Towards higher accuracy and better frequency response with standard multi-hole probes in turbulence measurement with remotely piloted aircraft (RPA)

Abstract

This study deals with the problem of turbulence measurement with
small remotely piloted aircraft (RPA). It shows how multi-hole
probes (MHPs) can be used to measure fluctuating parts of the
airflow in flight up to 20 Hz. Accurate measurement of the
transient wind in the outdoor environment is needed for the
estimation of the 3-D wind vector as well as turbulent fluxes of heat,
momentum, water vapour, etc. In comparison to an established MHP
system, experiments were done to show how developments of the system
setup can improve data quality. The study includes a re-evaluation
of the pneumatic tubing setup, the conversion from pressures to
airspeed, the pressure transducers, and the data acquisition
system. In each of these fields, the steps that were taken lead to
significant improvements. A spectral analysis of airspeed data
obtained in flight tests shows the capability of the system to
measure atmospheric turbulence up to the desired frequency range.

Full text

Atmos. Meas. Tech., 7, 1027–1041, 2014
www.atmos-meas-tech.net/7/1027/2014/
doi:10.5194/amt-7-1027-2014
© Author(s) 2014. CC Attribution 3.0 License.
Atmospheric
Measurement
Techniques
Open Access
Towards higher accuracy and better frequency response with
standard multi-hole probes in turbulence measurement with
remotely piloted aircraft (RPA)
N. Wildmann, S. Ravi, and J. Bange
Center for Applied Geoscience, Eberhard-Karls-Universität Tübingen, Tübingen, Germany
Correspondence to: N. Wildmann (norman.wildmann@uni-tuebingen.de)
Received: 8 August 2013 – Published in Atmos. Meas. Tech. Discuss.: 14 November 2013
Revised: 13 February 2014 – Accepted: 26 February 2014 – Published: 22 April 2014
Abstract. This study deals with the problem of turbulence
measurement with small remotely piloted aircraft (RPA). It
shows how multi-hole probes (MHPs) can be used to mea-
sure fluctuating parts of the airflow in flight up to 20Hz.
Accurate measurement of the transient wind in the outdoor
environment is needed for the estimation of the 3-D wind
vector as well as turbulent fluxes of heat, momentum, water
vapour, etc. In comparison to an established MHP system,
experiments were done to show how developments of the
system setup can improve data quality. The study includes
a re-evaluation of the pneumatic tubing setup, the conversion
from pressures to airspeed, the pressure transducers, and the
data acquisition system. In each of these fields, the steps that
were taken lead to significant improvements. A spectral anal-
ysis of airspeed data obtained in flight tests shows the capa-
bility of the system to measure atmospheric turbulence up to
the desired frequency range.
1 Introduction
In many applications multi-hole probes (MHPs) serve the
purpose of measuring the flow angle and speed of an
airstream. They are commonly used in wind-tunnel and road
tests for the automotive industry (Zimmer et al., 2001) as
well as in airborne measurements (Crawford and Dobosy,
1992). Many different designs and calibration techniques can
be found in literature (Telionis et al., 2009; Sumner, 2000;
Pfau et al., 2002; Lemonis et al., 2002). The minimum num-
ber of holes that are used for three dimensional flow measure-
ment is four, while probes with five holes are common and
seven-hole probes can also be found. With increasing num-
ber of holes, the range of the angle of incidence that can still
be measured with the probe increases. There are also probes
with only one pressure port, which is constantly turned inside
the probe (Schlienger et al., 2002). The shape of the probe
(conical, hemispherical or faceted) has an effect on the max-
imum incidence angle as well as on the sensitivity regarding
Reynolds number changes (Telionis et al., 2009), due to the
different points of flow separation. In airborne meteorology,
the MHP made by Goodrich Sensor Systems (Rosemount,
1982) has been the most commonly used probe for measure-
ments in the atmospheric boundary layer. Using flight cali-
bration maneuvers, these MHPs can be used for wind mea-
surement on-board manned aircraft (Friehe et al., 1996; Khe-
lif et al., 1999). The development of the BAT probe (Craw-
ford and Dobosy, 1992) enabled the measurement of the tur-
bulent heat flux by combining fast temperature sensors with
the existing system.
Within the last decade, RPASs (remotely piloted air sys-
tems) have become more and more affordable and suitable
for atmospheric measurements and some have also been
equipped with MHPs (Spieß et al., 2007; van den Kroonen-
berg et al., 2008; Thomas et al., 2012; Martin and Bange,
2014). The big advantage compared to manned aircraft is the
decreased disturbance of the airflow by the aircraft, due to
the smaller wingspan and wing load, which leads to smaller
upwash (Crawford et al., 1996) and the reduced overall size,
which decreases the disturbance of turbulence measurements
according to Wyngaard et al. (1985). Higher flexibility and
lower operating cost are other major advantages with small
RPAS. The Meteorological Mini Aerial Vehicle (M2AV) is
Published by Copernicus Publications on behalf of the European Geosciences Union.

