1) The document outlines tuning the braking characteristics of an aircraft model using flight test data. Key steps included generating test cases from the data, reconstructing the data for analysis, and performing a re-prediction analysis to identify discrepancies. 2) Regression analysis on acceleration errors was used to derive an improved braking friction coefficient table. Additional tuning of thrust reverser dynamics provided better matching of deceleration profiles. 3) Sanity checks confirmed the friction coefficients derived were feasible. The tuned model matched the flight data to tolerances required for pilot training simulation.

1. Key Aspects
INTRODUCTION
PROCESS
Test Case Generation
Setting-Up the Analysis
Identifying the Corrections
Thrust Reversers
SANITY CHECKS
CONCLUSIONS
AIRCRAFT MODELLING AND PERFORMANCE PREDICTION SOFTWARE
The J2 Universal Tool-Kit - Modelling and
Tuning Braking Characteristics

2. 1
INTRODUCTION
This white paper outlines the modelling capability of the j2 Universal Tool-Kit for matching flight test
data and the subsequent analysis.
In the scenario outlined below a model of a Business Jet has been developed for use in analysis of
various flight scenarios including accident investigation. The Business Jet is a twin jet with a seating
capacity of 14-19 persons. It has an operational ceiling of 45,000 ft, a range of more than 4,000 nmi
at a cruising speed of 0.8-0.85 Mach.
The Aircraft Model developed is a complete 6-DoF non-linear model including aerodynamics, all
control surfaces (including high lift devices), engines, mass, cg, and inertia. Fuel and payload can be
adjusted to suit variable scenarios. A previous analysis and tuning activity has matched the model for
thrust and drag characteristics, based upon flight data and studied the initial ground roll and
acceleration of the aircraft for take-off.
The next aspect to be tuned, was to determine the braking characteristics and thrust reversers to
enable appropriate stopping scenarios to be identified. The undercarriage and braking model has
been developed and the thrust for the thrust reversers detailed but these have yet to be matched
against the test data. The following white paper will describe and work through the process of
establishing test points and then matching/tuning the model within the j2 Universal Tool-Kit to match
the test points.
The j2 Universal Tool-Kit is a complete flight physics modelling and analyses software suite that can
be used on all aspects of flight physics analysis from conceptual design through detail design and
simulation and into accident investigations. This paper shows some of the tools and functionality built
into the j2 Universal Tool-kit that enable high fidelity models to be constructed and tuned in very short
time-scales.

3. 2
PROCESS
Test Case Generation
The first stage is to identify the test cases. No specific tests for evaluating the braking had been put
forward, apart from the final scenario, and so it was necessary to look through the available recorded
data to establish points where the aircraft was on the ground and decelerating.
It is also necessary to identify areas where it is only the brakes that are being used without the thrust
reversers. Three timed sections were found including the final scenario.
 146963s - 147000s
 147930s - 147960s
 147973.2s - 148026.2s (Accident scenario)
Following earlier investigation requests, and in order for a known start point to be used for the
analysis, a utility has already been developed by j2 that enables the raw FDR data provided to be sliced
into sections. This utility calculates angular velocities from the Euler angles and Kinematics. Non-
numerical signals are converted into numerical switch values based upon the header information in
the CSV file. From the runway information found, an altitude could be identified, assuming we are
only dealing with ‘on the ground’ roll cases. The ground speed and heading were used to estimate a
position. As the test cases were to be looking at the ground, the angle of attack is estimated to match
the pitch angle, whilst the sideslip is estimated to be the variation between the heading and the track
when accounting for the magnetic variation at the
airport too.
Over the chosen section of the flight, a high pass
filter estimates the noise, the utility outputs and
the standard deviation of the noise signals for use
in re-construction. Finally, the complete data set
is output in a j2 import format. Once the three
import files had been generated, so these were
imported…
…with all the units converted to SI,

4. 3
…and the signals associated with signals on the
model.
This process is all set up thropugh a series of
mapping templates that can be associated diretly
to an aircraft project. Once the templates are set-
up multiple test points can be imported
automatically and associated to a chosen aircraft
model for visualisation and.
With the data files now in the j2 Universal Tool-Kit these could be re-constructed to provide a
kinematically consistent set of aircraft states. The reconstruction process also enables us to smooth
the data whilst maintaining the consistency.
With this information the imported files could be reconstructed.
The reconstruction process uses integrated Kalman Filters and Smoothing algorithms along with
kinematics to take the coarse, noisy, and possibly biased flight test data and remove the noise and
bias whilst running the data signals through kinematics to identify a smooth consistent set of aircraft
states. The process can be applied to multiple test points simultaneously automatically calculating
bias and offsets for each flight.

