Pitching-Moment and Centre of Pressure Results
5. THEORETICAL ESTIMATES 15 5.1 Comparison of Theoretical and Experimental
Results 6. DISCUSSION 20 7. ACKNOWLEDGEMENT 25 REFERENCES 25 SYMBOLS 27 TABLE 1 ILLUSTRATIONS
1. INTRODUCTION
As part of a research programme to investigate the characteristics of bodies in curved flow as provided by the CoA Whirling Arm Facility, an ogive-cylinder body of fineness ratio 6:1 has been tested in the CoA Low-Speed Wind Tunnel to establish a datum case in straight uniform flow. As the results are of general interest, they are presented separately.
The pressure distributions over the body were measured and the pressures at each longitudinal station were integrated to give the local normal
force loading and pitching moment. These were integrated again to obtain the overall normal force and pitching moment on the model and hence the centre of pressure position.
Ward (ref. 1) has measured the same quantities on a similar model at Mach numbers between 0.4 and 2.0 using a strain-gauged balance.
The pressure distributions over the body have been calculated by the ring-source method developed by Christopher, Deo and Shaw (ref. 2 ) . Being an inviscid solution, these results are valid only at low incidences, but the calculations were made over the whole of the test range to see how well they predicted the experimental results.
2. EXPERIMENTAL DETAILS 2.1 The Model and Support
The model tested (Fig. 1) was an ogive-cylinder of overall fineness ratio of 6:1 with a nose fineness ratio of 2:1. The maximum body diameter was 9.5 inches (241.3 mm) thus giving an overall length of 57 inches
(1447.8 mm) and a nose length of 19.0 inches (482.6 m m ) . The model was designed as a balsa-wood shell which, except for a short hardwood nose cone, was split longitudinally to ease the installation of the pressure plotting
tubes and allow easy access to the Scanivalve pressure switches used to measure the pressures (Fig. 2 ) . Balsa was used as the tests in curved flow were done with the same model in the CoA Whirling Arm, where the model is subjected to a 6 g loading and thus light weight is an important parameter in the design so as to minimise stress and deflection. As lightweight balsa tends to tear easily and have a furry finish when machined, the model was turned slightly over-sized, the surface covered with a cellulose dope which was allowed to sink in and harden before the final machining. By this means a reasonable finish of acceptable accuracy was obtained. The outside of the model was then sprayed matt black so that it would be suitable for oil-flow visualisation tests.
The model was pressure plotted along two generators 180 degrees apart which were at 90 degrees to the split line so as to minimise any errors due to flow disturbances coming from any discontinuities etc at the split line. The joints were sealed and faired with plasticine to avoid leakage. As balsa is rather soft and porous as mentioned above, a small segment of a lightweight hardwood, gelutong, was incorporated along the pressure plotting generators to give a better anchorage for the pressure plotting tubes and also to ensure a smooth surface near the holes. One generator, referred to as the "mainline" generator was pressure plotted at intervals of 0.02 of the body length (L) from O.OL to 0.99L. The opposite ("auxiliary") generator had pressure holes at O.IL intervals between O.OIL and 0.91L together with
additional holes at 0.33L, 0.335L, 0.34L and 0.345L. The primary purpose of the auxiliary line of holes was to make the weight distribution of the model as symmetrical as possible so asto minimise the torque needed to rotate the model, especially under the '6 g' conditions prevailing on the Whirling Arm.
In the event of a serious anomaly occuring in the analysis of results, the data from the auxiliary line of holes would be available for confirmation purposes.
In addition the nose plug incorporated a pi tot tube and two additional pressure holes at the O.OIL station opposite each other and at right angles to the "mainline" generator. The pi tot and the four holes at O.OIL thus formed a 5-hole yawmeter that was used to determine the alignment of the model to the incident airflow.
The orientation of the model was such that in the datum position (0=0), the "mainline" row of holes was on the underside of the model at positive incidence.
In order to obtain a complete pressure distribution over the body, it was necessary to rotate it about its longitudinal axis. The model therefore was mounted on its supporting sting by two needle bearings and was intended to be rotatedin 5 degree intervals by a rotary solenoid with a 3:1 stepdown
gearbox. Unfortunately the gearbox failed at the beginning of the tests and thus the roll attitude had to be set manually by two thin strings which were wound around a group of 4 screws partially driven into the base of the model. The roll position was determined by means of a pointer attached to the sting which was aligned with a scale attached to the base of the model (Fig. 3 ) .
The clearance of the operating strings varied with incidence, but was typically 5 mm.
The model was supported on a parallel sting which was pivotted on an unfaired rectangular strut which spanned the tunnel and was attached to the rear of the top and bottom turntables (Fig. 4 ) . The diameter of the support sting was 2.0 inches (50.8 mm) and the base of the model was 36 inches (915 mm) in front of the leading edge of the support strut, giving a sting/base
diameter ratio of 0.21 and clearance of 3.79 body diameters (D) between the model base and the supporting strut. The effective sting diameter however was
somewhat greater owing to the presence of instrumentation wires and pressure leads that were strapped to the outside of the sting. In addition there was a group of 3 clips that were a necessary part of the support system together with the bridle attachment for the incidence adjustment system. The
resultant shape was somewhat irregular, but as the maximum overall diameter was still small compared with the base, it was considered that there would be no intereference with the pressure distribution over the body.
2.2 Transition Fixing
As the Reynolds number of the tests was only 310 000 based on body diameter, it was decided to ensure turbulent flow over the model by fixing transition by a band of roughness 0.1 inch (2.5 mm) wide halfway between the first and second pressure plotting stations i.e. at 0.02 L. This means that the 4 yawmeter pressure holes were in natural (laminar) flow. The roughness consisted of a sparse distribution of spherical glass balls (ballottini) which had been double seived so that they all had a mean diameter of approx 0.023 inches (0.06 mm) to give a roughness Reynolds number of 800 under the test conditions as recommended by Braslow (ref. 3 ) .
2.3 Instrumentation
The individual pressure taps were connected by short lengths of plastic tubing to two 48 port Scanivalve pressure switches symmetrically mounted inside the model. The pressures were then measured by Setra 0.1 psi differential pressure transducers.
The tunnel static pressure was obtained from a pi tot static probe
mounted 12 inches (30 mm) from the side wall of the working section in a plane 14 inches (350 mm) behind the nose of the model. This static pressure was used as a reference pressure for the transducers and also to check the zero
drift of the transducers by measuring their outputs when connecting the reference pressure to each side of the transducer during each pressure scan.
A PET microcomputer was used to step the Scanivalves and measure the transducer outputs by means of a 12 bit Analogue-to-Digital converter. Each pressure was measured 5 times and the mean value recorded on the system disc. The PET system also obtained the tunnel speed from the difference between the standard pitot and static pressure taps located in the settling chamber and at the entry to the working section. This pressure difference was measured by a 0.5 psi differential transducer and was recorded with each pair of pressure readings, to be used later to convert the readings to corrected pressure coefficients (Cp). The discrimination of the system was Cp = 0.003 approx, but due to tunnel unsteadiness, noise etc the overall inaccuracy was somewhat greater.
3. FIRST SERIES OF TESTS
As the model was to be tested in the CoA Whirling Arm facility at a speed of approx 70 fps (21.3 m / s ) , the tests in the 8ft x 6ft tunnel were done at approximately the same speed. However, in order to avoid a 10:1 change in amplifier gain which would have reduced the overall accuracy appreciably, a tunnel speed of 62.3 fps (18.96 m/s) was chosen. The test Reynolds number was 310,000 based on the maximum body diameter.
