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The Methods of Forecasting Some Events During the Aircraft Takeoff and Landing*
19th IFAC Symposium on Automatic Control in Aerospace September 2-6, 2013. Würzburg, Germany
The Methods of Forecasting Some Events During the Aircraft Takeoff and Landingà A.Kuznetsov,*A.Shevchenko**, Ju. Solonnikov*** * Moscow Institute of Electromechanics and Automatics (JSC “MIEA”), Moscow, Russia (e-mail: [email protected]) **Trapeznikov Institute of Control Sciences, Russian Academy of Sciences Moscow, Russia e-mail: [email protected]). *** Moscow Institute of Electromechanics and Automatics (JSC “MIEA”), Moscow, Russia (e-mail: [email protected] Abstract: The algorithmic methods of estimation current and forecasting of the future movement of the aircraft are offered. The methods are based on the energy approach to flight control of air vehicles. The energy balance equation is generalized on runway stages. Equation describes the process of changing the aircraft total energy in whole trajectory, including the ahead segment. The length of this segment is calculated from the conditions of achieving the required final energy state. For the takeoff stage the forecast algorithm calculates the position of the aircraft on runway, from which it is possible to speed up till the speed of steady level flight and to reach the altitude for overcoming the high-altitude obstacles. The length of braking distance is determined for the landing stage. The correction of the forecasting algorithms is proposed for the purpose of an increasing in likelihood of forecast. The results of the simulation of many takeoffs and landings of passenger aircraft with different weights with the obstacles presence and with the engine failure are given.
Keywords: flight control, energy approach, prediction, decision making.
known factors: temperature, RNW altitude, RNW slope, wind velocity, etc.
INTRODUCTION The problems of safety and accident- safety of air traffic have always been in the spotlight of aircraft operators and designers. As air traffic increase this problem becomes aggravated. The human factor plays a decisive role in ensuring the accident- safety. The most critical stages during each flight are the takeoff and landing stages which are carried out with obligatory participation of the pilot.
The existing technique of takeoff decision is usually based only on the moment of reaching by aircraft the so-called takeoff decision speed V1. As noted in several studies [Glubokaya (2008), Erusalimskiy (2011). Nikiforov (2002)] this technique cannot prevent accidents in abnormal situations. The reasons for these situations are follows: too low acceleration of the aircraft, the engine failure, exceeded takeoff weight, brake failure, runway (RWY) contamination or deviation from expected weather conditions. Despite successful methodical developments, such as [Sharov (2007), Zavershinsky (2009), Constans F.(2007)], the problem of the pilot information support is far from its solution.
In [Boeing (2012)] the data on distribution of accidents at different stages of the flight of civil aircrafts for the period 1959 through 2011 are submitted. As it follows from the analysis of these data more than half of all accidents occur at takeoff and landing stages. But 30% of all accidents occur only at takeoff roll and landing run though the duration of these stages is only 2% of average flight duration.
In our previous papers [Borisov et al. (2010), Shevchenko (2011), Shevchenko et al. (2012)], the methods of forming an objective flight image and predicting future scenarios of flight were offered. The methodological basis of development is the energy approach to flight control. Conceptually, the basic idea of the work is in line with new views on the control in class of terminal algorithms with fixed target function. In this paper the conditions for achievability of terminal state during takeoff in the presence of high-altitude obstacles and during landing with an engine failure are found. To improve the forecast reliability the adjustment of forecasting algorithms was introduced. Modelling of the forecasting algorithms has been carried out on the computer stand with the certified model of serial liner.
The role and responsibility of the pilot increase in emergency situations. However, the lack of time for decision-making and need of evaluating atypical situations result in stressful states. The problem of reducing the risk of air accidents has been widely discussed [Erusalimskiy (2011), Glubokaya (2008), Middleton et al (1994), Nikiforov (2002), Pinder (2002), Zammit-Mangion and Eshelby (2002), Bove and Andersen (2002). Kofman et al (2006)]. These and many other researches are based on knowledge of the nominal aerodynamic characteristics. Normalized diagrams are used to preplan the basic maneuvers according to the a priori
Ã
This study was financially supported by the Russian Foundation for Basic Research (Project No № 12-08-00651-a) 978-3-902823-46-5/2013 © IFAC
183
10.3182/20130902-5-DE-2040.00026
2013 IFAC ACA September 2-6, 2013. Würzburg, Germany
2. THE SUMMARY VERSION OF THE ENERGY APPROACH The distinctive feature of this approach is that the dynamic equations are written in the coordinate system related with the moving air mass. Therefore, the d'Alembert forces induced by translational acceleration have been added to the force equations.
Xdp Ddp
x(t)
ΔHE = ΔH +ΔH +ΔH D E
w E
Lr DVr LRNW
Hob Lob S
Fig. 1. The layout of specific points along the takeoff trajectory. the coordinate of a TDP, Lr is the rolling reserve from DMP.
The equation is written in deviations of specific energy:
HE ( ∗) = E ( ∗) mg = h + V 2 2 g .