5. 4
This data was now in a position where it could be used for the analysis.
Setting-Up the Analysis
Whilst it is possible to create manual inputs for the engines’ PLA values and brake pressure etc. this
normally requires a separate analysis to be set up for each test case, and all the signals from the flight
data are required to be entered as model inputs. The net result is a manual re-prediction. The
advantage is to perform a Re-Prediction Analysis built into j2 which does not require the manual
process.
The initial re-prediction model tracked all available control
surfaces. However, this showed that there was an offset on
the rudder as this was causing turning that didn’t exist. Rather
than developing a tracker, at this stage a simple Yaw Damper
was added to the Rudder Deflection on the model and the
tracker removed. The resulting tracking parameters are:
All control surfaces are tracked (except rudder), the engine
power lever and the brake pressure, along with the bank
angle.

6. 5
A series of trim rules were
set up to define the initial
conditions.
When tuning a simulator
to Level D for full pilot training, a throttle offset is allowed. This is calculated case by case during the
qualification tests by trimming the throttles to achieve the target initial accelerations and then
maintaining a constant offset throughout the test. A similar approach has been defined on the j2
model. In addition to the throttle values calculated through the actuators from the PLA values, there
is a small Trim Offset added from the Pilot Throttle. Thus, in the trim rules used, the first rule is used
to set the pitch angle to that from the flight and to find the throttle setting to achieve a target
acceleration. The next rule is used to define the fuel and payload weights for the test. The third trim
rule ensures that the model is initialised with the landing gear down. The final rule defines the altitude
of the terrain. Based upon the altitude of the aircraft and the altitude of the runway, a terrain height
is set that enables the aircraft to drop slightly (6”) and settle.
The 3 separate test points could now be run as a Re-Prediction Analysis. Re-Prediction analysis is a
technique that enables the model to be “driven” directly from the flight test data. This can be in the
form of driving control surfaces, with offsets found through trimming, for comparison/qualification of
a model. This type of re-prediction is similar to performing QTG tests on a simulator. The Re-
Prediction can track additional parameters to reduce the number of degrees of freedom to isolate
specific characteristics and can go right through to tracking all states and surfaces on the model to
identify the comparative variations between the flight data and the model aerodynamics for
automatic tuning of the model. Setting up and running the analyses is performed through the GUI
within the j2 Universal Tool-Kit enabling the engineers to rapidly build and assess multiple test cases.
The initial passes of the analysis showed the discrepancy in the accelerations and some issues with
the landing flight starting to early (prior to Weight on Wheels) and the test case had a small amount
of turning flight, so both cases had their start times adjusted.

7. 6
Identifying the Corrections
The corrections were to take the form of a new table that converted Brake Pressure (PSI) to a Friction
Coefficient. The initial stages focussed on identifying any corrections during the lower brake pressure,
these are the first two cases.
Baseline
We can see that the baseline results show very clearly that there is insufficient braking with the
original model.

8. 7
If we look at the final objective of the accident scenario we can see that the acceleration has already
been tuned to provide a suitable speed profile during the take-off phase. However, in the chart below,
we can see that when the brakes are applied at 40s there is almost no impact on the speed and nothing
happens until the thrust reversers are used at 44s.
The acceleration shows almost no impact of the brakes.
We can see the impact of the Thrust Reversers on the model behaviour but not the brakes. Thus, the
key is to generate corrections such that the brakes also decelerate the aircraft.

9. 8
Re-Normalising the Braking Factor
The first stage is to adjust the normalisation of the braking coefficient. The initial model has a linear
response from 0-1 with the braking pressure of 0-2845psi respectively with the high value being the
maximum pressure identified as the maximum value recorded on the FDR. However, that spike could
be an anomaly as the brake pressure never exceeds 1000psi during the accident. At the same time, it
is noticed that the pressure never drops to 0 and during the initial take-off run the values hover
between 50 and 100 psi. So, it is assumed that at 100psi the braking friction is zero. The brake pressure
is therefore re-normalised to 100-1000psi is equivalent to a braking factor of 0-1.
This is performed through a simple look-
up table. The initial coefficient of friction
used for 100% braking was 0.47. Thus the
braking factor table could be converted
into a friction coefficient table.
Re-charting the results then showed some improvements.
The initial landing and braking was able to reduce the terminal velocity down from 65kts to 51kts.

10. 9
The acceleration all remains within tolerance although, as it sits above the flight data, it causes the
velocity to deviate. The longer the test runs in time so the more chance of drift.
The low speed to stop scenario now all fits within a Level-D simulator tolerance.

11. 10
However, there is still little impact at the higher Brake Pressures seen in the test case.

12. 11
There is some change in the acceleration when the brakes are applied but not sufficient to slow the
aircraft down.

13. 12
Regression Analysis on the Acceleration Error
It was still necessary to identify the correct Braking Friction Coefficient, especially at higher Brake
Pressure, that would satisfy the accident scenario. By running some curve fitting analysis on the error
between the accelerations we were able to identify a set of Pressure ‘v’ Friction values that would
produce an improved result.
The curve fitting looked at the difference in the acceleration and converted it into a required braking
force. This could then be converted into a Friction Coefficient (μ) by dividing through by the vertical
force of the legs. As such we can get a μ (DMu). This could be added to the original value (Mu base)
to give the corrected value (Mu corr).
The corrected value is curve fitted and the curve fit is then used to define a new look-up table
(Mu tab) for the braking factor. Some factors were adjusted to bring in the maximum braking force
sooner.