3.1 Test Programme
The model was rigged so that its centre line was parallel to the tunnel side walls. Because of the position of the incidence pivot, the model moved appreciably as incidence was altered. In order to minimise the changes of model position in the tunnel, the tests were done with two vertical positions of the pivot. For angles between -2 and 4 degrees the pivot point was on the tunnel centreline; for angles between 6 and iO degrees the pivot point was 6.8 inches (170 mm) below the tunnel centreline.
The tests covered an incidence range of -2 to 4 degrees in one degree steps and from 6 to 10 degrees in two degree steps. The angular settings were determined with the tunnel at rest by means of an inclinometer on the parallel part of the body. As the normal force generated by the model at the tests speed was less than 1 lb (0.5 k g ) , no corrections for sting deflection were applied.
At each angle of incidence, pressure scans were made at 10 degree increments in roll angle between 0 and 180 degrees.
3.2 Analysis and Discussion of Results 3.2.1 Incidence flow determination
In order to determine the incident flow the yawmeter readings were examined over the incidence range at roll angles of 0, 90 and 180 degrees. The pressure coefficients, Cp, for the yawmeter holes have been plotted
against incidence (Fig. 5 ) , the main and auxiliary line holes for roll angles of 0 and 180 degrees and the port and starboard holes for a roll angle of 90 degrees.
Examination of the curves shows that although the pressure measured by the 'mainline' hole varied linearly with incidence, the actual pressure coefficients were considerably less than those measured at the other holes which were close to the expected theoretical values. Detailed examination
of the hole showed that it was located in a shallow depression caused by a tear in the wood. As the hole calibration was linear and the normal force and pitching moment contributions from this station were small, no corrective action was taken. However this error should be remembered when looking at the axial distributions of pressure coefficient. The calibration of the holes was obtained by linear regression analysis. This analysis showed that the incident flow approached the model from an angle of 1.22 degrees below the horizontal and at an angle of 0.54 degrees from the starboard side.
3.2.2 Loadings and pressure distributions
The local loadings at the pressure plotting stations were determined by numerical integration of the pressure coefficients. The overall normal force and pitching moment coefficients were obtained by further numerical integration and from these the centre of pressure position was derived. The moment centre was taken at the nose of the body and the reference length to be the model length. The variation of the overall normal force, pitching moment and centre of pressure position with incidence relative to the incident
flow is shown in Figs. 6, 7 and 8.
Analysis of the variation of normal force coefficient with incidence shows that the variation is linear over the test range but that the mean
line does not go through the origin and zero normal force occurs at -0.4 degrees of incidence (Fig. 6 ) .
Similar analysis of the pitching moment data (Fig. 7) showed that a straight line can be fitted to the data. However zero pitching moment occurs at -2.96 degrees incidence which is considerably different from the no-lift incidence. This shows that there is a considerable no-lift pitching moment which is unexpected with a symmetrical body.
The variation of the centre of pressure position with incidence (Fig. 8) shows thatathigh incidences, the centre of pressure position is at approximately 0.23L behind the nose and moves rearwards with reduction in incidence, slowly at first but with increasing rapidity as incidence approaches zero before
moving rapidly forward to be in front of the nose at negative incidences. This extremely rapid variation is primarily due to the large no-lifting pitching moment.
The variation of the normal force loading along the body with incidence is shown in Fig. 9. The graphs show that there is a positive loading over the rear of the body even at negative incidences and this this loading increases appreciably near the rear of the body, especially at low incidence. At -0.78 degrees incidence, this positive loading extends over the rear 60% of the body. As incidence is increased the loading over the last 20% of the body increases markedly up to about 5 degrees and then gradually reduces.
In order to investigate further the cause of these unusual loadings, the circumferential pressure distributions have been plotted at stations x/L = 0.95, 0.97 and 0.99 for the incidences tested (Figs. 10-12). The graphs show clearly that at the rearmost station there is a large positive peak in Cp centered on 0 = 40 degrees at incidences up to 5.22 degrees which becomes less prominent and moves inwards at higher incidences. This peak decreases at the more forward stations, but the longitudinal loading distributions show that its effect must extend as far forward as x/L = 0.4 at some incidences. These circumferential distributions also show that the distribution at x/L = 0.99 is dissimilar in character to those at the other stations as the main variation is with incidence rather than with roll angle.
Further investigation showed that one of the strings used to alter the roll angle crossed the base at approximately this position and gradually moved away as incidence was increased. It would therefore appear that, even though this string was less than 1 mm diameter, its presence close to the base interfered seriously with the afterbody pressure distributions. This was borne out by oilflow tests which showed a well defined separation line which extended forward from the point at which the string crossed the base (Fig. 3) to the junction between the ogival nose and the afterbody (Fig. 13).
The local loading distribution of 0 = 0.22 degrees also shows some unusual features. Although the calibration of the nose yawmeter holes shows that the model is at positive incidence, there is a well defined negative loading
distribution over the ogival region except for the most forward (O.OIL) station which has the expected positive loading. The local loadings obtained from the auxiliary line of holes showed that the local loading was negative at x/L = 0.01 and 0.11, but positive over the rest of the body with the peak value occuring rather farther aft than the expected position at x/L = 0.15. However as there are no pressure holes along the auxiliary line between x/L = 0.11 and 0.21, no detailed information is available on the manner of the change from negative to positive loading. Examination of the circumferential distribution of pressure
coefficient between x/L = 0.01 and 0.11 (Figs. 14 - 19) shows no obvious errors at 0.22 degrees incidence. However a systematic error seems to
be present at roll angles of 30 and 160 degrees at an incidence of 2.22 degrees; the sense of the error is such that in both cases a diminution in the normal force loading would result when the pressure distributions are integrated. While this may account for the rather low loads and irregular shape of the
loading distributions atthis incidence, it is felt that there is no satisfactory evidence to explain the apparently irregular change of sign of the local loading along the forebody except the possible sensitivity of the integration technique to small changes (inaccuracies) in pressure coefficient at low incidences.
Other factors that have been considered to explain these anomalies
are:-(a) The yaw of the model is rather large (0.54 degrees) so at an
incidence of 0.22 degrees, the inclination of the resultant flow to the vertical axis is nearly 70 degrees. As the pressures have only been measured over the range 0 = 0 to 180 degrees, the integrated normal force will be in error. However the sign should not be changed.
(b) The transition band is located between the O.OIL and 0.03L
stations. As positive normal force is generated at the front station, it may be possible that the transition band causes a separation over part of the forebody thus giving rise to the negative loading.
It is felt that the second explanation is the more likely, but there is no confirmatory evidence from other sources.
In order to investigate the general accuracy achieved by the analysis of the pressure distributions by numerical integration, the local loadings were further examined. In ref. 4 it was concluded that the variation of the peak forebody loading with incidence should be linear. This variation has been plotted (Fig. 20a) and shows that the variation is indeed linear with the greatest variation from the linear regression fit being at incidences of 0.22 and 2.22 degrees, i.e. the incidences where anomalies occur. As the peak loading is a somewhat arbitrary choice, it was decided to anlayse the results using the loading at x/L = 0.01 as this approximated closely to the initial slope of the loading distribution which would also be expected to vary linearly with incidence. This variation is plotted in Fig. 20b and again shows a good fit between the data and the linear regression line with the values at incidence of 0.22 and 2.22 degrees again showing the greatest variation from the mean line.
It is interesting to compare the no-lift angles obtained by these
methods with the mean value obtained from the nose yawmeter (the incidence datum used in plotting the results). The slope analysis gives a zero lift angle of -0.16 degrees, while the maximum loading analysis gives a zero-lift angle of +0.18 degrees. From this it is concluded the various methods of obtaining the alignment to the flow agree to within plus or minus 0.2 degrees.