1028 N. Wildmann et al.: Multi-hole probes with RPA
one of such RPAS and the measurement technique that was
used in this system will be referred to as a benchmark in this
study. New developments made as part of this study will be
compared to the M2AV where possible. Since the turbulent
wind vector and all turbulent flux measurements are strongly
dependent on the measurement of airflow angles and true air-
speed, a critical analysis of the systematic errors and sources
for noise in the measurement with a MHP will be conducted.
This analysis includes the complete measurement chain from
the pneumatic setup of the probe and the pressure transducers
until the sampling of the data.
The meteorological wind vector v(i.e. the wind vector in
the earth’s orthonormal, meteorological coordinate system)
can be calculated from navigation, flow and attitude measure-
ment aboard a research aircraft using
v=vgs +Mmf vtas +×sp(1)
(Williams and Marcotte, 2000). The ground-speed vector vgs
describes the movement of the origin of the aircraft-fixed
coordinate system (index f) with respect to the earth’s sur-
face and is determined using the on-board navigation system.
Aboard an RPA the latter is usually a combination of an iner-
tial measurement unit (IMU) and a global navigation satellite
system (GNSS). The determination of the ground speed vgs
and the rotation into the earth’s coordinate system Mmf using
the Eulerian angles are not subject of the present study, and
are described in literature (Haering, 1990; Leise and Mas-
ters, 1993; Boiffier, 1998; van den Kroonenberg et al., 2008;
Bange, 2009).
The true-airspeed vector vtas is the flow vector measured
by an in situ flow probe, in this study a MHP, preferably
mounted at the nose of the RPA. Thus vtas is defined in the
aircraft’s coordinate system f. The location of the MHP in
relation to the origin of the aircraft-fixed coordinate system f
is described by the lever-arm vector sp=(xp,yp, zp), which
points from the origin of the aircraft system fto the location
of the MHP. The vector of angular rotation rates contains
the angular velocities of the aircraft system frelated to the
meteorological system mand is among the primary output
data of the IMU.
In the following we focus on the determination of the true-
airspeed vector vtas defined by
vtas = − |vtas|
p1+tan2α+tan2β

