$1$/<6<62)7+(75,0&21',7,216
)LUVW$SSURDFK
To be able to run the EUROPA code and acquire meaningful and accurate results, all of the A109 helicopter input data specifications were collected. For some of the data, it was possible to attain the correct figures, in other cases the variables were calculated by their specific equations or estimated using Matlab. Once all the data had been collected the results were inputted into the correct location in the input file. Finally a FORTRAN programming code was run so that an executable EUROPA file could be produced.
+RYHU )LUVW$QDO\VLV
During this very first iteration different flight records were used and for all of them the Out of Ground Effect (OGE) condition were examined. Previous flight test records containing data on OGE hover performance were used as much as possible.
The wide choice of the flight test results permitted analysis of flight testing conducted at low and high altitude. In different all up mass configurations and different temperatures without rescue hoist, search light etc, etc.
These are the four flights conditions used in OGE. The testing was carried out in zero wind conditions and with the helicopter in a clean configuration, all having the start height of 60ft above ground, with the following characteristics:
Flight N° Initial Weight [Kg]
Final Weight [Kg]
OAT [C°]
HP
[ft] RPM C.G.
1 3446 2522 16 800 ft 102% mid/right
2 3264 2633 15 7600 ft 102% forward/right
3 3222 2511 14 9300 ft 102% forward/right
4 2710 2700 18 9400 ft 102% forward/right
7DEOH +RYHUIOLJKWWHVWUHFRUGVILUVWDQDO\VLV
In the first hover analysis phase the main focus was kept on the three parameters: Torque, Collective and Pedals to see how well they were matched. The flight test data was replayed and analysed using the Agusta PANDA program which is an interface to the Agusta flight test data base.
The three parameters were expressed in percentile form with the subsequent conventions:
Torque 100% when matched, a “datum” read in the file A109.BLD Collective 100% when all up, 0% all down.
Pedals 100% when the left pedal is fully down, 0% when the right pedal is fully down.
Simulation with EUROPA was attempted with constant temperature, altitude, height and C.G., while the weight changed every step using the multitrim conditions option in the case.dat file.
• 7RUTXH
Torque was the first parameter to be matched changing the CD0, CD2 values of the main rotor and DELTA0 and DELTA2 of the tail rotor files and the Hub Power in the build file. For the same flight test two extreme conditions were taken in terms of weight, then the matching was tried. The tests at different weights had to demonstrate a general behaviour for the Torque, but it was not known how far removed the single test would be from true general behaviour. For a first approach, even with this concern, it was assumed satisfactory. After that flight tests with similar weight but different altitudes were analysed. Overall the task was carried out without any major shortcomings.
• &ROOHFWLYH
After the matching with the Torque, Collective was optimised. The values of G01 and G02 were changed until a good match with the PANDA values could be achieved. The results were achieved without any major shortcomings.
G01: pitch of the main rotor blade referred to 0.75 R when the collective is at 0%.
G02 : pitch of the main rotor blade referred to 0.75 R when the collective is at 100%.
The main rotor blade range referred to a flapping angle of 0° and a lag angle of 6°.
• 3HGDOV
The same procedure used for the collective was used for the matching of the Pedals. In this case TH0MAX and TH0MIN were changed until good results were obtained.
Unfortunately it was impossible to match the results for different altitudes.
TH0MAX : pitch of the tail rotor blade referred to 0.75 R when the collective is at 0%.
TH0MIN : pitch of the tail rotor blade referred to 0.75 R when the collective is at 100%
The tail rotor blade range referred to a flapping angle of 0°.
&RQFOXVLRQV
The first analysis of the Hover underscored good matching for the Torque and the Collective. For the Pedals it was clear that a convergence was impossible if they were not at the same altitude.
Analysing the trend of the pedal command with increasing altitude, it was clear that there was a progressive divergence from the flight data. Matching a low altitude flight, EUROPA gave an 18% error for a 9000 ft flight test. At the start every parameter was changed trying to match the Pedals, without any appreciable result. It was considered that there was an error in the flight test data, but after some crosschecks with different parameters found inside the database, it was obvious it was not the case. It was assumed that this was due a lack in the accuracy of the mathematical model of the tail rotor and this also account for the strange behaviour of the Z –force in the tail rotor, as it was of the same order of magnitude of the Y-Force. Analysing the EUROPA source code it was finally found the mathematical model was indeed not sufficiently accurate, so it was modified for a better matching at different altitudes for the pedals.
See appendix B Tail rotor model.
When the modified mathematical model was applied to the code the error decreased to under a 3% for the pedal commands. This was more similar to the degrees of error of the other two parameters. Even the big Z-Force decreased, it became of the same order of the X-Force as expected.
After the development of the new tail rotor mathematical model the difference between the simulation and the test data was quite small for all the three parameters.
These input parameters for torque, pedal and collective only changed one specific command and nothing else, so at this time it was not necessary to do any cross checks.
Furthermore, there was not any data to do crosschecks with.