14. 13
This table of Friction Coefficients was then evaluated against the three tests again. In the Landing and
Brake scenario the results are significantly improved, with a large proportion of the flight staying
within tolerance and the final airspeed being in tolerance despite possible drift.
The bumps and oscillations could be due to atmospheric variations. As we can see the accelerations
stay well within tolerance.

15. 14
The brake to stop scenario still remains within tolerance.

16. 15
When we look at the accident flight the airspeed almost remains within tolerance …

17. 16
… but there is some drift towards the end before the braking starts.
Although the acceleration remains within tolerance.

18. 17
As previously mentioned, there is some drift which can result in some variations towards the end of
the test. As we are mainly interested in the braking in this case, the accident flight was started later
to allow the aircraft to settle prior to applying the brakes.
Starting further along the take-off acceleration (25s) we are able to demonstrate even more how the
braking matches the flight data as now we can eliminate some of the drift.

19. 18
Thrust Reversers
When we look at the accelerations on the accident scenario, we can see that when the thrust reversers
“kick in” there is an immediate step change in the acceleration on the model that is not present in the
flight data.
This implies there needs to be a delay for the thrust reversers to react. The second point of interest
is that the thrust reversers’ authority needs to be increased to increase the deceleration and finally
there is a slight overshoot in the deceleration along with a little oscillation.
The initial implementation of the thrust reversers is a simple step in the thrust when they are
deployed, hence the acceleration step. By having a transition towards the thrust reversers, we can
create a smoother dynamic response. This can be done by putting the switch through an actuator.
First order Actuators create a smoother dynamic response whilst a second order actuator can react
faster but, depending upon the values used, can create an overshoot or oscillation.

20. 19
Thus, a second order actuator was used and the gains adjusted along with a multiplier on the
effectiveness to create the appropriate response.
The resultant response shows an improved correlation for the Thrust Reverser Deployment too.

21. 20

22. 21
SANITY CHECKS
The required friction coefficient for the braking appears high as Airbus uses a value of 0.5 for their
handbook calculations. However, the ESDU data tables allow for a friction coefficient up to 0.8 in dry
conditions. Thus, a series of checks have been made to confirm the values found when using the
regression are realistic.
Starting with a basic “hand calculation”
1. Change in acceleration due to braking is +1.5m/s2
to -1.25m/s2
.
2. At the mass of 26,273kg the force required can be approximated using F= M*U’ = 72.25kN.
3. Therefore the Average Braking Force required by each main leg = 36.125kN
4. Average load carried by each main leg at the time of braking (Check Point) = 50.07kN
5. Thus, the average friction coefficient required is 36.125/50.07 = 0.72
In order to achieve the observed step change in acceleration requires a step change in force. The
possible sources are:

23. 22
 Change in configuration resulting in a step change in drag
The basic drag model has been qualified during the acceleration tests.
Whilst there are some changes in the control surfaces around the period of deceleration, there
are no major contributions (e.g. Ground Spoilers) that would add a significant drag change
 Reduction in thrust or thrust reverser
There is no change in the recorded PLA or EPR values, and thus the thrust during the initial braking
period. The basic thrust model has been qualified during the acceleration tests.
The thrust reversers are not applied until 46s.
Other aspects that can be considered includes examining if there is a greater load on the main gear
such that the ratio between vertical load and braking force reduces. In order for this to be achieved
we need to either move the CG further aft (more weight carried on the main gear and less on the
nose) or the aircraft needs to be heavier.
If we shift the CG further aft the change of the load is small and we move away from the CG position
identified.

24. 23
If we increase the mass of the aircraft, we also increase the braking force required (M*U’) thus the
braking friction coefficient will be very similar.
This means that the retarding force during the initial slowing down phase has to come from the brakes
and cannot be accounted for by making any other adjustments.

25. 24
CONCLUSIONS
The model has now been tuned, against the available data, for braking and for thrust reversal.
The magnitude of the braking coefficients, whilst high, are feasible and the forces cannot be attributed
to any other model variable.
The thrust reversers show the appropriate retarding force and dynamic characteristics.

26. 25

27. 26

28. 27
All cases fall within the acceptable tolerances for a Level-D pilot training simulator. If cases are left for
longer, so they can drift but the results are still acceptable.
The j2 Universal Tool-Kit has enabled the model build and qualification against flight test data to be
performed in a graphical environment in a matter of weeks. The model was constructed from multiple
data sources and external code to create complete flight model that is capable of being used for
dynamic analysis, simulation and accident investigation. The model was matched against flight data
to Level-D tolerances for take-off acceleration and braking/thrust reversers.