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ROYAL AIRCRAFT ~5~7'A~L!~N~4~NT
R. & M. No. 3037
(17,997)
A.R.C. Technical Report
<
MINISTRY
OF SUPPLY
AERONAUTICAL RESEARCH COUNCIL
REPORTS AND MEMORANDA
<
Pressure Probes Selected for
Threc,Dimensi0nal Flow Measurement
By
D. W. BRYER, A.F.R.Ae.S., D. E. WALSHE, B.Sc.
and H. C. GARNER, M.A.,
of the Aerodynamics Division, N.P.L.
© Crown copyright zy58
/
:-i
•
LONDON"
HER
MAJESTY'S
STATIONERY
1958
PRICE
95. 6d.
NET
OFFICE
Pressure Probes Selected for
Three-Dimensional Flow Measurement
By
I). W. BRYER, A.F.R.Ae.S., 1). E. WALSI{E, B.Sc.
and H. C. GARNER, M.A.,
of the Aerodynamics Division, N.P.L.
Reports and Memoranda No. 3 o 3 7*
November, 19 5 5
Suramary.--Seven pressure probes have been tested in a uniform stream in order to ascertain the best types for
measuring velocity and flow direction. Methods of calibration are discussed in section 8 together with the effects
of wind speed, flow direction and turbulence on the calibration factors (section 4).
The performance of three of the probes in the turbulent boundary layer of a flat plate is analysed and their
accuracies compared when they are used to estimate displacement and momentum thicknesses (section 6).
The Conrad probe is proved superior to other types for boundary-layer measurements. Further research on the
lines indicated in section 7 is necessary before the best type of probe for use in regions of separated flow can be
ascertained. The main features of the velocity-measuring probes are listed in Table 4.
For measuring static pressure in three-dimensional flow, a disc type of probe is described and shown to be insensitive to flow direction and scale effect (section 5).
1. Introduction.--In recent years, low-speed wind-tunnel research has been much concerned
with swept-back wings and the behaviour of the flow past them. Although qualitative flow
observations are fairly easily obtained, the detailed study of the three-dimensional-flow
characteristics demands the precise measurement of flow parameters at many positions around
the model. For this purpose it is necessary to consider means of improving flow-measuring
instrumentation which should not only provide data of acceptable quality but be capable of
rapid operation.
In general, there are two main types of flow in which measurements are likely to be required:
(a) The attached boundary layer where large changes in flow direction are confined to
planes parallel to.the wing surface, but where normal distance from the surface must be
known to a high degree of accuracy.
(b) Regions of separated flow such as the wake or part-span vortices where large changes
in flow direction may be encountered in any plane, but where measurem4nts to a
lesser degree of accuracy than for (a) are usually acceptable.
* Published with permission of the Director, National Physical Laboratory.
I
•t
I
Flow parameters in conditions similar to both (a) and (b) were obtained in the past b y separate
measurements of a number of flow quantities at one point, different instruments being used for
each quantity. This method, apart from the excessive time required, proved inaccurate because
of errors in the positioning of successive instruments. It became evident that a first step towards
an improved technique was to find a single instrument which could be used to measure all the
relevant quantities without the necessity of shutting down the tunnel to adjust or substitute
probes. W i t h this object, a number of instruments of tile pressure-probe type have been tried.
It was seen t h a t for (a), the probe must be small, but the component of flow normal to the wing
surface need not be measured. ' B y contrast, for (b). with less likelihood of interference, a larger
instrument can be tolerated but all the flow components are required. Therefore the probes
fall into two main categories, those suitable for use in flow of type (a) and those for type (b).
At the National Physical Laboratory, measurements in a swept-wing boundary layer were
first attempted b y the Conrad yaw-meter method due to Brebner (1950) ; the results in this
case were found to be unrepeatable owing to the inadequacy of the available traversing apparatus.
An accurate apparatus (Ref. 2, 1953) was then constructed with which repeatable results were
obtained, but some discrepancies remained and were attributed to the uncertain behaviour
of the calibration factors. To discover the cause of the discrepancies, a series of tests were
carried out in the N.P.L. Low-Turbulence Wind Tunnel where tile performance of various
probes was studied to determine the most satisfactory types for use in either boundary layers
or regions of separated flow. Tile results of the investigation form the subject of this report.
2. Details of Probes and A#paratus.--2.1. Choice a~d ComEruction of Probes.--Eight types
of pressure probe were tested. Drawings 0I these and their relevant dimensions are given in
Figs. l a to lh: Their selection was governed partly b y availability and ease of manufacture,
but they form a representative group of tile types used for wind-tunnel work in recent years.
Spherical and hemispherical probes were intentionally omitted. Past experience has shown
that probes of this type, small enough for most wind-tunnel work, are very difficult to make
accurately ; even if this can be achieved, they are then liable to excessive lag in the transmission
of pressure readings. Their properties have been discussed elsewhere by Winternitz 3 (1956).
The Conrad probe (Fig. la), evolved from a yaw meter design due to O. Conrad 4 (1950),
consists of two nickel tubes soldered together side-by-side with their forward ends ground to
form a point. Four of these probes were made in order to observe the effect of changing the
external diameter of the tubes, the ratio of the internal to external diametersj and the apex
angle between the forward faces.
The 3-tube and 5-tube probes (Figs. lb and lc) embody a central tube to which are attached
side tubes with their forward ends chamfered in the same manner as the Conrad tubes.
The chisel, conical and pyramid probes, shown respectively in Figs. ld, l e - a n d lf, are all
constructed in a similar manner from stainless-steel tubing. Individual tubes are selected to
fit into an outer sheath, the interstices packed with copper wire and the whole soldered together.
The forward end of the probe is then ground to its particular shape.
The axial probe, designed b y Templin ~ (1954) at the National Aeronautical Establishment,
Canada, has a solid tip (Fig. lg) to which are connected three hypodermic tubes encased b y a
tapered shroud. The three pressure holes in tile tip are drilled before final shaping.
Fig. l h shows details of the disc-static probe which will be discussed later in section 5. It
consists of a brass disc with its edge radiused and a small pressure hole drilled through its centre.
An internal passage connects the centrM hole to a hypodermic tube fixed to the edge of the disc.
In the manufacture of all these probes, the internal diameter of the pressure tubes was increased
from a position as close as possible to the measuring point. Thereby lag in the transmission of
pressures was reduced to a minimum,
2
2.2. A/5/saratus and Tests.--All the probes were calibrated in the N.P.L. Low-Turbulence
Wind Tunnel which had a 16-sided working-section with opposite faces 7 It apart. The probes
were mounted in turn on a traversing and yawing apparatus (Ref. 2) and provision was made
for the accurate setting of.pitch. Tests were carried out at wind speeds ranging between
50 It/sec and 110 It/sec. In some of the tests a steel-mesh screen was used to increase turbulence
in the tunnel stream. The screen was ~ in. thick with ~ in. square holes separated by ~ in. wide
strips and was fixed normal to the flow at a position 6 It upstream of the calibration position.
