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Appendix 2 to ETSO-C117b - Wind Field Models and Data

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###### Appendix 2 to ETSO-C117b – Wind Field Models and Data

*ED
Decision
2020/011/R*

This
Appendix contains data that defines the wind field models to be used
in conducting the tests specified in paragraph 4(d)(10) of this ETSO.
This material was developed by the National Aeronautics And Space
Administration (NASA), reference NASA Technical Memorandum 100632
[ref. 1].

The
downburst model parameters below provide the variables to be used to
obtain the representative test conditions: (1) and (2)

<table bgcolor="#d9d9d9" cellpadding="7" cellspacing="0">
<col/>
<col/>
<col/>
<col/>
<tr>
<td bgcolor="#808080">
Radius
				of Downdraft (ft)
</td>
<td bgcolor="#808080">
Maximum
				Outflow (ft/s)
</td>
<td bgcolor="#808080">
Altitude
				of Max. Outflow (ft)
</td>
<td bgcolor="#808080">
Distance
				from Starting Point (3) (ft)
</td>
</tr>
<tr>
<td bgcolor="#d9d9d9">
920
</td>
<td bgcolor="#d9d9d9">
37
</td>
<td bgcolor="#d9d9d9">
98
</td>
<td bgcolor="#d9d9d9">
20000
				(-9000)
</td>
</tr>
<tr>
<td bgcolor="#d9d9d9">
1180
</td>
<td bgcolor="#d9d9d9">
47.6
</td>
<td bgcolor="#d9d9d9">
98
</td>
<td bgcolor="#d9d9d9">
15000
				(-14000)
</td>
</tr>
<tr>
<td bgcolor="#d9d9d9">
2070
</td>
<td bgcolor="#d9d9d9">
58.4
</td>
<td bgcolor="#d9d9d9">
131
</td>
<td bgcolor="#d9d9d9">
25000
				(-4000)
</td>
</tr>
<tr>
<td bgcolor="#d9d9d9">
4430
</td>
<td bgcolor="#d9d9d9">
68.9
</td>
<td bgcolor="#d9d9d9">
164
</td>
<td bgcolor="#d9d9d9">
30000
				(1000)
</td>
</tr>
<tr>
<td bgcolor="#d9d9d9">
9010
</td>
<td bgcolor="#d9d9d9">
72.2
</td>
<td bgcolor="#d9d9d9">
262
</td>
<td bgcolor="#d9d9d9">
30000
				(1000)
</td>
</tr>
<tr>
<td bgcolor="#d9d9d9">
3450
</td>
<td bgcolor="#d9d9d9">
88.2
</td>
<td bgcolor="#d9d9d9">
197
</td>
<td bgcolor="#d9d9d9">
25000
				(-4000)
</td>
</tr>
<tr>
<td bgcolor="#d9d9d9">
3180
</td>
<td bgcolor="#d9d9d9">
53.1
</td>
<td bgcolor="#d9d9d9">
262
</td>
<td bgcolor="#d9d9d9">
30000
				(1000)
</td>
</tr>
<tr>
<td bgcolor="#d9d9d9">
1640
</td>
<td bgcolor="#d9d9d9">
46
</td>
<td bgcolor="#d9d9d9">
164
</td>
<td bgcolor="#d9d9d9">
25000
				(-4000)
</td>
</tr>
<tr>
<td bgcolor="#d9d9d9">
5250
</td>
<td bgcolor="#d9d9d9">
81.3
</td>
<td bgcolor="#d9d9d9">
197
</td>
<td bgcolor="#d9d9d9">
30000
				(1000)
</td>
</tr>
<tr>
<td bgcolor="#d9d9d9">
1250
</td>
<td bgcolor="#d9d9d9">
67.6
</td>
<td bgcolor="#d9d9d9">
100
</td>
<td bgcolor="#d9d9d9">
25000
				(-4000)
</td>
</tr>
</table>

(1) From analytic microburst model documented in NASA TM-100632.
These parameters are based on data from Proctor’s Terminal Area
Simulation System (TASS) model.

(2) For the takeoff case, the downburst centre is positioned at the
point the aeroplane lifts off the runway for all test cases.

(3) For the approach/landing case, the downburst centre is positioned
as stated. The test is begun with the aeroplane at an initial
altitude of 1 500 feet on a 3° glideslope (touchdown point
approximately 29 000 feet away). The distance from the starting
point indicates where the centre of the downburst shaft is located
relative to the starting point. The number in parentheses next to it
indicates the relative distance of the microburst centre from the
touchdown point (not the end of the runway). A negative number
indicates that the microburst centre is located before the touchdown
point, positive indicates it is past the touchdown point.

