On Runway Capacity and Wake Vortex Safe Separation Distance (SSD)

On Runway Capacity and Wake Vortex Safe Separation Distance (SSD) L.M.B.C. Capos CCTAE (Center for Aeronautical and Space Science and Tecnology), Instituto Superior Tecnico, Lisbon Technnical University. Av. Rovisco Pais, 049-00 Lisboa, Portugal. luis.capos@istl.utl.pt J.M.G. Marques Universidade Lusófona de Huanidades e Tecnologias (ULHT), Capo Grande, Lisboa, Portugal, and CCTAE. jgarques@ulusofona.pt Abstract The capacity of ATM is liited by the runway availability at airports. The nuber of take-off and landings fro the sae runway is liited by wake vortex separation distances. Currently the safe separation distances (SSD) are established by epirical rules using as sole criterion the classification of the leading and following aircraft into three weight categories light, ediu and heavy. The Boeing B757 has been the subject of an exception to the rules increasing the separation distance on the basis of flight incidents; the Airbus A380 has been subject of an extended separation distance for super heavy aircraft as a safety precaution. The purpose of the present paper is to obtain a forula for wake vortex separation distances that involves a nuber of assuptions and siplifications, but does include ore paraeters rather than just the weight of the leading and following aircraft. The predicted SSD for pairs of typical light (Citation 500), ediu (B737-300) and heavy (B747-400) aircraft are coparable to the ICAO iniu separation rules, suggesting that the latter are oderately conservative on the safe side. The special case of B757-00 is considered justifying the increased separation. In the case of A380-00, the special ultra-heavy rules appear to be excessively conservative highlighting the need for a ore scientific approach to the subject, especially in cases where a long experience fro the past is not available. Keywords- capacity, separation, safety, wake hazard. I. INTRODUCTION The ICAO rules on iniu separation distances between aircraft at take-off and landing deterine the capacity of runways, airports and the whole terinal area air traffic. These epirical rules have proved to be generally safe in a long past experience and should not be changed lightly. However the lack of a scientific basis begs soe questions: Are current separations rules too conservative, unnecessarily liiting capacity? Is there any reliable way a saller separation could be introduced without reducing safety? Not too uch can be expect fro epirical rules using as sole criterion three weight categories for the leading and following aircraft. This begs another set of questions: What other paraeters besides weight affect the safe separation distance (SSD)? Can we have soe idea of whether current SSD are either (a) too conservative or (h) safe without excessive argin? Two particular aircraft highlight the issues with current separation rules: After several incidents the separation distance for the B757 has been increased beyond its weight category ; On the A380, the first super-heavy aircraft, have been iposed uch larger separation distance than for a heavy B747, apparently ore as a safety precaution than on the basis of clear knowledge due to the lack of precedent. The present paper does not clai to provide definitive answers to any of these questions, but rather to introduce a ore scientific approach that can be copared with epirical separation rules. The ethod adopted derives an analytical forula for the SSD that shows ore clearly the paraeters influencing the result than the nuerical approaches in the literature [-7]. A siple analytical forula for the SSD between aircraft is obtained in three steps with soe approxiations. First, the wake of a aircraft and its evolution in the atosphere, in the presence of wind, shear and ground effects is a coplex fluid phenoenon [8]. Rather than use CFD with turbulence odels [9], in order to arrive at a siple forula for the SSD, the wake vortex strength of the leading aircraft is assued to decay [0] according to a diffusion equation with convection (step : section II). The worst case scenario is considered (step : section III) where the following aircraft flies straight into the axis of the vortex syste of the leading aircraft, so that the induced rolling oent is axiu. It is assued (step 3: section IV) that only a fraction f of the axiu roll control power of the following aircraft is used to counter the rolling oent induced by the wake of the leading aircraft. This leads to a forula for the SSD separation distance that has two solutions (section V), naely an unsafe close distance and a safer larger distance. The latter is found to agree broadly with the ICAO separation rules, that are found to be oderately conservative for typical aircraft pairs in the light, ediu and heavy categories. The special case of larger separation distance for the B757 is also explained (section VI), whereas in the case of the A380 as sole representative of the new Third SESAR Innovation Days, 6 th 8 th Noveber 03