Pressures were measured with a sloping-tube alcohol manometer which could be read to 0.01 in. ;
this gave an overall accuracy within approximately 1 per cent of the dynamic pressure in the
worst case, this being the lowest wind speed of test.
In order to carry out boundary-layer measurements, a flat plate of 0.625 in. thickness, 4 ft
span and 14 ft. chord was rigged horizontally in the working-section ; incidence could be set to
either 0 or + 3 deg and surface pressure holes were disposed chordwise along its centre at intervals
of 1 ft. To ensure a turbulent boundary layer, a trip wire was fixed to the surface at a short
distance behind the faired leading edge. To increase the turbulence in certain tests, a spoiler
of 1 in. square section was fitted to the surface immediately behind the trip wire. Before making
measurements with the various probes, total-head a n d static-pressure traverses normal to the
surface were carried out at selected positions along the centre-line of the flat plate. For these,
a 0.048 in.-diameter total-head tube and a 0.063 in.-diameter static tube were used, both
instruments having been carefully calibrated against an N.P.L. sub-standard pitot-statie tube
in the calibration position. It was considered that, in the absence of yaw and a change of pitch
of less than 3 deg, the measurements so obtained were accurate to plus or minus ½ per cent of
the dynamic pressure at the edge of the boundary layer except in positions very close to the
surface or when the spoiler was present.
3. Princi/sles of Calibration.--In a steady stream, the magnitude and direction of the flow
at any point may be defined by four independent parameters, the angle of pitch 0, the angle
of yaw ~0, the total head H and the static pressure ~b. In order to calculate these from windtunnel observations, at least four quantities must be measured at the point and their relationship
to the flow parameters ascertained by calibration of the measuring instrument. We now examine
methods of calibrating tile velocity measuring probes described in section 2.1.
3.1. 2-Tube Method.--For use in boundary layers where the velocity component normal to
the surface may be ignored, we consider first the simple Conrad yaw meter (Fig. la). It is
seen from Fig. 2a that, when the probe is yawed about the vertical axis through its apex, the
difference in pressure in the two tubes (/51 --/52) behaves linearly with ¢ , the angle between the
longitudinal axis of the probe and the local flow direction for [ ¢I < 15 deg. Moreover, as shown
in Fig. 1 of Ref. 1, the values of (/51 --152) are substantially greater than those obtained with
other types of yaw meter. Having recognized that a pressure probe could be fairly easily
arranged to rotate about the vertical axis through its apex, Brebner has given in the Appendix
• to Ref. 1 a method of operation which may be simplified in the following way.
The probe is yawed until the pressures in the two tubes are equal, i.e.,/51 = t52 = 150, say.
At this position (¢ = 0), t50 is noted together with the angle of yaw. The probe is then rotated
to ¢ = ± 1 0 deg and the values of pl and ~b2 recorded for both positions. Then, with the aid
of the calibration factors K1 and K2 :
H = ~o + K1A /
t
o
where
= ½{(A) + ~o -- (P~)+ ~o = (A)-1o + (P~)- ~o}.
3
(1)
The choice Of ¢ ~- q-10 deg is large enough to ensure 1 per cent accuracy in measuring ¢ , yet
well within the range for linear A (Fig. 2a).
For all the probes illustrated in Figs. lb to lf, the behaviour of the side-tube pressures with
yaw is similar to that of the Conrad probe, so that the method described above might be applied
to any of them. F o r example, Fig. 2b shows the effect of yawing or pitching the symmetrical
pyramid probe (Fig. If), whose upper and lower tubes couldbe used to indicate changes in pitch.
3.2. 3-Tube Methods.--The addition of a central tube to the Conrad probe to form the 3-tube
probe (Fig. lb), enables total head to be observed directly when the probe is rotated in the plane
of the tubes until the side-tube pressures are equal (2#1----2#~ -----2#0). If 2#8 is the pressure in the
centre tube:
H ~-- 2#8
(2)
2# -----2#0 + K3(2#a -- 2#0)
where K3 is obtained from calibration.
Kiichemann 6 (1955) describes a method due to Crabtree, who suggests that the 3-tube probe
might be used without rotation. This method relies on three conditions being satisfied; the
difference between the pressures in both pairs of adjoining tubes must be linear and their sum
in one pair must remain constant with respect to yaw. In practice, the first condition appears
to be satisfied, but Fig. 3 shows that the sum of the presures in adj oining tubes is approximately
constant only in limited ranges of yaw, 28 deg < [~[ < 47 deg for this particular 3-tube probe.
By increasing the apex angle of the probe to 146 deg these ranges could be brought together to
give an approximately constant sum for l~l < 15 deg. This renders the method impracticable,
since the sensitivity (2#1-- 2#~)/¢, which varies roughly as the cosine of half the apex angle, would
be reduced by a factor of about one third.
3.3. 5-Tube Methods.--The methods mentioned so far in this section are intended primarily
for conditions where the angle of pitch is negligible or its effect on the measured pressures is
small within a limited range of 0. Where the flow is truly three-dimensional, it is necessary
to measure a fourth quantity, either angle or pressure, to obtain all four flow parameters. Such
measurements are usually required at positions far enough from the surface, to permit the use of
a larger probe without introducing any serious interference effects.
The most direct method of measurement is to use a 5-tube probe (Fig. le), which can be aligned
directly into wind so that the pressures in the four side tubes are equal; the angles of pitch
and yaw are indicated by the traversing apparatus, H is read from the centre tube and 2# can
be obtained from equation (2) as for the 3-tube probe. Unfortunately, the mechanical problems
involved in making the traversing apparatus are difficult to solve. It is therefore necessary
to investigate other methods which require rotation of the probe about only one axis.
The following method has been examined. The 5-tube probe is yawed to obtain equal pressure
readings in the side tubes, so that 2#1 : 2#2 : 2#o. If 2#8 and 2#~ are the pressures ill the upper
and lower tubes and 2#5 the centre-tube pressure:
o =
c(2#,
-
2#8)/(25 -
{ =
H - - 2# =
po)
K(2#5 - - 2#0)
H = 2#5 + F ( o ) q
where C, K and F(O) are obtained from calibration.
4
og
QI
1o
4 5
~ t
(3)
3.4. Temibiin's Method.--Another method, due to Templin 5, is to use a probe of the pattern
shown in Fig. lg. In this case, the probe is rotated about its longitudinal axis until the side-tube
pressures are equal, when this pressure/50 and the centre-tube pressure/58 are recorded. Then
the velocity vector lies in the plane containing the longitudinal axis and the normal to the plane
through the side tubes. The probe is then rotated through 90 deg and the larger of the side-tube
pressures t5' is recorded ; from this reading/5', together with/50 and fla from the previous position,
the remaining flow parameters may be deduced from calibration curves. In the presence of
scale effect at large flow angles, the method outlined above would require calibration charts.
To facilitate the reduction of results when the angle 0 between the velocity vector and the axis
of the probe does not exceed 15 deg, however, it is suggested here that calibration factors could
be applied instead, the flow parameters being computed from the equations:
o = c'(p' - p0)/(p
q = H--p
- p0)
=
P0)
t
(,
(4)
H = P0 + F'q + G ' ( p ' - / 5 0 ) )
where C', K', F', G' may depend on wind speed.