At the moment of overcoming an obstacle the aircraft total energy Eob is defined by its geometrical height Hob and level flight airspeed V2:
Specific energy measure unit is the meters; therefore it is called also as energy height. Here ΔH E is the increment of total energy height of the vehicle;
is the distance to a point of achievement of rotation speed, Ddp is the distance to a takeoff decision point (TDP), Xdp is V2
Considering together dynamical equations of the air vehicle translational motion in the air, kinematic equations, and equation of total energy we have obtained the energy balance equation [Kurdjukov et al. (1998), Borisov et al. (1999), Pavlov et al. (2003)] : eng E
Here x(t) is current coordinate of the aircraft, Hob and Lob are height of an obstacle and distance to it, V2 is the minimum airspeed of steady level flight, S is a distance for accumulation of total energy, LRWY is length of a RWY, DVR
Eob ≥ m
ΔHEeng , ΔHED
, ΔH specific engine work, expenditure of energy for overcoming of harmful drag, and wind work, respectively. For each term the integral expressions has been found [Kurdjukov et al (1998)]. w E define
V2 2 + mgH ob 2
(1)
During aircraft maneuvering it is possible to predict the accumulated energy if the trajectory is known. It is calculated as the sum of current total energy and the work of all applied forces along the flight trajectory up to the obstacle. Neglecting the small flight path angle and the engine inclination angle we will write down the equation:
However, additional resistance force of the chassis appears when moving on the RWY. Therefore we have offered to generalize the energy balance equation to RWY modes by
E (t ) = m
adding the term ΔH representing the energy consumption to overcome the resistance force: b E
V (t ) 2 + mgh(t ) + S ∑ Fi (t ) 2 i
(2)
Among the applied forces Fi (t ) the most significant ones are the engine thrust, the aerodynamic drag, and the undercarriage reaction.
ΔH E = ΔH Eeng + ΔH ED + ΔH Eb + ΔH Ew
The new term is presented in the form:
This equation may be interpreted as a method for predicting the aircraft energy sufficient for climbing above the obstacle. The required condition is expressed as follows:
t2
ΔH Eb = ∫ Vkb dt , t1
E (t ) ≥ Eob
where kb is the generalized braking factor depending on wheels adhesion with RWY pavement and degree of wheel’s brake blocking.
Modelling of all forces Fi (t ) is a nontrivial task. Instead of Modelling we have offered to use a certain measurable behavioral equivalent, namely a longitudinal acceleration:
So the energy balance equation reflects uniformly the interconnections of all energy sources and consumers in system “flying object – power plant – surroundings”.
Σ Fi = ma(t )
(3)
i
3. FORECAST OF THE POSSIBILITY OF THE AIRCRAFT TAKEOFF WITH THE OBSTACLES PRESENCE
which is defined by the measured load factor nx
a(t ) = gnx (t )
During a takeoff run unforeseen contingencies may arise. Among them there are engine failures, the raised ambient air temperature in high mountains at excessive loadings, RWY damage and so on. In such situations it is extremely necessary to estimate the capability of the aircraft to carry out takeoff within the RWY edges and to gain sufficient height above an obstacle ahead. Let’s consider a takeoff trajectory (Fig.1).
(4)
From (1) and (2) taking into account (3) and (4) it is possible to find a distance sufficient to accumulate the required energy Eob:
(
Ddpf (t ) = g ( H ob − h(t ) ) + 0.5 (V2 2 − V (t ) 2 ) − Lob
)
gnx (t )
Note that the resulting expression is invariant relative to the aircraft mass. Behind this distance the safe takeoff is 184
2013 IFAC ACA September 2-6, 2013. Würzburg, Germany
obstacle height of 50m are shown. At the distance of 800 m from a start point the engine failure was imitated.
available. Then, the takeoff decision point coordinate may be defined as follows:
X dp (t ) = x(t ) + Ddpf (t )
The following table shows the forecasted coordinates X dpf
It is obvious, that the information concerning the distance remaining till the end of a RWY is rather important for the pilot. This remaining distance, or reserve Lr (t ) , may be calculated very simply:
Lr (t) = LRNW − Xdp (t) . Figure 2. The forecast of takeoff decision point and rotation speed point. and the coordinates of the points where the rotation speed is achieved actually XV1, for an aircraft of different takeoff weights.
Forecasting method based on the energy approach made it possible to predict another characteristic point in the takeoff trajectory. In emergency situations the pilot must assess not only the opportunity to continue the takeoff, but also the position of the aircraft on the RWY where he can start the nose-wheel lifting. For each type of aircraft there is the rotation speed Vr at which it is allowed to increase the pitch angle. The distance from the current aircraft position till the point of rotation speed is expressed by the formula:
DVr ( t ) =
(Vr )
2
− V (t )
2 gnx ( t )
Table. Comparison of forecasted and real coordinates f Weight, (t) V1, (km/h) XV1,(m) X dp,(m) Vr, (km/h) XVr, (m)
70 90 105
2
204 220 238
515 764 1095
153 508 837
210 228 245
547 825 1203
Comparison of coordinates shows that the ability to fly over an obstacle is predicted long before the plane gets takeoff decision speed ordered by flight operation manuals.
,
Objective estimation of this distance, unlike intuitive one, improves situational awareness of the pilot and thus reduces the preconditions for erroneous actions. The moment of zeroing this distance serves as a signal to begin the aircraft rotation at takeoff pitch. The warning information may be presented to the pilot in the form of a text announcement, or graphic symbols or a voice command.
