985592

Recent NASA Wake-Vortex Flight Tests,

Flow-Physics Database and Wake-Development Analysis
Dan D. Vicroy
NASA Langley Research Center

Paul M. Vijgen, Heidi M. Reimer, Joey L. Gallegos and Philippe R. Spalart

Boeing Commercial Airplane Group

This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

ABSTRACT dependent on the atmospheric state (e.g. stratification,

wind magnitude and direction, ambient turbulence) [3,4].
A series of flight tests over the ocean of a four engine tur-
Numerous laboratory experiments and analytical models
boprop airplane in the cruise configuration have provided
have been developed to study and simulate wake vortex
a data set for improved understanding of wake vortex
flow physics. (Reference 3 provides a recent overview of
physics and atmospheric interaction. An integrated data-
wake-vortex flow physics issues and understanding.)
base has been compiled for wake–characterization and
However, there is very little full-scale data available for
validation of wake-vortex computational models. This
comparison with and validation of the experimental and
paper describes the wake-vortex flight tests, the data pro-
computational results. Many of the previous wake-mea-
cessing, the database development and access, and
surement flight tests have obtained only qualitative or lim-
results obtained from preliminary wake-characterization
ited quantitative data on the atmospheric state, which can
analysis using the data sets.
have a direct influence on wake-flow physics. The flight
test data described in this paper are an attempt to
INTRODUCTION develop a wake measurement data set with the accom-
panying atmospheric state information. This data set has
Several of today’s major airports are operating near their been compiled into a database that can be used by wake
capacity limit, leading to an increase in airport congestion vortex researchers to compare with experimental and
and delays. The ability to relieve the congestion through computational results. This paper provides an overview
airport expansion or new airport construction is limited of the wake-measurement flight tests and the database
and increasingly difficult. NASA, the Federal Aviation development and access. In addition, preliminary wake-
Administration (FAA), airport operators, the aircraft indus- characterization results obtained with the data set are
try and the airlines are all interested in methods to presented.
improve airport capacity. NASA is conducting a Terminal
Area Productivity (TAP) Program with the goal of provid- WAKE-MEASUREMENT FLIGHT TESTS
ing the necessary research to support the FAA and
industry in safely achieving clear-weather (visual flight
The objective of the flight tests was to develop a full-scale
rules) airport capacity in instrument meteorological con-
wake measurement test method to obtain a detailed
ditions (IMC). The flight test described in this paper is
wake-development data set with the accompanying
part of the Reduced Spacing Operations element of the
atmospheric state information, as discussed in the intro-
TAP Program [1].
duction. The tests used two NASA airplanes as illustrated
The spacing required to avoid the wake turbulence of the in figure 1.
preceding airplane is one of the limiting factors in safely
The NASA-Wallops Flight Facility’s Lockheed-Martin
reducing in-trail spacing. A wake vortex upset is most
C-130, shown in figure 2, was the wake generator. It was
hazardous for aircraft near the ground during landing and
outfitted with wing tip smokers to mark the wake. It
takeoff. The degree of upset mainly depends on the rela-
weighed between 95,000 and 113,000 pounds during the
tive size of the vortex generating and vortex encountering
test with a geometric wingspan of 132 feet 7 inches. The
airplanes and the extent of wake decay. In addition to the
tests were all flown with the C-130 in the “clean” configu-
spacing between commercial aircraft, some elements of
ration (i.e. flaps up and gear retracted), resulting in a trail-
paratrooper airdrop procedures are also limited by loca-
ing wake with a single vortex pair representative of a
tion and strength of trailing vortices from preceding air-
transport aircraft during climb-out, cruise or initial
craft [2]. The strength of the encountered wake is highly
approach. The tests were conducted over the ocean
along the eastern shore of Virginia.
1
 the wake as a function of distance can be seen in the
image.
The OV-10 was also equipped to measure the ambient
weather conditions for correlation with the wake transport
and decay characteristics. Temperature, pressure and
humidity measurements are continuously recorded to
complement available ground-station weather balloon
data, while the local wind velocities are derived from the
onboard inertial and GPS based navigation systems. An
extensive overview of research instrumentation and mea-
surement capabilities of the OV-10 is presented in refer-
ence 5.

Figure 1. Wake measurement flight test setup.

The NASA-Langley North-American Rockwell OV-10A

measured the wake and atmospheric conditions. The
OV-10 was equipped with a three-boom, flow-sensor
arrangement to measure the flow-field characteristics of
the wake. The booms were located on each wing tip and
the right side of the nose as shown in figure 3. As is cus-
tomary, the booms were designed to place sensors as far
ahead of the aircraft as possible yet have sufficient stiff-
ness and low mass (high natural frequency) to prevent
unwanted vibration influence on the sensor measure-
ments. Standard NACA pitot-static probes with balsa
angle-of-attack and sideslip vanes were mounted at the
end of each wingtip. A 5-hole pressure probe was Figure 3. OV-10 major instrumentation systems
mounted at the end of the nose boom to provide flow
direction, airspeed and static pressure measurements.
Wind-tunnel calibrations have been obtained for the three
probes and airspeed calibration flights have been con-
ducted to correct the probes for residual airframe-
induced flow perturbations.