4. Calibration Factors.--The utility of any velocity measuring probe will depend ultimately
on the manner in which the calibration factors vary with flow conditions. Changes in flow
direction, Reynolds number, turbulence and velocity gradient are likely to have some effect.
The uniform-stream calibration was intended to estimate the relative magnitude of the effects
due to the first three of these variables. On the resuIt of this, three of the probes were selected
and the behaviour of their calibration factors was further examined in the presence of total-head
gradient.
The apparatus used in the calibration tests has been described in section 2.2. Changes of
flow direction were simulated by altering the attitude of the instruments in relation to the
wind direction. Reynolds number was varied with wind speed and small-scale turbulence
introduced by fitting the steel-mesh screen. To observe the effect of total-head gradient,
measurements were made in the fiat-plate boundary layer where turbulence could be further
increased by attaching the spoiler. In no case was turbulence measured, but the perturbation
of silk tufts held at tile measuring positions showed that an appreciable increase resulted from
either of the devices described.
4.1. 2-Tube Method.--Uniform Stream.--Results from the uniform-stream calibration of six
types of probe to which the 2-tube method (section 3.1) could be applied are given in Figs. 4a, 4b,.
5a, 5b, 6 and 7. As regards the various types of Conrad probe, it is seen in Fig. 4a and Fig. 6
that the effect of pitch on the sensitivity ratio (/51 --P~)/q$ for [0] < 6 deg is small in all cases
and will scarcely affect the accuracy of measurement except when the sensitivity ratio itself
is low. This is the case for the Conrad-(iii) probe, whose large apex angle reduces sensitivity
by about 40 per cent. In Fig. 4b, scale effect is seen to be appreciable for the Conrad@) probe,
but tends to disappear when the external diameter of the tubes is increased ; scale effect does
not appear to depend on the internal diameter, but reduction in the ratio did lowers the
sensitivity. The introduction of small-scale turbulence by means of the screen (section 2.2)
has no serious effect on the behaviour of the Conrad probes which are therefore likely to be
suitable for boundary-layer exploration. For tests in boundary layers, the Conrad-(i) was
selected as being conveniently small, and the Conrad-(iv) as being insensitive to scale effect;
with these two probes, it was possible to study further the effect of varying the ratio diD.
It is quite clear from Figs. 5a and 5b that of the five probes compared, all except the pyramid
• probe show a degree of sensitivity to pitch sufficient to preclude their use with the 2-tube method.
5
It Iollows that the chisel probe can be used only as a yaw meter. The conical probe can be
used to measure flow direction, but, lacking a central tube, cannot at the same time provide
sufficient data to estimate velocity. The pyramid probe, being reasonably insensitive to pitch,
scale effect and small-scale turbulence, was selected as the third probe for boundary-layer tests.
A comparison of the Conrad- (i) , Conrad- (iv) and pyramid probes in
of practically uniform sensitivity. In Fig. 7, the calibration factor
to obtain total head, is plotted against 0 for each of the three probes.
to be independent of the flow conditions, provided that ]01 < 6 deg.
calibration factors defined in equation (1) are taken as follows:
Probe
K1
Conrad@)
Conrad-(iv)
Pyramid
1"13
1 "42
0"90
Fig. 6 shows them to be
K1 = ( H - 1)o)/A, used
In each case, K1 appears
Constant values of the
ar~2
-- 0"935
-- I. 535
In the case of the Conrad@) probe, there is an appreciable scale effect, which can be represented
by the formula:
-- K2 =
1.03
where q0 = ½pV2, when V ---- 110 ft/sec.
-- 0.20
log1012 6- _ ~ _ A ,
q0
•.
.
.
.
.
.
.
(5)
In all cases the dynamic pressure is q = (KI -- K2)A.
4.2. 2-Tube Method.--Boundary Zayers.--The calibration factors, K~, K2 and ( K ~ - K2)
obtained from boundary-layer measurements with the Conrad@), Conrad-(iv) and pyramid
probes are given in Figs. 8a, 8b and 8c respectively. For the Conrad probes corrections of
0.18D have been applied to the vertical displacement, as suggested by Young and Maas 7 (1936)
for total-head tubes. The calibration quantities, plotted against wind speed, include results
from positions at the edge of the boundary layer, and at 0-5 and 0.2 of the boundary-layer
thickness ~ ; a few results in the separated turbulent flow behind the spoiler (section 2.2) are
also included. For each calibration factor a full-line curve indicates the values taken from the
uniform-stream calibration.
For the Conrad-(i) and Conrad@v) probes, it is seen that the values of K1 and Ks from tile
uniform-stream calibration are in fair agreement with those estimated from measurements
taken in the presence of a velocity gradient ; of these two probes, the Conrad-(i) shows the least
scatter. In the case of tile pyramid probe, the boundary-layer values are somewhat lower
than in the uniform stream, which suggests that free-stream Values of K~ and K~. would tend to
overestimate total head and underestimate static pressure when used for boundary layers. As
may be expected, values of K~ and K2 at the edge of the boundary layer are generally close to
the uniform-stream value, whilst for the larger probes at 0.26 they are occasionally subject
to interference effects. The effect of increasing the scale of turbulence is seen to be small.
4.3. 3-Tube and 5-tube Methods.--The 3-tube probe has been calibrated in a uniform s t r e a m
on the basis of equation (2). From these measurements, the sensitivity ratio (ib8 --Po)/q has
been plotted against velocity (0 = 0) and against angle of pitch O(V = 110 ft/sec) in Fig. 9.
Sensitivity and scale effect are compared with results from the Conrad@) and 5-tube probes;
tile effect of 0 is compared with the 5-tube probe. The scale effect on (/98 -- Po)/q is seen to be
similar to the effect on (Pl --1~2)/q4 for tile Conrad-(i) probe, but the 3-tube probe has only
about three quarters of the sensitivity of the Conrad-(i) when ~ = 4- 10 deg. The lower sensitivity is quite offset by the rapidity of the 3-tube equi-balanced method ; however, its extreme
sensitivity to pitch renders it unsuitable for use in a n y but purely two-dimensional flow.
6
When upper and lower tubes are added to the 3-tube probe to form the 5-tube probe, the
effect of pitch on (P5 --flo)/q is small (Fig. 9), but the scale effect remains appreciable. This
scale effect must be taken into account when calibrating for the 5-tube method using equations (3).
The calibration factors from the uniform-stream calibration of the 5-tube probe are given in Fig.
10. W i t h this method, it is seen that the accuracy of dynamic-pressure measurement diminishes
rapidly for 101 > 15 deg, but the method could be used up to I01 -- 20 deg if an accuracy of
plus or minus 4 per cent is acceptable. I t should be noted t h a t this method can utilize the same
type of traversing apparatus as t h e 2-tube method.