Examination of the local loading distribution at the higher incidences (Fig. 9b) shows that there is a slight bump occuring in the distributions just aft of the shoulder of the body (x/L = 0.35) which becomes larger as incidence increases. This may be an indication of a local separation at the shoulder.
In view of the errors in the results due to the interference of the roll positioning strings with the afterbody pressure distributions, it was decided to retest the model with the strings removed. In addition, shortly after the test series was completed, it was found that the settling chamber screen had become partially unfastened and had to be made secure. It is more than likely that the screen was becoming progressively unfastened during the present tests as the flow inclination measured during tests on a similar body shortly before the present tests (Ref. 4) was only 0.75 degrees compared with the 1.22 degrees measured in these tests.
4. SECOND SERIES OF TESTS
As a replacement system for rotating the model in roll was not completed before the start of the tests, the model was rotated while the tunnel was running by pushing on the screws fixed into the base around which the string had been wrapped in the first series of tests. In order to ensure that they would not affect the flow over the afterbody, the screws had been moved inwards towards the sting. A friction device was also installed to ensure that the model did not rotate after its roll position had been set.
For these tests the model was tested inverted i.e. positive incidence is measured nose downwards, with the sting pivot point located 6.0 inches
(150 mm) above the tunnel centre line. These changes were dictated by geometrical considerations necessary to enable the tests to be extended to higher
incidences but still keeping the model near the centre of the tunnel. These high incidence tests will be reported separately.
Preliminary tests were made at 0 = 0, 90, 180 and 270 degrees to recalibrate the yawmeter head and to determine the inclination of the incident flow to the horizontal. The model was aligned in the tunnel so that the parallel afterbody was horizontal, but was inclined 0.5 degrees to starboard of the tunnel centre
line to correspond to the yaw measured in the first series of tests. A
preliminary check showed that the model was considerably misaligned in yaw and that a better approximation would be with the model yawed 0.5 degrees to port of the tunnel centre line. The model datum position was altered accordingly and this datum was used throughout the test series.
Pressure measurements were made at incidences of - 1 , 0, 1, 2, 4, 6, 8 and 10 degrees from datum. At each incidence the pressure distribution was measured at roll angles between 0 and 180 degrees in 10 degree
intervals.
As previously the pressure readings were converted to pressure coefficient form and were then numerically integrated first to give the local loadings and then the overall normal force and pitching moments and hence the centre of pressure position. The pressure distributions, local loadings and moments are tabulated in the second part of this report together with plots of the circumferential pressure distributions at the pressure plotting stations.
4.1 Yawmeter and Incident Flow Calibration
As the calibration was done at roll angles of 0,90,180 and 270 degrees of roll, it was possible to fully calibrate each hole individually even though the incidence range was limited by the necessity of keeping the model reasonably near the tunnel centre line.
The general form of the calibration was as before, with the bottom (mainline) hole giving a considerably smaller reading than expected as noted previously. Over the range of incidence tested, the variation of pressure at a given hole was linear and a mean line was fitted to the data by the least squares linear regression technique. As the calibraitons of three of the holes are close together and therefore difficult to separate on a graph, the results are presented in tabular form. The equation of each calibration line is
assumed to be of the form:-Cp = A + B0
where A and B are determined from the linear regression fitting method. If we take the calibration lines for a particular hole when it is located on the top and bottom generators, then their intersection will determine accurately the inclination of the incident flow in the vertical plane as the hole characteristics are the same.
The table below summarises the results of this analysis. The coefficients when the hole is on the lower generator are denoted by A and B, and by A' and B' when the hole is on the top generator. G is the incidence at which the calibration curves intersect.
HOLE
A
B
A'
B'
0'
Bottom 0.3706 0.01812 0.3644 -0.01954 -0.1646Top
0.5428 0.02134 0.5332 -0.02176 -0.2220 Port 0.5264 0.02245 0.5230 -0.02283 -0.0750 Starboard 0.5433 0.02382 0.5391 -0.02382 -0.0830Meaning the values of the intersections of the calibration lines, the model nose yawmeter is aligned to the tunnelflow when it is at an incidence of -0.14 degrees relative to the horizontal (positive incidence nose down). In physical terms this means that the incident flow is inclined 0.14 degrees downwards from the roof of the tunnel.
As it was difficult to move the model safely in yaw when the tunnel was running owing to backlash between the top and bottom turntables to which the model support system was attached, the direction of the incident flow in the yaw plane was determined from the difference in pressure between the port and starboard yawmeter holes making allowance for the difference between the yaw settings for alignment with the mean flow and for zero pressure difference between the port and starboard yawmeter holes as obtained from the calibration in the vertical plane.
The incident flow relative tothemodel datum was found to be 0.13 degrees to port which, allowing for the initial datum alignment and model inversion, corresponds to the incident flow coming from 0.37 degrees to port of the tunnel centre line.
All incidences quoted henceforth are relative to the incident flow.
4.2 Circumferential Pressure Distributions around the Body in the Neighbourhood of the Base
Comparison of the circumferential pressure distributions at x/L = 0.95, 0.97, and 0.99 in this series of tests (Figs. 21 - 23) with the previous results (Figs. 10 - 12) showed
that:-(a) the pronounced pressure peaks near 40 degrees roll angle are no longer present. Some irregularities are still presentinthe curves, but these are thought to be more of an indication of the accuracy of measurement than of any interference effect.
(b) the pressures at roll angles of 0 and 180 degrees are more nearly equal in the second series of tests. Although the minimum pressure
coefficient seems rather greater in the first series of tests, the agreement is much closer if the datum is taken as the line between the values at 0 and 180 degrees roll, as the differences between these coefficients is much greater in the first series of tests.
(c) although the variation of pressure coefficient with incidence at a given station is similar, the axial variation near the base is rather less in the second test series.
(d) in the second series of tests there is also a rapid change in the slope of the curves near zero incidence at x/L = 0.99 as compared with the variation at higher incidences. As before the pressures at this station vary more with incidence than with roll angle.
It would appear therefore that the strings had a considerable effect on the pressure distributions over the rear of the body.
4.3 Local Load Distributions and General Aerodynamic Characteristics
The pressure distributions at each station were numerically integrated to give the local loading which is plotted against longitudinal position in Fig. 24.
At the lower incidences the axial variation is rather irregular. Although the forebody loading now changes sign with incidence the peak loading at -0.86 degrees incidence seems too small in comparison with the 0.14 degree case which in turn seems much too large for an incidence so close to zero.
At the higher incidences the distributions become smoother and compare well with the first series of tests (Fig. 9 ) .
The loading distributions obtained in the second series of tests however still show an increase In loading over the rear of the body even though the inteference effects from the roll control strings have been eliminated. This is most noticeable at incidences of less than 2 degrees, where the rear loading accounts for a large part of the total normal force.
The loadings over the main part of the parallel afterbody are approximately zero at low incidences and become slightly negative at the highest incidence tested. At this incidence there again seems to be a slight increase in loading just aft of the junction of the ogive with the parallel afterbody. This is probably due to a local separation at the junction and its presence is confirmed by the local loadings obtained from the auxiliary line of holes.
In the first series of tests, the local loadings over the parallel afterbody between x/L = 0.40 and 0.80 were small and positive. Indicating that the interference effects extended over this region.
The local loadings have been analysed as previously to give an estimate of the no-lift angle. The maximum loading analysis. Fig. 25a, gives a no-lift angle of 0.34 degrees whilst the slope analysis gives -0.14 degrees (Fig. 25b).
As has been noted above, it is considered that the forebody load distributions at incidences of -0,86 and 0.14 degrees are in error. These errors can affect the analysis appreciably as both errors tend to make the no-lift angle more negative, especially in the case of the maximum loading analysis, thus explaining to some extent the poor no-lift estimates.