&RQWUROODELOLW\
Controllability/performance flight records were needed to examine the controllability behaviour of the EUROPA - code. ,WLVLPSRUWDQWWRQRWLFHWKHWHVWIOLJKWVZHUHPDGHZLWK
WKH KHOLFRSWHU PRYLQJ LQ UHVSHFW WR WKH JURXQG ZKHUH LQ UHDOLW\ WKH &RQWUROODELOLW\ LV
UHTXLUHG ZKHQ KRYHULQJ ZLWK DODWHUDO ZLQG 7KLV GLIIHUHQFH MXVWLILHV VRPH GLVFUHSDQF\ RI
WKHFRGHZLWKWKHWHVWV,QIDFWWKHFRGHLVDEOHWRVLPXODWHODWHUDOZLQGDWGLIIHUHQWVSHHGV
EXWLQUHDOLW\WKLVLVDOPRVWLPSRVVLEOHWRGR:RUWK\RIQRWHLVWKHIRUFHGDQJOHRI\DZ
RI WKH (8523$ FRGH LQ HYHU\ VLPXODWLRQ DQJOH DOPRVW LV LPSRVVLEOH WR PDLQWDLQ IRU
WKHSLORWVGXULQJIOLJKWWHVWV
There is always some angle of yaw and some angle of roll. Some is always bigger than the other mostly depending on how the pilots prefer to fly. Zero angle of yaw and/or at the same time zero angle of roll is impossible. The tests of interest were basically the same as for hover: clean configurations, different weight, outside temperature, density altitude, centre of gravity positions as well as zero wind condition.
These are the two flight conditions used for lateral flight, with the following characteristics:
Flight N° Weight
[Kg] Centre of Gravity OAT [C°]
HP
[Ft] RPM
1 3200 Forward/right 25 500 100%÷102%
2 3264 Very forward/left 21 600 100%÷102%
7DEOH &RQWUROODELOLW\IOLJKWWHVWUHFRUGV
This issue of controllability just considered the tests done for 90 and 270 degrees of azimuth, which are lateral flight to the right and to the left from a helicopter pilot point of view. For these tests Torque, Collective and Pedal PANDA values were handed in for different velocities as 0, 10, 20, 30 and 40 knots.
The variables to be optimised for the controllability of flight were some parameters in the fin input called fin drag constant for α = 0°, fin second order drag coefficient, fin drag coefficient for α = 90° and the KLAMF for the wake of the main and tail rotor on the fin.
As well as the PLAN and SIDE constants in the fuselage input file. After some consideration, it was decided to discard the changes in the PLAN and SIDE variables because of the effects they could have on the hover performance, so the coefficients involved in the fuselage file were directly changed, always looking to the output files and the α and β angle of attack of the fuselage, for a better focus on the right variable.
For the optimisation of the different variables, the strategy was to keep the other variables constant and then change one, until there was a satisfactory outcome and it achieved the desired result.
Simulation with EUROPA was attempted with constant temperature, altitude, height, C.G., gross weight and wind direction while the speed changed during every step using the multitrim condition option in the case.dat file.
• 7RUTXH
The main focus was to get the Torque to be as close as possible to the real value.
Increased effort was required due to the increased variables involved in the process of optimisation. The main variables involved in the process of optimisation were the C at 90° for the fin and the PLAN and SIDE reference area for the D fuselage(see above).
• &ROOHFWLYH
Greatly correlated with the Torque, the Collective was used as a secondary matching variable. This was due to the link and intrinsic behaviour of the Collective with the Torque, so defining this variable alone was impossible, requiring a constant link with the Torque.
• 3HGDOV
The main purpose of the assessment was to test the effectiveness of the pedals. This was carried out with the helicopter flying at 90° degrees, at 30 and 40 knots lateral speed. During this test the main concern was that there would be a decline in the effectiveness of the tail rotor.
&RQFOXVLRQV
When all iterations and optimisations of the variables were done, it was decided to put most attention to the flight that was carried out 20 knots, since it was the most critical one.
Pretty soon it was discovered that the fin drag constant for α = 0° and fin second order drag coefficient did not have any significant influence, so those values were to be kept as the initial ones. So in the end the three variables to be optimised was the KLAMF, the fin drag coefficient for α = 90° degrees and the fuselage coefficients.
Analysing the Pedals and Torque, a good matching was obtained for the Torque, especially for flight 2 with 90° and 270° wind.
In the subsequent figures green dots represent flight test data while blue simulated data.
The red line is just a second order curve approximating the flight test data.
0 5 10 15 20 25 30 35 40 0
10 20 30 40 50 60 70 80 90 100
Pedals vs Wind
Wind (knots)
Pedals in %
0 5 10 15 20 25 30 35 40
0 10 20 30 40 50 60 70 80 90 100
Torque vs Wind
Wind (knots)
Torque in %
Controllability: Flight 2 90 °
)LJXUH )OLJKW:LQG
0 5 10 15 20 25 30 35 40 0
10 20 30 40 50 60 70 80 90 100
Pedals vs Wind
Wind (knots)
Pedals in %
0 5 10 15 20 25 30 35 40
0 10 20 30 40 50 60 70 80 90 100
Torque vs Wind
Wind (knots)
Torque in %
Controllability: Flight 2 270 °
)LJXUH )OLJKW:LQG
For flight 1 at 90°, it was obvious that there was a shift due to a recorded gust of wind
which negated good results.