**SUMMARY**

A
simple downburst model has been developed for use in batch and
real-time piloted simulation studies of guidance strategies for
terminal area transport aeroplane operations in wind shear
conditions. The model represents an axisymmetric stagnation point
flow, based on velocity profiles from the Terminal Area Simulation
System (TASS) model developed by Proctor [ref. 3,4] and satisfies the
mass continuity equation in cylindrical coordinates. Altitude
dependence, including boundary layer effects near the ground, closely
matches real-world measurements, as do the increase, peak, and decay
of outflow and downflow with increasing distance from the downburst
centre. Equations for horizontal and vertical winds were derived, and
found to be infinitely differentiable, with no singular points
existent in the flow field. In addition, a simple relationship exists
among the ratio of maximum horizontal to vertical velocities, the
downdraft radius, depth of outflow, and altitude of maximum outflow.
In use, a microburst can be modelled by specifying four
characteristic parameters. Velocity components in the x, y, and z
directions, and the corresponding nine partial derivatives are
obtained easily from the velocity equations.

**INTRODUCTION**

Terminal
area operation of transport aircraft in a wind shear environment has
been recognised as a serious problem. Studies of aeroplanes
trajectories through downbursts show that specific guidance
strategies are needed for aeroplanes to survive inadvertent downburst
encounters. In order for guidance strategies to perform in
simulations as in actual encounters, a realistic set of conditions
must be present during development of the strategies. Thus, aeroplane
and wind models that closely simulate real-world conditions are
essential in obtaining useful information from the studies.

Wind
models for use on personal computers, or for simulators with limited
memory space availability, have been difficult to obtain because
variability of downburst characteristics makes analytical models
unrealistic, and large memory requirements make the use of numerical
models impossible on any except very large capacity computers.

Bray
[ref. 2] developed a method for analytic modelling of wind shear
conditions in flight simulators, and applied his method in modelling
a multiple downburst scenario from Joint Airport Weather Studies
(JAWS) data. However, the altitude dependence of his model is not
consistent with observed data and, although flexibility in sizing the
downbursts is built into the model, it does not maintain the physical
relationships which are seen in real-world data among the sizing
parameters. In particular, boundary layer effects should cause the
radial velocity to decay vertically to zero at the ground, as does
the vertical velocity.

In a
study conducted at NASA Langley Research Center, three different
guidance strategies for a Boeing 737-100 aeroplane encountering a
microburst on take-off were developed [ref. 3-4]. These strategies
were first developed using a personal computer, and then implemented
in a pilot-in-the-loop simulation using a very simple wind model in
both efforts. The wind velocities used are depicted in Figure 1. This
model consisted of a constant outflow outside of the downburst radius
and a constant slope headwind to tailwind shear across the diameter
of the downburst.

![](/static/files/file_jytjXw2lpRK/image041.png)

***Figure
1 — Wind Model Used in Guidance Studies***

It
was recognised that a more realistic wind model could significantly
alter the outcome of the trajectory. For the subsequent part of this
study, which involves altering the aeroplane model to simulate
approach to landing and escape manoeuvres and additional take-off
cases, a more realistic wind model was preferred. The simple
analytical model outlined in this report was developed for this
purpose.

**SYMBOLS**

<table cellpadding="7" cellspacing="0">
<col/>
<col/>
<tr valign="top">
<td>
JAWS
</td>
<td>
Joint
				Airport Weather Studies
</td>
</tr>
<tr valign="top">
<td>
NIMROD
</td>
<td>
Northern
				Illinois Meteorological Research on Downbursts
</td>
</tr>
<tr valign="top">
<td>
R
</td>
<td>
radius
				of downburst shaft (ft)
</td>
</tr>
<tr valign="top">
<td>
r
</td>
<td>
radial
				coordinate (distance from downburst centre) (ft)
</td>
</tr>
<tr valign="top">
<td>
TASS
</td>
<td>
Terminal
				Area Simulation System
</td>
</tr>
<tr valign="top">
<td>
u
</td>
<td>
velocity
				in r-direction (or x-direction) (knots)
</td>
</tr>
<tr valign="top">
<td>
v
</td>
<td>
velocity
				in y-direction (knots)
</td>
</tr>
<tr valign="top">
<td>
w
</td>
<td>
velocity
				in z-direction (knots)
</td>
</tr>
<tr valign="top">
<td>
wmax
</td>
<td>
magnitude
				of maximum vertical velocity (knots)
</td>
</tr>
<tr valign="top">
<td>
umax
</td>
<td>
magnitude
				of maximum horizontal velocity (knots)
</td>
</tr>
<tr valign="top">
<td>
x
</td>
<td>
horizontal
				(runway) distance, aeroplane to downburst centre (ft) 