superheavy class the extra separation distance relative to the heavy class appears excessive. In conclusion (section VII) a siple forula has been obtained for the SSD due to wake vortex effects, that takes into account ore than just the weight of the leading and following aircraft, and ay represent a sall step forward in a scientific approach to the subject. II. DECAY OF WAKE VORTEX STRENGTH WITH DISTANCE The wake vortex syste of the leading aircraft is represented in the siplest possible for by the vortex circulation strength [] of the wing of the leading aircraft (index ): cw r U S where W is the weight, r c the root chord, the air density, S the wing area and U the airspeed. Note that the wake vortex strength is proportional to the wing loading W S of the leading aircraft. The wake vortex decays in the atosphere due to turbulent diffusion as it is convected by abient flows. The siplest representation is an equation for the vorticity : Substituting (4), (5) and () in (3) specifies the vorticity as a function of position behind the leading aircraft: x cw r b U exp. Sx 800 x The vorticity (Figure ) initially increases in the wake of the leading aircraft, goes though a peak at a distance x : Wc r x eu a b U a,b 800 and then decays. This specifies the wake encountered by the following aircraft, and the rolling oent it induces (section III). w y z x. t z x y including [] diffusion by a turbulent viscosity and convection by downwash velocity w of the leading aircraft. The vorticity is generated by the wake vortex strength () of the leading aircraft, and t is tie and x is the longitudinal coordinate in the direction of the flight path, and yz, transverse Cartesian coordinates. The forced solution of () specifies the evolution of the vorticity as a function of tie and position: b z t, x, y, z exp. t z / w t z / w This forula is siplifies further assuing that: (i) the transverse coordinate is the core radius a related to the span b of the leading aircraft: / y z a b / 0 (ii) the downwash velocity is sall relative to the airspeed of the leading aircraft: zu / w x U t Figure. The vorticity in the wake of an aircraft initially increases with distance fro the trailing edge of wing tip and ultiately decays due to vortex breakdown, erging and turbulent diffusion, iplying that it has a axiu at interediate distance. III. EFFECT OF THE WAKE OF THE LEADING ON THE FOLLOWING AIRCRAFT The worst case scenario is considered in which following aircraft flies straight into the axis of the vortex wake of the following aircraft thus being subject to a vertical velocity: w x, y y yr r x y y x, where r, are the vorticities of the right and left wing tip vorticities of the leading aircraft, whose axis are respectively at positions y r and y. The vertical velocity (8) has a constant ter that does not affect the rolling oent, and a ter proportional to the spanwise coordinate w x y y x, involving the difference of vorticities due to the right- and leftwing vortices: Third SESAR Innovation Days, 6 th 8 th Noveber 03

3 x x x, r that is given by the wake (6) of the leading aircraft.. where c is the ean geoetric chord and h a diensionless paraeter: b/ h y c ydy, 3 cb b/ specified by the shape of the wing. It is unity h for rectangular wing c. The rolling oent on the c y following aircraft is proportional to: (i) the vorticity induced by the leading aircraft; (ii) the airspeed U and wing area S c b of the following aircraft; (iii) the span of the following aircraft appears to the square b (or cube b 3 including S ) because an aircraft with larger span catches ore of the vortex further outboard contributing ore to the rolling oent. IV. INDUCED ROLLING MOMENT VERSUS CONTROL POWER The rolling oent induced by the wake of the leading on the following aircraft ust be copensated by the available control power of the following aircraft that is given by: R a CA ax U Saba, Figure. The worst case scenario of a wake vortex encounter is when the following aircraft flies straight into the axis of the vortex wake of the leading aircraft catching the two wing tip vortices. The difference of vorticities induces a vertical velocity upward on one wing and downward on the other wing causing to a rolling oent. The lift on a section of the wing of the following aircraft is given [3] by: where y c yu U y c y is the