0 5 10 15 20 25 30 35 40
0 10 20 30 40 50 60 70 80 90 100
Pedals vs Wind
Wind (knots)
Pedals in %
0 5 10 15 20 25 30 35 40
0 10 20 30 40 50 60 70 80 90 100
Torque vs Wind
Wind (knots)
Torque in %
Controllability: Flight 1 90 °
)LJXUH )OLJKW:LQG
0 5 10 15 20 25 30 35 40 0
10 20 30 40 50 60 70 80 90 100
Pedals vs Wind
Wind (knots)
Pedals in %
0 5 10 15 20 25 30 35 40
0 10 20 30 40 50 60 70 80 90 100
Torque vs Wind
Wind (knots)
Torque in %
Controllability: Flight 1 270 °
)LJXUH )OLJKW:LQG
The pedals are well matched with a 90° wind for both of the flights, reaching the loss of the tail rotor effectiveness, EUROPA simulated the 100% pedal command at 35 Knots for flight 1 and 37 Knot for flight 2. More problems arose for the flights with 270° wind; a 10% shift. Keeping in mind some issues, this behaviour can be acceptable. Referring to the code, the simulated helicopter is flying at 0° angle of yaw, which is never reached nor maintained in reality. From the pilot’s point of view, manoeuvring the helicopter to the left is a little trickier as the pilot handles the aircraft from the right hand seat. They need visibility, especially when trying to fly at 30 or 40 knots. So a subconscious little “more than needed” angle of yaw it is maintained in the flight test. With these differences in mind the EUROPA code can be assumed to be sufficiently accurate.
/HYHO)OLJKW
After Controllability, Level flight performance was analysed; the core evaluation for the trim conditions were reached. For level flight seven flight records were used. The number of parameters chosen was due to the significance of the evaluation and the importance of the outcome of the analysis for the company.
These are the seven flights conditions used for the level flight, with the following characteristics:
Flight N°
Generalized Weight
[Kg]
Mean Weight
[Kg]
Centre of Gravity
OAT [C°]
Mean HP [ft]
Speed [Kn]
1 2733 2595 mid/left 8 2099 40÷135
2 3030 2829 forward/left 7 2645 40÷135
3 3511 3130 forward/left 11 3522 40÷135
4 4039 3120 forward/left 10 7432 40÷135
5 4475 3141 mid/left -1 10942 40÷135
6 4968 3136 mid/left -8 14282 40÷130
7 5212 2983 forward/left -15 17357 40÷115
7DEOH /HYHOIOLJKWWHVWUHFRUGV
Generalized Weight it is a common term in the helicopter world, it is generally used to compare different flight tests at different altitudes and different gross weight.
Generalized Weight GW2
= n
σ , where
0
ρ(h)
σ = ρ and RPM
n= nominal RPM
Usually it takes time to do a flight test and meanwhile the fuel is burned. The helicopter becomes lighter and it needs to fly higher to maintain the same generalized weight. During
the level flight Performance tests, different altitudes, weight and temperatures were recorded, so mean values had to be calculated for those inputs matching the generalized weight. In the EUROPA code the means of weight and altitude matching for the generalized weight were accepted because the code experiences difficulties changing more than one parameter at the same time. Airspeed was limited during the EUROPA evaluation. During the flight testing, airspeed was limited further as for our purposes it was pointless continuing at high speeds.
For all the records, true values for Torque, Collective, Pedal, Longitudinal cyclic, Lateral cyclic and theta were collected from PANDA. For each flight record these parameters were plotted with Matlab© in several graphs, to get a good overview of the situation. From the results, the flight tests a curve of best fit was drawn, to make it easier to compare with the EUROPA – code simulated results. It also reduced the natural scatter that comes along with the flight test values. Matlab© was used also to plot forces and moments of all the components for a better understandings of the output results. This was a great improvement in the evaluation and sped up the whole process of optimisation.
Due to the involvement of almost all the helicopter components, a great number of parameters were involved in the evaluation and into the matching of level flight data. CD0 and CD2 for the main rotor and DELTA0, DELTA2 for the tail rotor were modified along with G01, G02, G0S0, G1S1, G1C0 and G1C1. Moreover, TH0MAX and TH0MIN were modified in the tail rotor file. As in the controllability other coefficients were changed in the fuselage input file. The parameters in the fin and tailplane files were modified noticeably. Fin setting angle, second order drag coefficient, drag constant for α = 90° were changed for the fin while setting angle, drag coefficient for α = 0°, drag coefficient for α = 90° and the main rotor wake contraction factor were changed for the tailplanes.
As in the Controllability for the optimisation of the different variables, the strategy was to keep the other variables constant and then change one, until the desired effect was achieved.
Moreover, every variable was heavily linked to multiple commands. This required hard work and consideration of all the implications of modifying “only” one parameter. This behaviour implied reflective iterative work, always looking back at the other commands and at the consequences of every modification.