</td>
</tr>
<tr valign="top">
<td>
y
</td>
<td>
horizontal
				(side) distance, aeroplane to downburst centre (ft)
</td>
</tr>
<tr valign="top">
<td>
z
</td>
<td>
aeroplane
				altitude above ground level (ft)
</td>
</tr>
<tr valign="top">
<td>
zh
</td>
<td>
depth
				of outflow (ft)
</td>
</tr>
<tr valign="top">
<td>
zm
</td>
<td>
height
				of maximum U-velocity (ft)
</td>
</tr>
<tr valign="top">
<td>
zm2
</td>
<td>
height
				of half-maximum U-velocity (ft)
</td>
</tr>
<tr valign="top">
<td>
z*
</td>
<td>
characteristic
				height, out of boundary layer (ft)
</td>
</tr>
<tr valign="top">
<td>
e
</td>
<td>
characteristic
				height, in boundary layer (ft)
</td>
</tr>
<tr valign="top">
<td>
λ
</td>
<td>
scaling
				factor (s-1)
</td>
</tr>
</table>

**DEVELOPMENT
OF VELOCITY EQUATIONS**

Beginning
with the full set of Euler and mass continuity equations, some
simplifying assumptions about the downburst flow conditions were
made. Effects of viscosity were parameterised explicitly, and the
flow was assumed to be invariant with time. The downburst is
axisymmetric in cylindrical coordinates, and characterized by a
stagnation point at the ground along the axis of the downflow column.
The flow is incompressible, with no external forces or moments acting
on it.

The
resulting mass conservation equation is

(1)

Written
out in full, equation 2 is

(2)

This
equation is satisfied by solutions of the form

(3a)

(3b)

provided
that

(4a)

(4b)

Note
that

. To solve this system of equations, solutions were assumed for two
of the functions and the other two were obtained from equations 4a
and 4b.

It
was desired that the velocity profiles of this analytic model exhibit
the altitude and radial dependence shown in the large-scale numerical
TASS (Terminal Area Simulation System) weather model [ref. 6-9]. The
TASS model is based on data from the Joint Airport Weather Studies
(JAWS) [ref. 10], and provides a three- dimensional velocity field,
frozen in time, for given locations of an aeroplane within the shear
[ref. 11-12].

![](/static/files/file_jytjXw2lpRK/image049.png)

***Figure
2 — Vertical Profile of Microburst Outflow (Non-dimensional)***

Figure
2 shows dimensionless vertical profiles of horizontal velocity, u,
for TASS data, laboratory data obtained by impingement of a jet on a
flat plate, and data from NIMROD (Northern Illinois Meteorological
Research on Downbursts) [ref. 13-21]. Specific points of interest are
the maximum horizontal velocity (located 100-200 metres above the
ground), below which is a decay region due to boundary layer effects,
zero velocity at the stagnation point on the ground, and an
exponential decay with altitude above the maximum velocity altitude.
Vertical velocity profiles from TASS data are shown in Figure 3, also
exhibiting a decay to zero at the stagnation point.

VERTICAL
PROFILES OF VERTICAL VELOCITY FOR 30 JUN 82 CASE:
SENSITIVITY TO
RADIUS OF PRECIPITATION SHAFT

![](/static/files/file_jytjXw2lpRK/image050.png)

***Figure
3 — Vertical Profile of Microburst Downflow***

The
radially varying characteristics desired for the horizontal wind were
two peaks of equal magnitude and opposite direction located at a
given radius, with a smooth, nearly linear transition between the
two. Beyond the peaks, the velocity should show an exponential decay
to zero. The vertical velocity was required to have a peak along the
axis of symmetry (r = 0), and to decay exponentially as the radius
increases.

A
pair of shaping functions that gave velocity profiles matching the
TASS data as required are given below.

The
remaining solutions were found by integrating equations 4a and 4b,
yielding:

Figures
4 and 5 show plots of these shaping functions.