4.4. Axial-Probe Methods.--Uniform-stream calibration curves for the axial probe are shown
in Fig. l l a where values from the Canadian tests (Ref. 5) are also plotted. The wind speed
of the Canadian tests was 50 ft/sec. Calibration of the axial probe reveals a marked scale effect
at the higher values of 0 and there is a discrepancy between the values of (Ps --Po)/q obtained
with the N.P.L. instrument and the values from Ref. 5. It is difficult to account for this
discrepancy as the probe examined here is a fairly exact copy of the Canadian design ; at the
same time, the reasonably constant values of (P3 --Po)/q for 0 < 15 deg given b y the N.P.L.
instrument facilitate the application of calibration factors (equation (4)) for limited flow angles.
The behaviour of such factors under various flow conditions is illustrated in Fig. 1 lb where a
possible accuracy of plus or minus 2 per cent on velocitymeasurement is indicated for IOl < 15
deg. If this is acceptable, equation (4) can be used with the values:
C' = 25.3 deg ,
F'=0.55,
G'=0.07
K ' = 1-69 -- 0. 125 log10ib~ -- P0,
q0
and
.. . . . . . .
(6)
where q0 = ½pV2, when V = 110 ft/sec.
5. Disc-Static _Probe.--Although not entirely relevant to this paper, the disc-static probe
has been included as a type of static-pressure probe which is insensitive to changes of flow direction
in one plane and is not subject to scale effect. The instrument, described in section 2.1 and
illustrated in Fig. lh, is shown to have the above properties in Fig. 12. Furthermore, if provision
is made to rotate the disc about the vertical axis through its centre (Fig. 12), it can be used in
three-dimensional flow where very large changes in flow direction Occur. The probe was first
calibrated in the N.P.L. 18-in. Octagonal Tunnel at wind speeds up to 70 ft/sec. It was observed
to have negligible scale effect and a low degree of sensitivity to pitch. As shown in Fig. 12, the
recorded pressure attained a well-defined maximum, as the disc was rotated in yaw to about
minus or plus 4 deg from the 'into wind' position. Within these limits the recorded pressure
remained practically constant ; it is apparent t h a t this property can be employed to align the
disc approximately along the wind direction when this is unknown. Further tests in the
Low-Turbulence Tunnel show that scale effect remains small between 50 and 110 ft/sec and t h a t
the reading is little affected b y turbulence in the tunnel stream. The readings obtained with
the present instrument require correction b y about 0.12 of the dynamic pressure so t h a t an
approximate estimation of total head is necessary before the static pressure can be deduced to
an accuracy of plus or minus 1 per cent of the dynamic pressure. B y altering the edge shape or
thickness ratio of the disc it would be possible to reduce this correction.
6. Boundary-Layer Traverses.--Neasurements of boundary-layer velocity are most frequently
undertaken in order to estimate the displacement thickness and momentum thickness:
01=
0 1--~
.
~2= oU
7
.
.
.
.
.
.
.
.
.
.
(7)
I t is therefore of major interest to compare the performance of the Conrad@), Conrad@v) and
pyramid probes when measurements with each are used to evaluate the above integrals. Results
from nine different boundary-layer profiles on the flat plate have been taken. Initially, careful
measurements were made with pitot and static tubes; the traverse positions and associated
data arelisted in Table 1. Two typical traverses are illustrated i n Fig. 13a and Fig. 13b, where
the total-head and static pressure deduced from measurements with the three probes are plotted
together with curves obtained with the pitot and static tubes. The tendency for the pyramid
probe to overestimate velocity is clearly shown. For the Conrad probes, no consistent effect
appears to accompany a change in the ratio diD. Tables 2 and 3 show respectively the values
of dl and d2 obtained with the pitot and static tubes together with available values from the
three probes. To obtain these values rapidly from a minimum number of observations, use
has been made of the formulae which are included under Table 3 and fully discussed in Ref. 8
(Garner. 1956). The use of these formulae is well justified by the comparison in Tables 2 and 3
of integrated values of ~1 and d~ with those obtained with the formulae for each of the nine pitot
and static traverses. Values computed by the two methods agree to within 1 per cent in nearly
all cases. Figs. 14 and 15 are intended to illustrate the degree of correlation in ~1 and d2 between
results from the three probes and pitot and static measurements. The Conrad-(i) results are
seen to be nearest to tile line representing perfect correlation, although with this instrument,
experimental scatter can be up to plus or minus 4 per cent. The general tendency of the pyramid
probe to underestimate values of ~ and d2 is thought to be due partly to interference and partly
to a change in K1 and K2 (section 4.2) associated with a total-head gradient.
The effect of flow conditions on the accuracy of velocity measurement does not alone dictate
the type of probe best suited to boundary-layer exploration. Other factors, which may have
no direct bearing on the overall accuracy but influence the choice of pressure probe, are ease of
manufacture, size and rapidity of operation. Pressure probes comprising a simple arrangement
of tubes are readily manufactured to a high degree of accuracy. The maximum size is usually
limited by the minimum boundary-layer thickness to be encountered whereas the minimum
size will depend both on the pressure-transmission lag and the accuracy attainable in manufacture.
It has been seen here that no particular merit attaches to tile use of tubing of ratio did less
than 0-60, so that standard hypodermic tubing of this ratio can be used.
7. Concluding Reread'ks.--7.1. Assessment of Probes.--An assessment of the various pressure
probes is given in Table 4, which lists their advantages and disadvantages when used to measure
velocity and flow direction by the methods described in section 3. In summarizing tile salient
features of tile probes and their methods of operation, consideration has been given to the
overall requirements of pressure probes for wind-tunnel work:
Small size with structural stiffness
(b)
(c)
(d)
(e)
(f)
(g)
All measurements as nearly as possible at a point
Rapid pressure response
Calibration unaffected by flow conditions
Simplicity of accurate construction
All the required measurements from one instrument
Rapid measurements at a number of points by remote control.
The last two properties are almost essential for detailed exploration of three-dimensional
flows.
7.2. Boundary-Layer Measurements.--For velocity measurement in the attached three-dimensional boundary layer, the Conrad probe (Fig. la) is suitable and can be calibrated in the manner
described in section 3.1.
8
From the free-stream calibration (Figs. 4b, 6 and 7) the Conrad@v) appears slightly superior
to the Conrad-(i) mainly on account of smaller scaIe effect. Further calibration in the boundary
layer (Figs. 8a and 8b) reveals this to be misleading, as variations in the calibration factors
K1 and K2 under boundary-layer conditions suggest for velocity measurement an accuracy of
plus or minus 2.4 per cent for the Conrad-(iv) and plus or minus 1.6 per cent for the Conrad@).
The pyramid probe (Fig. lf) does not measure velocities in boundary layers more accurately than
plus or minus 3-3 per cent.
From boundary-layer traverses with the Conrad@), Conrad-(iv) and pyramid probes, the
ro0t-mean-square error in tile estimation of displacement thickness ~1 (Fig. 14) is respectively
3-5, 5 and 11 per cent, and for momentum thickness (Fig. 15) is 3, 4.5 and 9 per cent.
Besides showing more consistently accurate results, the Conrad@) probe is preferred to the
Conrad-(iv) because the ratio d i d = 0.6 allows for a smaller probe with less pressure transmission
lag or danger of blockage due to dust particles.