At larger distances to obstacles (over 2000 m) forecast shows the ability of takeoff almost from the initial point for any aircraft including an aircraft of maximum takeoff weight. This is understandable since the forecast takes into account the energy accumulating both on the ground and in the air.
4. SIMULATION OF TAKEOFF WITH THE OBSTACLES PRESENCE
When modelling the distances till achieving the rotation speed XVr. also were calculated. For TU-204 these speeds are equal to 210, 228 and 245 km/h, respectively, for three download options.
Testing of the forecasting technique has been carried out at the computer stand with the certified model of the serial aircraft TU-204. The full dynamic model contained the engine model. The equivalent engine time constant was 1.5 sec. Failure of one engine was imitated by reduction of total thrust by half (on 50 %).
These distances XVr are marked on the Xdp graphs in Fig. 2. Analysis shows that on the airfields with obstacles located far enough from the rear edge, further than 1500 m, the forecast of successful takeoff happens earlier than the rotation speed is achieved. This speed will limit the start of lift-off from the RWY.
The operator's console allowed to assign the weight and centering of the aircraft, climate conditions, airfield altitude and to compile the takeoff scenario in accordance with the flight manual operation.
In the case of closely located obstacles the rotation speed achieving does not guarantee a successful climb. For such climbing the aircraft must accumulate sufficient energy while running on the RWY because at the short air segment of takeoff the aircraft may accumulate only a small portion of the required total energy. In such situations the takeoff roll should be continued to the TDP.
The purposes of modelling were to get multiple estimates of TDP and to compare them with the recommendations of the standard piloting techniques.
5. FORECAST OF SAFE BRAKING DISTANCE
Series of takeoffs of the aircraft with different weight (from minimum to maximum) have been modelled. Takeoffs with one failed engine in the initial part of the takeoff run were of particular interest. The obstacle height varied from 50 to 150m and the distance to obstacles varied from 500 to 3000m.
After an unsuccessful touchdown or in situation of rejected takeoff the overrunning beyond the RWY threshold may occur. Overrunning occurs by several reasons such as overshoot at landing, blocking up the RWY by extraneous objects, RWY damage, RWY icing, etc. In such situations it is very important to estimate the possibility of emergency braking or executing an alternative maneuver e.g. go-around.
In Fig. 2 predictive coordinates of the TDP for aircrafts with different takeoff weights in function of the distance till an 185
2013 IFAC ACA September 2-6, 2013. Würzburg, Germany
Db _ cor = kcor Db
The situations on the RWY occurring during braking process are represented in figure 3.
The most powerful influences on the dynamics have thrust reverse and engine failure. After engine failure the overall thrust is restored within 3-5 seconds. Therefore, it was decided to take only the reverse level into account. So, the correction factor was toggled concurrently with the change of the reverse command. 2 if reverse=max ⎪⎧1.49kb − 3.14kb + 2.62 kcor = ⎨ 3 2 ⎪⎩−0.98kb + 3.08kb − 2.53kb + 1.82 if reverse=min
Figure 3. The various factors at landing and ground rolling. The decision whether to continue the landing in normal mode or to use the emergency braking depends on the forecasted braking distance. The prediction can be calculated from the condition of the reducing aircraft kinetic energy (or speed) to some small value ε close to zero. After touchdown the total aircraft energy varies in accordance with the law:
E(t ) = m
V (t ) 2
2
+ S ∑ Fi i
7. MODEL TESTS OF THE ALGORITHM OF THE BRAKING DISTANCE FORECASTING The main purposes of braking process modelling were • Demonstration of correction algorithm operability on a set of regular and abnormal situations, • Obtaining the estimations of forecast errors.
.
The forecasted braking distance Db _ cor of the TU-204 of maximum, nominal and minimum weights for different brake factors kb in the function of initial speed V0 are resulted in Fig. 4. The distances for intermediate values of the brake factor are easily interpolated.
Taking into account the same assumptions as above we get the formula for prediction of braking distance Db: Db = S = 0.5 (V (t ) 2 − ε 2 ) g * nx (t )
Note that forecasting the distance is based on the current measurement of acceleration which in turn reflects the resultant reaction of all applied forces including undercarriage friction. Comparing the forecasted braking distance and current aircraft position relative to the RWY threshold the warning inscription about the reserve of distance may be generated in the pilot field-of-view:
Dreserv = LRWY − x(t ) − Db 6. CORRECTION OF FORECASTING ALGORITHM
Figure 4. The braking distance forecasting at ground rolling.
The most simple and obvious forecast of the braking
It is seen, that at bad conditions of a RWY such as icing or sleet along the whole RWY the braking distance can reach 2500m. These calculations should be considered for landing planning on short RWY. Note that braking processes have been simulated at extremely low braking factor and an engine failure.
f
distance X dp is calculated being based on current energy and actuating external forces. It is obvious that all forces vary during movement process according to the AFM or under unforeseen circumstances. Therefore the forecast cannot coincide with real process and always contains an error or uncertainty. For increasing the forecast likelihood the method of forecasting algorithms correction is offered in the given work.
Introducing the forecasting algorithms into the structure of onboard information system depends primarily on the confidence of aircraft operators to the forecasting technique.