![](/static/files/file_jytjXw2lpRK/image055.png)

***Figure
4 — Characteristic Variation of Horizontal Shaping Functions***

![Picture 43](/static/files/file_jytjXw2lpRK/image056.png)

***Figure
5 — Characteristic Variation of Vertical Shaping Functions***

Combining the functions as in equation 3, the horizontal and vertical
velocities are expressed as

(5)

(6)

By
taking derivatives of equations 5 and 6 with respect to r and z,
respectively, and substituting in equation 2, it can be shown that
the velocity distributions satisfy continuity.

The
parameters z\* and ε were defined as characteristic scale lengths
associated with ‘out of boundary layer’ and ‘in boundary layer’
behaviour, respectively. Analysis of TASS data indicated that z\* =
zm2, the altitude at which the magnitude of the horizontal
velocity is half the maximum value.

It
was also noted that the ratio

To
determine the location of the maximum horizontal velocity, the
partial derivatives of u with respect to r and z were set equal to
zero. The resulting equation for the r-derivative is

The
resulting equation for the z-derivative is

Recalling
that zm/z\* = 0.22, the values 1.1212 and 12.5 were
obtained from iteration for the ratios r/R and z\*/ε, respectively.

Using
these values, the maximum horizontal velocity can be expressed as
umax = 0.2357 λ R. The maximum vertical wind is located
at r = 0 and z = zh, by definition, and is given by

A
ratio of maximum outflow and downflow velocities can be formed

The
Scaling factor, λ, was determined by using either of equations 5 or
6 for horizontal or vertical velocity, and setting it equal to the
maximum velocity, umax or wmax, respectively.
Solving for λ results in:

The
velocity equations were easily converted to rectangular coordinates,
as shown in the Appendix. Partial derivatives with respect to x, y,
and z were obtained by differentiating the velocity equations, and
are also listed in this Appendix.

**DISCUSSION
AND RESULTS**

Vertical
and horizontal velocity profiles for u and w are shown in Figures 6
and 7.

![Picture 44](/static/files/file_jytjXw2lpRK/image065.png)

***Figure
6 — Vertical Velocity Profiles for the Analytical Model***

![Picture 45](/static/files/file_jytjXw2lpRK/image066.png)

***Figure
7 — Radial Velocity Profiles for the Analytical Model***

Four
profiles are shown for each component. The horizontal wind profiles
in figure 6 were taken at the radios of peak outflow (r = 1.1212 R)
and at about one-fourth that radius (r = 0.3 R), where the maximum
outflow is approximately half the value at the peak outflow radius.
The vertical wind profiles were taken at the radius of peak downflow
(r = 0) and at r = 0.3 R. Horizontal wind and vertical wind profiles
in figure 7 were taken at altitudes of h = zm (maximum
outflow), h = z\* (half-maximum outflow), and h = zh (depth
of outflow).

This
analytical model is compared with TASS, laboratory, and NIMROD data
in figure 8. The figure shows that, when non-dimensionalised by the
altitude of half-maximum outflow (z\*) and by the maximum outflow (u =
umax), the analytical model agrees closely with the other
data.

![](/static/files/file_jytjXw2lpRK/image067.png)

***Figure
8 — Comparison of Wind Model Vertical Profiles***

Different
shears can be modelled by specifying four parameters, and the
location of the downburst centre relative to the aeroplane flying
through it. The four parameters are: 1) a characteristic horizontal
dimension; 2) the maximum wind velocity; 3) the altitude of maximum
outflow; and 4) the depth of outflow. The characteristic horizontal
dimension specified is the radius of the downdraft column, noting
that this is about 89 % of the radius of the peak outflow. The
maximum wind velocity can be either horizontal or vertical.

**CONCLUDING
REMARKS**

The
analytic microburst model developed for use in real-time and batch
simulation studies was shown to agree well with real-world
measurements for the cases studied. The functions chosen for the
model showed boundary-layer effects near the ground, as well as the
peak and decay of outflow at increasing altitudes, and increasing
downflow with altitude. The exponential increase and decay of the
downflow and outflow (in the radial direction) are also characterised
by the model. Equations for horizontal and vertical winds are simple
and continuously differentiable, and partial derivatives in
rectangular or cylindrical coordinates can be easily obtained by
direct differentiation of the velocity equations. The governing
equation for this system is the mass conservation law, and the
analytic velocity functions developed here satisfied this condition.
The model is sustained by a strong physical basis and yields high
fidelity results, within the limitations of maintaining simplicity in
the model, and variability of the microburst phenomenon.
Parameterization of some of the characteristic dimensions allows
flexibility in selecting the size and intensity of the microburst.