The 3-tube, 5-tube, chisel, pyramid and conical probes are unlikely to be of use for
measurements in three-dimensional boundary layers (sections 4.1, 4.2 and 4.3).
7.3. Measuren, ents in Detached Flow.--It is premature to suggest that any pressure probe
will give acceptable results under all possible conditions of detached flow. Generally, a sharpedged instrument is preferred to a rounded one, boundaryqayer transition at the nose being
affected less by Reynolds number.
The 5-tube probe could be used equi-balanced, or with two calibration factors and one curve
(Fig. 10), providing the angle of pitch is less than 15 deg.
Similarly, the axial probe could be used with calibration factors for values of themean-flow
angle 0 less than 15 deg (Fig. l lb). For 0 > 1 5 deg, the calibration requires two charts and
a single curve for ~ (Fig. lla).
Where very large changes in flow direction occur, static pressure could be measured with a
disc probe (section 5). Tests show the disc-static probe (Fig. lh) to be essentially free from scale
effect at wind speeds below 110 ft/sec.
7.4. Future Work.--It is probable that the best results in detached flow would be obtained
using instruments of the 5-tube type with apparatus capable of aligning the probe to the local
mean flow direction. An apparatus of this type due to Fail (Ref. 6) has been used at the Royal
Aircraft EstabliShment; development of a remotely controlled apparatus is being undertaken
at N.P.L.
In a programme of tests about to be started at N.P.L., it is proposed to examine the behaviour
of Conrad probes in the boundary layer of a two-dimensional model aerofoil. The 5-tube and
axial probes will be tested in the wake of the aerofoil with separated flow of high turbulence
intensity and low mean velocity. Under these conditions it is known that different pressure
probes give inconsistent measurements of mean flow. In the opinion of the authors, this may
be due to the relative sensitivities of the probes to fluctuations in flow direction. It is hoped
that from hot-wire turbulence measurements and a knowledge of the steady-flow characteristics
of the probes it may be possible to ascertain to what extent they measure the true mean velocity.
8. Acknowledgements.--The authors wish to acknowledge the help of Miss S. M. Passmore,
who carried out much of the computation, and Miss I. G. Davidson, who assisted Mr. Walshe
with the experimental work. Mr. J. H. Warsap was responsible for the calibration of the discstatic probe.
9
NOTATION
D
d
H
External diameter of individual probe tube or of circular-section probe
Internal diameter of probe tube
Total head
o
KI, K2
Calibration factors (2-tube method)
P
t)o
Static pressure
Pressure in side tubes when probe is orientated until these give equal
readings
2b,~
Pressure in tube ~ of probe (n = 1, 2, . . . 5)
Pressure in side tube of axial probe (section 3.4)
Dynamic pressure (---- ½pV2)
2'
q
qo
R~
Reference value of q (V = 110 ft/sec)
Reynolds number of boundary layer ( = U(~2/v)
U
Velocity at edge of boundary layer
Velocity at distance z from surface
V
Velocity
Normal distance from surface
z
A
Average pressure difference between side tubes {equation (1)}
(3
dl
Thickness of boundary layer
~2
Momentum thickness
0
Angle of flow relative to axial probe (section 3.4)
0
Angle of pitch
Displacement thickness
Kinematic viscosity
¢
Density of fluid
Angle of probe in yaw (relativeto ~)
~o
Angle of flow in yaw
P
10
REFERENCES
No.
Author
Title, etc.
1
G . G . Brebner
....
..
Pressure and boundary-layer measurements on a 59 deg swept-back
wing at low speed and compaSison with high-speed results on a
45 deg swept wing. C.P. 86. P a r t I. February, 1949. P a r t II.
August, 1950.
2
D . W . Bryer
....
..
A remotely controlled traversing yaw meter for boundary-layer
exploration. J. Sci. Inst. Vol. 33, pp. 173-175. May, 1956.
3
F . A . L . Winternitz
..
Probe measurements in three-dimensional flow.
28. No. 330, pp. 273 to 278. August, 1956.
4
O. Conrad
....
..
Geraete zur Messung yon Stroemungsrichtungen.
Technisches Messen. V 116-2. October, 1950.
5
R . J . Templin
....
..
Flow characteristics in a plane behind the trailing edge of a low
aspect-ratio wing as measured b y a special pressure probe• N.A.E.
Lab. Memo. AE-58. April, 1954.
6
D. Kiichemann
..
Boundary layers on swept wings: their effects and nleasurement.
R.A.E. Tech. Note Aero. 2370. April, 1955. Proceedings of the
7th meeting of the A.G.A.R.D. Wind-Tunnel and Model-Testing
Panel. Canada. June, 1955.
7
A . D . Young and
•.
The behaviour of a pitot-tube in a transverse total-pressure gradient.
R. & M. 1770. September, 1936.
8
H. C. "Garner
..
Thickness parameters b y rapid integration of turbulent boundarylayer profiles. J. Roy. Aero. Soc. Vol. 61, pp. 278-280. April,
1957.
J.
....
..
51. Maas
11
Airc. Eng.
Archiv
Vol.
fuer
TABLE 1
Boundary-Layer Data
Case
1
2
3
4
5
6
7
8
9
Incidence
(de~
0
0
0
0
0
3
3
3
3
Position
(ft)
2
8
12
12
12
4
12
4
12
U
(ft/se~
113
113
115
67
54
116
116
68
68
~1/~2
d
(in.)
0.53
1.35
2.00
1.90
2"30
1"00
2.20
1-10
2.25
1"385
1"355
1.35
1.37
1.33
1"365
1-33
1"37
1"35
R ~ X 10 - 3
3.3
8.0
11.5
7-2
6.3
6.0
13-1
3-9
8.4
TABLE 2
Values of ~ (in.)
Probe
Case
1
2
3
4
5
6
7
8
9
P i t o t and Static
Integrated
0"0761
0"1837
0"2587
0.2785
0.2937
0.1345
0-2866
0"1498
0-3167
Formula
0"0754
0"1819
0"2557
0.2763
0.2954
0-1347
0"2860
0"1490
0.3141
TABLE
,
Probe
Case
1
2
3
4
5
6
7
8
9
(53 1 - 0" 8 7 6 9 -
-
o
Conrad-(iv)
Pyramid
Formula
0"0717
0-1839
0-2414
0.2662
0.2806
0.1355
0"2803
0"1520
0-3236
Formula
--0"2434
-0.2765
0.1244
0-2776
0"1448
0.3107
Formula
-0-1701
0"2260
--0.1171
-0"1308
--
Conrad-(i)
Conrad-(iv)
Pyramid
Formula
0.0522
0"1373
0.1810
0"1989
0-2116
0-0995
0"2112
0.1102
0"2414
Formula
--0"1822
-0"2088
0.0922
0.2092
0.1059
0.2318
Formula
-0.1292
0.1724
--0.0880
-0.0977
--
3
Values of o~ (in.)