Figure 4. OV-10 tail video of wake 2.4 nmi in trail.

The general flight test procedure was as follows. The

OV-10 would fly to the flight test area and begin a series
of “weather” runs. These would begin with one or two
“turbulence” runs, which were 2-minute, level, constant
Figure 2. C-130 wake generator airplane. heading flight segments 1000 feet below the test altitude.
The test altitude was generally 4000 or 5000 feet. This
The OV-10 flew through the wake at various downstream was followed by a “weather profile” run, which was a con-
distances measuring its velocities and position. A picture stant speed, constant heading climb from 1000 feet
of a wake measurement taken from the video camera below to 500 feet above the test altitude. Another series
mounted on the left tail of the OV-10 (as noted in figure 3) of turbulence runs would then follow 500 feet above the
is shown in figure 4. The smoke clearly denotes the vor- test altitude. After completing the weather runs, the
tex pair in the C-130 trailing wake. Some perturbation of OV-10 would rendezvous with the C-130 and start a
series of “wake measurement” runs. The C-130 would fly

2
a constant speed and heading at the test altitude. The • Time-tagged, VHS video recordings from the tail
OV-10 measured the wake by flying slower than the camera and both wing-tip cameras.
C-130 and making a series of wake penetrations at • Flight notes from the test pilot and flight engineers of
increasing ranges behind the C-130. At the conclusion of event times and conditions
a series of wake measurement runs an additional series
• Time-tagged data tape from the experimental data
of weather runs were then conducted. Although the OV-
system
10 made measurements over the entire length of the
wake visualized by smoke, the measurements do not • Time-tagged Ashtech differential Global Positioning
constitute a ‘frozen wake’. In other words, the measure- System (GPS) data
ments at increasing distance behind the generator air- The flight notes and video data are reviewed and used to
craft are made in different parts of the atmosphere. (As establish a precise log of event times and test conditions
an example, the OV-10 travels about 30 nmi during an called the “flight event” file. This information is then used
encounter run that spans 9 nmi of trailing wake.) to extract the pre- and post-flight instrument calibration
The ideal data set for wake development and decay anal- data and the data for the calibration check flight maneu-
ysis would be a series of instantaneous, 3-dimensional vers. This calibration data is used to establish the instru-
wake measurements within a fixed air mass at multiple mentation zero bias values, which are saved as a “flight
streamwise distances, from initial wake roll-up until final constants” file for each flight. The event and constants
decay or breakup. However, there currently is no practical files and the data from the onboard data acquisition sys-
test method or instrumentation system to make such a tem (DAS) are input for the OV-10 Data Reduction and
global measurement. Analysis Program (OVDRA). This program applies the
instrument calibration and bias corrections to the DAS
FLIGHT DATA REDUCTION PROCESS data and computes the inertial referenced wind compo-
nents. The output of OVDRA is a calibrated data file for
The data flow of the flight-data reduction process is each run of the test flight. These run data files are used
shown in figure 5. For each flight the OV-10 generates to compute turbulence levels and generate wind and tem-
four data products: perature profiles.

Figure 5. Flight data reduction process.

3
 OV-10 was flying through the wake from left to right. The
airplane flew through the left vortex but passed below the
right vortex. Each boom traces a different path in space,
which is clearly seen as the airplane banks about 35
degrees left at the end of the measurement pass (fig. 8).

Figure 7. Horizontal profile of OV-10 wake measurement

pass (Flight 558, Run 26, Event 1).

The pilot notes from the C-130 provide weight and test
condition information used to estimate the initial circula-
Figure 6. Wake axis system.
tion strength of the wake for comparison with circulation
derived from the wake measurements.
The OV-10 and C-130 inertial positions are known from
differential GPS measurements collected at 1 Hz. The
NONDIMENSIONALIZATION – Several of the data val-
Wake_Vel program (fig. 5) uses this position information
ues are nondimensionalized for comparison with other
and the OVDRA output to translate the measured wake
data sets. The nondimensionalization parameters are
velocity data to an inertial-referenced wake axis system.
defined as follows:
The wake axis system, shown in figure 6, is aligned with
The length scale is the initial spacing between vortices
the heading between the OV-10 and C-130 at the time of
based on an elliptical span load.
the wake vortex encounter ( t ref ). The origin of the coor-
dinate system (C-130 position at t o ) is the C-130 posi-
b∗ = π4 b
tion when it generated the wake being measured at t ref . (Eq. 1)