4.4 Overall Normal-Force, Pitching-Moment and Centre of Pressure Results The local loadings and moments were integrated to give the total normal force and pitching moment coefficients, from which the centre of pressure positions could be obtained. The variation of these quantities with incidence is plotted in Figs. 26 - 28.
Unlike the first series of tests, the variation of both normal force and pitching moment with incidence is no longer linear, both curves having an appreciably greater slope in the neighbourhood of zero incidence. As already discussed, this is due to the appreciable load present over the last 20% of the body which constitutes a large part of the total normal force at low incidence.
The variation of the centre of pressure positions at positive Incidences shows a gradual shift forward as incidence increases, altering linearly from a value of x/L = 0.36 at 0.2 degrees to x/L = 0.18 at an incidence of 10 degrees. The curve has not been extended to negative incidences because of the uncertainties noted in the loading distributions at incidences of -0.86 and 0.14 degrees which make the derived values of the centre of pressure positions somewhat doubtful.
5. THEORETICAL ESTIMATES
Theoretical estimates of the body pressure distributions and local loadings have been made using the ring source method (ref. 2 ) . This method has been developed as a rapid means of calculating the loading and pressure distributions over axially symmetrical bodies. Experience has shown that the program is easier to operate and is about twice as fast in operation as a program using panel methods (SPARV), but at the same time there is close agreement between the results. It should be noted that in the ring source method a sinusoidal variation in source strength around the circumference is assumed, and on this assumption, the loading distributions are calculated
without specifically working out the circumferential pressure distribution. In fact the program as it is written at present only derives the axial distribution of pressure along one chosen generator. If the pressure distribution along another generator is required the program has to be rerun.
In all methods of estimation of the pressure distributions over bodies having blunt bases it is necessary to specify some method of closure to the body, but unfortunately there is no general agreement as to what the closure shape should be. The three most popular proposals
are:-(a) extending the body in a tangential straight line from the base for a reasonable distance
(b) terminating the body in a cone, again of suitable length
(c) trying to represent the dividing streamline between the cavity and external flows by some quadratic curve which is tangential to the afterbody at the base. The most usual choices are an ellipse or an ogive with the ogive being the most favoured because of the separations that must occur over the bluff rear of the ellipse.
In order to assess the effect of different afterbody closures the pressure distributions over the body were calculated at zero incidence for the following
cases:-(1) cylindrical extensions of lengths OD, ID and 3D (2) conical extensions of lengths ID, 3D and 5D (3) ogival extensions of lengths ID, 3D and 5D
The results together with the experimental distributions obtained along the top generator at an incidence of 0.22 degrees in the first series of tests are presented in Table 1.
The results show that the length of the parallel extension has no effect on the calculated distributions over the body but that the pressures over the rear of the body differ appreciably from those measured
experimentally.
Variation in length of the ogival extensions cause changes in the
pressure distribution over most of the cylindrical afterbody; it would appear that the best representation of the experimental pressure distribution is with a 3D extension.
The effect of changing the length of the conical extension is much greater than that noted in the other cases. Because of the discontinuity in curvature at the base, small cone angles are desirable but even so the
agreement with the experimental results is not as good as with the ogival extensions.
It was decided that the best closure was the 3D ogive and accordingly the pressure distributions at roll angles of 0 and 180 degrees together with the local loading distribution along the body were calculated for the range of attitudes tested in the second series of tests.
5.1 Comparison of Theoretical and Experimental Results
The theoretical and experimental longitudinal pressure distributions are plotted for the range of incidences tested (Figs. 29-36). In all cases the experimental data at x/L = 0.01 should be ignored because it is known that these values are in error due tothe condition of the body near the pressure plotting hole (see section 3.2.1). Also it would appear that the pressure hole at x/L = 0.29 is consistently reading too high as compared with the adjacent stations.
The experimental results follow the shape of the theoretical solutions up to x/L = 0.90 but the pressure coefficients are more positive by approximately 0.02. Aft of this, the agreement is good near zero incidence as would be
expected because of the choice of base closure. However as incidence Increases the agreement gets steadily worse as the experimental pressures near the base become progressively more negative than predicted by theory. It is suggested that this may be due to the inadequate representation of the base flow by the chosen body closure. If the base closure is to represent the base cavity adequately, then its shape should vary with incidence, in which case the axis of the base closure should not be straight but have a variable camber so that the rear of the closure is aligned with the free stream direction. Although
there is little difference between the pressures on the 0 and 180 degree generators over much of the parallel part of the body, a difference occurs over the last 10% of the body which is more pronounced in the experimental results. This is particularly noticeable at x/L = 0.99 where not only is the difference large even near zero incidence but the pressure difference changes sign very rapidly as the incidence goes through zero as has been noted already in the discussion on the circumferential pressure distributions at this
station (Fig. 2 3 ) .
The theoretical and experimental variation of local loading along the body are plotted in Figs. 37 - 44. Both the local loadings derived from the main and auxiliary (check) lines of pressure holes are plotted, but the comments in this section refer solely to the main line of holes which define the axial variation of loading at closer intervals. The difference between the two sets of loadings is considerable in places, but this is discussed more fully in Section 6.
The agreement between the theoretical and experimental results is not very good at the lower incidences especially at -0.86 and 0.14 degrees.
The experimental forebody loadings are much too small at -0.86 degrees Incidence and much too large at 0.14 degrees. It might be though that this , could be an indication of an alignment error, but previous analysis has
shown that these two loading distributions seem inconsistent with the others and are thus likely to be in error.
The enlarged scale used for plotting the results up to 2.14 degrees incidence shows clearly the large scatter in the experimental results, particularly at the two lowest incidences and gives some idea of the discrimination to be expected in practice.
The theoretical estimates do not predict the large increase in loading that occurs over the last 20% of the body length. This is disappointing as the base closure was tailored to give the appropriate pressure distribution over the top and bottom generators in this region. However as shown in Fig. 23, the experimental pressure distributions in the base region (x/L = 0.99) vary in an unexpected and unexplained manner with incidence to account for the large rear loadings that are present.
At incidences of 2.14 degrees and above a more consistent pattern emerges in which
(a) The experimental forebody loading distributions are similar in shape to the theoretical estimates but are smaller in magnitude by an approximately constant amount.
(b) The experimental and theoretical loadings over most of the parallel afterbody (x/L = 0.33 to 0.80) agree well up to an incidence of 8.14 degrees. At 10.14 degrees incidence however the experimental results differ appreciably from the theoretical predictions and show a marked reduction in loading around x/L = 0.40.
(c) The rear loadings present are not predicted, but as their magnitude does not change appreciably with incidence they contribute a
6. DISCUSSION
The tests have shown that the flow over the model is very sensitive to interference in the base region as evidenced by the major changes in pressure distribution and local loadings caused by the presence of a thin string normal to the stream just behind the base. For this particular model with a
parallel afterbody, the pressure gradients over most of the afterbody are small and thus it would be expected that the boundary layer would be reasonably
sensitive to imposed disturbances such as produced by the string. As the amount of rear loading on the body was unexpected, especially at low incidence an examination was made of published experimental results on similar bodies.
As already mentioned a similar model had been tested by Ward at Mach numbers between 0.4 and 2.0 in the RAE Bedford 3ft x 3ft transonic and
supersonic windtunnel (ref. 1) at a Reynolds number of 820 000 based on body diameter. Although the models were similar. Ward's tests were made primarily to investigate the variation of forebody drag at transonic and supersonic
speeds and hence the balance data was obtained over a large range of Mach number at large (5 degree) intervals of incidence. More important however was the support system used, the model being supported in the tunnel by a sting which was effectively a long extension of the parallel afterbody with a narrow circumferential slot at the base to allow for the measurement of base pressure. The theoretical investigation into the effect of base closure on the pressures over the
afterbody (section 5) had shown that this arrangement would not have the same basic pressure distribution over the rear of the afterbody as the model and support system used in the present tests. Thus the overall forces and moments obtained in the two experiments were not expected to agree closely especially as transition was not fixed in Ward's experiment.