The correction was defined on the basis of statistical processing of results of model experiments. All experiments were spent with the certified model of serial liner TU-204. The set of flight conditions included the scatter of landing weight, airspeed and braking factor. The failure of one of engines was simulated by reduction of total thrust by half.
For confirmation of forecast likelihood the special researches of forecasting errors have been carried out. The averaged error of the current distance calculation with respect to the real process was accepted as the measure of the forecast likelihood. To have the possibility of comparing predictive estimations with real process the modelling of each flight was carried out twice. In the first run the real process was recorded and in the second one the predictive braking distance was calculated.
Increase of the forecast likelihood in our work is reached by introducing the scale factor Kcor in forecasting algorithm. So, the corrected braking distance is presented in a form 186
2013 IFAC ACA September 2-6, 2013. Würzburg, Germany
In Fig. 5 an example of the correction effectiveness is demonstrated. The simulated conditions were as follows: the weight=105t, the braking factor = 0.4, the initial airspeed = 210 km/h. The graphs show the forecast braking distances without correction (Db) and with correction (Db_cor). In the later case the average error (ERR) relative to the actual process is within –22÷+22m. The errors of forecast in another most unfavorable conditions did not exceed 50-70m.
Constans F.(2007) Landing assistance device and method for aircraft. FR 0605157. 21.12.2007 Erusalimskiy M.A. (2011). Analysis of a decision-making about rejection or continuation of takeoff in flight accident and incidents. Aviation Explorer, 07.11.2011. http://www.aex.ru/docs/4/2011/11/7/1447/ Glubokaya M.G. (2008). The onboard system for the decision-making support during the passenger aircraft takeoff. Technology of Air Fleet .Vol.82. №1,pp 21-30
Db_cor
Kofman V.D., Poltavetc V.A., Teimurazov R.A. (2006). The comparative analysis of safety of domestic and foreign aircrafts flights. Problems of flight safety. 2006. № 1. pp. 6-15. http://www.transafety.ru/issue/20054/articals/102.html.
ERR D_real
Kurdjukov A.P., Natchinkina G.N., Shevtchenko A.M. (1998). Energy Approach to Flight Control. AIAA Guidance Navigation and Control Conf., AIAA Paper 984211, Boston, MA.
Figure 5. The effectiveness of forecast correction. Eventually, it has been established, that the aircraft of the maximum and minimum weight with failed engine and all deployed braking devices is able to slow down from landing speed till taxing speed at the most modern airports.
Middleton D., Srivatsan R., Person L. Jr. (1994). Flight Test of Takeoff Performance Monitoring System Indicates Successful Use in Research Vehicle. Flight Safety Foundation Digest. Vol. 13 № 10.
8. CONCLUSION The methods of predicting the possibility of terminal states achieving at the takeoff and landing stages are developed. The methodological basis of these methods is the energy approach to motion control in the space. This approach has been extended to the land-based fragments of the flight trajectory. The most important property of every forecast is its likelihood. For its increasing the methods of adjusting the forecasting algorithms are proposed in the article. The model tests of the forecasting algorithms over a wide range of situations at takeoff and landing stages, including the engine failure and the presence of the closely located obstacles have been executed.
Nikiforov S.(2002).The onboard takeoff monitoring system effective means of the transport aircraft safety increase Technology of Air Fleet. Vol.76. № 3. Pavlov B.V., Shevchenko A.M., Nachinkina G.N. (2003). Energy Approach and its Usage for Flight Control System Design. Actual Problems of Aviation and Aerospace, vol.8, №2(16), pp 24-43. Pinder S.D. (2002).Aircraft Takeoff Performance Monitoring in Far-Northern Regions: An Application of the Global Positioning System. Ph.D. thesis. University of Saskatchewan.
The results of simulation have confirmed the possibility of advance warning or notifying pilot about the possibility of continuing safe takeoff or landing. Such notifications can improve the situational awareness of the pilot and, thus, reduce the probability of the erroneous actions of the crew.
Sharov V. D. (2007). The method of evaluation of runway overrun probability for aircraft on landing. Nauchnyi vestnik MGTU Grazhdanskoi Aviatcii, № 122, pp 61-66. Shevchenko A.M.(2011). Some means for informational support of airliner pilot. 5th International Scientific Conference on Physics and Control (Physcon 2011). Leon, Spain. 2011. p. 1-5. http://lib.physcon.ru/doc?id=78f90e41e746/
REFERENCES Boeing (2012). Statistical Summary of Commercial Jet Airplane Accidents. Worldwide Operations 1959 – 2011. July 2012. http://www.boeing.com/news/techissues/pdf/statsum.pdf.
Shevchenko A.M., Pavlov B.V., Nachinkina G.N. (2012) Method of aircraft takeoff forecasting in the presence of high-altitude obstacles. Proceedings of the Southern Federal University. Technical sciences. 2012. №3. pp. 167-172.
Borisov V.G., Nachinkina G.N., Shevchenko A.M. (1999) Energy approach to flight control. Automation and Remote Control. Vol.60, №6, pp.805-813. Borisov V.G., Pavlov B.V., Shevchenko A.M. (2010). Means of information support of the pilot. 7nd scientific and technical conference «Mechatronics, Automation, Control» (MAC-2010), St.Petersburg, Russia, pp. 74-77.