The wake velocity algorithm Wake_Vel translates the For the C-130 b∗ is 104 feet.
OVDRA wind measurements to the wake coordinate sys-
tem. Each wake measurement event has it own wake
coordinate system. Since the wake translates with the
airmass the wake origin location must be iteratively deter-
mined based on the known C-130 track and OV-10 mea-
surement location, and an assumed average wind
component. The wake-origin location also determines the
wake age. The wakes translation with the wind also
requires that the wake measurement positions be cor-
rected to account for the drift of the wake over the mea-
surement period.
The OV-10 could measure the wake velocity at 3-points
in space at any instant in time. A wake measurement
pass consists of 3 streams of wake velocity data col- Figure 8. Vertical profile of OV-10 wake measurement
lected at 128 Hz, over a 5 to 10 second period (i.e. about pass (Flight 558, Run 26, Event 1).
600 to 1000 data samples are taken). An example of a
wake velocity measurement from the three booms is The initial circulation is computed as:
shown in figures 7 and 8. These figures show the hori-
zontal and vertical profiles of the wake measurement W
pass along with the wake velocity vectors. The figures Γ∗ =
b∗ ρVt
show that during this particular wake measurement the (Eq. 2)

4
The initial wake descent velocity is computed as: • Encounter Data Type: Data at 128 Hz that covers the
duration of an individual OV-10 wake measurement
Γ∗ pass. This file type contains wake-velocity data as
V∗ =
2πb∗ shown in figures 7 and 8, in addition to other parame-
(Eq. 3) ters that may be used for wake profile analysis. The
The time scale is the time for the wake to descend one Main-Run data set includes references to the occur-
length scale. rence of wake measurement passes.
• Weather Run Data Type: Data that cover the duration
b∗ of a weather run is included at a rate of 128 Hz. A
t∗ =
V∗ reduced set of parameters for analysis of turbulence
(Eq. 4) and atmospheric state is retained.
The nondimensionalization values derived from some of • Wake Video Data Type: Digital image files captured
the flight-test results discussed later in this report are from the OV-10 tail camera are included for many
listed in table 1. encounters. These images can be used towards
characterization of the wake shape. The Main-Run
Table 1. Nondimensionalization parameter values. data set includes reference to the availability of the
video images.
Flight Run Γ∗ V∗ t∗
In addition to data related to the OV-10 measurement
2
ft /s ft/s sec systems, additional data sets are provided:
558 26 1706 2.6 39.8 • Weather data: Available vertical weather profile data
705 27 2123 3.2 32.0 obtained from standard weather balloons are
included as a separate data category in the data-
705 28 2206 3.4 30.8
base.
705 29 1482 2.3 45.8
• Encounter-event Descriptions: Detailed OV-10 flight-
705 30 1464 2.2 46.4 log description files are included that serve as over-
705 37 2033 3.1 33.4 views of the OV-10 flight profiles and provide some
encounter characterization.
DATA BASE • Wake velocity plots: Processed wake-encounter
velocity profiles (such as shown in figures 7, 8 and
The flight test data obtained from seven flights conducted 16a) are included to assist the user in familiarization
in 1995 and 1997 have been compiled into an organized with the data quality.
structured database that may be used by researchers for • Data-reduction documentation: Source code used to
detailed wake vortex analysis. The main purpose of the reduce the OV-10 flight measurements to wake-pro-
database is the integration of all relevant flight data into file velocity data are provided.
an organized and structured data set.
• Instrumentation documentation: Pertinent informa-
The data set includes relevant (dimensional and non- tion about sensors and instrumentation systems
dimensional) measured and reduced OV-10 and C-130 installed on the OV-10 aircraft are included (see also
parameters used to determine the wake velocities and Ref. 5).
location from the wake measurement runs, as well as
Figure 9 summarizes the flight-data categories described
weather parameters obtained during the measurement
above. A summary of the data contained from each of the
runs and dedicated weather runs. A total of nearly 200
seven flights is provided in Table 2. The presently ASCII-
parameters are included in the data set, with some
formatted database can be used as stand-alone data-
redundant measurements retained to allow comparison
base. The user would extract desired data using time as
of instrumentation systems. Selected parameters are
independent parameter from the data base and port the
nondimensionalized for comparison between runs at dif-
set to his own data-analysis routines. Alternately, the
ferent speeds of the generator aircraft and for compari-
user could load the integrated data set into a suitable
son with other experimental results. The database also
relational database for searching and post processing.
includes weather balloon data and captured frames from
The high data rates used in Main-Run and Weather-Run
the OV-10 tail camera video images (such as shown in
categories together with the approximately 200 encoun-
figure 4).
ters obviously result in a rather large database. However,
The database is comprised of several different data cate- detailed spatial information is now preserved for wake
gories. Four categories are centered on the OV-10 mea- encounter and atmospheric-turbulence analysis.
surements:
• Main Run Data Type: Data is included at 32 Hz rate
covering the duration of each OV-10 run. This file
type would be used for wake location analysis.

5
 First, aspects of atmospheric conditions during the flights
conducted are summarized with ambient turbulence lev-
els quantified using different parameters. Next, wake-
descent profiles, vortex velocity profiles and circulation
development are illustrated.