1
tanβ
tanα
,(2)
(see also Lenschow, 1986; Leise and Masters, 1993;
Williams and Marcotte, 2000; van den Kroonenberg et al.,
2008; Bange, 2009) with angle of attack α(positive for air
flow from below) and sideslip β(positive for flow from star-
board). All three variables α,β, and |vtas|in Eq. (2) can be
derived from MHP pressure measurements.
Fig. 1. Research RPA MASC. The position of the MHP approxi-
mately 15cm in front of the fuselage nose tip is depicted with the
red ellipse.
Research RPA MASC
At the University of Tübingen the research platform MASC
(Multi-purpose Airborne Sensor Carrier) is operated and
equipped with a MHP, fast temperature sensors, a barome-
ter and a humidity sensor to enable the measurement of ther-
modynamic, turbulent scalars as well as the 3-D turbulent
wind vector and turbulent fluxes of water vapour, sensible
heat and momentum (Fig. 1 and Wildmann et al., 2013). The
electrically powered motor-glider airplane with a wingspan
between 2.60 and 3.40 m has a total weight of 5–7 kg depend-
ing on the battery and payload. Wind-tunnel experiments re-
vealed that the fuselage and running pusher engine did not
have a significant influence on the airflow at the location of
the MHP. The aircraft is equipped with the autopilot ROCS
(Research Onboard Computer System), which has been de-
veloped at the Institute for Flight Mechanics and Control
(IFR) at the University of Stuttgart (Haala et al., 2011). The
autopilot controls a constant airspeed of 24±1m s−1and
constant altitude with a precision of ±2m. Navigation to pre-
defined waypoints is done relative to the take-off position.
The flight tests that were performed to validate the results of
this study were done with a MASC RPA.
2 The probe
2.1 Mechanical design of the probe
The MHP used at the University of Tübingen has a conical
head, nine holes and was designed and manufactured at the
Institute for Fluid Dynamics (ISM) of the Technische Univer-
sität Braunschweig, Germany. The arrangement of the holes
can be seen in Fig. 2. In addition to the five holes on the cone,
which are used to measure the flow angles, it has a ring with
four holes in a 90◦offset pattern in front of it. These holes
merge into one pressure port and provide a reference static
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N. Wildmann et al.: Multi-hole probes with RPA 1029
Fig. 2. Probe by ISM Braunschweig, picture and dimensions in mil-
limetres.
pressure, which is less sensitive to the flow angle compared
to normal static ports of a Prandtl sonde. This pressure port
is then used in the standard calibration described in Sect. 2.2.
The same probe was also used in the M2AV. Figure 3 shows
a computational fluid dynamic (CFD) simulation of the probe
done with OpenFOAM at two different angles of attack.
2.2 Differential pressure to flow angle conversion
The conversion between differential pressures of the six pres-
sure ports of the probe-to-flow angles and true airspeed is
usually based on wind-tunnel calibration and can be done in
several ways (see Sasangko, 1997; Bohn and Simon, 1975;
Treaster and Yocum, 1979). A typical solution is a poly-
nomial fit between normalized pressure differences and air-
flow angles, true airspeed and static pressure respectively.
The ISM probe was intensively used in field campaigns (e.g.
Martin et al., 2011; van den Kroonenberg et al., 2011; Spieß
et al., 2007) with the M2AV. Table 1 shows how dimension-
less coefficients are defined from the pressures at the probe.
The definitions on the left are taken from Bohn and Simon
(1975), for an English summary see Spieß (2006). They are
referred to as the M2AV conversion method in the following.
The definition of the pressure ports and differential pressures
is described in Figs. 4 and 5. The coefficients kαand kβare
directly calculated from the pressures at the MHP ports (see
Table 1 for different methods to do so). Using a polynomial
fit with coefficients that were determined in a wind-tunnel
calibration, the angle of sideslip, angle of attack and the co-
efficients kqand kpcan be calculated from kαand kβ. To find
dynamic and static pressure, the expressions for kqand kpin
Table 1 need to be solved for qand p, respectively. A de-
tailed description is given in Appendix A. The true airspeed
as used in Eq. (2) has to be calculated using the measured to-
tal air temperature Ttot, the static pressure pand the dynamic
pressure q:
|vtas|2=2cpTtot 1−p
p+qκ(3)
with the Poisson number κ=R/cp, where R=
287 J kg−1K−1is the gas constant for dry air and
cp=1005 J kg−1K−1is the specific heat for dry air.
In the M2AV conversion the ring pressure ports are used to
find qand pto get a more angle-independent measurement.
However, it was identified that in certain flight conditions the
ring can cause problems for turbulence measurement, since
the ring port pressure shows an increased noise level, which
is induced by the probe itself. Figure 6 shows the result of
measurements during the calibration procedure of the MHP
in a jet wind tunnel with a turbulence intensity of about 1%.
At a constant airspeed of 22ms−1and angle of attack of 10◦
the angle of sideslip βwas varied between −20 and 20◦in
steps of 2◦. Each position was held for 10s and the standard
deviation of the ring port pressure was measured. It can be
seen that at certain angles of sideslip, the fluctuations of the
measured pressure is higher than at other angles. This can be
considered to be aerodynamic noise introduced by the probe.
To avoid measuring turbulence that is not primarily related
to the atmosphere, a different pressure conversion method
(see Table 1, right column) that avoids using the ring port
pressure was tested. The method was initially proposed by
Treaster and Yocum (1979) and is one of the most basic five-
hole probe calibration methods. It only uses one front hole
and four side holes.
The calibration results with the occurring nonlinearities
are depicted in Figs. 7, 8 and 9. Below 10◦the nonlinear-
ities are comparably small, but at higher angles the use of
a ninth-order polynomial in calibration becomes necessary
to represent the characteristics of the probe. Higher degree
polynomials only marginally increase accuracy. The maxi-
mum deviation from the resulting polynomial in the calibra-
tion procedure is 0.47◦for α, 0.59◦for βand 0.15m s−1for
airspeed. These values also cover variations of wind-tunnel
speed and inaccuracies in the angle settings.
Figure 10 shows the measurement of the airflow angles
and true airspeed in one flight leg of 1000m (including parts
of the turns at the beginning and the end). The flight was done
at late afternoon on 23 September close to the Lindenberg ob-
servatory of the German Meteorological Service. The flight
altitude was 100 m above ground in an atmospheric boundary
layer with weak stability.
The pressures from the five-hole probe were converted
in both ways, with the M2AV method and with the MASC
method, avoiding ring-port measurements. While the air-
flow angles do not show a difference, it can clearly be seen
that true airspeed is much less noisy in the latter method.
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1030 N. Wildmann et al.: Multi-hole probes with RPA
