Landing Distance Minimization to Prevent Overrun Accidents Using Field Theory and Stabilizing Air Traffic – A Novel Approach

Airplane is considered to be the pinnacle of engineering as it has proven that it is possible for a manmade object to fly. Before its invention, flying was just a dream for mankind. In such an esteemed domain, landing is the most challenging part and it is where a large number of accidents occur, especially due to overrun. As the name suggests, overrun accidents occur due to insufficient runway length. In the present study, the concept of planar electromagnetic fields is incorporated to minimize the landing distance of an aircraft, thus preventing the overrun accidents. As a result, unexpected losses can be avoided. In addition to this, the stability of air traffic control can be perpetuated and the fuel consumed during loitering time can be diminished.


Introduction
One of the major problems associated with aircrafts is the number of accidents due to over-run. According to the NTSB, 379 of 1332 runway accidents (1995 and 2007) were due to overruns causing 680 fatalities [1]. It is seen that 35% of the accidents have occurred due to landing overrun (LDOR), which is a serious snag [2]. There are lots of accidents that had occurred due to insufficient runway space. For an instance, Air India Express -811/812 landed 5200 ft from the beginning of Runway 24 of Mangalore International Airport in 2010. It overran, falling over a cliff and catching fire, leading to the demise of 158 lives [3]. Also, Cubana de Aviación Flight 1216 suffered an accident as a result of an overshoot on a wet runway and exiguous deceleration in 1999 [4]. All such accidents have occurred due to insufficient runway length. On the other hand, Air Traffic Control has become difficult to implement during rush hours. The number of commercial flights handled globally is 102,465 per day [5]. The traffic control has to be maintained at any cost, to avoid irregular handling of aircrafts. The aircrafts must wait till it is permitted to land during the time of which it loiters around the airspace, wasting a considerable volume of fuel. It is seen that the air traffic is continuously increasing since 2012 [6]. If this continues to exist, traffic management will be subjected to question in the future. A mutual solution to both these problems can be provided by reducing the landing distance.

Mechanics of Landing
In order to minimize the landing distance, it is essential to obtain an expression for the same. Figure 1 shows the forces associated with an airplane while landing, namely Lift (L), Drag (D), Thrust (T), Weight (W), Rolling Friction (R) [7]. The instantaneous acceleration acting in the opposite direction, is given by Newton's equations of motion [7], where µ r is the friction coefficient whose value is 0.4 for a paved runway [7]. During landing, the thrust is theoretically zero [7]. Hence, Substituting equation (2) in [7], we have Newfangled aircrafts make use of thrust reversal (T R ) during the landing ground roll, by ducting air from the jet engines and blowing it in the upstream direction, opposite to the usual downstream when normal thrust is produced [7]. This aids the deceleration and shortens the ground roll. Hence equations (2) and (3) become, (4) and, respectively. The above expression for is the minimum landing distance required by an ideal aircraft to complete its landing.

Decelerating Planar Field
It has been seen that, though the reverse thrusters have been deployed, overrun continues to occur. To decrease the landing distance, thereby reducing the air traffic and hence the accidents due to over-run, this paper proposes the solution in this section. The deceleration concept is based on Lenz's law and production of Foucault currents (loops of electrical current induced within conductors by a changing magnetic field in the conductor in planes, perpendicular to the field [8]). Superconductors (red bars) are laid below the asphalt layer (green plane) as in figure 2. The landing aircraft (grey cylinder) moves along . The wings are neglected as they are parallel to the field.

Figure 2. Flux, force and eddy current Representation
When current (I) is passed through the superconductors, the field ( is produced horizontally. The direction of is given by cork rule. By Fleming's right hand rule, these Foucault currents are produced normally. Now, according to Fleming's left hand rule, a decelerating force ( ) is generated in the opposite direction to the aircraft's movement. Such a huge amount of field can be generated by means of high temperature superconductors [9]. The charges are restricted to the surface as the aircraft body is a Faraday's cage [10].

Expression for Decelerating force ( )
The decelerating force aids the drag (D), adding up to the net opposing forces. This results in the minimization of the landing distance. If is the emf induced in a straight conductor [11], the differential form of Lorentz force is given by [12],   It is seen that the force generated is proportional to the square of the flux density (B).

Interface constraints
The superconductors produce the magnetic field (B), approximately given by [12], (8) where is ground permeability. Figure 4 shows the vector component representation of flux density as the flux travels from ground to air. is the flux density in the ground medium and is that of the air medium. and make an angle and α with the barrier, respectively. The flux density varies normally and tangentially (i.e) as and and as and . From figure 4, these are given as , , and and the resultant flux density is given by,

Figure 4. Vector representation of ground-air Barrier
From the boundary conditions [12], . Substituting the known values, From ratios of trigonometry, . Substituting the values of r, cosɸ and sinɸ, can be expressed as, Substituting the value of in equation (7), we obtain The g-force bearable by an average passenger inside an aircraft is 1.16 g [13]. But in case of fighter jets, the pilots alone are considered. They are trained to endure higher g-forces [14]. Now, equation (4) is updated as, Now the minimum landing distance equation with respect to equation (13) is, The above expression for gives the minimum landing distance in terms of F e . All the other quantities in equation (14) are fixed. By varying the value of F e , s L is varied inversely.

Results and discussions
Let us consider an Airbus A380 for analysis. Table 1 shows the values of the forces associated with landing and other data [15]. The aircraft body is usually made up of aluminium and other composites to bring about homogeneity [16]. Three cases are simulated namely the normal landing (red), planar field landing (blue) and the imprudent landing (green), as shown in figure 5. Now let us consider that an external force is generated with the help of planar field when an Airbus A380 is landing. For typical landing (red), the landing distance is 1931.8 m. The same A380 associated with planar fields (blue), takes only 1072.6 m (55.52% of typical distance). The corresponding value of F e is calculated to be 266.9 kN. The blue curve in the velocity graph shows a linear decrease which indicates a smooth landing. Taking into account the passenger comfort, the maximum reducible distance (green) is found to be 500 m from simulations. But the g-force is just below the maximum bearable limit of 1.16 as shown in figure 6. This can be implemented under absolutely emergency conditions, but not recommended for normal cases. Due to this reason, it can be referred to as imprudent landing.

Conclusion
It has been verified that, on applying the concept of planar fields, it is possible to minimize the landing distance of an aircraft. Subsequently, overrun of aircrafts can be avoided and the accidents due to it can be circumvented, with the features of typical landing. As the landing will be completed quickly, air traffic becomes easy to manage. The volume of fuel that is wasted due to loitering, can be conserved. This idea can be applied to the aircraft carrier ships having shorter runways and the places minimum a distance is inevitable. The discussed braking technique is comparatively superior, as it is applied to the whole aircraft body and the stress is distributed uniformly. Hence, this technique is safe and electrically compatible as the field is restricted to the surface. The value of the externally generated force (F e ), is limited due to the g-force bearable by humans. However, this concept can be extended to the cases where F e has no limit, which includes defense applications such as decelerating a high speed missile and hindrance to bombings.