chord, U is the airspeed, the sall angle-of-attack in the first ter; the vorticity in the second ter is positive 0increases lift on the port wing and decreases lift on the starboard wing seen fro the front in the Figure causing a rolling oent: R b/ b/ y l y dy, where b is the span of the following aircraft. If the aircraft has a syetrical wing (all current airlines do), only the second ter of () contributes to the rolling oent induced on the following aircraft by the wake of the leading aircraft: 3 R x hu c b x. where CA ax is the axiu lift coefficient of the ailerons, Sa their area and ba the oent ar. The following aircraft should keep a safety argin by using only a fraction 0 f of the axiu roll control power to copensate the rolling oent induced by the leading aircraft: a R f R x. Substituting the induced (3) and control (5) rolling oents in (6) specifies f h S b S b C U b 6 / / / /, a a Aax as the axiu wake vorticity of the leading aircraft that the following aircraft can cope with. The axiu wake vorticity fro the leading aircraft that the following aircraft can copensate (7) is: (i) proportional to the fraction of the axiu available roll control power that is used; (ii) proportional to the roll control effectiveness defined as the product of the ratios of the aileron to wing area and aileron oent ar to wing span: b S / b S a a because the wing is affected by the wake vortex and the aileron counter this effect; (iii) proportional to the axiu lift coefficient of the ailerons, that deterine the axiu Third SESAR Innovation Days, 6 th 8 th Noveber 03

4 available roll control power. Substituting the weight of the following aircraft: W 0.5CL S U in the axiu vorticity (7) that can be copensated: f Sa ba CAax W / S h S b C b U L it follows that it is: (i) proportional to the ratio of aileron to wing lift coefficients, because the wing reacts to the wake vortex and the aileron opposes it; (ii) proportional to the wing loading, so that a higher wing loading opposes a stronger vorticity; (iv) inversely proportional to air density, airspeed and wing span, that is larger values lead to saller vorticity that can be countered. Figure 3. The following aircraft can copensate with aileron deflection the rolling oent induced by the wake of the leading aircraft (Figure ) at two positions with equal vorticity (Figure ). The closest position is unsafe because increasing the separation leads to a larger rolling oent. The farthest position is the safe separation distance such that as increase in separation reduces the rolling oent. V. FORMULA FOR THE SAFE SEPARATION DISTANCE The wake vorticity (6) depends on the distance behind the leading aircraft (Figure ). For a given following aircraft (Figure ) the induced wake rolling oent (3) and the roll control oent (5) balance when (0) is a equality: cw b U S b C exp S x 00 x h S b C b U r 4 f a a A ax W / S L forward position the following aircraft has only one option: keep distance or coe closer to the leading aircraft. The second root of () corresponds to the region of decaying vorticity after the peak vorticity xii x that is safe: if the wake vorticity of the leading aircraft is too strong the following aircraft should increase the separation distance until the available roll control power is sufficient. If the second root of () satisfies (a) b U 00 x II : x II cr b U h Sb W / S CL a,b 4 f S b W / S C S a a Aax the exponential in () is approxiately unity and the safe separation distance (SSD) is given by (b). The forula (b) for the SSD shows that it increases if: (i) the leading aircraft has a higher wing loading, because it causes a stronger vortex wake; (ii) the following aircraft has a lower wing loading because it is ore susceptible to the wake of the leading aircraft; (iii) for saller aileron area and oent ar that reduces the roll control power; (iv) larger wing area of the following aircraft that catches ore of the wake vortex; (v) larger wing span of the following aircraft to the square because it catches ore of wake vortex further outboard; (vi) larger root chord of the leading aircraft that increases the wake vortex strength; (vii) larger airspeed of the following aircraft that increases the rolling oent induced by the wake of the leading aircraft; (viii) larger ratio of wing to the aileron lift coefficient of the following aircraft; (ix) saller fraction of the axiu available roll control power used; (x) saller turbulent diffusivity iplying that the wake vortex decays ore slowly with tie and distance; (xi) larger wing geoetry paraeter (4), e.g. an unswept wing h is ore affected than a delta wing h / because it has ore outboard area affected by the wake vortex. TABLE I. AIRCRAFT WEIGHT CLASSIFICATION ICAO classification Exaple chosen Designation Weight W Aircraft Maxiu Landing weight W (kg) Heavy (h) W > 36 t Boeing 747-400 W =396 893 Mediu () 7 t < W < 36 t Boeing 737-700 W =70 080 Light (l) W< 7 t Cessna Citation 55 W =5 375 Equation () has two roots (Figure 3). The first root corresponds to the following aircraft close to the leading aircraft in the region of increasing vorticity before the peak x I. This is an unsafe position because if the following aircraft loses power or falls behind for any reason x xi the vorticity increases beyond the available roll control power; in the unsafe Third SESAR Innovation Days, 6 th 8 th Noveber 03