P i t o t a n d Static
Integrated
0.0550
0.1357
0.1915
0.2035
0.2206
0.0985
0.2155
0.1092
0.2348
Conrad-(i)
Formula
0.0543
0.1359
0.1915
0.2044
0.2228
0"0987
0.2154
0.1086
0"2340
0" 3 3 7 0 ( Uu ) o . 1~~ 6 s o -
o
' -o
12
0" 5289(U)o.6195~
u S
o1
@}
o-
TABLE 4
Summary of Probe Characteristics
The following probes are assessed for boundary-layer work only requiring measurements of
yaw and velocity.
Probe
Conrad
Fig. No.
Method
la
2-tube
Advantages
Disadvantages
i Easily manufactured. Measurements nearly at a point.
Practically insensitive to -}- 6
deg of pitch
Requires accurate yawing apparatus
Small (suitable for boundary-
Scale effect must be taken into
account
i
Conrad-(i)
la
2-tube
layer measurement).
accurate
i High sensitivity.
effect
Most
Conrad-(ii)
la
2-tube
Conrad-(iii)
la
2-tube
No special advantages
Low
sensitivity.
scale effect
Conrad-(iv)
la
2-tube
No scale effect
Large for boundary-layer work
(if reduced, internal diameter
too small)
3-tube
lb
equi-balanced
Direct reading of total head.
Very rapid
Sensitive to pitch and scale effect
3-tube
lb
2-tube
Direct reading of total head
Sensitive to pitch and scale effect
Requires accurate yawing apparatus
Chisel
ld
2-tube
No special advantages
Very sensitive to pitch. Unsuitable for 3-dimensional work.
Slow response.
Difficult to
No scale
Large for boundary-layer work
manufacture
13
Appreciable
TABLE 4--continued
Summary of Probe Characteristics
The following probes are somewhat large for boundary layers and are assessed for other threedimensional work. In addition to yaw and velocity, the angle of pitch is obtainable with all
these probes.
Probe
5-tube
. Fig _No.
Method
Advantages
1
equi-balanced
Direct reading of total head.
Rapid
Requires elaborate yawing and
pitching apparatus. Appreciable scale effect
Disadvantages
5-tube
2-tube
High sensitivity
Sensitive to pitch and scale effect.
Accurate yawing required
5-tube
5-tube
Requires only to be yawed
Unsatisfactory
(> 20 de~)
for large
pitch
Conical
le
2-tube
No special advantages
Difficult to manufacture.
sensitive to pitch
Very
Pyramid
If
2-tube
Insensitive to limited pitch.
No scale effect
Difficult to manufacture
,
Axial
lg
Templin
(section 3.4)
Requires rotation about'probe
axis only
Requires careful manufacture.
•Appreciable scale effect '(requires cMibration charts)
Axial
lg
Equation (4)
Requires rotation about probe
axis only. Simple calibration
Scale effect.
to 15 deg
14
Flow angles limited
(a-)
D
(i)
(ii)
(i/i)
(iv)
Conrad probes
_~ angle
Apex
o.o31" O'bO
0"063" O'bO
0.0bs" 0'be
0"063" 0"32
70~
7o °
1200
700
~ Apex
1,
angle
(b)
I
~-
bubeRrobe
5 - ~ube Rro~e
(c)
o.o0++,o.~o aA~;"+l
"o'o~b"/3
70* I
------Apex
I
oDe
angle
70°
I
(e)
Io
-- ahgle
I ° o'n19
°+1
90 °
O'Oe8"
Conical probe
0'121 "
0"17
~ngle
g~o
(f)
I
lot
Apex
\
Il II I ii
I
I II
I
I II
I
I
I
I
I
I
I
I
I
I iI I
1II i
I
I
I I
hI,
I I
l ,,
Top
Top vrew
lop vFew
Fronb view
Front view
iI
and s~de
v;ew
Topand~ide
Top view
+o+
G_!
view
view
Io
v+
IN',
i-,,-,a
cn
(h)
(,9) Ax,al probe
d = 0-020"
H o.eo"
,,
~+-_k___:/! ~ ]
o.3o'~
•
Diac-sga~c probe
Rogagmn
I
Top view
51de view of disc
Holes I 2and 3
o.o,'# Rad--'l--I'-" ° ' ° J
] Trans/abon
t
+~ o.o,o.o,a
8
Topviewof probegip
Apex
angle
l ll!lI:
lilIMi',
IllrlIi
II
5ide v~ew
Apex anBle = ao °
90° J
I',!',I,!
llJ'l,l
ii
II
I I
a~le I
...
Ii
I I', ',',
II
I~I
I','I ii
"
probe
P_~ram/d
~
,',
I
f
I
I
I
I i
i
I I
I I
I
Apex
,'L~. ~
Ch,sel probe
(d)
d
Frone v;ew
Side view
Frontviewof d;~c
FIGS. l a to lh.
Details of v a r i o u s probes.
#op and
view
_
Frong ~
v;ew
~;de vJ'ew
--?-;~d
o
!
~0 = ~2 (~Vo
+
V
Conrad
Conr&d
I
o7 ]
vo = I10 f t / ~ e c
where
D = 0"063"
D = 0"063"
d = 0-60 D
d:o.~2
D
Wind
direcBion
0"6-
V= uo ft/~ec
5~ream
0"5i--
,
0"4
/
,t
X-,/
./a,~+~
0"2 --
/
--rl
¢
/
I
~
_ ~ ..
P~ramid
4~.7
&P = P,-P2 agains~ # ( ~ o = o)
zXp =Pz-P* against 0 (£~ 0= O)
06
/
/ /
V = tJo
.0'5
'
f~/sec
Free 5Lr~a.m
\
\
/
z
Pklramid
/
.0-4
\
.0-3
[
0'2
0"1
0"1
Ap
V = 54 ft/sec
Turbulent~tream
qo o
V=54
%o
Turbu/en ~ 5~re_.&m
"-0-1
-0'
-0'3
-0'3
//
-0"5~
-0"4
-0"~,
-0"5
-O'b
-O'b i
-0'7
I
-15 °
FIG. 2a.
-I0 °
-50
0
-0"7
5°
Angle of probe in gaw (~)
Effect of yawing.
I0 °
15°
Conrad probes at zero pitch,
_15o
_]@o
_50
0
5°
I0 °
15 o
Angle of robag)on (# or-e)
FIC. 2b.
Effect of rotating Pyramid probe in yaw and pitch.
1.0
(p2.r p~)= consLant.
0"9
/
0.8
0.7
G÷I%-2p
2q
/
/
I
El V=IIOf~/sec
+ V= 50fL/sec
]
115eful range
~=0
28° < ~/~47 °
'-4
0"6
" ,,',2"
/
J
0"5
I
i
0-4
0"5
-20
FIG, 8.
-I0
I)
10
-20
30
40
50
Limitation of non-rotating 8-tube probe.
Free
Tur-b.
sV~ream ~tceam
(i)
.----o
('i)
--o . . . .
(ib
--+
(ii1
(iii)
--+ ....