40 60 80 100 120 0
20 40 60 80 100
Torque vs TAS
TAS
Torque
40 60 80 100 120
0 20 40 60 80 100
Longitudinal vs TAS
TAS
Longitudinal
40 60 80 100 120
0 20 40 60 80 100
Lateral vs TAS
TAS
Lateral
40 60 80 100 120
0 20 40 60 80 100
Collective vs TAS
TAS
Collective
40 60 80 100 120
0 20 40 60 80 100
Pedals vs TAS
TAS
Pedals
40 60 80 100 120
−4
−2 0 2 4
Θ vs TAS
TAS
Θ
Flight Test Polyfit Europa
Level Flight N ° 1
)LJXUH /HYHO)OLJKW1IW
[%] [%] [%] [%]
[%]
[Kts] [Kts]
[Kts] [Kts]
[Kts]
[Kts]
[deg]
40 60 80 100 120 0
20 40 60 80 100
Torque vs TAS
TAS
Torque
40 60 80 100 120
0 20 40 60 80 100
Longitudinal vs TAS
TAS
Longitudinal
40 60 80 100 120
0 20 40 60 80 100
Lateral vs TAS
TAS
Lateral
40 60 80 100 120
0 20 40 60 80 100
Collective vs TAS
TAS
Collective
40 60 80 100 120
0 20 40 60 80 100
Pedals vs TAS
TAS
Pedals
40 60 80 100 120
−4
−2 0 2 4
Theta vs TAS
TAS
Theta
Flight Test Polyfit Europa
Level Flight N ° 2
)LJXUH /HYHO)OLJKW1IW
[%] [%]
[%] [%]
[%]
[Kts]
[Kts]
[Kts] [Kts]
[Kts]
[Kts]
[deg]
40 60 80 100 120 0
20 40 60 80 100
Torque vs TAS
TAS
Torque
40 60 80 100 120
0 20 40 60 80 100
Longitudinal vs TAS
TAS
Longitudinal
40 60 80 100 120
0 20 40 60 80 100
Lateral vs TAS
TAS
Lateral
40 60 80 100 120
0 20 40 60 80 100
Collective vs TAS
TAS
Collective
40 60 80 100 120
0 20 40 60 80 100
Pedals vs TAS
TAS
Pedals
40 60 80 100 120
−4
−2 0 2 4
Theta vs TAS
TAS
Theta
Flight Test Polyfit Europa
Level Flight N ° 3
)LJXUH /HYHO)OLJKW1IW
[%]
[%] [%] [%]
[%]
[Kts]
[Kts]
[Kts]
[Kts]
[Kts]
[Kts]
[deg]
40 60 80 100 120 0
20 40 60 80 100
Torque vs TAS
TAS
Torque
40 60 80 100 120
0 20 40 60 80 100
Longitudinal vs TAS
TAS
Longitudinal
40 60 80 100 120
0 20 40 60 80 100
Lateral vs TAS
TAS
Lateral
40 60 80 100 120
0 20 40 60 80 100
Collective vs TAS
TAS
Collective
40 60 80 100 120
0 20 40 60 80 100
Pedals vs TAS
TAS
Pedals
40 60 80 100 120
−4
−2 0 2 4
Θ vs TAS
TAS
Θ
Flight Test Polyfit Europa
Level Flight N ° 4
)LJXUH /HYHO)OLJKW1IW
[%]
[%] [%] [%]
[%]
[Kts]
[Kts]
[Kts]
[Kts]
[Kts]
[Kts]
[deg]
40 60 80 100 120 0
20 40 60 80 100
Torque vs TAS
TAS
Torque
40 60 80 100 120
0 20 40 60 80 100
Longitudinal vs TAS
TAS
Longitudinal
40 60 80 100 120
0 20 40 60 80 100
Lateral vs TAS
TAS
Lateral
40 60 80 100 120
0 20 40 60 80 100
Collective vs TAS
TAS
Collective
40 60 80 100 120
0 20 40 60 80 100
Pedals vs TAS
TAS
Pedals
40 60 80 100 120
−4
−2 0 2 4
Theta vs TAS
TAS
Theta
Flight Test Polyfit Europa
Level Flight N ° 5
)LJXUH /HYHO)OLJKW1IW
[%]
[%] [%]
[%] [%]
[Kts]
[Kts]
[Kts] [Kts]
[Kts] [Kts]
[deg]
40 60 80 100 120 0
20 40 60 80 100
Torque vs TAS
TAS
Torque
40 60 80 100 120
0 20 40 60 80 100
Longitudinal vs TAS
TAS
Longitudinal
40 60 80 100 120
0 20 40 60 80 100
Lateral vs TAS
TAS
Lateral
40 60 80 100 120
0 20 40 60 80 100
Collective vs TAS
TAS
Collective
40 60 80 100 120
0 20 40 60 80 100
Pedals vs TAS
TAS
Pedals
40 60 80 100 120
−4
−2 0 2 4
Theta vs TAS
TAS
Theta
Flight Test Polyfit Europa
Level Flight N °6
)LJXUH /HYHO)OLJKW1IW
[%] [%] [%] [%]
[%]
[Kts]
[Kts]
[Kts]
[Kts]
[Kts] [Kts]
[deg]
60 80 100 0
20 40 60 80 100
Torque vs TAS
TAS
Torque
60 80 100
0 20 40 60 80 100
Longitudinal vs TAS
TAS
Longitudinal
60 80 100
0 20 40 60 80 100
Lateral vs TAS
TAS
Lateral
60 80 100
0 20 40 60 80 100
Collective vs TAS
TAS
Collective
60 80 100
0 20 40 60 80 100
Pedals vs TAS
TAS
Pedals
60 80 100
−4
−2 0 2 4
Theta vs TAS
TAS
Theta
Flight Test Polyfit Europa
Level Flight N ° 7
)LJXUH /HYHO)OLJKW1IW
[%] [%] [%]
[%] [%]
[Kts] [Kts]
[Kts]
[Kts]
[Kts] [Kts]
[deg]
Simulation with EUROPA was attempted with constant temperature, altitude, height, C.G., weight, while the speed changed every steps using the multitrim conditions option in the case.dat file.