Fig. 3. OpenFOAM flow simulation around the probe tip at 24ms−1total airspeed at 0◦angle of sideslip in both figures, 0◦angle of attack
in the left figure and 10◦angle of attack in the right figure. The colour scale shows differential pressure to the environment in pascals.
Fig. 4. Tubing system as used by the TU Braunschweig and described in Spieß et al. (2007) for the M2AV. The pressure transducer mea-
surements dP0iare differential pressure readings of the low pressure port (LP) connected to the holes P1–P4 and the ring portholes Pstatic
compared to the high pressure port (HP), which in this case is the common port P0. Ps represents a barometric pressure sensor.
The spectra of the velocities estimated through the M2AV
(Fig. 11) shows that the noise introduced by the ring-pressure
ports manifest as “white-noise” at higher frequencies, while
the MASC method shows significantly reduced noise and the
presence of the k−5
3slope (Kolmogorov distribution for lo-
cally isotropic turbulence in the inertial subrange).
It should be noted that the large difference between the
two methods shows up explicitly at certain airflow angles,
which were included in the presented time series. However,
even though errors are smaller at other angle combinations,
they can be completely avoided if the ring port pressure is
not used for true airspeed calculation.
3 Tubing response and calibration of the probe
As transient velocities are of particular interest, the pneu-
matic dynamic response of tubing and transducer needs to
be investigated to ensure measurements within a certain error
band in the target frequency range. The tubing system within
the MHP consists of a combination of a steel tube with an
inner diameter of 0.7mm and another tube of different ma-
terial (e.g. PVC – polyvinyl chloride) and diameter. The dy-
namic response of the system depends not only on the length
and diameter of the tubing, but also on the air volume inside
the pressure transducers. The magnitude and phase response
of tubing systems has been well investigated by Bergh and
Tijdeman (1965). They derived theoretical estimates of the
response of a single tube connected to either a single or mul-
tiple transducers connected in series with the variable tubing
length, tubing diameter and transducer volume. Further stud-
ies by Semaan and Scholz (2012) investigated the validity of
the model for short-tubing length and proved it suitable for
tubing longer than 150mm; however, their model does not
account for branched tubing systems.
Since differential pressures are required for airflow angle
estimation, one strategy would be to connect the holes of
a five-hole probe to pressure transducers and calculate the
flow angles from the measured differential pressures as de-
scribed in Spieß et al. (2007) for the M2AV. The schematic
of such a setup is shown in Fig. 4. This setup has a strongly
branched tubing system at the high pressure port of all trans-
ducers (P0is branched six times), whereas the low pressure
port is in most cases directly connected to one hole of the
probe. This setup cannot be simulated by a simple model like
the one described by Bergh and Tijdeman (1965).
Alternatively, the holes in the probe can be connected
to the transducers in the manner presented in Fig. 5. This
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N. Wildmann et al.: Multi-hole probes with RPA 1031
Fig. 5. Alternative tubing setup without branches as used in MASC. The pressure transducer measurements dP i are differential readings of
all single port pressures of the probe (P0–P4 and Pstatic, high pressure, HP) compared to one common reference port (low pressure, LP).
Table 1. Comparison of two methods to define dimensionless coefficients for five-hole probe measurements.
Bohn et al. (1975) (M2AV) Treaster and Yocum (1979) (MASC)
1P 1
5P4
i=0Pi−1
5P4
j=0Pj21
2+hP0−1
4P4
i=1Pii(dP1+dP2+dP3+dP4)
4
kαdP01−dP03
1P dP1−dP3
dP0−1P
kβdP02−dP04
1P dP2−dP4
dP0−1P
kqq−dP0s
1P
dP0−q
dP0−1P
kpPs+dP0s−p
1P
Ps+1P −p
dP0−1P
−20 −10 0 10 20
0
1
2
3
4
5
6
7
8
β (deg)
σp (Pa)
Fig. 6. Standard deviation of the pressure ports Pstatic in front of
the ring of the ISM probe during a wind-tunnel calibration. Angle
of attack 10◦, angle of sideslip shifted from −20 to 20◦.
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
kα
kβ
β = 0o
α = −20o
β = 20o
α = 20o
α = 0o
β = −20o
Fig. 7. Two-dimensional plot of kβover kα. The figure shows the
nonlinearities that are larger for higher airflow angles αand β.
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1032 N. Wildmann et al.: Multi-hole probes with RPA
−20 −10 0 10 20
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
β (deg)
kq
α = 0o
α = −10o
α = −20o
Fig. 8. Calibration coefficient kqfor dynamic pressure against cali-
bration angle βfor three attack angles α.
method of tubing connection was used in MASC. The mea-
sured pressures can be converted to the same measurement
as in the M2AV setup as follows:
dP0i =dP0−dPi
with i=1,...,4,s. (4)
To compare the M2AV and MASC setups with respect to
the tubing system, the model of Bergh and Tijdeman can-
not be used because it does not account for branches. There-
fore, an experiment was set up to assess the response of the
two different tubing strategies (see Fig. 12). What is depicted
as “tubing under investigation” in the sketch is in a first ex-
periment replaced with the M2AV’s branched tubing system
as shown in Fig. 4 between the hole P0 and the high pres-
sure port (HP) of transducer dP0s. In a second experiment,
the tubing is replaced with MASC’s single tube, as shown in
Fig. 5 between hole P0 and the HP port of transducer dP0.
For all connections, PVC tube of a length similar to the ac-
tual setup that would be implemented in MASC (in this case
0.18m) was used. Instead of the connection to the P0 hole
of the probe, the free end of the tube is connected to a sealed
volume attached to a speaker. A reference measurement was
made by placing another transducer directly on the cabin wall
without any tubing in between the pressure source and the
transducer. The speaker was able to play sine waves with fre-
quencies from 10 to several 100Hz. The measurement com-
puter was logging the transducer output at a rate of 1kHz.
The maximum investigated frequency was 200 Hz, which is
higher than the sampling rate that is used in flight.
Initially, the response of the transducers themselves were
tested. The transducers included sensors of the type P4V-
Mini by the company AllSensors and sensors of type LBA by
the company Sensortechnics. The P4V-Mini sensors work on
the principle of a membrane that is displaced by the pressure
N. Wildmann et al.: Multi-hole probes with RPA 5
Bohn et al, 1975 (M2AV) Treaster and Yocum, 1979 (MASC)
∆P1
5P4
i=0 Pi−1
5P4
j=0 Pj21
2
+P0−1
4P4
i=1 Pi(dP1+dP2+dP3+dP4)
4
kαdP01−dP03
∆P
dP1−dP3
dP0−∆P
kβdP02−dP04
∆P
dP2−dP4
dP0−∆P
kqq−dP0s
∆P
dP0−q
dP0−∆P
kpPs+dP0s−p
∆P
Ps+∆P−p
dP0−∆P
Table 1. Comparison of two methods to define dimensionless coefficients for five hole probe measurements.
−20 −10 0 10 20
0
1
2
3
4
5
6
7
8
β (deg)
σp (Pa)
Fig. 6. Standard deviation of the pressure ports Pstatic in front of the
ring of the ISM probe during a wind-tunnel calibration. Angle of
attack 10◦, angle of sideslip shifted through −20 to 20 ◦.