Zammit-Mangion D., Eshelby M. (2002) An Operational Evaluation Of A Take-Off Performance Monitoring Algorithm. ICAS2002 Congress. http://lu.fme.vutbr.cz/icas2002/paper7105.pdf
Bove T., Andersen H.B. (2002). The effect of an advisory system on pilots' go/no-go decision during take-off. Reliability Engineering and System Safety. Vol. 75, № 2, pp 179-191.
Zavershinsky V.V. (2009) The device for prevention the aircraft overrunning beyond of the runway. RU2373115. 20.11.2009 187
The Methods of Forecasting Some Events During the Aircraft Takeoff and Landingà A.Kuznetsov,*A.Shevchenko**, Ju. Solonnikov*** * Moscow Institute of Electromechanics and Automatics (JSC “MIEA”), Moscow, Russia (e-mail: [email protected]) **Trapeznikov Institute of Control Sciences, Russian Academy of Sciences Moscow, Russia e-mail: [email protected]). *** Moscow Institute of Electromechanics and Automatics (JSC “MIEA”), Moscow, Russia (e-mail: [email protected] Abstract: The algorithmic methods of estimation current and forecasting of the future movement of the aircraft are offered. The methods are based on the energy approach to flight control of air vehicles. The energy balance equation is generalized on runway stages. Equation describes the process of changing the aircraft total energy in whole trajectory, including the ahead segment. The length of this segment is calculated from the conditions of achieving the required final energy state. For the takeoff stage the forecast algorithm calculates the position of the aircraft on runway, from which it is possible to speed up till the speed of steady level flight and to reach the altitude for overcoming the high-altitude obstacles. The length of braking distance is determined for the landing stage. The correction of the forecasting algorithms is proposed for the purpose of an increasing in likelihood of forecast. The results of the simulation of many takeoffs and landings of passenger aircraft with different weights with the obstacles presence and with the engine failure are given.
Keywords: flight control, energy approach, prediction, decision making.
known factors: temperature, RNW altitude, RNW slope, wind velocity, etc.
INTRODUCTION The problems of safety and accident- safety of air traffic have always been in the spotlight of aircraft operators and designers. As air traffic increase this problem becomes aggravated. The human factor plays a decisive role in ensuring the accident- safety. The most critical stages during each flight are the takeoff and landing stages which are carried out with obligatory participation of the pilot.
The existing technique of takeoff decision is usually based only on the moment of reaching by aircraft the so-called takeoff decision speed V1. As noted in several studies [Glubokaya (2008), Erusalimskiy (2011). Nikiforov (2002)] this technique cannot prevent accidents in abnormal situations. The reasons for these situations are follows: too low acceleration of the aircraft, the engine failure, exceeded takeoff weight, brake failure, runway (RWY) contamination or deviation from expected weather conditions. Despite successful methodical developments, such as [Sharov (2007), Zavershinsky (2009), Constans F.(2007)], the problem of the pilot information support is far from its solution.
In [Boeing (2012)] the data on distribution of accidents at different stages of the flight of civil aircrafts for the period 1959 through 2011 are submitted. As it follows from the analysis of these data more than half of all accidents occur at takeoff and landing stages. But 30% of all accidents occur only at takeoff roll and landing run though the duration of these stages is only 2% of average flight duration.
In our previous papers [Borisov et al. (2010), Shevchenko (2011), Shevchenko et al. (2012)], the methods of forming an objective flight image and predicting future scenarios of flight were offered. The methodological basis of development is the energy approach to flight control. Conceptually, the basic idea of the work is in line with new views on the control in class of terminal algorithms with fixed target function. In this paper the conditions for achievability of terminal state during takeoff in the presence of high-altitude obstacles and during landing with an engine failure are found. To improve the forecast reliability the adjustment of forecasting algorithms was introduced. Modelling of the forecasting algorithms has been carried out on the computer stand with the certified model of serial liner.
The role and responsibility of the pilot increase in emergency situations. However, the lack of time for decision-making and need of evaluating atypical situations result in stressful states. The problem of reducing the risk of air accidents has been widely discussed [Erusalimskiy (2011), Glubokaya (2008), Middleton et al (1994), Nikiforov (2002), Pinder (2002), Zammit-Mangion and Eshelby (2002), Bove and Andersen (2002). Kofman et al (2006)]. These and many other researches are based on knowledge of the nominal aerodynamic characteristics. Normalized diagrams are used to preplan the basic maneuvers according to the a priori
Ã
This study was financially supported by the Russian Foundation for Basic Research (Project No № 12-08-00651-a) 978-3-902823-46-5/2013 © IFAC
183
10.3182/20130902-5-DE-2040.00026
2013 IFAC ACA September 2-6, 2013. Würzburg, Germany
2. THE SUMMARY VERSION OF THE ENERGY APPROACH The distinctive feature of this approach is that the dynamic equations are written in the coordinate system related with the moving air mass. Therefore, the d'Alembert forces induced by translational acceleration have been added to the force equations.
Xdp Ddp
x(t)
ΔHE = ΔH +ΔH +ΔH D E
w E
Lr DVr LRNW
Hob Lob S
Fig. 1. The layout of specific points along the takeoff trajectory. the coordinate of a TDP, Lr is the rolling reserve from DMP.