AMBIENT ATMOSPHERIC CONDITIONS – The seven

flights included in the database were conducted in three
types of ambient atmospheric conditions (see Table 3
and Ref. 6). Some flights were conducted at altitudes
near (cumulus) cloud layers, likely resulting in strong
local variations in updraft and ambient atmospheric tur-
bulence. Weather and overall wake development (shape)
are summarized in Table 3. Measurements in the data-
base should allow additional meteorological characteriza-
tion (see also reference 6).
Flights 556, 557 and 558 were conducted in a nearly
unstable stratified atmosphere (low Brunt-Vaisala fre-
quency) with relatively high turbulent kinetic energy levels
(to be discussed below). Flight 560, 561 and 705 were
conducted in a rather stable atmosphere and in absence
of clouds. Flight 559 had an intermediate level of stability.

AMBIENT TURBULENCE LEVELS – The OV-10 made

dedicated “turbulence runs” of two minutes in length to
gather data on the atmospheric turbulence in the area of
the encounter runs. These “turbulence-run” data can be
used to quantify variation in the atmospheric turbulence
from one flight to another.

Figure 9. Database components and structure. Ambient Turbulent Kinetic Energy – Turbulent kinetic
energy (TKE) is a measure to characterize atmospheric
The database contained on optical disks can be obtained turbulence. TKE is determined from the 128 Hz measure-
by contacting the first author at: NASA Langley Research ments of the three wind velocity components (u, v, and w)
Center, MS 153, 100 NASA Road, Hampton, VA as follows:
23681-2199.
(
TKE = 12 σ u2 + σ v2 + σ 2w ) (Eq. 5)
Table 2. Summary of database content.
Flight Encounter Individual Weather Wake where σu, σv and σw are the standard deviations of the
Number Runs Encounters Runs Images corresponding velocity components over some sample
556 9 49 2 37 time. The range of TKE’s obtained from the various “tur-
557 4 21 2 16 bulence” runs in each flight is indicated in Table 3.
558 6 42 2 6 Clearly, Flight 556 has overall much higher turbulence
559 4 24 1 11
levels than Flight 705. A disadvantage of using TKE is the
560 4 8 2 9
strong dependence of its magnitude on the duration of
561 4 4 2 14
705 4 84 4 0
the measurement window used to evaluate equation 5.
Total 35 232 15 94 To obtain measurements that include relatively large
wavelengths (on order of the Crow mechanism) long
PRELIMINARY WAKE CHARACTERIZATION sampling times (on order of 2 minutes) are needed.

Using the reduced OV-10 data contained in the database,

preliminary results of wake and atmospheric character-
ization are presented. Results are given here as an illus-
tration of the possible use of the available data for wake
analysis. Detailed discussion of wake characterization is
beyond the scope of this paper.

6
 Figure 10. Spectral density from 2 minute “turbulence” run (Flight 556, Run 29).

Table 3. Summary of ambient atmospheric conditions

Flt. Flight Weather TKE Brunt-Vaisala Wake Shape Summary
No. Altitude Summary 2 min sample frequency (Oscillation Amplitude)
ft ft2/sec2 1/sec
556 2000-3400 Near cloud base, turbulent 4.5-36 (-0.00002) Large wake oscillations, bursting at 2.5-4 nm, and
Crow onset at < 1nm, linking later
557 2700-5200 Near cloud base, turbulent 1.2-13 0.0089-0.022 Large wake oscillations, bursting at 1.5-2.5 nm, Crow
onset at 1 nm, linking later
558 4100-5700 High clouds 1.1-1.2 0.0055-0.0089 Large wake oscillations, bursting at 5 nm, Crow onset
at 1-2 nm
559 ~ 5000 High clouds .98-7.3 0.0077-0.01 Moderate wake oscillations
560 4000-5500 Clear sky .25-1.77 0.017 Small wake oscillations,
561 4000-5500 Clear sky 0.3-1.9 0.013 Small wake oscillations
705 6200-8000 Hazy, low turbulence stable 0.4-3.4 0.01-0.015 Very small oscillations, Crow onset after 5 nm

Spectral Distribution of Ambient Turbulent Energy and resolved over a range of about 3 decades of wavenumber
Dissipation Rate – The “turbulence” run measurements in these 2-minute data samples. The most-unstable
were analyzed in the frequency domain using ensemble- wavelength of the Crow instability (at about 8.6 ⋅b∗ , see
averaged Fourier analysis. Ref. 13) occurs at a wave number of approximately 0.001
for the conditions in these plots, i.e. near the lower end of
As an example, spectral density results obtained from the
the resolved inertial range. The data in the inertial range
2-min. “turbulence” runs from Flights 556 and 705 are
from both samples show that small-scale atmospheric
shown in Figs. 10 and 11, respectively. The power-spec-
turbulence is isotropic, as expected. Similar levels and
tral density is shown as function of the wavenumber for
trends are obtained from each of the three OV-10 probes.
each wind components individually (for each boom), as
Consistent with the TKE levels shown in Table 3, Flight
well as combined (parameter labeled ‘All’). The wave
705 spectral energy densities are at much lower levels
number is the frequency multiplied by 2π Vt , where Vt is
than in Flight 556, allowing measurement noise effects to
the true airspeed of the OV-10. (The wave number is pro-
become apparent, particularly at the highest wavenum-
portional to the inverse of the turbulent-eddy size.) In
bers. Nose-boom instrumentation resonance is visible in
general, the measurements generally follow the “-5/3”
the low-turbulence data of Flight 705. The highest wave
slope predicted by Kolmogorov’s theory for eddies in the
numbers extend into a frequency range with instrumenta-
inertial range of isotropic turbulence. The inertial range is
tion limitations (such as pneumatic lag for the nose-boom