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
kα
kβ
β = 0o
α = −20o
β = 20o
α = 20o
α = 0o
β = −20o
Fig. 7. Two dimensional plot of kβover kα. The figure shows the
nonlinearities that are larger for higher airflow angles αand β.
−20 −10 0 10 20
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
β (deg)
kq
α = 0o
α = −10o
α = −20o
Fig. 8. Calibration coefficient kqfor dynamic pressure against cali-
bration angle βfor three attack angles α.
−20 −10 0 10 20
0.2
0.3
0.4
0.5
0.6
0.7
β (deg)
kp
α = 0o
α = −10o
α = −20o
Fig. 9. Calibration coefficient kpfor static pressure against calibra-
tion angle βfor three attack angles α.
Fig. 9. Calibration coefficient kpfor static pressure against calibra-
tion angle βfor three attack angles α.
difference and its deflection is measured by piezoresistivity.
The LBA sensors estimate pressure difference through a ther-
mal mass-flow measurement.
To visualize the response of the pressure measurement sys-
tem, the amplitude and phase response as the two parts of the
transfer function Hof the system are calculated:
H (ω) = |H (ω)|eiφ (ω),(5)
where ωis the angular frequency and φthe phase shift. The
amplitude response is presented as the ratio between the stan-
dard deviation σof the tubing system being investigated and
the reference:
|H (ω)| = σP0(ω)
σPref(ω) .(6)
To find the phase response of the system, the cross-
correlation function %P0,Pref between the two sensors was
calculated for each frequency and the time shift between the
two signals needed for maximum correlation was estimated.
This time shift was converted to a phase angle in the follow-
ing manner:
1t =t (max|%P0,Pref|), (7)
φ=1t ·ω·180
π.(8)
The tests with the P4V-Mini sensors showed consider-
able variations in the response of each individual transducer.
Therefore, the experiment was carried out only with the LBA
sensors by Sensortechnics. In Sect. 4 further reasons are
given for choosing this type of sensor in future flight mea-
surements. The amplitude and phase response of the two
tubing systems are presented in Fig. 13. In the same figure,
the theoretical response for the single tube of same length
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N. Wildmann et al.: Multi-hole probes with RPA 1033
260 270 280 290 300 310 320 330
0
5
10
15
20
time (s)
β (deg)
260 270 280 290 300 310 320 330
0
5
10
15
20
time (s)
α (deg)
260 270 280 290 300 310 320 330
22
24
26
28
30
32
time (s)
|vtas| (m s−1)
M2AV
MASC
Fig. 10. True airspeed, measured with the five-hole probe and calculated with the M2AV and MASC methods respectively. Angle of attack
throughout the leg approximately 10◦; angle of sideslip approximately 8◦. See text for flight conditions.
Fig. 11. Spectra of the true airspeed measurement in flight with standard calibration and new method. The red line shows the k−5
3slope.
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1034 N. Wildmann et al.: Multi-hole probes with RPA
Fig. 12. Schematic drawing of the experiment to measure the tub-
ing response. While the HP port of the reference transducer (Pref)
is directly connected to the acoustic box, the HP port of the pressure
measurement under investigation (P0) is connected with the neces-
sary tubing of the real system. Ps is the common ambient pressure
on the LP port of the transducers.
without branches as calculated with the Bergh and Tijdeman
model is presented.
It can be seen that both tubing setups resemble oscillatory
dynamic systems with at least one resonance frequency. The
first resonant frequency of the M2AV system was found to
be at around 80Hz, while it is out of the measurement range
for the alternative setup. The damping factor of the M2AV
setup is much higher than for the alternative setup, hence
the resonance amplitude was much smaller. The phase re-
sponse attenuates towards −180◦, which is characteristic for
a second-order dynamical system.
It should be recalled that in the M2AV setup, one side of
the differential transducers was connected to the side holes
of the probe directly, while the other side of the transducers
was connected to the front hole with a branch to five other
transducers. In light of the acoustic tests performed here, it
was identified that the tubing responses on either side of the
transducer differ significantly. Though the two tubing sys-
tems have a nominally similar amplitude response, a phase
shift ϕbetween each other would exist. Therefore an artifi-
cial signal Smwould be measured, which can be described as
follows:
Sm=sinωt −sin(ωt +ϕ),
=sinωt −sinωt ·cosϕ+cosωt sin ϕ,
=(1−cosϕ) sinωt +sinϕcosωt ,
knowing that
a·sinωt +b·cosωt =Acos(ωt −α)
with
A=pa2+b2,(9)
tanα=b
a,(10)
the artificial signal is
Sm=q(1−cosϕ)2+sinϕ2·cosωt −arctan sinϕ
1−cosϕ,
=p2(1−cosϕ) ·coshωt −cot−1ϕ
2i,
=2sin ϕ
2·coshωt −cot−1ϕ
2i.(11)
From Fig. 13, at 20Hz the two tubing connections have
a difference in phase shift of about 10◦. This implies the
transducer would measure a differential signal with an am-
plitude of 2 sin 10◦
2=0.174 times the original absolute sig-
nal, which is added to the measurement and can thereby be
defined as an error of almost 20%.
To see the real behaviour of the two tubing strategies and
the artificial signals that are measured due to phase shift ef-
fects, a setup equal to that present in the M2AV was tested.
That is, both ends of a transducer were connected to the
acoustic box whereby one port was connected to the box
through a branch with five other transducers connected in
parallel and the other port of the transducer was directly
connected to the acoustic box via a 18cm tube. In subse-
quent tests, both ports of the transducers were connected via
18cm tubes to the acoustic box, this would resemble the al-
ternate tubing strategy that is now being used on MASC.
Ideally, as both ends of the transducers are connected to the
same “source” (acoustic box), the pressures in the transduc-
ers should nullify one another and no pressures should be
logged. The results of a time series measuring a sweep from
10 to 100 Hz (in steps of 10Hz and a rest time of 10s at each
step) are shown in Fig. 14, left. The increase in amplitude of
the pressure signal is not only due to an increasing phase
shift, but also due to the increasing power of the speaker
at the same gain setting. Figure 14, right, shows a normal-
ized result for the measured frequency range, where the mea-
sured signal was divided by the prevailing pressure in the box
that was measured with a second transducer. It can be seen
that the relative error for 20Hz is less than theoretically es-
timated, but it is also obvious that the effect can be observed
in real measurements and can be avoided with the point-to-
point tubing connections.
4 The pressure transducers
The volume of the pressure transducers adds to the pneumatic
transfer function, and variation between different transduc-
ers can lead to a significantly different amplitude and phase
response of the sensor at higher frequencies. Besides that,
most pressure transducers are also sensitive to vibrations. In
many MEMS (microelectromechanical system)-based differ-
ential pressure transducers, deformation of a membrane ex-
posed to the applied pressure is measured by the means of
piezoelectricity (in our study the sensor of type P4V-Mini,