No numerical results were given in Ward's report so the values plotted in Figs. 26 - 28 have been obtained from the graphs in ref. 1 and are somewhat inaccurate. The agreement in overall normal force is excellent at 4 degrees incidence, but the shape of the curves is different in that the present tests the slope of the normal force curve decreases slightly with increase in
Incidence while the reverse occurs in the Ward's tests. The same comparison holds good in comparing the pitching moment results. The centre of pressure position obtained in the two tests varies almost linearly between the same values between 0 and 10 degrees incidence, but the sense of the variation is different, giving the same centre of pressure position at 5.7 degrees incidence.
A somewhat similar body has been tested by Tinling and Allen (ref. 5) at subsonic speeds. Their model had a 3:1 finess ratio ogival nose with a cylindrical afterbody 7.7 diameters long. Again the main purpose of the tests was rather different, being to investigate the behaviour of the separated body vortices at incidences of 10 degrees and greater and their effect on the overall normal force on the body. The body was similarly pressure plotted along the 0 and 180 degree generators and the overall pressure distributions were obtained by rotating the model in 10 degree steps. The number of stations for which data is presented is 23, but the farthest aft station is 10 body diameters from the nose (x/L = 0.935) which unfortunately is in front of the position where the rear loading begins to increase appreciably in the present tests. The model was held in the tunnel by a rear sting support of which no details were given, but from a photograph of the rig it would appear that the general proportions of the sting relative to the body were similar to those used in the present tests. The tests were made with free transition but at the lowest Mach number (M = 0.30), tests were made at Reynolds number of 400 000 and 3 000 000 to investigate any scale effects present in the tests. Luckily this is the Mach number most comparable to the present tests. The graphs showing the effect of Reynolds number on the overall lift characteristics and the local normal force distributions at 10 degrees incidence are reproduced in Figs. 45 and 46. Although no loading distributions were presented at 5 degrees incidence, they were obviously obtained as a value of the overall normal force coefficient was plotted.
It should be noted that the increase in Reynolds number caused an appreciable increase in normal force curve slope and the shape of the curve drawn at the higher Reynolds number is such that it would not pass through the origin unless the initial slope of the curve at the origin is greater than at an incidence of 5 degrees (Fig. 4 5 ) . Thus although this analysis depends on the value of the normal force obtained at 5 degrees incidence, it indicates that the normal force variation with incidence obtained in the present tests is
possible.
Tinling notes that although the differences between the circumferential pressure distributions at the two Reynolds numbers appeared to be small, the Integrated effect of these changes was considerable (Fig. 46) in that there was a marked effect on the loading distributions over the parallel afterbody especially just aft of the nose junction with a linear increase of loading along the afterbody to a value of 0.04 at a distance of 10 diameters from the
nose (x/L = 0.935). The general shape of theloading distributions in the present tests approximates closely to the high Reynolds number tests indicating that the transition band is effective. However it should be noted that the loads over the afterbody in the present tests are slightly negative instead of slightly positive.
Initial analysis of the high incidence tests on the present model are showing several interesting features. As it was anticipated that the vortex development over the model might be asymmetrical for a variety of reasons, the pressure distribution along the main generator and measured for roll angles from 0 to 360 degrees in steps of 10 degrees. However owing to storage limitations on the PET computer the local loadings for the port and starboard were worked out separately and showed that there were considerable discrepancies between the two sides which became more pronounced with increase in incidence.
Because of this and various features of the present tests, it was decided to look at the load distributions obtained from the auxiliary line of holes which have also been plotted in Figs. 37 - 44.
At the two lowest incidences where agreement between the experiment and theory had been poor, the forebody loadings obtained from the check holes now agreed well with the theoretical estimates. At the same time both experimental values of the afterbody loadings agreed well, even to the increase in loading measured over the rear of the afterbody which is not only much greater than predicted by theory but is of the opposite sign. The four closely spaced holes grouped adjacent to the junction of the forebody and afterbody show some irregularities in that the loadings obtained from the rear three (which are at the beginning of the parallel section) are almost the same and are somewhat greater than the first which is located on the forebody. The differences however are within the probable accuracy of the experiment.
At an incidence of 1.14 degrees (Fig. 39), the forebody loadings obtained from the check holes are considerably less than those obtained previously, but the mean of the two values is approximately equal to the theoretical prediction. However the loadings over most of the afterbody obtained from the check holes are more positive than both the main experimental data and the theoretical prediction and verify the increase in loading over the rear of the afterbody. The agreement between the check results are theory is excellent between x/L = 0.20 and 0.80, but the peak forebody loadings are less than
predicted and again the large increase in loading over the rear of the afterbody is not predicted.
At 6.14 degrees incidence (Fig. 42) the two sets of experimental
resuls agree well up to x/L = 0.21 but the check results give higher loadings over the rest of the body. The forebody loadings are again lower than the theoretical estimates, but the mean of the experimental afterbody loadings agree well with the theoretical estimates until x/L = 0.80.
At the two highest incidences, 8.14 and 10.14 degrees (Figs. 43 and 4 4 ) , the loadings obtained from the check holes show increasingly greater loadings over those obtained previously over the whole length of the body except beyond x/L = 0.70 where the differences become smaller. The mean of the two sets of experimental data give forebody loadings that are slightly smaller than the theoretical values and slightly greater over the afterbody up to the point where the results diverge (x/L = 0.80).
It should be noted that the check holes at x/L = 0.335,0.340 and 0. 345 tend to show very little variation in loading at any incidence and do not follow the general slope of the loading curves. As the forebody/afterbody junction is at x/L = 0.333, it is thought that the appearance of a length of constant loading immediately aft of the shoulder may indicate a small region of flow separation. While this region appears quite small at low incidence, it becomes more
pronounced at the higher incidences and is confirmed by the main set of data. Summarising, at low incidence the forebody load distributions obtained from the check holes are considerably more negative than those obtained previously but there is good agreement between the two sets of data over the afterbody.
As incidence is increased, the agreement between the forebody loadings improves and at 6.14 degrees they are identical. Over this range the check holes give consistently higher loadings over the afterbody, but the magnitude of the difference increases only slowly with incidence in this range. At higher Incidences the loadings from the check holes are greater than the main set of loadings over thewhole body and this difference increases rapidly with
incidence.
As has been mentioned, tests on the same model at incidences greater than 10 degrees shows that the discrepancy in loading between the two sides of the body grows more marked as incidence increases and at the highest incidence tested the total load on the port side (the side scanned by the check holes in the present tests) was nearly double that of the starboard side. As the trend was the same throughout the incidence range, it was felt that there must be
some consistent reason for the flow asymmetry. As the only physical asymmetry in the system is the support strut from which the model is mounted (Figs. 3 and 4 ) , possible results of this asymmetry were considered.
As incidence increases from zero, the body crossflow develops eventually leading to flow separation and the formation of a pair of trailing vortices which grow in size and strength as incidence increases. If initially for geometric reasons the vortices pass on one side of the bluff support strut, as the
Incidence is further increased and the vortices grow stronger it seems logical that they should remain on the same side of the strut. If this is so, the vortices in the neighbourhood of the strut will be progressively displaced
from the vertical plane of symmetry of the model. It is then possible that this asymmetry is fed forward to displace the body vortices in roll thereby causing the aerodynamic plane of symmetry to roll relative to the physical plane. The large variations noted are possible because, as has already been noted, it only needs small changes in the pressure distribution to cause appreciable changes in the local loading. The changes in the pressure distribution that would result from the postulated displacement of the body vortices are such as to give the variations in loading noted.