7
probe), obscuring the detection of the viscous range in As an example, the estimated dissipation rates for the 2-
the turbulence spectrum. min turbulence-run data shown in Figure 10 (Flight 556,
Run 29) is shown in figure 12 as function of wavenumber.
Nearly constant levels of dissipation rates can be
Table 4. Dissipation Rate and Turbulence Categories observed for wavenumbers between 0.003 and 0.3 (wing-
during “Turbulence Runs”. tip boom sensors). Table 4 summarizes the range of dis-
sipation rates for these wavenumbers computed for the
Flight Range of MacCready Turbulence
No. Turbulent Category [7] turbulence runs of each of the six flights. The dissipation
Dissipation Rate categories as described by MacCready [7] are included
(ft2/s3) in Table 4 to characterize ambient atmospheric turbu-
lence. Using these categories, the ambient turbulence
556 0.01 Moderate
levels encountered in the tests varied between “moder-
557 0.01-0.04 Moderate ate” and “negligible”. This characterization based on dis-
558 0.0002-0.001 Negligible/Light sipation rate is in agreement with qualitative reports of
559 0.0001 Negligible turbulence levels given by the OV-10 pilots in the present
flights.
560 0.0001 Negligible
705 0.00002 Negligible The overall wake development (such as distance needed
for onset of Crow instability growth) as summarized in
Besides the TKE, another indicator of atmospheric turbu- Table 3 appears to correlate with the level of atmospheric
lence previously used to characterize flight-test data turbulence.
(e.g., Ref. 7) is the turbulent dissipation rate, which is a
measure of the rate of dissipation of turbulent kinetic Local Variations in Ambient Turbulence – Preliminary
energy by action of viscosity. For isotropic turbulence, the analysis of the video data obtained from the “encounter
dissipation rate ε can be estimated from the energy den- runs” indicates that rather large local variations in the
sity E at each wavenumber k in the inertial range: wake shape (i.e., amplitude of apparent Crow oscillation)
can occur in a short period of time as the OV-10 trails the
3 C-130.
 5  2
ε =  3.6 Ek 3 
  (Eq. 9)

Figure 11. Spectral density from 2 minute “turbulence” run (Flight 705, Run 25).

8
As an example, results from Flight 558, Run 28 with the
OV-10 flying encounters at about 1.8 nautical miles
behind the C-130 are discussed. The wake was fairly
straight and steady at the beginning of the run, but
quickly became wavy and oscillatory, both vertically and
horizontally, at a short time thereafter. This occurred over
approximately 1 minute and 10 seconds. The OV-10 had
flown a maneuver at the beginning of the run near the
wake, but outside its influence, supplying 10 seconds of
clean data. Another 10 seconds of measurements out-
side the wake are also available between two encounters
(encounters 4 and 5) later in the run. The spectral con-
tent of the velocity perturbations for these samples are
shown in Figure 13, together with the data for “turbu-
lence” Run 25. The left most plot is the 10 seconds at the
beginning of the run, the middle plot is near the end of
the run, and the right plot is the nearest 2-minute turbu-
lence run. The 10-sec data window allows only reduced
wavenumber resolution as compared to the 2-min turbu-
lence run. However, the fact that the “-5/3 Kolmogorov”
slope is clearly observed also in the 10-sec data sets
allows direct extrapolation to smaller wavenumbers in the Figure 12. Turbulent dissipation rate (Flight 556, Run 29).
range of the Crow wavelength. As noted above, for the
altitude range of this flight test, the Crow wavelength is
within or close to the inertial wavenumber range.

Figure 13. Comparison of local and ambient spectral density data (Flight 558, Run 25 and 28, Nose boom data).