(iv)
----v---
(,iv)
--~ . . . .
e--
+--
--x-~--
D
d/D
0.03('
0.60
O' 031"
0"60
o.o6f
0.60
0.063"
o. 0~ 3"
0.60
0.32
o. ~2
o. o6~"
o. o63"
0.60
Apex
angle
70 o
70 °
70 °
70 ~'
120 a
700
700
V
II0
50
II0
S0
II0
110
50
P-Fee
Tur-b
~L~-eam 5 t r-e.a.m
q =~PV 2
¢=±i0 °
0.050
Ci)
(ii)
(]ii)
----o-.~
--x--
+
(iv)
-----v---
v
0 "050
o
Apex
D
did
O'OBI a
O,06B"
O' 053/I
0'60
0'60
70 °
70 °
0" 60
1"20°
0'065"
0'52
70 °
4-
e,ngle
q = Y2pV 2
0
O =
~ = +-I0 ~
I
÷
+
+
0"048
0' 048
0'046
0. o46
l
/ I
0'04-4
0" 044 ~
0"04.2
0' 0 4 2
~
V
7
L
P , - P2
O0
q f)
0"060
q ~ 0.040
0"038
0"038
0"0.36
0"036
'
0" 034
0'032
0"057
/ X
0'0 3 0
0"028
0
Z 6°
Angle
FIG. 4a.
~12 °
0'028
40
/
/
50
60
70
/
80
90
100
II0
J20
of pi~,ch (.e)
Sensitivity of Conrad probes in measuring v e l o c i t y . Effect of pitch.
FIC. 4b.
Sensitivity of Conrad probes in measuring v e l o c i t y . Effect of velocity.
5~rnbol
Probe
~-~ube
5-gube
Chisel
Conical
Pqramid
P~ramid
P~lramid
Apex
V
ahgle :Wsec
700
7o 0
Ii0
IIo
~e °
Ito
9o 0
9o 0
90 °
90 °
IIo
II o
50
5#
5bream
Free
ffree
Free
Free
Free
Free
Turbulen~
r¢ =~ pvZ
5cjmbol
Probe
Apex
angl e
= ± I0o
+
__¢.--
3-bube
700
--D.--
O'OOO
5bream
Free
~o °
Free
90 °
Free
900
Free
90 ° i Turbulenb
5-bube
Conical
PLjr&mlc~
PLjr~mid
q = J/2p v 2
e=O
=
*
i0 o
0"060
f
O"058
j
,
J
J
J
J
O' O ~ l
\
\
0'052
PI-~2
c.O
0"050
\
O'05~
PI - P=
q~
0.050
0'048
0.048,
0'046
0.046
0'044
O"044
0"042
0"04-,
3
¢
0"040
42
G
0"038
0
± 6o
An91¢ of
FIG. 5a.
pitc~h(o)
+12 °
Sensitivity of various probes in measuring velocity.Effect of pitch,
40
50
60
70
ve ioc, y
80
~0
I ec)
IDD
I10
1"20
FIG, 5b,--Sensitivity of various probes in measuring velocity.Effect o¢ velocity.
¢ f~/~ec 5~ream
--o-- -o-
-
--e--
Ho
50
5*
Dymbo/ iProbeCFig i)
Free
Free
rurbulen;-
o
I~obabion of probe in yaw
5ymbol Probe (Fig. 1)
V f~./~.c 5~.rea~
C o n r a d O)
Conrad Or)
Pyramid
o
=- +_i0°
--o--
110
Fr6e
o
Conrad (i)
--o--
50
Free
~
Conrad (iv)
--0°-
54 Turbul~nl
I3
Pyramid
Ro~,&bion of" probe in y&w
0
048
A
PI
- P2
q~
¢S= +_1o°
I.I
~ ' ~
~C&'i~)r~iOn Con,5~2an~ = l'13 I
I
0"04-4
.....
~--..~
I.O/
I
J
- -
o. 04-2
1.5
bO
1,4,
o.o,o[
cafibra~lon
l
T_
H - Po
'
Calibr&Bion consb.&n{: = 1'4-2
c/=2.s% (p,-p~) ab (D=*-Io°
1.2
1
0 "044I-0'042
P, - P2
%0,o
o~1 C~.liUra~.,on
o.o381
0
FIG. 6.
±b o
Angle of pi~ch ( o )
*12 °
V e l o c i t y - m e a s u r i n g p r o b e s of p r a c t i c a l l y
uniform sensitivity.
0
FIG. 7.
con~~l
_.&o
Angle of pibch (0)
.L._12o
C a l i b r a t i o n c o n s t a n t s for o b t a i n i n g
total head.
K, - Kx = H - R
&
KI
o
•
= ~_~o
Xt
Po-p
-K~
Y
= ~
Cal.ibra~/on curve
Uniform free ~i:ream
Uniform Durbulen~s~re&rn
6oundarH lager ~ =B
6oundar 5 lager ~} = o.~
Kt - K2 =
H
P
&
t
x
A
N i,. = _~o
5epar&l;ed #Orbule"n&flo~
Calibration curve
Uniform free s~ream
Unifor,m burbulen~ sl;ream
Boundary laijer,,~=8
Boundar~ I~jer,. ~ = 0"5
Boundary lager. ~=o'28
5eparabed bur,bulen[-, flo~'
A
Y
Po- P
2"4
D~n.amic pr-e~ure
2.5
x
2"4
Kj-I< 2
Dgnarnic ~ressure
2
23
KI-K ~
2"2
x
~rt
%
x
2.3
Y
x
¥
2.1 ¸
2'2
I,B
1'6
To~al head
bO
To~al head
12
x
KI
x
I'1
y÷
1"5
-~
x
x+
ol-
f
o
x
K~
+
x
Y+
x
x---&
.+
Y-&
x~
x
Y
Y
&
I'0
1"5
I,.a
I.I
5i:aBic pr.es~ure
5ratio
pressure
I-0
-I< 2
&
-K 2
&
x
I.I
0.9
x
I'0
40
FIG. 8a.
50
60
70
80
/
90
Velocity (f~/sec)
I00
++*
I10
+
y
+
X
-I-
y
6
4-
N.
x
"dr
120
Dependence of c a l i b r a t i o n on f l o w c o n d i t i o n s . - Conrad-(i) probe.
0.8
40
FIG. 8b.
50
60
70
80
/
90
vero~i~g(f~/~e~)
I{)0
II0
120
D e p e n d e n c e of c a l i b r a t i o n on flow c o n d i t i o n s . - Conrad-(iv) probe.
Calibration curve
o
a
+
x
Y
Kj- K2= " ~
KI
H -Po
=T
'= -~----~
-K 2
3-Lube
UnFform f r e e 5 ~ r e a m
U n i f o r m Lurbulen/; s~ream
Boundary laver, } = 6
boundar 9 Jayer. ?=0'56
13oundarg l a y e r . ~ = o - 7 5
Separated ~urbul%n~ flow
obe (p~-po)/#
5-eu0e probe (Ps-po)/q
0"72
0"0#8
o=o
0'69
2.6
0"046
/
Dynamic pressure
(Ps- Po)/¢
2.5
0"66
gl-g 2
2'4
u
X
2-3
n
x
I
x"x
Y
Y l /
/
/
/
+++"
P,- P2)
q~
0"044
/
4>.~. /
0"63
0"042
/
I'0
0"60
royal head
b0
b0
0,9
Kt
70
80
040
90
t00
IfO
+++
X'K
Y
0-8
60
K
O--%5
+
50
I
0"70
V = IIo fE/sec
0'68
0"7
o
1"7
5~agic pres,ure
Cm po)lq
0"64
t'6
D
--J<2
+
+÷t
o
I-5
I-~40
FIc. 8c.