• 7RUTXH
As seen before, the first parameter to be matched was the Torque. Main rotor CD0 and CD2 were the most important parameters doing the biggest changes, tail rotor DELTA0 and DELTA2 were used as refining parameters. The problems arose when other variables needed to be changed, especially for changing the slope of the torque curve. Tailplane and fin drag coefficients at 0° were particularly important, but also the tailplane drag coefficient at 90° at low speeds due to the relative wind direction seen by the tailplanes due to the main rotor wake . The setting angle of the tailplanes had a little effect to be considered too. Unfortunately all these parameters had big consequences also in Collective, Pedals, Longitudinal, Lateral and the pitching attitude of the rotorcraft.
• &ROOHFWLYH
With more than adequate correlation with the Torque, very little fine tuning was needed for the Collective; apart from the main rotor CD0/2 every other parameter that changed the Torque changed the collective command. G01 and G02 shifted the curve up and down in the graph, but great difficulties were found when modifying the slope of the curve without changing the behaviour of the Torque curve at the same time. Only the tail rotor DELTA0 and DELTA2 and the Main rotor lift curve slope had some benevolent effect. Due to the different behaviour of the collective curve from the Torque, especially at low speed, a small error was tolerated.
• 3HGDOV
ThePedals mostly showed good positioning from the start, but refining the position was another matter. TH0MAX and TH0MIN shifted the curve up and down only,
not affecting the curvature of the command. As expected, the main rotor CD0/2 made a greatly difference modifying the curve up and down. Drag parameters had some influence on the behaviour, as noticed above, but the other commands also had to be remembered. Tail plane drag constants at 0° or 90° modified the Pedal commands at low or high speeds as the fin drag constant for α = 90° and the fin setting angle.
• /RQJLWXGLQDO
Generally the behaviour was satisfactory and needed little effort to correlate with the lateral command and the pitching angle θ. Again G0S0 and G1S1 shifted the curve up and down, with a little increase in the curvature due to the G1S1 at low speeds. The other parameters were not so straightforward. Tailplane setting angle, drag coefficients at 0° end 90°, max lift coefficient and KLAMF, fin setting angle, drag coefficient at 0° and finally the fuselage X-Force and pitching coefficients changed the longitudinal command.
• /DWHUDO
Little improvement was achieved in the lateral command showing a minor diverging attitude. Fortunately the error was close to the flight test behaviour. As usual, G1C0 and G1C1 shifted the curve up and down, while tailplane drag coefficients at 0° end 90°, fin setting angle and fin drag coefficient at 0° had little effect.
• 7KHWD
Great care was given to this parameter due to the importance of general behaviour.
Almost all the drag parameters of the fin and tailplanes affected the pitching attitude, as did the tailplane setting angle. For good matching if was necessary to lower the fuselage pitching coefficient, otherwise excessive tailplanes setting angles were required, not mentioning the general bad behaviour at low speeds.
&RQFOXVLRQV
Good matching was achieved for Pedals, Theta and Longitudinal commands. Torque and Collective showed strange behaviour especially at low speeds. In the preceding analysis, Hover and Controllability, always showed the same general curvature and good matching.
Looking at the graphs it is evident the Torque curve is more “closed” while the Collective seems stretched in the TAS axis. Much was done to modify this discrepancy but the results were modest.
More problems were found analysing the Lateral command. It seems from the graph, the simulated command has a curvature symmetric to a 90 Knots vertical axis. Much effort was made to correct this and produce good matching but nothing seemed to work in the right direction. After some consideration, it was accepted as a consequence of the 0° angle of Yaw. Referring to the EUROPA code, the simulated helicopter was flying at 0° angle of yaw, but never reached nor maintained this in reality. However due to the minor gap between the simulated Lateral command and the real test data this divergence was tolerated.
The flights at high altitude caused concern. As when the density decreased, it was calculated in the graphs that there was a tendency for the Torque, Collective and Pedals to diverge at high speeds. In the beginning it was assumed to be due to bad input data, but when an effort was made to get better results it was evident that there was a discrepancy in the simulation model of the EUROPA code.
The problem lies, probably, in the main rotor mathematical model. In the flight tests, the Torque curve seems to close and shift to upper percentile values when the altitude increase, while the EUROPA code gives a more wider curve misjudging at all the behaviour.
EUROPA seems to follows the simple relation “lower density” , ”lower drag”.