As has been previously mentioned, the large rear loading on the body at low incidences results from large changes in the circumferential pressure distributions over the rear of the afterbody as the incidence changes sign.
In order to investigate this further, the variation of the pressure coefficients at roll angles of 0 and 180 degrees has been plotted against incidence for
stations near the rear of the body (Fig. 47). The results show clearly that large changes of pressure coefficient at a particular pressure hole occur as the incidence changes sign. It would be expected that the pressures would be the same on the top and bottom generators at zero incidence for reasons of symmetry and thus give zero loading. If large rear loadings exist on the body at small incidences, then large pressure changes must take place almost instantaneously as the body moves from zero incidence. The increments in incidence are too large to show whether such a step change takes place, but the graph shows clearly that large changes in pressurecoefficient do occur rapidly near zero incidence in the region where the unexpected afterbody loadings occur and are a maximum at the rear of the body where the local loading is a maximum. Smooth curves drawn through each set of experimental points Intersect at -0.6 degrees
incidence at each station. Such good agreement is likely to be coincidental and a result of the spacing of the data as there is no other confirmation that this interpretation is more likely than the suggested step change.
The sensitivity of the pressure distributions over the rear of the body to changes in the base conditions had been indicated theoretically when the effect of various afterbody closures was investigated to determine a closure which closely represented the experimental results at zero incidence (section 5 ) . Table 1 shows that the pressure coefficient at x/L = 0.99 could be varied from -0.004 to -0.692 by alteration of the closure shape as compared with the value of -0.063 obtained experimentally, while the effect of the closure shape
could be detected as far forward as approximately x/L = 0.25 taking a difference of 0.005 as significant. Thus, with hindsight, the forward effect of the
string near the base of themodel might have been anticipated even if the magnitude could not have been predicted.
With increase in incidence the pressures measured experimentally over the rear of the body decrease appreciably while the theoretical values hardly alter (Figs. 29 - 36). Both theoretically and experimentally the difference in pressure between the 0 and 180 degree generators increase as incidence increases. However the increase appears almost instantaneously experimentally as the incidence changes from zero and then remains almost constant with further increase in incidence whilst the theoretical variation increases gradually with incidence. Most importantly however the theoretical increase is of the opposite sign to the experimental results leading to a reversal in the loading as
previously noticed.
This sensitivity of the afterbody pressure distributions to base
conditions is somewhat surprising as the pressure gradient over the rear of the afterbody is favourable and thus the flow might be expected to be reasonably stable instead of apparently having a symmetrical flow only in a small region near zero incidence and an unpredictable but stable flow away from zero
incidence.
Further investigation into the effect of further alterations of the body closures such as adding camber may achieve better agreement with the
experimental results as it has been demonstrated that the choice of closure can have large effects in comparison with the differences with which we are concerned.
7. ACKNOWLEDGEMENT
The work reported here is part of the work done under Agreement
No:-2028/131-XRAW from Royal Aircraft Establishment, Farnborough, Hants.
REFERENCES
1. Ward, L.C. Force measurements at transonic speeds on
axisymmetric forebodies to determine the
effects of bluntness.
Royal Aircraft Establishment Technical Report 76088
July 1976
2. Christopher, P.A.T., A ring source method for predicting the
Deo, H.S. aerodynamic characteristics of bodies of
Shaw, C.T. revolution.
C.I.T. Cranfield College of Aeronautics
Report 8609, March 1984
3. Braslow, A.L. A review of factors affecting boundary layer
transition.
NASA Technical Note NASA TN D-3384, August 1966
4. Christopher, P.A.T., The subsonic aerodynamic characteristics of a