9
Comparison of the plots in Fig. 13 for the encounter runs due to local variations in the vertical wind, temperature
shows an order of magnitude increase in turbulent profile (stratification), or ambient turbulence (see also Ref
energy levels for resolved wavenumbers (i.e., 0.05) 3) as the OV-10 samples the wake in different locations of
between the two 10-sec data segments. In other words, the atmosphere. Recent numerical simulations indicate
the measured change in local ambient turbulence corre- that wake rebound is predicted for sufficiently strong
lates with apparent locally increased Crow amplification stratification [14].
and highly oscillatory wake shape as observed in the
Figure 15 summarizes in a histogram the relative vertical
video data. The viscous dissipation rate obtained from
location of the C-130 wake obtained from the OV-10 mea-
short data sets (i.e., on the order of several seconds) at
surements at various downstream distances for a variety
rather high wavenumbers can be useful to characterize
of C-130 airspeeds. The average wake descends as a
ambient turbulence levels at scales relevant to Crow
function of the separation distance. However, there are
instability. Proper sensors (e.g., vanes) and aircraft
several encounters where the wake location is at or just
instrumentation (e.g. inertial and GPS navigation sys-
above the flight altitude of the C-130. In the flight with the
tems as installed in the OV-10), combined with appropri-
lowest ambient turbulence (Flight 705), the wake could
ate data-analysis routines, may allow useful qualitative
be observed and had measurable wake-perturbation
turbulence measurements towards in-situ prediction of
velocities as far back as 10 nmi.
aspects of wake development.
During Flight 705, short rectilinear flight segments were
included to allow sufficient data sets for characterization
of possible local ambient turbulence levels. The very low
level of turbulence in this flight (see Table 4), however,
may preclude detection of quantifiable differences in
ambient turbulence levels during an encounter run.

Figure 15. Histogram of wake locations (from all

encounters) at various separation distances.

WAKE VORTEX VELOCITY PROFILES – The OV-10

encounters provide wake vortex velocity profiles in a ref-
erence system attached to the local wake (see Flight
Data-Reduction Process section above). In total about
230 encounters are available (see Table 2).
Figure 14. OV-10 measured wake descent of a C-130
As an example of typical measurements available, Figure
(Run 26, Flight 558).
16a shows the horizontal and vertical wake induced
velocities corresponding to the trajectories provided in
In summary, the OV-10 nose and tip-boom instrumenta-
Figures 7 and 8. The location of the vortex pair can
tion and data-reduction system allows quantitative char-
clearly be inferred from the velocity profiles; the approxi-
acterization of ambient atmospheric turbulence during
mate vortex spacing is 100 ft (i.e. close to b*). Several
the dedicated “turbulence” runs as well as during time
data points are obtained in or near the core of the left vor-
windows from the “encounter” runs away from the wake.
tex. As mentioned with figures 7 and 8, the OV-10 was
flying from left to right and flew very near the center of the
WAKE DESCENT PROFILES – The vertical position of
left vortex but below the right. This was typical of most of
the trailing wake relative to the (constant) flight altitude of
the wake measurement passes. The encounter with the
the C-130 generator aircraft is determined from each OV-
first vortex would usually push the OV-10 below the sec-
10 wake encounter. Figure 14 shows an example of the
ond vortex. This resulted in measurements like figure 16a
wake decent against non-dimensional time. During the
that clearly shows the large perturbation velocities of the
first 2.5 time units the wake descends in a manner in fair
first vortex compared to the data from the second.
agreement with wake circulation ( ∆h = b∗ ⋅ ∆t / t∗ ).

However, during the remaining time the wake descent is

considerably different and an apparent “rebound” is
observed. The apparent “rebound” of the wake may be

10
 the vortex models proposed by Burnham [8], Hoffman
and Joubert [9], or Spalart [3]. The vortex model used in
this analysis was developed by the first author of this
paper based on available analysis of the OV-10 mea-
sured data. The empirical model is similar to the Hoff-
man-Joubert and Spalart models.

(a) Measured horizontal velocity profile (Flight 558,

Run 26, Event 1).

Figure 17. Vortex model circulation profile.

The vortex model used here is based on the circulation

(b) Measured vertical velocity profile (Flight 558, profile shown in figure 17. The circulation profile is
Run 26, Event 1). related to tangential velocity through:
Figure 16. Γ∞ Γ(r )
Vθ (r ) =
2πr Γ∞
The horizontal and vertical velocities measured in the (Eq. 6)
flight test can be used to evaluate analytical models for
trailing-vortex flows (discussed below), and to estimate The model circulation profile is defined as:
the circulation strength of the vortex pair. The measured
centerline downwash velocity together with the spacing 
 Ar 2 , r ≤ r1
of the vortices can also provide an estimate of the 
strength of the trailing vortex pair. 
Γ(r )  r 
a
Although not shown here, measurements of the axial = , r1 < r ≤ r2
velocities when a probe traversed a vortex core are avail- Γ∞  r2 
able in the database. 
1 , r > r2

WAKE-CIRCULATION DECAY ANALYSIS – Quantifica- 
(Eq. 7)
tion of possible decay of circulation with wake age as
function of atmospheric conditions is of interest in view of where:
wake-prediction model systems studied for possible
advanced air-traffic control [12]. In particular, flight data 2 ln r1 + ln A
a=
are of interest to evaluate aspects of “continuous-decay” ln r1 − ln r2
and “catastrophic-event” wake-development theories (Eq. 8)
(see Ref. 3). and
To estimate the vortex characteristics such as circulation
Γ∞
strength, core location, and core radius, theoretical vor- Vθ = Vθ (r1 ) = Ar1
tex models are fit to the measured wake velocities. In this max 2π (Eq. 9)
analysis a pair of independently oriented, counter-rotat-
ing, axially symmetric line vortices modeled the wake. with the constraints:

V (r )
The velocity field about each line vortex was represented
by its tangential velocity profile θ , where r is the per- 0 < r1 < r2
(Eq. 10)
pendicular distance from the line vortex. There are a vari-
ety of vortex models that can be used for the tangential 0< A≤ r1−2
(Eq. 11)
velocity profile such as a Lamb or Rankin point vortex or

11
For each wake measurement a multi-variable search is
conducted to determine the location and orientation of
the line vortex pair and the values of the vortex model
parameters (r1 , r2 , Γ∞ , A) that best fit the measured data.