5 TABLE II. AIRCRAFT DATA Index h-heavy l s v Boeing Cessna Boeing 737- Citatio 757-300 n 500 00 Sybol Unit Boeing 747-400 Airbus 380-00 W kg 60360 58060 4400 8980 38000 S 54.6 5.00.30 85.5 90* b 64.44 34.3 4.6 38.05 79.80 c t.50*.00* 0.80*.47* 3.87* S a 0.90.00* 0.30* 4.46 40.00* b a 3.00*.00* 5.00*.00* 34.00* V s s - 60.7 5.5 4. 54.3 53.8* c 8.40 3.64.56 4.87.53 c r 5.30 6.8.33 8.7 9.6 h - 0.65 0.596 0.756 0.65 0.668 0 s - 707 330 63.5 430 859 w s -. 0.98 0.454.5 0.77 a 3..7 0.7.90 3.99 U s - 78.9 66.9 54.9 70.6 70.0* W/S kg.- 48 464 97 484 44 W/(Sb) kg.- 3 7.46 3.54 3.84.74 5.9 bs/b as a - 7.5 95 44 54 3 s - 409 99 39.5 80 557 x 46 0300 4.5 33 580 x / b * - estiated - 6.60 3.00.0 3.49 7.7 VI. COMPARISON OF THE THEORETICAL SSD WITH EMPIRICAL SEPARATION RULES The forula (b) for the safe separation distance is applied to three aircraft typical (Table I) of the light, ediu and heavy categories, respectively the Cessna Citation 500, the Boeing 737-300 and Boeing 747-400. The data used for these aircraft appears in the Table II. The forula (b) for the SSD involves an unknown paraeter naely the diffusivity of the atosphere. Its value was deterined 0.96 s - by fitting the SSD of two heavy aircraft to the ICAO value xhh 4 n, that is therefore exact in the Table III. The faction of the axiu available roll control power used CAax f f C L is indicated at the botto of the Table III. There are no other free paraeters in the coparison of the theoretical SSD with the ICAO separation rules in the Table III. The calculated SSD is always less than the ICAO rule by a sall aount, suggesting that the iniu separation distances used are safe without being too conservative. Only in the case of ediu leading and following aircraft is the ICAO separation slightly less than the prediction. This leads to the case of the B757 that is treated as special because it has larger separation distance than other ediu aircraft (Table IV). The calculated SSD for the special aircraft is again lower and close to the FAA separation rules, suggesting that they are safe without being too conservative. The reason why the special B757 aircraft has stronger wake effects than other ediu aircraft is explained by the forula (b) for the SSD taking into account A the data for the Boeing 757-00 in the Table II: (i) the special aircraft has a roll control authority (8) interediate between that of the uch larger aircraft and that of a ediu aircraft; (ii) the volue loading defined as the ration of the weight to the product of wing area by span: W W bs bc for the special aircraft is coparable to that of ediu and light aircraft, and uch higher than for the heavy aircraft; (iii) the special aircraft has an approach speed interediate between those of the ediu and heavy aircraft; (iv) the downwash velocity of the special aircraft is larger than for the ediu aircraft, and exceeds slightly that of the heavy aircraft, which indicates a strong wake. Although none of the effects (i) to (iii) is draatic in isolation, they all add in the sae direction, of giving the special aircraft a stronger wake than its weight category would suggest as confired by its downwash velocity higher than all the others. This is also shown by a peak vorticity x 33 behind the aircraft, which in ters of wing spans x / b 3.49 is interediate between ediu and heavy aircraft, in Table II. TABLE III. SAFE SEPARARTION DISTANCES IN NAUTICAL MILES ICAO RULES (CALCULATED VALUES IN BRACKETS) Leading a/c a/c Following h Heavy (B 747-400) Mediu (B 737-00) l (Citation 500) h Heavy (B 747-400) xh xhh 4 ( xh xhh 4 ) xh 5 ( xh 4.87 ) xh 6 Mediu (B 737-300) xh 3 ( xh.66 ) x x 3 ( x x 3.4 ) x 4 l Light (Citation 500) x h 3 ( x h.08 ) x 3 ( x.54 ) x x 3 ( xh 5.40 ) ( x 3.55 ) x x f 0.5 0.3 0.06 TABLE IV. CALCULATED (B) SEPARATION DISTANCES Following aircraft Special B757-00 Leading aircraft Ultra-heavy A380-00 (.8 ) Identical xss 4.00 xss 4.00 xvv.47 xhh 4.00 Heavy (> 5t) xsh 3.63 xsh 4.00 xvh 3.3 xhh 4.00 Large (8.6 t< W< 5t) xs 4.44 xs 5.00 xv 4.9 xh 5.00 Light (<8.6t) xs 4.9 xs 6.00 xv 4.49 xh 6.00 f 0.3 0.5 Third SESAR Innovation Days, 6 th 8 th Noveber 03