Hussain, Z. body of revolution - A revised experiment.
Shaw, C.T. C.I.T. Cranfield, College of Aeronautics
Report 8408, March 1984
5. Tinling, B.E. An investigation of the normal-force and
vortex-Allen, C.Q. wake characteristics of an ogive cylinder
body at subsonic speeds.
SYMBOLS
A
Cm
dCp^/dxCN
dC[^/dxS
D
M
N
P
po
q
R
0
0
maximum body cross-sectional area pitching moment coefficient (M/qAL) local pitching moment contribution normal force coefficient (N/qA) local normal force loading
pressure coefficient ((p - po)/q) maximum body diameter
pitching moment, measured about nose total normal force
local static pressure
free stream static pressure free stream dynamic pressure
free stream Reynolds number based on D Incidence angle
0 . 0 1 0 . 0 3 O . O i 0 . 0 7 0-0'< 0 . 1 1 0 . 1 3 0 . 1 5 0 . 1 7 0 . 1 1 o . ^ l 0 . ^ 3 0 . 2 5 0 . 2 7 O . i i 0 . 3 1 0 . 2 3 0 . 3 5 0 . 3 7 0 . 3 i O . f c l 0 . ' i 3 O . * ? 0 . * 7 0 •>• < 0 . 5 1 0 . 5 1 O . S J 0 . 5 7 0 . 5 * 0 . 6 i 0.>>3 0 . 6 5 0 . 6 7 0 . 6 i 0 . 7 1 0 . 7 3 0 . 7 5 0 . 7 7 0 . 7 ; * O.fel 0 . 6 3 U . 8 5 0 . 6 7 0 . S 9 0 . ^ 1 0 . 9 3 0 . 9 5 0 . 9 / 0 . < 9 0 . 5 2 2 Ö . 3 6 7 0 . 2 6 1 0 . 17 7 0 . 1 0 3 3 . j * 9 - 0 - 0 0 1 - d - 0 < . 3 - 0 . 0 7 - T - O . l l O 0 . 1 3 -- 0 -- 1 5 3 - 0 - 1 6 5 - J . 1 7 3 - 0 . 1 7 1 - 3 . 1 5 9 - 0 . 1 2 5 - 0 . 0 9 7 - 0 . 0 6 . - 0 . 0 5 1 - 0 . 0 < . 3 - ) . 0 3 6 - 3 . 0 3 2 - 3 . 0 2 5 - 0 . 0 2 5 - 0 - 0 2 2 - 0 . 0 2 0 - 0 . 0 1 3 - 0 . 3 1 5 - 0 - 0 1 5 - 0 . 3 1 » - 0 - 0 1 3 - 0 . 9 1 2 - 0 . 0 1 1 - 0 - 3 1 0 - 0 . 0 0 9 - 0 . 0 0 3 - O . O O J - 0 . 0 0 •! - 0 . 0 0 7 - 0 . 0 0 7 - O . O O i - 0 . 3 0 6 - 0 . 0 0 6 - 0 . 0 0 6 - 0 - 0 0 5 - 0 . 0 0 5 - 0 . 0 0 5 - O . 0 O 4 - 0 . 3 0 » 1 . 5 2 ; 0 . 3 6 7 0 - 2 6 1 0 - 1 7 7 0 . 1 0 3 0 . 0 * 9 - 0 . 0 0 1 - 0 . 0 * 3 - 3 . 0 7 9 - 0 . 1 1 0 - 0 . 1 3 " . - 0 . 1 5 3 - 0 . 1 6 6 - j - 1 7 3 - 0 . 1 7 1 - 0 - 1 5 3 - 3 . 1 2 5 - 0 . 0 8 7 - O . O i i - 0 - 0 5 1 - a - 0 - 3 - 0 . 0 3 6 - 3 . 0 3 2 - 0 . 3 2 5 - 0 . 0 2 5 - 0 . 3 2 2 - 0 . 3 2 3 - 0 . 0 1 3 - 0 . 0 1 5 - 0 . 3 1 5 - O . O l f c - 0 . 0 1 3 - 0 . 3 1 2 - 3 . 3 1 1 - 0 . 0 1 3 - 0 . 0 0 9 - 0 . 0 0 9 - 0 . 3 0 H - 0 . 3 0-i - 3 . 3 0 7 - 0 . 0 0 7 - 0 . 0 0 7 - 0 . 0 0 5 - 0 . 0 0 6 - 0 . 0 0 6 - 0 . 0 0 5 - 0 . 0 0 5 - 3 . 0 0 5 - 0 . 0 0 5 - O . Ü O » 0 . 5 2 2 0 . 3 6 7 0 . 2 6 1 0 . 1 7 7 0 . 1 0 3 0 . 0 < . 9 - 0 - 0 0 1 - 0 . 0 * 3 - 0 . 0 7 9 - 0 - 1 1 0 - 0 . 1 3 * - 0 . 1 5 3 - 0 . 1 6 6 - 0 . 1 7 3 - 0 . 1 7 1 - 0 - 1 5 » - 0 . 1 2 S - 0 . 0 9 7 - 0 . 0 6 " . - 0 . 0 5 1 - 0 . 0 * 3 - 0 . 0 3 6 - 0 . 0 3 2 - 0 . 0 2 3 - 0 . 0 2 5 - 0 - 0 2 2 - 0 . 0 2 0 - 0 - 0 1 9 - 0 - 0 1 6 - 0 . 0 1 5 - 0 . 0 1 * - 0 . 0 1 3 - 0 . 0 1 2 - 0 . 0 1 1 - 0 - 0 1 0 - 0 . 0 0 9 - 0 . 0 0 9 - O . O O B - 0 - 3 0 9 - 0 . 0 0 7 - O . 0 O 7 - 0 - 0 0 7 - 0 . 0 0 6 - 0 . 0 0 5 - 0 . 0 0 6 - 0 . 0 0 5 - 0 - 0 0 5 - 0 . 0 0 5 - 0 . 0 0 5 - 0 . 0 0 * 0 . 5 2 1 j . 3 6 5 0 . 2 5 9 0 . 1 7 5 0 . 1 0 5 0 . 0 * 6 - O . Ö O * - 0 . 0 * 7 - 0 . 0 8 3 - 0 . 1 1 * - 0 . 1 3 9 - 0 . 1 5 S - 0 . 1 7 1 - 0 - 1 7 8 - 0 . 1 7 7 - 0 . 1 6 * - 0 . 1 3 1 - 0 . 0 9 3 - 0 . 0 7 1 - 0 . 0 5 8 - 3 . 0 5 0 - 0 - 0 * * - 0 - 0 * 0 - 0 - 3 3 6 - 0 . 0 3 * - 0 . 0 3 1 - 0 . 0 3 0 - 0 . 3 2 9 - 0 . 0 2 9 - 0 . 0 2 7 - 0 . 0 2 7 - 0 . 0 2 7 - 0 . 0 2 7 - 0 . 0 2 8 - 0 . 0 2 9 - 0 . 0 3 0 - 0 . 0 3 2 - 0 . 0 3 * - 0 . 0 3 7 - 0 . 0 * 0 - 0 . 0 * 5 - 0 - 0 5 0 - 0 . 0 5 7 - 0 . 0 6 6 - 0 . 0 7 8 - 0 - 0 9 2 - 0 - 1 2 2 - 0 . 1 7 7 - 0 . 2 9 2 - 0 . 6 9 2 0 . 5 2 1 0 . 3 6 5 0 . 2 5 9 0 . 1 7 5 0 . 1 0 6 0 . 0 * 7 - 0 . 0 0 * - 0 . 0 * 6 - 0 . 0 8 3 - 0 . 1 1 3 - 0 . 1 3 3 - 0 . 1 5 7 - 0 . 1 7 1 - 0 . 1 7 7 - 0 - 1 7 6 - 0 - 1 6 3 - 0 . 1 3 0 - 0 . 0 9 2 - 0 . 0 7 0 - 3 . 0 5 7 - 3 . 0 * 8 - 0 . 0 * ? - 0 . 0 3 8 - 0 . 0 3 5 - 0 . 0 3 2 - 0 . 0 3 0 - 0 . 0 2 3 - 0 . 0 2 7 - 0 . 0 2 b - 0 . 0 2 5 - 0 - 0 2 * - 0 . 0 2 * - 0 . 0 2 * - 0 . 0 2 * - 0 . 0 2 5 - 0 . 0 2 5 - 0 . 0 2 6 - 0 - 0 2 7 - 0 . 0 2 9 - 0 . 0 3 1 - 0 . 0 3 3 - 0 . 0 3 6 - 0 . 0 * 0 - 0 . 0 * 5 - 0 . 0 5 2 - 0 - 0 6 0 - 0 . 0 7 5 - 0 . 0 9 8 - 0 . 1 * 4 - 0 . 2 7 2 0 . 5 2 1 0 . 3 6 5 0 . 2 5 9 0 . 1 7 6 0 . 1 0 6 0 . 0 * 7 - 0 . 0 0 3 - 0 . 0 * 5 - 0 . 0 8 2 - 0 . 1 1 3 - 0 . 1 3 9 - 0 . 1 5 7 - 0 . 1 7 0 - 0 . 1 7 7 - 0 . 1 7 5 - 0 - 1 6 2 - 0 . 1 2 9 - 0 . 0 9 2 - 0 . 0 6 9 - 0 . 0 5 6 - 0 . 0 * 8 - 0 - 0 * 2 - 0 - 0 3 7 - 0 . 0 3 * - 0 . 0 3 1 - 0 . 0 2 9 - 0 . 3 2 7 - 0 . 0 2 5 - 0 . 0 2 * - 0 . 0 2 3 - 0 . 0 2 2 - 0 . 0 2 2 - 0 . 0 2 2 - 0 . 0 2 2 - 0 - 0 2 2 - 0 . 