The main rotor mathematical model has several simplifications. It does not consider the interaction of the other components on the main rotor especially the effect of the fuselage:
the main rotor flies alone without any disturbance. The main rotor wake is considered uniform and variable only with the azimuth, while in reality the fuselage deflect and divide
the altitude increase they start to work in the non linear part. In the EUROPA code the rotor lift force is a linear function of local blade incidence and the drag force is a simple quadratic function of lift. Moreover the retreating blade stall has to be considered. At high altitude the blades are working at high incidence near the stall, which is often triggered by the sharp local incidence perturbations induced by the trailing tip vortex from previous blades.
At one time, during the simulations, the DERA (Defence Agency Evaluation Research) aerodynamic model was tried in the main rotor input file instead of the Padfield model, to see if that could give a more accurate main rotor drag model and naturally better results.
But that was a disappointment though; the curves were shifted upwards or downwards depending on output parameter but for the main parameter Torque, the change in the shape of the curve was unsatisfactory.
After all these considerations, the EUROPA code was reputed accurate for our purposes even at high altitude. The low speed part of the graphs, under 80/100 Knots, were sufficiently close to the test data. So further investigation was not considered necessary.
Further research for the development of a better main rotor model at high speed and altitude is considered necessary if the EUROPA-code needs to cover even these extreme flight conditions.
&OLPE
In the same way as for the Performance flight for the level case the climb records were done for different weight, outside temperatures, altitudes and C.G.; this comprised for seven flight tests.
These are the seven flights conditions used for the climb, with the following characteristics:
Flight N°
Min power speed [Kn]
Mean Weight
[Kg]
Centre of Gravity
OAT [C°]
Mean HP [ft]
RoC [ft/min]
1 75 2694 forward/left 3 3000 300÷2500
2 75 2988 forward/left 4 3000 300÷2400
3 75 3089 forward/left 3 3000 300÷2000
4 75 2979 forward/mid -6 10000 300÷2000
5 75 3094 forward/left -7 10000 300÷1800
6 75 3006 far forward/left -15 15000 200÷1000
7 60 2705 forward/left -27 18000 200÷1200
7DEOH &OLPEWHVWUHFRUGV
For all the test flights the speed for minimum power was used, which is the speed when the helicopter can use the maximum delta of power for the climb.
Mean weight is the mean weight for the whole flight, while mean Hp is the mean altitude tested, because usually the start and finish altitude vary during the same flight. Rate of climb (RoC) is the rate tested.
To compare different flight tests an equivalent RoC and an equivalent Power was used, calculated with these formulas:
mean
ew true
true
Power Power W
= σ W
mean
ew true
true
RoC RoC W
= σ W
Usually it takes time to do a flight test, meanwhile the fuel is burned. The helicopter becomes more and more lighter so it is used a normalizing factor to compare to the mean weight, while, to evaluate different flights, a normalizing density factor is needed.
In the EUROPA - code the mean weight and altitude were always used for this simulation.
And for running the EUROPA – code the continues incremented parameter in the case.dat file was the component for vertical speed in the Z – direction at the same time having constant temperature, altitude, height, centre of gravity, weight and forward speed. For all the records, true values for power, collective, pedal, longitudinal cyclic, lateral cyclic and theta were collected from Panda. Power was then normalized in equivalent power and after that it was generated the equivalent torque. The same was made for the EUROPA resulting power. Rate of climb was also normalized, as the power, both for the Panda values and for the EUROPA results.
For each flight record these parameters were plotted with Matlab© in several graphs, to get a good overview of the situation. Along test points of the flight test a curve of best fit was drawn, to make it easier to compare with the EUROPA - code simulated results. It also reduced the naturally scatter that comes along with the flight test values. Matlab© was used also to plot forces and moments of all the components for a better understandings of the output results, with a great improvement for the evaluation, also speeding up all the process.
Looking backward to the Hover and Level Flight few parameters were changed. Only some parameters in the tailplanes files were modified: drag coefficient for α = 90° and the tailplanes maximum lift coefficient. The strategy was to keep the other variables constants as in the Level Flight and then changing one, till a “good feeling”, with the variable and the effects that it did, was achieved.
Moreover, even if the variables were not heavily linked to multiple commands, an iteration work was necessary, always looking back at the consequences in the Level Flight.