6 For the ultra heavy aircraft A380-00 the peak vorticity is even farther x 580 or x / b 7.7 wing spans than for the special and heavy aircraft; copared with the heavy aircraft, the ultra-heavy has a peak vorticity at a larger absolute distance, and larger relative distance in ters of wing spans. The sae Table II suggests that the very large aircraft ight not have special wake separation probles, starting with a roll control power higher than that of the heavy aircraft; the volue loading is lower than for a heavy aircraft and uch lower than the special aircraft. In addition, the downwash velocity is uch lower for the ultra-heavy than for the heavy and special aircraft; in fact the downwash velocity of the ultra-heavy is interediate between the ediu and light aircraft, which is a rearkable result, considering the size difference. Thus the ultra-heavy aircraft ay require a separation distance not uch larger than the heavy aircraft (Table IV). The ICAO and FAA rules for the iniu separation distance take into account only the weight of the leading and following aircraft. The forula (b) for the safe separation distance shows that a ore relevant paraeter is the ratio of wing loadings: W/ S W / S The wing loading of the ultra-heavy aircraft (Table II) is lower than that of the heavy aircraft, that is coparable with the special aircraft. The forula (b) for the SSD also involves other paraeters like the roll control effectiveness that can vary significantly between aircraft. REFERENCES [] Stuever, R. A. & Greene, G. C. 994 An analysis of relative wakevortex hazards for typical transport aircraft, AIAA-94-080, NASA Lagley Research Center, Hapton, AIAA 3th Aerospace Sciences Meeting, Reno, Nevada. [] Landau, L.D. & Lifshitz, E.M. 956 Fluid Mechanics. Pergaon Press. [3] Capos, L.M.B.C. 00 Coplex Analysis with Applications to Flows and Fields, CRC Press. [4] Perry, R. R., Hinton, D. A. & Stuever, R. A. 996 NASA wake vortex research for aircraft spacing, AIAA paper. [5] Hinton, D. A. 996 An Aircraft Vortex Spacing Syste (AVOSS) for dynaical wake vortex spacing criteria, 78th Fluid Mechanics Panel & Syposiu on the Characterization and odification of wakes fro lifting vehicles in fluids, Trondhei, Norway. [6] Hinton, D. A., Charnock, J. K., Bagwell, D. R. & Grigsby, D. 999 NASA Aircraft Vortex Spacing Syste Developent Status, AIAA 37th Aerospace Sciences Meeting, Reno, Nevada. [7] Shen, S., Ding, F., Han, J., Lin, Y-L., Arya, S.P. & Proctor, F.H. 999 Nuerical odeling studies of wake vortices: real case siulations, AIAA Paper 99-0755, 37th Aerospace Sciences Meeting, Reno, Nevada. [8] Rossow, V.J. 999 Lift-generated vortex wakes of subsonic transport aircraft, Progress in Aerospace Sciences 35, 507-600. [9] Spalart, P. R. 009 Detached-Eddy Siulation, Annual Review of Fluid Mechanics 4, 8-0. [0] Ginevsky, A.S. & Zhelannikov, A. I. 009 Vortex wakes of aircrafts. Springer. [] Capos, L.M.B.C. & Marques, J.M.G. 004 On wake vortex response for all cobinations of five classes of aircraft, Aeronautical Journal 08, 95-30. [] Capos, L.M.B.C. & Marques, J.M.G. 00 On aircraft response and control during a wake encounter. In Progress in Industrial Matheatics at ECMI 008, ed. Fitt, A.D.; Norbury, J.; Ockendon, H.; Wilson, E., 747-75. ISBN: 978-3-64-09-8. London: Springer-Verlag. VII. CONCLUSION In the cases of the light, ediu, heavy and special aircraft for which there is a very substantial experience the theoretical forula for the SSD gives results broadly in agreeent with the epirical iniu separation rules, suggesting that the latter are safe without being too conservative, or unnecessarily liiting capacity at airports. In contrast the ultraheavy aircraft ay be penalized with excessive separation distances as a safety precaution against an unprecedented case without the benefit of long experience. The analytical forula does provide useful indications of what paraeters have the greatest effect on the SSD. The objective of deriving an analytical forula for the SSD has iplied a nuber of siplifications; the final result also involves two paraeters naely the diffusivity that depends on atospheric conditions and the fraction of axiu roll control power used that is a pilot choice. The evolution of a vortex wake does depend on atospheric and ground conditions, and thus epirical of theoretical separations are only a guide. The ethods used to calculate the SSD can be extended [] to the response of an aircraft to a wake vortex encounter, including the effect of controls and aerodynaic daping []. Third SESAR Innovation Days, 6 th 8 th Noveber 03