as used in the M2AV for example). The piezoelectric voltage
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N. Wildmann et al.: Multi-hole probes with RPA 1035
0 20 40 60 80 100 120 140 160 180 200
0
1
2
3
Frequency (Hz)
Amplitude amplification factor
Amplitude response of pressure measurement system
MASC theoretical
M2AV experiment
MASC experiment
0 20 40 60 80 100 120 140 160 180 200
−150
−100
−50
0Phase response of pressure measurement system
Frequency (Hz)
Phase shift φ (deg)
Fig. 13. Amplitude and phase response of the pressure measurement systems, including tubing, branches, transducer, etc. The MASC setup
was investigated in an experiment (grey line) and theoretically with the Bergh and Tijdeman model (dashed line). The M2AV setup cannot
be calculated with the model and thus is only investigated in an experiment (black line).
Fig. 14. Acoustic test of the MASC and the M2AV tubing system
in comparison. Left: raw measurement of the transducers. Right:
percentage of prevailing pressure that is measured as an artefact due
to different phase shifts at the high and low pressure ports of the
transducer.
is amplified and a voltage linear to the applied pressure is
put out by the sensor. However, the membrane can also be
deformed by accelerations perpendicular to the membrane
surface. Since aircraft are always subject to vibrations and
accelerations it is important to consider this effect in the pres-
sure measurements when membrane-based pressure trans-
ducers are used. The way to reduce the errors made due to
this effect can be to calibrate the sensors for the sensitiv-
ity regarding acceleration and measure the given accelera-
tions in flight to subtract the acceleration-induced signal from
the transducer output signal. A way to avoid the issue of
sensitivity to accelerations completely is to choose a differ-
ent measuring principle which is not based on a membrane
deformation. A suitable alternative are sensors that work on
thermal flow measurement (in our study the sensor of type
LBA, as used in MASC). Figure 15 shows a comparison be-
tween a membrane-based sensor and a thermal flow sensor
which were at the same time exposed to accelerations by
mounting them on one solid board and applying shock accel-
erations in three different orientations. It can be seen that the
accelerations in the direction perpendicular to the membrane
orientation (here the ydirection) affect the membrane-based
sensor, but not the thermal flow sensor. In the test, accelera-
tions of up to 5 ms−2were applied. Similar accelerations can
be found in straight-leg flights with the MASC system. Other
aircraft might have less or more vibration depending on the
propulsion and flight dynamics. The resulting pressure trans-
ducer noise with amplitudes of up to 3Pa adds to the higher
frequency turbulence measurement and causes higher rela-
tive errors at lower turbulence intensity.
5 Sampling and anti-aliasing
So far, errors by aerodynamic and mechanical effects that af-
fect the signal that is passed on by the pressure transducer
were discussed. The next step in the measuring chain is to
convert this analog 0–5V signal from the pressure trans-
ducer to a digital signal and logging the data of all chan-
nels synchronously to one file. All data acquiring systems
(DAQ) need to address the effect of aliasing in the mea-
sured frequency scales. Aliasing is critical in two ways: first,
high frequency noise signals can alias into the sampled fre-
quency range, if they are not filtered. Second, the signal
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1036 N. Wildmann et al.: Multi-hole probes with RPA
Fig. 15. Vibration/acceleration applied to pressure transducers in distinct directions
of the physical variable to be measured with frequencies
slightly higher than half the sampling frequency can fold into
the sampled frequency range and then lead to overestimates
in the power of the signal at low frequencies. Commercial
DAQ are generally unsuitable for RPA because they are ei-
ther too heavy, too big or need too much power. The Univer-
sity of Tübingen developed the measuring computer AMOC
(Airborne Meteorological Onboard Computer) in coopera-
tion with the University of Applied Sciences Ostwestfalen-
Lippe. The computer is equipped with two STM32 micro-
controllers, a 24bit, 16 channel analog-to-digital converter,
a telemetry interface, a SD (Secure Digital)-card slot for
data logging and various other interfaces (see also Wild-
mann et al., 2013). To obtain reliable turbulence measure-
ments within an error band of 10%, an anti-aliasing filter
was designed and implemented on the measuring computer
which contains the following parts.
1. A first order analog filter (RC-low pass) with cut-off
frequency at 160Hz: only 50% of the original ampli-
tude of signals with 160Hz passes the filter, and only
10% of the signal at 500 Hz. The amplitude response
of the analog filter can be seen in Fig. 16 as a dashed
blue line.
2. Oversampling of the signal at 500 Hz on-board the
measuring computer: only signals above 500Hz ap-
pear as aliases in the measured signal on-board the
measuring computer. As described above, these signals
are already damped to less than 10% of the original
signal.
3. Digital moving average filter with cut-off frequency at
70Hz in real-time on-board AMOC: the moving aver-
age filter is chosen because of its simple implemen-
tation, needing only little computing power in real-
time processing and giving an optimal noise reduction
while keeping sharp step responses (Smith, 1997). The
rather poor performance of the filter in frequency sepa-
ration is still good enough for the given task. From the
red dashed line in Fig. 16, it can be seen that the filter
still has a quasi-flat response at 10Hz and still more
than 91% of the signal amplitude is passed at 20 Hz,
while at 100Hz only 25 % passes and, thanks to the
complementary analog filter, the response of signals
above 150Hz is always damped to a maximum of 6%
of the original signal.
4. The log onto the SD-card at 100 Hz: logging at 100 Hz
is another oversampling step to achieve anti-aliased
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N. Wildmann et al.: Multi-hole probes with RPA 1037
Fig. 16. Amplitude response of the applied filters in the analog
channels of the MASC DAQ. The effective filter (red) is a com-
bination of an analog RC low-pass filter (blue) and a digital moving
average filter (green). The dashed lines represent the theoretical be-
haviour of the filters with the applied parameters. The solid lines
represent measurements of the real sensor response in an acoustic
box experiment.
data of up to at least 20Hz. Sampling at 100 Hz, sig-
nals between 100 and 150Hz can fold into the fre-
quency range of up to 50Hz. The previous steps ex-
plained how these signals are already damped to less
than 25%. Frequencies above 150Hz are damped to
less than 6%.
This means that in the frequency range from 0 to 50Hz a
maximum error caused by aliasing of 25% is theoretically
possible. In reality, the measured signal is a turbulent flow,
wherein the power of the signal decreases with increasing
frequency (power law k−5/3in the inertial subrange of lo-
cally isotropic turbulence, Kolmogorov, 1941). This means