500 1000 1500 2000 2500 0
20 40 60 80 100
Torque vs ROC
ROC
Torque
500 1000 1500 2000 2500 0
20 40 60 80 100
Longitudinal vs ROC
ROC
Longitudinal
500 1000 1500 2000 2500 0
20 40 60 80 100
Lateral vs ROC
ROC
Lateral
500 1000 1500 2000 2500 0
20 40 60 80 100
Collective vs ROC
ROC
Collective
500 1000 1500 2000 2500 0
20 40 60 80 100
Pedals vs ROC
ROC
Pedals
500 1000 1500 2000 2500 0
1 2 3 4 5
Theta vs ROC
ROC
Theta
Climb Flight N ° 1
)LJXUH &OLPEIW.J
[%] [%]
[%] [%]
[%]
[ft/min] [ft/min]
[ft/min] [ft/min]
[ft/min] [ft/min]
[deg]
500 1000 1500 2000 2500 0
20 40 60 80 100
Torque vs ROC
ROC
Torque
500 1000 1500 2000 2500 0
20 40 60 80 100
Longitudinal vs ROC
ROC
Longitudinal
500 1000 1500 2000 2500 0
20 40 60 80 100
Lateral vs ROC
ROC
Lateral
500 1000 1500 2000 2500 0
20 40 60 80 100
Collective vs ROC
ROC
Collective
500 1000 1500 2000 2500 0
20 40 60 80 100
Pedals vs ROC
ROC
Pedals
500 1000 1500 2000 2500 0
1 2 3 4 5
Theta vs ROC
ROC
Theta
Climb: Flight N ° 2
)LJXUH &OLPEIW.J
[%] [%] [%] [%] [%]
[ft/min]
[ft/min]
[ft/min]
[ft/min]
[ft/min] [ft/min]
[deg]
500 1000 1500 2000 0
20 40 60 80 100
Torque vs ROC
ROC
Torque
500 1000 1500 2000
0 20 40 60 80 100
Longitudinal vs ROC
ROC
Longitudinal
500 1000 1500 2000
0 20 40 60 80 100
Lateral vs ROC
ROC
Lateral
500 1000 1500 2000
0 20 40 60 80 100
Collective vs ROC
ROC
Collective
500 1000 1500 2000
0 20 40 60 80 100
Pedals vs ROC
ROC
Pedals
500 1000 1500 2000
0 1 2 3 4 5
Theta vs ROC
ROC
Theta
Climb: Flight N ° 3
)LJXUH &OLPEIW.J
[%] [%] [%] [%] [%]
[ft/min]
[ft/min]
[ft/min]
[ft/min]
[ft/min] [ft/min]
[deg]
500 1000 1500 2000 0
20 40 60 80 100
Torque vs ROC
ROC
Torque
500 1000 1500 2000
0 20 40 60 80 100
Longitudinal vs ROC
ROC
Longitudinal
500 1000 1500 2000
0 20 40 60 80 100
Lateral vs ROC
ROC
Lateral
500 1000 1500 2000
0 20 40 60 80 100
Collective vs ROC
ROC
Collective
500 1000 1500 2000
0 20 40 60 80 100
Pedals vs ROC
ROC
Pedals
500 1000 1500 2000
0 1 2 3 4 5
Theta vs ROC
ROC
Theta
Climb: Flight N ° 4
)LJXUH &OLPEIW.J
[%] [%] [%] [%] [%]
[ft/min]
[ft/min]
[ft/min]
[ft/min]
[ft/min] [ft/min]
[deg]
500 1000 1500 0
20 40 60 80 100
Torque vs ROC
ROC
Torque
500 1000 1500
0 20 40 60 80 100
Longitudinal vs ROC
ROC
Longitudinal
500 1000 1500
0 20 40 60 80 100
Lateral vs ROC
ROC
Lateral
500 1000 1500
0 20 40 60 80 100
Collective vs ROC
ROC
Collective
500 1000 1500
0 20 40 60 80 100
Pedals vs ROC
ROC
Pedals
500 1000 1500
0 1 2 3 4 5
Theta vs ROC
ROC
Theta
Climb: Flight N ° 5
)LJXUH &OLPEIW.J
[%] [%] [%]
[%] [%]
[ft/min]
[ft/min]
[ft/min]
[ft/min]
[ft/min] [ft/min]
[deg]
400 600 800 1000 0
20 40 60 80 100
Torque vs ROC
ROC
Torque
200 400 600 800 1000
0 20 40 60 80 100
Longitudinal vs ROC
ROC
Longitudinal
200 400 600 800 1000
0 20 40 60 80 100
Lateral vs ROC
ROC
Lateral
200 400 600 800 1000
0 20 40 60 80 100
Collective vs ROC
ROC
Collective
200 400 600 800 1000
0 20 40 60 80 100
Pedals vs ROC
ROC
Pedals
200 400 600 800 1000
0 1 2 3 4 5
Theta vs ROC
ROC
Theta
Climb: Flight N ° 6
)LJXUH &OLPEIW.J
[%] [%] [%]
[%] [%]
[ft/min]
[ft/min]
[ft/min]
[ft/min]
[ft/min] [ft/min]
[deg]
200 400 600 800 1000 1200 0
20 40 60 80 100
Torque vs ROC
ROC
Torque
200 400 600 800 1000 1200 0
20 40 60 80 100
Longitudinal vs ROC
ROC
Longitudinal
200 400 600 800 1000 1200 0
20 40 60 80 100
Lateral vs ROC
ROC
Lateral
200 400 600 800 1000 1200 0
20 40 60 80 100
Collective vs ROC
ROC
Collective
200 400 600 800 1000 1200 0
20 40 60 80 100
Pedals vs ROC
ROC
Pedals
200 400 600 800 1000 1200 0
1 2 3 4 5
Theta vs ROC
ROC
Theta
Climb: Flight N ° 7
)LJXUH &OLPEIW.J
[%] [%]
[%] [%] [%]
[ft/min]
[ft/min]
[ft/min]
[ft/min]
[ft/min]
[ft/min]
[deg]
Simulation with EUROPA was attempted with constant temperature, altitude, height, C.G., weight, forward speed while the vertical speed changed every steps using the multitrim conditions option in the case.dat file.
• 7RUTXH/DWHUDO3HGDOV&ROOHFWLYH
These commands were not touched by the variation of the tailplanes variables, or it was so little that it was insignificant. The difference before and after the matching is negligible. was It not satisfactory change other parameters other than the mentioned ones because the implication in the other performance tests.