Figure 18a shows the measured vertical and horizontal

velocity data and the model fit results for flight 558 run
26, event 1 (corresponding to figures 7 and 8).

Figure 20. Left vortex tangential velocity profile (Flight

558, Run 26, Event 1).

Compiling available model-fit results as a function of

(non-dimensional) wake age for a given measurement
run can provide a characterization of wake development
and possible wake decay. Figure 19 shows the wake
decay trend for three wake measurement runs of Flight
(a) Measured and modeled horizontal velocity profile
705. Large values and variations in the circulation relative
(Flight 558, Run 26, Event 1).
to the initial level (see Table 1) are noticeable for nondi-
mensional wake-age values up to about 1.5. Run 27 has
measurements only up to an age of 2. A simple linear fit
of the data provides a nondimensional decay rate of –
0.127, -0.091 and –0.104 for Runs 27, 28 and 37 respec-
tively, or approximately 10% per nondimensional time
unit. Run 37 however, has a nearly constant strength
from 2.0 to 5.0 time units (i.e., corresponding to a separa-
tion distance of almost 10 nmi at the C-130’s airspeed).
A second method to compute circulation strength was
employed for comparison with the model fit values and
ground-based wake-vortex field measurements. A 3 to 10
meter spatial average of the measured single-vortex cir-
culation, as recently proposed by Hinton and Tatnall
(b) Measured and modeled vertical velocity profile [10,11], was computed.
(Flight 558, Run 26, Event 1). 32.81
1
22.97 9.∫84
Γ3,10 = Γ ( r ) dr (ft 2 /s)
Figure 18.
(Eq. 12)
This required the velocity contribution from the second
vortex be subtracted from the measured wake velocity to
obtain a single vortex measurement. This was accom-
plished by subtracting the model-fit derived second-vor-
tex velocity contribution from the measured data. An
example of the resultant single vortex rotational velocity
and circulation profile are shown in figures 20 and 21,
respectively, for Flight 558, Run 26, Event 1. The figures
show the data from all three booms. The terms “inboard”
and “outboard” refer to the single-vortex measurement
location relative to the wake. For example, when measur-
ing the left vortex, the inboard side would be on the right
and the outboard side the left. The inboard measurement
is more sensitive to errors in the model fit of the opposite
vortex.
Figure 19. Nondimensional wake development obtained
from model fit (Flight 705).
12
 CONCLUDING REMARKS

Using the uniquely instrumented OV-10A research air-

craft, NASA recently conducted flight tests towards char-
acterization of trailing vortex wake development and
ambient atmospheric conditions. A total of about 230
wake encounters (penetrations) at different atmospheric
conditions are available at different initial-wake circulation
levels.
An integrated database has been compiled that com-
bines relevant reduced dimensional and nondimensional
flight data at appropriate data rates needed for wake-
characterization analysis. In-situ and weather-balloon
atmospheric data are included in the database, as well as
Figure 21. Left vortex circulation profile (Flight 558, Run frames obtained from video recordings of the wake
26, Event 1). shape.

Figure 22 shows the nondimensional 3-10 meter aver- Some wake-characterization analysis results are pre-
aged circulation development for Runs 27, 28 and 37 of sented in this paper to illustrate the possible uses for the
Flight 705. The figure shows a development trend similar data contained in the database. Some observations can
to Figure 19, but with reduced variations between be made based on the preliminary analyses presented:
sequential measurements, particularly for nondimen- • Ambient-turbulence measurements obtained with the
sional age less than 1.5. Note that the averaged circula- OV-10 show that the inertial turbulence range is well
tion as computed here is less sensitive to the curve-fit resolved and includes wavenumbers corresponding
modeling errors, resulting in less variation within and to most unstable wavelengths of the Crow instability.
between the runs. It also shows a very low decay rate. A
• Computed ambient turbulence kinetic energy (TKE)
linear fit through the average circulation yields a nondi-
levels and dissipation rates appear to correlate with
mensional decay rate of –0.089, -0.025 and –0.015 for
the wake development (i.e., onset of Crow instability
Runs 27, 28 and 37 respectively. The figure also distin-
as viewed from video images) and the pilots’ descrip-
guishes between the left and right vortex but show no
tions.
definitive difference.
• The trailing single-pair wake generally shows a con-
tinuous descent as a function of wake age. However,
several cases where the wake ‘rebounds’ to the flight
altitude of the generator aircraft are observed.
• Wake strength (circulation) development can be
obtained from the available data sets. Results
obtained from curve-fitting a newly formulated vortex-
circulation profile model for a flight with extremely low
ambient turbulence allowed estimation of wake circu-
lation up to a non-dimensional wake age of about 4,
with almost no decay.
Additional comprehensive analyses of data contained in
the database, including further correlation with available
weather data are needed for characterization of the
present wake-vortex flight tests.
Figure 22. Nondimensionalized wake decay from 3 to 10
meter average of the 3 booms (Flight 705). ACKNOWLEDGMENT