The equation is written in deviations of specific energy:
HE ( ∗) = E ( ∗) mg = h + V 2 2 g .
At the moment of overcoming an obstacle the aircraft total energy Eob is defined by its geometrical height Hob and level flight airspeed V2:
Specific energy measure unit is the meters; therefore it is called also as energy height. Here ΔH E is the increment of total energy height of the vehicle;
is the distance to a point of achievement of rotation speed, Ddp is the distance to a takeoff decision point (TDP), Xdp is V2
Considering together dynamical equations of the air vehicle translational motion in the air, kinematic equations, and equation of total energy we have obtained the energy balance equation [Kurdjukov et al. (1998), Borisov et al. (1999), Pavlov et al. (2003)] : eng E
Here x(t) is current coordinate of the aircraft, Hob and Lob are height of an obstacle and distance to it, V2 is the minimum airspeed of steady level flight, S is a distance for accumulation of total energy, LRWY is length of a RWY, DVR
Eob ≥ m
ΔHEeng , ΔHED
, ΔH specific engine work, expenditure of energy for overcoming of harmful drag, and wind work, respectively. For each term the integral expressions has been found [Kurdjukov et al (1998)]. w E define
V2 2 + mgH ob 2
(1)
During aircraft maneuvering it is possible to predict the accumulated energy if the trajectory is known. It is calculated as the sum of current total energy and the work of all applied forces along the flight trajectory up to the obstacle. Neglecting the small flight path angle and the engine inclination angle we will write down the equation:
However, additional resistance force of the chassis appears when moving on the RWY. Therefore we have offered to generalize the energy balance equation to RWY modes by
E (t ) = m
adding the term ΔH representing the energy consumption to overcome the resistance force: b E
V (t ) 2 + mgh(t ) + S ∑ Fi (t ) 2 i
(2)
Among the applied forces Fi (t ) the most significant ones are the engine thrust, the aerodynamic drag, and the undercarriage reaction.
ΔH E = ΔH Eeng + ΔH ED + ΔH Eb + ΔH Ew
The new term is presented in the form:
This equation may be interpreted as a method for predicting the aircraft energy sufficient for climbing above the obstacle. The required condition is expressed as follows:
t2
ΔH Eb = ∫ Vkb dt , t1
E (t ) ≥ Eob
where kb is the generalized braking factor depending on wheels adhesion with RWY pavement and degree of wheel’s brake blocking.
Modelling of all forces Fi (t ) is a nontrivial task. Instead of Modelling we have offered to use a certain measurable behavioral equivalent, namely a longitudinal acceleration:
So the energy balance equation reflects uniformly the interconnections of all energy sources and consumers in system “flying object – power plant – surroundings”.
Σ Fi = ma(t )
(3)
i
3. FORECAST OF THE POSSIBILITY OF THE AIRCRAFT TAKEOFF WITH THE OBSTACLES PRESENCE
which is defined by the measured load factor nx
a(t ) = gnx (t )
During a takeoff run unforeseen contingencies may arise. Among them there are engine failures, the raised ambient air temperature in high mountains at excessive loadings, RWY damage and so on. In such situations it is extremely necessary to estimate the capability of the aircraft to carry out takeoff within the RWY edges and to gain sufficient height above an obstacle ahead. Let’s consider a takeoff trajectory (Fig.1).
(4)
From (1) and (2) taking into account (3) and (4) it is possible to find a distance sufficient to accumulate the required energy Eob:
(
Ddpf (t ) = g ( H ob − h(t ) ) + 0.5 (V2 2 − V (t ) 2 ) − Lob
)
gnx (t )
Note that the resulting expression is invariant relative to the aircraft mass. Behind this distance the safe takeoff is 184
2013 IFAC ACA September 2-6, 2013. Würzburg, Germany
obstacle height of 50m are shown. At the distance of 800 m from a start point the engine failure was imitated.
available. Then, the takeoff decision point coordinate may be defined as follows:
X dp (t ) = x(t ) + Ddpf (t )
The following table shows the forecasted coordinates X dpf
It is obvious, that the information concerning the distance remaining till the end of a RWY is rather important for the pilot. This remaining distance, or reserve Lr (t ) , may be calculated very simply:
Lr (t) = LRNW − Xdp (t) . Figure 2. The forecast of takeoff decision point and rotation speed point. and the coordinates of the points where the rotation speed is achieved actually XV1, for an aircraft of different takeoff weights.
Forecasting method based on the energy approach made it possible to predict another characteristic point in the takeoff trajectory. In emergency situations the pilot must assess not only the opportunity to continue the takeoff, but also the position of the aircraft on the RWY where he can start the nose-wheel lifting. For each type of aircraft there is the rotation speed Vr at which it is allowed to increase the pitch angle. The distance from the current aircraft position till the point of rotation speed is expressed by the formula:
DVr ( t ) =
(Vr )
2
− V (t )
2 gnx ( t )
Table. Comparison of forecasted and real coordinates f Weight, (t) V1, (km/h) XV1,(m) X dp,(m) Vr, (km/h) XVr, (m)
70 90 105
2
204 220 238
515 764 1095
153 508 837
210 228 245
547 825 1203
Comparison of coordinates shows that the ability to fly over an obstacle is predicted long before the plane gets takeoff decision speed ordered by flight operation manuals.