**REFERENCES**

1. Oseguera, M. and Bowles R. L.: A Simple, Analytic 3-Dimensional
   Downburst Model Based on Boundary Layer Stagnation Flow, Rosa,
   July 1988.
2. Bray, R. S.: Application of Data to Piloted Simulations. Wind
   Shear/Turbulence Inputs To Flight Simulation and Systems
   Certification, NASA CP-2474, 1987, pp. 97-115.
3. Hinton, D. A.: Aircraft Trajectory Guidance During Wind Shear
   Encounters. Master’s Thesis, George Washington University,
   January 1988.
4. Hinton, D.A.: Flight management strategies for escape from
   microburst encounters, NASA TR 4057, 29, pp. 1988.
5. Hinton, D.A.: Relative merits of reactive and forward-look
   detection for wind shear encounters during landing approach for
   various microburst escape strategies, NASA TM-4158,
   DOT/FAA/DS-89/35, 1990.
6. Proctor, F.H.: The Terminal Area Simulation System, Volume I:
   Theoretical Formulation, NASA Contractor Report 4046, April
   1987.
7. Proctor, F. H.: Numerical simulations of an isolated
   microburst. Part I: Dynamics and structure, J. Atmos. Sci., 45,
   pp. 3137-3160, 1988.
8. Proctor, F.H.: The Terminal Area Simulation System, Volume II:
   Verification Cases. NASA Contractor Report 4047, April 1987.
9. Proctor, F. H., 1989: Numerical simulations of an isolated
   microburst. Part II: Sensitivity experiments, J. Atmos. Sci.,
   46, pp. 2143-2165.
10. Frost, W.: Modeling and Implementation of Wind Shear Data. Wind
    Shear/ Turbulence Inputs to Flight Simulation and Systems
    Verification, NASA CP-2474, 1987, pp. 49-66.
11. Proctor, F. H.: NASA Wind Shear Model -- Summary of Model
    Analysis. Airborne Wind Shear Detection and Warning Systems,
    NASA CP-10006, 1988, pp. 29-66.
12. Proctor, F. H., and Bowles, R. L.: Three-dimensional simulation
    of the Denver 11 July 1988 microburst-producing storm,
    Meteorol. and Atmos. Phys., 49, 1992, pp. 107-124.
13. Fujita, T. T.: Tornadoes and Downbursts in the Context of
    Generalized Planetary Scales. Journal of Atmospheric Sciences,
    vol. 38, no. 8, August 1981, pp. 1511-1534.
14. Oseguera, R. M.; Bowles, R. L.; and Robinson, P. A., 1992:
    Airborne In Situ Computation of the Wind Shear Hazard Index,
    AIAA Paper 92-0291, 1992.
15. Lewis M. S., Robinson P. A., Hinton D. A., Bowles R. L.: The
    relationship of an integral wind shear hazard to aircraft
    performance limitations, NASA TM-109080, 1994.
16. Arbuckle, P. D., Lewis M. S., Hinton D. A.: Airborne systems
    technology application to the windshear threat, 20th Congress
    of the International Council of the Aeronautical Sciences, ICAS
    Paper No. 96-5.7.1, pp. 1640-1650, 1996.
17. Airborne Windshear Detection and Warning Systems. First
    Combined Manufacturers’ and Technologists’ Conference, NASA
    CP-10006, DOT/FAA/PS-88/7, 1988.
18. Airborne Windshear Detection and Warning Systems, Second
    Combined Manufacturers’ and Technologists’ Conference, NASA
    CP-10050, 1990.
19. Airborne Windshear Detection and Warning Systems, Third
    Combined Manufacturers’ and Technologists’ Conference, NASA
    CP-10060, DOT/FAA/RD-91/2-1, 1991.
20. Airborne Windshear Detection and Warning Systems, Fourth
    Combined Manufacturers’ and Technologists’ Conference, NASA
    CP-10105, DOT/FAA/RD-92/19-1, 1992.
21. Airborne Windshear Detection and Warning Systems, Fifth and
    Final Combined Manufacturers’ and Technologists’
    Conference, NASA CP-10139, DOT/FAA/RD-94/14-1, 1994.

[Amdt ETSO/16]