Y
50
60
66
- Po)l
70
" 80
.
90
Velocity (fl: leer)
_
0"62
~e x x
x
I00
IlO
1"20
Dependence of calibration on flow conditions.-Pyramid probe,
0"60
0
l
2
4
6
Angle of
Fro. 9.
8
I0
pitch e(deg)
12
;¢
Usefulness of equi-balanced 3-tube probe.
16
/
V : IiOfl;/sec
V 5ofV./sec
o
+
I
/
P4-P3
P5 -P~
/
/
-2
/
<>__
Canadnan
El
PresenL
Presenb
+
De~ermJnabon
cahbrabon V = 5ofL lsec
c a l i b r a t i o n V = l l o f & lsec
c a l i b r e & i o n Y = s 0 f /sec
of flowangle
0
#
3
,
p - po
P~-Ps
Flowangb ~ :1o-6 ~
deg
/
P~-Po 2
/~"
-3
-30
-20
0"70
o
=
I
-10
A
x
o
0 (de@)
¢
o ±m°:,s°~-2o°
Io
I
30
20
0
go=~? v~ whenV= Ilof~/sec
r'O
10°
20 °
30° t @ 400
50 °
+
Ps"Po ,
go.6o
0'5!
50
500
Debermznabon of dgnamFc pressure g
0'65
bO
/
0.&
Dyn~m,o p~e~sure g =(p - po) [,.s,-o., Iog, o .Ps-% Po
I
I
0o
7o
I
oo
I
I
9o
,o0
]
/
• &-Po
g
/t
0"6 _
u
i
I
0
/
~_o==~ '
,,o
0.4 ~
0"20
o
*
H
rl --P5
q
/
Cali~rabion for
bobal head
0'16
V = IIO
V
0
0"12
20 °
30°± @
4"0°
•
500
60 °
De~errntnabron o f 5baSic pressure p
/
fb~sec
5o f~/sec
10°
IO
l
p-p
~//
0.8,
0'08,
0"6 ]
.,#
.o
0'04
0
0
-30
-20
-10
0
e (~9)
FIG. 10.
10
20
30
Calibration of g-tube probe for limited flow angles.
t0 °
FIc. l l a .
20 °
30° 5 ~ 40°
50 °
Calibration of axial probe.
~0 °
v(f~/sec)
0"5
5~rearn
D
I10
Free
+
5o
Free
O
5¢
Turbu len~
Yaw
/
/
0"5
I
P-G
/
,ve pibch
7~ = sbabJC pressure
PD = recorded dbc pr~sure-
Ii
I
q °/29v 2
\
o.3o
,./
0"1
~
WJnd
0"4
Vamablon wi~.h yaw
Var,~bion wi~.h pibch
IS in. bunnel ----o
Y =50
fb/sec
--.x---
I
Flowangle I el
0"25
= 25.3
I
0
i0 °
+_@
0"7
0-6
o
lel=O
,,,
×
1®l=6 °
1@1=12°
12 o
14. 0
G
P Po 0.20
go = ~zgV2 when V=IIoffJsec
C~
k)
I
0'15
"X"
x
[,3
q
0"5
DLjnamtc pressure q
0"4
40
l
I
I
50
60
70
"
O" 05
=(p~-po)O.ag-o'l:5 Io9,0
I
I
90
lOP
t
80 ,
120
1/0
0
Velocibuj (lb./see)
-200
-15 °
-10 °
-50
5°
0
I0°
20 °
15 °
Pi~;ch and Lj~w
0"5
ca
+
fro fb l~ec
50 Fb~/sec
®
5*f~/sec
.°
~o/
0"7
p'-p
g
59m601 Tunnel
•
18in. Od:&9 .
a
Low Turb.
Low Turb
/
/
O"b
/
/+ff
P -Po
0
0'05
,
I
0-10
0'15
l
t
0-20
I
0"25
o
0"10
l
0".30
0"35
p-po
FIG. l l b .
n
q
a.k_.lc pressure ~o = O'07p ~'0"93po-0.4-5q
0"4
Free
Free
Turbuleng
0"15
/
0"5
5bream
Calibration of axial probe for limited flow angles.
O"05
20
30
4O
50
bO
70
$0
90
v~lo~ u (e~ l~ec)
FIG. 19,
Calibration of disc-static probe.
I00
110
f£f.~
1.0
o/
0"9
0,7
e
I'0
0.9
r~ ~"
J
.
0"8
~
ba
CJrl
/
0'4
,~,
o
m
v
[]
Pitob ~,si;&tlo
Conrad (i)
0.6
Conrad (iv)
PLjramid
0"4
0":3
0'3
0"2
0"2
0'1
O'l
-0"1
o
FIG. 13a.
/
0'6
5~/mbol Probe(5)
/
0'5 0 /
/
0"7
n
0"6
&b. ~he surface
= dLjnamic pressure aP. edge of boundarLj layer
p~ = 51:;a/~sc p r e s s u r e
Pw = 51=al;ic pressure ab bhe auPface
Q = dgnamic pressure a~ edge of boundarg laLjer
f/
/
5~jmbol
Probe(~)
Pitot ~ sta~.ic
o
v
Conrad (i)
Conrad(iv)
PwamJd
-O,I
o.,
o.~ } ( i n . ) l . 2
I.e
7.0
B o u n d a r y - l a y e r traverse. C o m p a r i s o n of probes.
---- 2"0 in. u = 110 ft/sec.
0
FIG. 13b.
o.7
o.4
o.G ~0n)°'8
lo
H
Boundary-layer traverse. Comparison of probes.
=l.lin.
u =65ft/sec.
.,+
o
5gmbol
Probe
o
V
Conrad(.i)
Conrad (iv)
U
P~ramid
.=
5ymbot
o/
0"30
Probe
o
Conrad ( i )
V
o
Conrad (iv).
Pgramld
0"25
O.~i
)
~2 In
8~ in
inch~s
Jnche~
0"15
/
Qb
( Probe
(Probe ,
~raverse
Oq
0"J~
0"0
0'10
0"05i
/
0"05
o-to
o-15
0-20
51 in inches(Pil:ot;-51:ab.ic
FIG. 14.
o-2s
o.~o
~raver~e)
/
u
o.os
o-lo
o.Js
0.20
o-2s
• S'2 Jn inches (Pi~o~-5~a~ic ~raverse)
o.3~
A c c u r a c y in estimation of displacement thickness.
/
/
/
/
FIG. 15.
A c c u r a c y in estimation of m o m e n t u m thickness.
R. & hi. No. 303
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