,
Objective estimation of this distance, unlike intuitive one, improves situational awareness of the pilot and thus reduces the preconditions for erroneous actions. The moment of zeroing this distance serves as a signal to begin the aircraft rotation at takeoff pitch. The warning information may be presented to the pilot in the form of a text announcement, or graphic symbols or a voice command.
At larger distances to obstacles (over 2000 m) forecast shows the ability of takeoff almost from the initial point for any aircraft including an aircraft of maximum takeoff weight. This is understandable since the forecast takes into account the energy accumulating both on the ground and in the air.
4. SIMULATION OF TAKEOFF WITH THE OBSTACLES PRESENCE
When modelling the distances till achieving the rotation speed XVr. also were calculated. For TU-204 these speeds are equal to 210, 228 and 245 km/h, respectively, for three download options.
Testing of the forecasting technique has been carried out at the computer stand with the certified model of the serial aircraft TU-204. The full dynamic model contained the engine model. The equivalent engine time constant was 1.5 sec. Failure of one engine was imitated by reduction of total thrust by half (on 50 %).
These distances XVr are marked on the Xdp graphs in Fig. 2. Analysis shows that on the airfields with obstacles located far enough from the rear edge, further than 1500 m, the forecast of successful takeoff happens earlier than the rotation speed is achieved. This speed will limit the start of lift-off from the RWY.
The operator's console allowed to assign the weight and centering of the aircraft, climate conditions, airfield altitude and to compile the takeoff scenario in accordance with the flight manual operation.
In the case of closely located obstacles the rotation speed achieving does not guarantee a successful climb. For such climbing the aircraft must accumulate sufficient energy while running on the RWY because at the short air segment of takeoff the aircraft may accumulate only a small portion of the required total energy. In such situations the takeoff roll should be continued to the TDP.
The purposes of modelling were to get multiple estimates of TDP and to compare them with the recommendations of the standard piloting techniques.
5. FORECAST OF SAFE BRAKING DISTANCE
Series of takeoffs of the aircraft with different weight (from minimum to maximum) have been modelled. Takeoffs with one failed engine in the initial part of the takeoff run were of particular interest. The obstacle height varied from 50 to 150m and the distance to obstacles varied from 500 to 3000m.
After an unsuccessful touchdown or in situation of rejected takeoff the overrunning beyond the RWY threshold may occur. Overrunning occurs by several reasons such as overshoot at landing, blocking up the RWY by extraneous objects, RWY damage, RWY icing, etc. In such situations it is very important to estimate the possibility of emergency braking or executing an alternative maneuver e.g. go-around.
In Fig. 2 predictive coordinates of the TDP for aircrafts with different takeoff weights in function of the distance till an 185
2013 IFAC ACA September 2-6, 2013. Würzburg, Germany
Db _ cor = kcor Db
The situations on the RWY occurring during braking process are represented in figure 3.
The most powerful influences on the dynamics have thrust reverse and engine failure. After engine failure the overall thrust is restored within 3-5 seconds. Therefore, it was decided to take only the reverse level into account. So, the correction factor was toggled concurrently with the change of the reverse command. 2 if reverse=max ⎪⎧1.49kb − 3.14kb + 2.62 kcor = ⎨ 3 2 ⎪⎩−0.98kb + 3.08kb − 2.53kb + 1.82 if reverse=min
Figure 3. The various factors at landing and ground rolling. The decision whether to continue the landing in normal mode or to use the emergency braking depends on the forecasted braking distance. The prediction can be calculated from the condition of the reducing aircraft kinetic energy (or speed) to some small value ε close to zero. After touchdown the total aircraft energy varies in accordance with the law:
E(t ) = m
V (t ) 2
2
+ S ∑ Fi i
7. MODEL TESTS OF THE ALGORITHM OF THE BRAKING DISTANCE FORECASTING The main purposes of braking process modelling were • Demonstration of correction algorithm operability on a set of regular and abnormal situations, • Obtaining the estimations of forecast errors.
.
The forecasted braking distance Db _ cor of the TU-204 of maximum, nominal and minimum weights for different brake factors kb in the function of initial speed V0 are resulted in Fig. 4. The distances for intermediate values of the brake factor are easily interpolated.
Taking into account the same assumptions as above we get the formula for prediction of braking distance Db: Db = S = 0.5 (V (t ) 2 − ε 2 ) g * nx (t )
Note that forecasting the distance is based on the current measurement of acceleration which in turn reflects the resultant reaction of all applied forces including undercarriage friction. Comparing the forecasted braking distance and current aircraft position relative to the RWY threshold the warning inscription about the reserve of distance may be generated in the pilot field-of-view:
Dreserv = LRWY − x(t ) − Db 6. CORRECTION OF FORECASTING ALGORITHM
Figure 4. The braking distance forecasting at ground rolling.
The most simple and obvious forecast of the braking
It is seen, that at bad conditions of a RWY such as icing or sleet along the whole RWY the braking distance can reach 2500m. These calculations should be considered for landing planning on short RWY. Note that braking processes have been simulated at extremely low braking factor and an engine failure.
f
distance X dp is calculated being based on current energy and actuating external forces. It is obvious that all forces vary during movement process according to the AFM or under unforeseen circumstances. Therefore the forecast cannot coincide with real process and always contains an error or uncertainty. For increasing the forecast likelihood the method of forecasting algorithms correction is offered in the given work.