0 2 2 - 0 . 0 2 2 - 0 . 0 2 3 - 0 . 0 2 * - 0 . 0 2 5 - 0 . 0 2 7 - 0 . 0 2 9 - 0 . 0 3 2 - 0 . 0 3 5 - 0 . 0 3 9 - 0 . 0 * 5 - 0 . 0 5 * - 0 . 0 6 9 - 0 . 0 9 T - 0 . 1 7 1 0 - 5 3 0 3 . •• 0 7 0 - 2 7 9 0 . 2 0 7 0 . 1 2 ' ï 0 . 3 7 1 0 . 0 2 3 - 0 . 0 2 2 - 0 . 0 5 0 - 0 . 0 9 6 - 0 . 1 2 1 - 0 . 1 3 7 - 0 . 1 * 7 - 0 . 1 6 7 - 0 - 1 * 0 - 0 - 1 * 7 - 0 - 1 1 1 - 0 . 0 7 3 - 0 . 0 6 1 - 0 - 0 * 8 - 0 . 0 3 9 - 0 . 0 3 2 - 0 . 0 3 2 - 0 . 0 1 8 - 0 . 0 2 0 - 0 . 0 1 5 - 0 . 0 1 6 - 0 . 0 1 7 - O . O l l - 0 . 0 0 7 - 0 . 0 1 2 - 0 - 0 0 9 - 0 . 0 0 9 - 0 . 0 1 1 - 0 . 0 1 0 - O . O U - O . O l * - 0 . 0 0 3 - 0 . 0 0 9 - 0 . 0 1 2 - O . O l l - 0 . 0 0 7 - 0 . 0 1 2 - 0 . 0 2 1 - 0 . 0 2 1 - 0 , 0 1 7 - 0 . 0 2 7 - 0 . 0 3 6 - 0 . 0 * 7 - 0 . 0 6 3 0 . 5 2 2 0 . 3 6 6 0 . 2 6 0 0 . 1 7 6 0 . 1 0 6 0 . 0 * 9 - 0 . 3 0 3 - 0 . 0 * 5 - 0 . 0 8 2 - 0 . 1 1 2 - 0 . 1 3 7 - 0 . 1 5 6 - 0 . 1 6 9 - 0 . 1 7 5 - 0 . 1 7 * - 0 . 1 6 1 - 0 . 1 2 9 - 0 . 0 9 0 - 0 . 3 6 7 - 0 - 0 5 * - 0 . 0 * 6 - 0 . 0 * 0 - 0 - 0 3 5 - 0 . 0 3 2 - 0 - 0 2 9 - 0 . 0 2 6 - 0 . 0 2 * - 0 . 0 2 2 - 0 . 0 2 1 - 0 . 0 2 0 - 0 . 0 1 9 - 0 . 0 1 9 - 0 . 0 1 7 - 0 . 0 1 7 - 9 . 0 1 6 - 0 . 0 1 6 - 0 . 0 1 6 - 0 . 0 1 6 - 0 . 0 1 6 - 0 . 0 1 4 - 0 . 0 1 6 - 0 . 0 1 7 - 0 . 0 1 7 - 0 . 0 1 8 - 0 . 0 1 9 - 0 . 0 2 0 - 0 . 0 2 2 - 0 . 0 2 * - 0 . 0 2 7 - 0 . 0 3 3 0 . 5 2 2 0 . 3 6 6 0 - 2 6 0 0 . 1 7 6 0 . 1 0 6 0 - 0 * 7 - 0 - 0 0 3 - 0 - 0 * 6 - 0 . 0 9 2 - 0 . 1 1 2 - 0 - 1 3 7 - 0 - 1 5 6 - 0 - 1 6 9 - 0 . 1 7 6 - 0 . 1 7 * - 0 . 1 6 1 - 0 . 1 2 3 - 0 . 0 9 1 - 0 . 0 6 9 - 0 . 0 5 5 - 0 . 0 * 6 - 0 . 0 * 0 - 0 . 0 3 6 - 0 . 0 3 2 - 0 . 0 2 9 - 0 . 0 2 7 - 0 . 0 2 5 - 0 . 0 2 3 - 0 . 0 2 2 - 0 . 0 2 1 - 0 . 0 2 0 - 0 . 0 1 9 - 0 . 0 1 8 - 0 . 0 1 9 - 0 . 0 1 8 - 0 . 0 1 8 - 0 - 0 1 9 - 0 . 0 1 8 - 0 . 0 1 8 - 0 . 0 1 8 - 0 . 0 1 9 - 0 . 0 1 9 - 0 . 0 2 0 - 0 . 0 2 1 - 0 . 0 2 3 - 0 . 0 2 5 - 0 . 0 2 7 - 0 . 0 3 0 - 0 . 0 3 5 - 0 . 0 * 3 0 . 5 2 1 3 . 3 6 6 0 . 2 6 0 0 . 1 7 6 0 . 1 0 6 0 . 0 * 7 - 0 . 0 0 3 - 0 . 0 * 6 - 0 . 0 9 2 - 0 . 1 1 3 - 0 . 1 3 7 - 0 . 1 5 6 - 0 . 1 7 0 - 0 . 1 7 6 - 0 . 1 7 5 - 0 . 1 6 2 - 0 . 1 2 9 - 0 . 0 9 1 - 0 . 0 6 9 - 0 . 0 5 5 - 0 . 0 * 7 - 0 . 0 * 1 - 0 . 0 3 7 - 0 . 0 3 3 - 0 . 0 3 0 - 0 . 0 2 9 - 0 . 0 2 6 - 0 . 0 2 * - 0 . 0 2 3 - 0 . 0 2 2 - 0 . 0 2 1 - 0 - 0 2 1 - 0 - 0 2 0 - 0 . 0 2 0 - 0 . 0 2 0 - 0 . 0 2 0 - 0 . 0 2 0 - 0 . 0 2 0 - 0 . 0 2 1 - 0 . 0 2 2 - 0 . 0 2 3 - 0 . 0 2 * - 0 . 0 2 5 - 0 . 0 2 7 - 0 . 0 3 0 - 0 . 0 3 3 - 0 . 0 3 7 - 0 . 0 * 2 - 0 . 0 * 9 - 0 . 0 6 2 0 . 5 2 1 0 - 3 6 5 0 - 2 5 9 0 - 1 7 5 0 - 1 0 5 0 - 0 * 6 - 0 - 0 0 * - 0 . 0 * 7 - 0 - 0 8 3 - 0 . 1 1 * - 0 - 1 3 9 - 0 . 1 5 8 - 0 - 1 7 1 - 0 - 1 7 8 - 0 . 1 7 6 - 0 . 1 6 3 - 0 - 1 3 0 - 0 . 0 9 3 - 0 . 0 7 0 - 0 . 0 5 7 - 0 . 0 * 9 - 0 . 0 * 3 - 0 . 0 3 9 - 0 . 0 3 5 - 0 . 0 3 3 - 0 . 0 3 0 - 0 . 0 2 9 - 0 . 0 2 7 - 0 . 0 2 7 - 0 . 0 2 6 - 0 . 0 2 5 - 0 . 0 2 5 - 0 . 0 2 5 - 0 . 0 2 6 - 0 . 0 2 6 - 0 . 0 2 7 - 0 . 0 2 9 - 0 . 0 3 0 - 0 . 0 3 1 - 0 . 0 3 * - 0 . 0 3 6 - 0 . 0 * 0 - 0 . 0 * 5 - 0 . 0 5 0 - 0 . 0 5 8 - 0 . 0 6 7 - 0 . 0 8 0 - 0 . 1 0 2 - 0 - 1 3 9 - 0 . 2 1 9
T A S L : 1 - COMPARISON 3F THEORETICAL PRESSURE D I S T R I B U T I O N S AT ZERO INCIDENCE OVER AN OGIVE CYLINDER 3 0 3 Y WITH VARIOUS BASE CLOSURES
View fronn rear
Location of pressure holes.(7o of body length)
Main l i n e , ( < ^ = 0 ) : - 0 , 1 - 997o in increments of 2 7o
Auxiliary line,(<^=180) :- 11,21,31,33.33.5,34,345,41,51,61,71,81,917,
Yaw meter , ((^ = 0,90,180,270) :- 17.
bulkhead
Sting
support
fitted for these \
tests) \
Centre \
bulkhead - ^
housing
Forward \
bulkhead —
transition band)
i?:!
1
Tunnel floorSide view
Model and Tunnel X CD •Model and TunnelPlan view
Key 1 Model 2 Model sting c l o m p 3 Sting extensionA Sting extension clamp 5 Rotary disc (pivot point) 6 S u p p o r t column 7 Fixing bracket 8 I n s t r u m e n t a t i o n leads 9 Incidence wire 10 Weight wire 11 Roll s t r i n g s
0 . 7 0 : 0.G0 0 , 5 0 0 . ^ 0
Cp
0 . 2 0 0 . 1 0 0 . 0 0 : _ 0 . 3 0 : -2 •^ INCIDENCE 10FIG 5 Calibration oF nose yawmeter
First series oF tests
0.30: 0.20 0.10 0.00 -.10
INCIDENCE
FIG S Variation oF C,, with incidence
X10" 0.00 -.20 ,40
'^m
-.60 -2First test series
X ^S . . . X \ x\^ " ^"^^ ' "^" 10 12
INCIDENCE
FIG 7 Variation oF C^ with incidence
m
0.80 0.40 ^CP 0.00
!["Kultura historyczna dawna i współczesna. Studia i szkice", Jerzy Maternicki, Warszawa 1979 : [recenzja]](data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==)