that the aliases naturally have a lower amplitude compared
to the true signal at a specific frequency, which also means
that the maximum error that was estimated is overestimated,
except for unnatural noise signals. Note that electromagnetic
noise typically begins at much higher frequencies that are fil-
tered by the analog filter.
6 Comparison of MASC and M2AV data
In order to demonstrate that the design considerations in
the airflow measurement system, as described above, do
show the desired improvement in turbulence measurement,
an analysis of the frequency response of the system in flight
was carried out. Kolmogorov’s theory of locally isotropic tur-
bulence in the inertial subrange provides theoretical slopes of
variance spectrum and structure function. If measured data
is compared to this theory, the quality of turbulence mea-
surement can be evaluated. Figure 17 shows the result of this
analysis for true airspeed measurements. To prove that real
Fig. 17. A variance spectrum and a structure function of true air-
speed measured with the MASC RPA in comparison to a measure-
ment with the M2AV RPA. In both plots, the result is an average
over 15 legs of 27s each. The structure function is normalized by
2σ2and therefore dimensionless. In both plots, MASC results are
shifted towards lower values for better readability. The dashed lines
indicate an estimation of the entry point of the inertial subrange. See
text for flight conditions.
enhancements compared to established measurement sys-
tems like the M2AV were achieved, the result is compared
to measurements of the M2AV in very similar meteorological
conditions. The M2AV flight was in summer on 10 July 2010.
The MASC flight in late spring, 8 May 2013, both in the al-
ready mixed layer in the late morning at an altitude of 200
and 100 m respectively. It can be seen that the MASC system
follows the theory very well up to 10Hz. Slight damping ac-
cording to the theory in Sect. 5 can be observed at higher
frequencies. According to the experiments that were done,
comparing tubing strategy, pressure transducers and probe
calibration, it would be expected that the M2AV system is
subject to more noise. The data does not reflect this. Instead,
in the structure function, a strong damping is observed in the
system starting at a time lag of approximately 0.5s, which
corresponds to turbulent signals with a frequency of 2Hz.
This suggests that the noise was reduced by a low-pass fil-
ter in the pressure measurements of the probe. This cannot
be ascertained in the absence of more information on the
DAQ used in the M2AV. However, it can be stated that the
MASC MHP setup meets the desired frequency response bet-
ter than the M2AV system. Analysis of seven more flights of
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1038 N. Wildmann et al.: Multi-hole probes with RPA
the M2AV in campaigns between 2007 and 2011 were anal-
ysed and supported the findings.
7 Conclusions
It was shown in this study how a standard MHP can be opti-
mized for turbulence measurements by following a few, easy
steps. It is of high importance to know the frequency re-
sponse of each piece in the measuring chain, starting with
the pneumatic response of the MHP itself, the tubing and
the pressure transducers. The common error of vibration
sensitivity in membrane-based pressure transducers was dis-
cussed, and to avoid this effect we suggest to use thermal
flow sensors instead. It was also shown how the data acqui-
sition has to be optimized for nondisturbed turbulence mea-
surement in the desired frequency range. The effect of anti-
aliasing can be minimized by an appropriate filter design.
Considering these points, precise measurements of mean
flow and turbulent fluctuation of up to 20Hz can be achieved
with the given MHP and DAQ system. To use the MHP in
RPA applications for wind and flux measurement, it has to
be embedded into a measurement system consisting of the
aircraft itself, inertial measurements and an autopilot in best
case. Issues such as flow distortion by the fuselage and wings
have to be discussed for each individual aircraft type (Craw-
ford et al., 1996; Wyngaard et al., 1985). The fusion of air-
flow data with inertial measurements to calculate wind is al-
ready described by van den Kroonenberg et al. (2008).
Acknowledgements. The authors would like to thank the anony-
mous reviewers for their valuable comments and suggestions to
improve the quality of the paper. We would furthermore like to
thank Maximilian Ehrle and Markus Auer for their great job as
safety pilots and Bernd Peters and the IAG Stuttgart for the sup-
port and time with the jet wind tunnel. The measuring equipment
would not have been ready to work without the help of Jens Dünner-
mann and Burkhard Wrenger from the University of Applied Sci-
ences Ostwestfalen-Lippe. We acknowledge the support from Dr.
Ing. Peter Scholz at the University of Braunschweig for questions
regarding the MHP design.
We acknowledge support by Deutsche Forschungsgemeinschaft
and Open Access Publishing Fund of Tübingen University.
Edited by: S. Malinowski
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1040 N. Wildmann et al.: Multi-hole probes with RPA
Appendix A
Five-hole probe pressures to airflow vector conversion
For a better understanding, a detailed step by step description
of the measurement with a five-hole probe will be given here.
The description needs to be divided into the wind-tunnel cal-
ibration procedure and the actual instantaneous measurement
of the airspeed vector.
A1 Wind-tunnel calibration
A wind-tunnel calibration is essential for the measurement
with a multi-hole probe. The goal of the wind-tunnel cali-
bration is to find a relationship between the measured pres-
sures dPiand the airflow angles αand β. Besides this, the
probe needs to be calibrated to measure the correct dynamic
and static pressure at any airflow angle (within the calibra-
tion range). In order to make this fit robust against changes
in airspeed (i.e. changes in Reynolds number), a polynomial
fit is not directly applied to the raw pressure readings, but
dimensionless coefficients are defined (see Table 1).
The presetting of the wind tunnel is a certain dynamic
pressure qand static pressure p, which should be continu-
ously measured with an independent measuring system dur-
ing the calibration routine. kαand kβserve as the variables
of the polynomial functions for α,β, and kp, and kq.kpand
kqcan be understood as correction values for dynamic pres-
sure and static pressure with regards to the airflow angle at
the probe.
α=fα(kα,kβ)
β=fβ(kα,kβ)
kp=fs(kα,kβ)
kq=fq(kα,kβ)(A1)
The functions fx(kα,kβ)are arranged as a polynomial of
order mand the two variables:
fx(kα,kβ)=
m
X
i=0
(kα)i"m
X
j=0
Xij (kβ)j#,(A2)
with Xij the coefficients cα,ij ,cβ ,ij,cs ,ij and cq,ij , for the
estimation of α,β,kpand kqrespectively. To achieve a good
accuracy with the polynomial fit, calibration with angle steps
of 2◦is recommended. The calibration range for the MHP
under investigation is suggested to be not larger than 20◦in
all directions. A sufficiently large number of calibration set-
tings yields four overestimated systems of linear equations,
which can be presented in matrix notation:






1kβ0k2
β0... kα0kα0kβ0kα0k2
β0... kn
α0kn
β0
1kβ1k2
β1... kα1kα1kβ1kα1k2
β1... kn
α1kn
β1
.
.
.
1kβn k2
βn . . . kαn kαn kβn kαn k2
βn . . . kn
αnkn
βn











cα,0
cα,1
.
.
.
cα,n











1kβ0k2
β0... kα0kα0kβ0kα0k2
β0... kn
α0kn
β0
1kβ1k2
β1... kα1kα1kβ1kα1k2
β1... kn
α1kn
β1
.
.
.
1kβn k2
βn . . . kαn kαn kβn kαn k2
βn . . . kn
αnkn
βn











cβ,0
cβ,1
.
.
.
cβ,n











1kβ0k2
β0... kα0kα0kβ0kα0k2
β0... kn
α0kn
β0
1kβ1k2
β1... kα1kα1kβ1kα1k2
β1... kn
α1kn
β1
.
.
.
1kβn k2
βn . . . kαn kαn kβn kαn k2
βn . . . kn
αnkn
βn











cs,0
cs,1
.
.
.
cs,n











1kβ0k2
β0... kα0kα0kβ0kα0k2
β0... kn
α0kn
β0
1kβ1k2
β1... kα1kα1kβ1kα1k2
β1... kn
α1kn
β1
.
.
.
1kβn k2
βn . . . kαn kαn kβn kαn k2
βn . . . kn
αnkn
βn











cq,0
cq,1
.
.
.
cq,n





.
(A3)
A solution for the coefficients ccan be found with a least
squares method. For the coefficients cα,i this would, for ex-
ample, yield
α=K·cα,
S(cα)=
m
X
i=1αi−
n
X
j=1
Kij cα,j 2=
α−K·cα
2,
ˆ
cα=argmin
cα
S(cα), (A4)
where Sis the minimization criterion and ˆcαis the best fit
for the given calibration. For linear independent columns,
a unique solution can be found by solving the normal equa-
tion:
KTK·ˆ
cα=KTα,
ˆ
cα=(KTK)−1·KTα.(A5)
Thus, the output of the wind-tunnel calibration are the co-
efficients cα,cβ,csand cq.
A2 Measurement with the multi-hole probe
Once the probe has been calibrated, velocity and flow angles
in arbitrary flows may be estimated as follows.
–The instantaneous pressures across each hole of the
probe are converted to instantaneous 1P, kα, and kβ
according to Table 1.
Atmos. Meas. Tech., 7, 1027–1041, 2014 www.atmos-meas-tech.net/7/1027/2014/

N. Wildmann et al.: Multi-hole probes with RPA 1041
–Subsequently, kp,kq,αand βare estimated:
α=K·cα,
β=K·cβ,
kp=K·cs,
kq=K·cq.(A6)
–Finally, the static pressure and the dynamic pressure
are calculated solving the equations in Table 1 for p
and q, respectively.
Table A1. Calculation of static and dynamic pressure from five-hole
probe measurements with two different methods.
Bohn et al. (1975) Treaster and Yocum (1979)
p Ps+dP0s −kp·1P Ps+1P −kp·(dP0−1P )
qdP0s +kq·1P dP0−kq·(dP0−1P )
www.atmos-meas-tech.net/7/1027/2014/ Atmos. Meas. Tech., 7, 1027–1041, 2014