Introducing the forecasting algorithms into the structure of onboard information system depends primarily on the confidence of aircraft operators to the forecasting technique.
The correction was defined on the basis of statistical processing of results of model experiments. All experiments were spent with the certified model of serial liner TU-204. The set of flight conditions included the scatter of landing weight, airspeed and braking factor. The failure of one of engines was simulated by reduction of total thrust by half.
For confirmation of forecast likelihood the special researches of forecasting errors have been carried out. The averaged error of the current distance calculation with respect to the real process was accepted as the measure of the forecast likelihood. To have the possibility of comparing predictive estimations with real process the modelling of each flight was carried out twice. In the first run the real process was recorded and in the second one the predictive braking distance was calculated.
Increase of the forecast likelihood in our work is reached by introducing the scale factor Kcor in forecasting algorithm. So, the corrected braking distance is presented in a form 186
2013 IFAC ACA September 2-6, 2013. Würzburg, Germany
In Fig. 5 an example of the correction effectiveness is demonstrated. The simulated conditions were as follows: the weight=105t, the braking factor = 0.4, the initial airspeed = 210 km/h. The graphs show the forecast braking distances without correction (Db) and with correction (Db_cor). In the later case the average error (ERR) relative to the actual process is within –22÷+22m. The errors of forecast in another most unfavorable conditions did not exceed 50-70m.
Constans F.(2007) Landing assistance device and method for aircraft. FR 0605157. 21.12.2007 Erusalimskiy M.A. (2011). Analysis of a decision-making about rejection or continuation of takeoff in flight accident and incidents. Aviation Explorer, 07.11.2011. http://www.aex.ru/docs/4/2011/11/7/1447/ Glubokaya M.G. (2008). The onboard system for the decision-making support during the passenger aircraft takeoff. Technology of Air Fleet .Vol.82. №1,pp 21-30
Db_cor
Kofman V.D., Poltavetc V.A., Teimurazov R.A. (2006). The comparative analysis of safety of domestic and foreign aircrafts flights. Problems of flight safety. 2006. № 1. pp. 6-15. http://www.transafety.ru/issue/20054/articals/102.html.
ERR D_real
Kurdjukov A.P., Natchinkina G.N., Shevtchenko A.M. (1998). Energy Approach to Flight Control. AIAA Guidance Navigation and Control Conf., AIAA Paper 984211, Boston, MA.
Figure 5. The effectiveness of forecast correction. Eventually, it has been established, that the aircraft of the maximum and minimum weight with failed engine and all deployed braking devices is able to slow down from landing speed till taxing speed at the most modern airports.
Middleton D., Srivatsan R., Person L. Jr. (1994). Flight Test of Takeoff Performance Monitoring System Indicates Successful Use in Research Vehicle. Flight Safety Foundation Digest. Vol. 13 № 10.
8. CONCLUSION The methods of predicting the possibility of terminal states achieving at the takeoff and landing stages are developed. The methodological basis of these methods is the energy approach to motion control in the space. This approach has been extended to the land-based fragments of the flight trajectory. The most important property of every forecast is its likelihood. For its increasing the methods of adjusting the forecasting algorithms are proposed in the article. The model tests of the forecasting algorithms over a wide range of situations at takeoff and landing stages, including the engine failure and the presence of the closely located obstacles have been executed.
Nikiforov S.(2002).The onboard takeoff monitoring system effective means of the transport aircraft safety increase Technology of Air Fleet. Vol.76. № 3. Pavlov B.V., Shevchenko A.M., Nachinkina G.N. (2003). Energy Approach and its Usage for Flight Control System Design. Actual Problems of Aviation and Aerospace, vol.8, №2(16), pp 24-43. Pinder S.D. (2002).Aircraft Takeoff Performance Monitoring in Far-Northern Regions: An Application of the Global Positioning System. Ph.D. thesis. University of Saskatchewan.
The results of simulation have confirmed the possibility of advance warning or notifying pilot about the possibility of continuing safe takeoff or landing. Such notifications can improve the situational awareness of the pilot and, thus, reduce the probability of the erroneous actions of the crew.
Sharov V. D. (2007). The method of evaluation of runway overrun probability for aircraft on landing. Nauchnyi vestnik MGTU Grazhdanskoi Aviatcii, № 122, pp 61-66. Shevchenko A.M.(2011). Some means for informational support of airliner pilot. 5th International Scientific Conference on Physics and Control (Physcon 2011). Leon, Spain. 2011. p. 1-5. http://lib.physcon.ru/doc?id=78f90e41e746/
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Zammit-Mangion D., Eshelby M. (2002) An Operational Evaluation Of A Take-Off Performance Monitoring Algorithm. ICAS2002 Congress. http://lu.fme.vutbr.cz/icas2002/paper7105.pdf
Bove T., Andersen H.B. (2002). The effect of an advisory system on pilots' go/no-go decision during take-off. Reliability Engineering and System Safety. Vol. 75, № 2, pp 179-191.
Zavershinsky V.V. (2009) The device for prevention the aircraft overrunning beyond of the runway. RU2373115. 20.11.2009 187