Both analysis approaches show the wake decay trend up Efforts by the Boeing Commercial Airplane Group (data-
to the highest non-dimensional wake age (corresponding base compilation and aspects of turbulence and wake-
to a separation distance of almost 10 nmi at the C-130’s development analysis) were supported under NASA Con-
airspeed) for a flight with extremely low ambient turbu- tract NAS1-20267 (Task 21).
lence. Uncertainty analysis of the measured data is
underway and will be included in the published database.

13
REFERENCES NOMENCLATURE

1. Perry, R. B.; Hinton, D. A.; and Stuever, R. A.: “NASA Wake a : vortex model variable (eq. 8)
Vortex Research for Aircraft Spacing,” AIAA 97-0057, 35th
A : vortex model parameter, 1/ft2
Aerospace Sciences Meeting & Exhibit, Reno, NV, January
9-10, 1997. b : wing span, ft
2. Blake, W. B., “Development of the C-17 Formation Airdrop
b∗ : initial vortex spacing, ft
Element Geometry,” J. Aircraft, Vol. 35, No. 2, March-April
1998. E : spectral density, ft3/s2
3. Spalart, P. R.: “Airplane Trailing Vortices,” Annual Review
k : wavenumber, 1/ft
of Fluid Mechanics, Vol. 30, pp. 107-138, 1998.
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AIAA 98-0592, 36th Aerospace Sciences Meeting & r1 : vortex model parameter, ft
Exhibit, Reno, NV, January 12-15, 1998.
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of the Preparation and Use of an OV-10 Aircraft for Wake t o : time when wake generated, sec
Vortex Flight Experiments,” AIAA 95-3935, September
1995. t ref : time when wake measured, sec
6. Zak, J. A. and Rodgers, W. G.: Documentation of Atmo- t ∗ : time scale, sec
spheric Conditions During Observed Rising Aircraft Wakes, TKE: turbulent kinetic energy, ft2/s2
NASA CR-4767, April 1997.
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from Aircraft,” Journal of Applied Meteorology, Vol. 2, pp. u : longitudinal wind component, ft/s
439-449. v : lateral wind component, ft/s
8. Hallock, J. N.: “Aircraft Wake Vortices: An Assessment of
the Current Situation,” DOT-FAA-RD-90-29, January 1991. V∗ : initial wake descent, ft/s
9. Hoffman, E. R. and Joubert, P. N.: “Turbulent Line Vorti-
V θ : vortex tangential velocity, ft/s
ces,” J. Fluid Mech., Vol. 16, Part 3, pp. 395-411, July
1963. Vθ : maximum tangential velocity, ft/s
10. Hinton, D. A. and Tatnall, C. R.: “A Candidate Wake Vortex max
w : vertical wind component, ft/s
Strength Definition for Application to the NASA Aircraft Vor-
tex Spacing System (AVOSS),” NASA TM-110343, Sep- W: weight, lbs
tember 1997. X w : longitudinal wake axis coordinate, ft
11. Tatnall, C. R.: “An Investigation of Candidate Sensor
Observable Wake Vortex Strength Parameters for the Yw : lateral wake axis coordinate, ft
NASA Aircraft Vortex Spacing System (AVOSS),” NASA Z w : vertical wake axis coordinate, ft
CR-1998-206933, March 1998.
12. Hinton, D. .A.: “An Aircraft Vortex Spacing System ∆h : change in wake height, ft
(AVOSS) For Dynamical Wake Vortex Spacing Criteria,” ∆t : wake age, sec
AGARD 78th Fluid Dynamics Panel Meeting and Sympo-
sium on the Characterization & Modification of Wakes from
ε : eddy dissipation rate, ft2/s3
Lifting Vehicles in Fluids, Trondheim, Norway, AGARD CP- ρ : air density, slugs/ft3
584, Paper 23, May 20-23, 1996. Γ : vortex circulation, ft2/s
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Conventional Aircraft," AGARDograph No. 204, May 1975. Γ3,10 : 3 to 10 meter average circulation, ft2/s
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Stratified Fluid,” J. Fluid Mech., Vol. 327, pp. 139-160, Nov.
1996. Γ∞ : vortex model total circulation, ft2/s
σ u : standard deviation of longitudinal wind component,
ft/s
σ v : standard deviation of lateral wind component, ft/s
σ w : standard deviation of vertical wind component, ft/s

14