• /RQJLWXGLQDO
The tailplanes drag coefficient for α = 90° were modified to match the curve at high rates of climb, while at low or mid climb rates the maximum lift coefficient was adjusted for a better correspondence.
• 7KHWD
Theta was heavily affected by the variation of the tailplane maximum lift coefficient, particularly in the mid and low rates of climb. At the high climb rates it was more affected by the drag coefficient for α = 90°.
&RQFOXVLRQV
Torque, Longitudinal, Collective and Theta have a good matching with the EUROPA code.
Torque and Collective did not require an optimisation process; they nearly matched the flight test results.
Longitudinal needed some evaluation because in the mid rates of climb, the maximum lift coefficient had some evident effect, while the drag at 90° TO the tailplane needed to be increased to a better result.
These effects where much more evident in the Theta angle.
It was perceivable looking at the graphs that the tailplane was in a stall condition, otherwise the pitching attitude at low/mid rates of climb were mismatched. The helicopter, with unstalled tailplanes, had a “high alpha” nose up attitude. A little correction was also needed in the tailplane drag at high RoC.
Pedals showed perfect matching at low rates but after that, the code results started to diverge from the flight tests. Lateral command had the same behaviour but the divergence was much more pronounced. The model was validated by an assessment of the purpose of our model. High rates of climb were not significant.
Another problem arose at high altitude, for Torque, Collective and Pedals. According to the code, with the helicopter flying at 75 knots and 15000 ft , the helicopter enter a hazardous area of the flight envelope. As seen in Level Flight there is good matching for low speed after that the code is not sufficiently complex to take care of reality. For high altitude flight tests these parameters start to diverge, the EUROPA code always predicts results lower than reality; as expected. Analysis of the last flight provided evidence of good matching, at 18000 ft. This is due to a lower forward speed, ( 60 Knots) meaning the helicopter is flying in an area where EUROPA is still able to simulate the flight tests with little error.
It is worthy of notice that there is a discrepancy in theta in the first flight, this is possibly due to an incorrect calculation of the C.G. by the Flight test engineer, as the C.G. was too far aft.
+RYHU )LQDO$QDO\VLV
It was necessary to return to the Hover performance after the climb to review the behaviour of the model more accurate and final fine tuning was necessary.
Naturally the same flight tests were used, as in first analysis of the hover, but further conditions were also considered.
These are the two flights conditions with the following characteristics:
Flight N°
Initial Weight [Kg]
Final Weight [Kg]
OAT [C°]
HP
[ft] RPM Height C.G.
1 3446 2522 16 800 100÷102% IGE/OGE mid/right
2 3264 2633 15 7600 100÷102% IGE/OGE forward/right
7DEOH +RYHUIOLJKWWHVWUHFRUGVILQDODQDO\VLV
As can be seen in the table, different RPM percentages were used for In Ground Effect and Out of Ground Effect. In the first analysis phase for the hover the main focus was kept on the three variables Torque, Collective and Pedals to see how well they were matching.
Following the first analysis phase Longitudinal, Lateral and Theta were also analysed.
Simulation with EUROPA was attempted using constant temperature, altitude, height and C.G., while the weight changed in each step using the multitrim condition option in the case.dat file. Another run was made taking into account the change in the C.G. as the weight of the ballast was reduced.
Now it was almost impossible to freely change the parameters without affecting the work previously done. It was changed only by the Coefficient at 90° for the Z-Force as the Torque showed a little gap. This did not affected the previous work done on performance analysis.
25000 3000 3500 20
40 60 80 100
Torque vs GW
GW
Torque
25000 3000 3500
20 40 60 80 100
Longitudinal vs GW
GW
Longitudinal
25000 3000 3500
20 40 60 80 100
Lateral vs GW
GW
Lateral
25000 3000 3500
20 40 60 80 100
Collective vs GW
GW
Collective
25000 3000 3500
20 40 60 80 100
Pedals vs GW
GW
Pedals
25000 3000 3500
1 2 3 4 5
Theta vs GW
GW
Theta
Flight Test Polyfit
Europa (High Gw) Europa (Low Gw) Hover: Flight 1 IGE 100%
)LJXUH +RYHU1,*(1U
[%] [%]
[%] [%] [%]
[Kg]
[Kg]
[Kg]
[Kg]
[Kg] [Kg]
[deg]
25000 3000 3500 20
40 60 80 100
Torque vs GW
GW
Torque
25000 3000 3500
20 40 60 80 100
Longitudinal vs GW
GW
Longitudinal
25000 3000 3500
20 40 60 80 100
Lateral vs GW
GW
Lateral
25000 3000 3500
20 40 60 80 100
Collective vs GW
GW
Collective
25000 3000 3500
20 40 60 80 100
Pedals vs GW
GW
Pedals
25000 3000 3500
1 2 3 4 5
Theta vs GW
GW
Theta
Flight Test Polyfit
Europa (High Gw) Europa (Low Gw) Hover: Flight 1 IGE 102%
)LJXUH +RYHU1,*(1U
[%] [%]
[%] [%] [%]
[Kg] [Kg]
[Kg] [Kg]
[Kg] [Kg]
[deg]
