Aircraft manufacturers are incorporating new advanced braking systems that are designed to minimize the amount of time that an aircraft occupies an airport runway upon landing. Minimizing runway occupancy time improves the efficiency and safety of the runways and maximizes the use of the airport's resources. To minimize an aircraft's duration of the runway usage, the aircraft must decelerate from its touchdown speed to a safe taxiing speed in the most expeditious manner. For safety and reduced wear and tear on the aircraft, it is important to have the aircraft safely brake in a controlled manner that is neither too quickly nor too slowly. In use, these systems allow a pilot to select a selected runway to land and exit the aircraft, and the braking system will decelerate the aircraft hard enough, but just hard enough, to slow the plane to taxi speed by the turnoff that leads to the selected taxiway or terminal. Once the pilot selects the appropriate runway exit during the approach to landing, the system regulates the aircraft's deceleration after touchdown. This enables the aircraft to reach any chosen exit at the correct speed under optimum conditions, no matter what the prevailing conditions are, including poor weather and visibility. A focus of these new systems is that they optimize the braking so that the aircraft gets to the taxiway intersection sooner (i.e., the aircraft does not decelerate too hard too soon, keeping speed up to minimize time spent on the runway) and also prevents overshooting of the intersection, which would then result in a relatively slow taxi to the next available turn off.
One such system is proposed in U.S. Pat. No. 9,102,404 entitled Method For Controlling The Deceleration On The Ground Of A Vehicle, the contents of which are incorporated herein by reference. In order to determine the appropriate braking force needed to precisely decelerate the vehicle, several parameters must be known. One very important consideration is the estimation of a precise distance estimate between vehicle touchdown and exit location/runway overshoot location; furthermore, the distance estimate between the aircraft's current position and the selected exit point would be continuously computed as the aircraft decelerates on the runway. Some navigational systems rely on a branch of spherical mathematics called geodesics to calculate the distances between points on or above the Earth. A common approach is that proposed by Sodano and Robinson in their paper, “Direct And Inverse Solutions Of Geodesics” U.S. Army's Technical Report No. 7. For integration of real-time, braking distance calculations into aircraft that utilize geodesics in the navigation software may require a form of this type of mathematics.
The problem with the use of geodesics to conduct distance calculations is that they require an iterative approach to arrive at a solution, which is taxing on a computational system such as a brake system controller, especially when the computations are required in real-time. In many cases, the distance calculations can overwhelm the system. What is needed is a simplified approach that preserves the necessary accuracy of the braking system runway distance estimates but can reduce the calculations to arithmetic functions rather than iterative functions.
By using a simplified aircraft brake distance estimation, calculations can be performed continuously in real-time that precisely determine and control braking to achieve the selected speed when the aircraft reaches the selected taxiway exit. Additionally, by using this simplified aircraft brake distance estimation, calculations can be used to create a warning of potential runway end excursions and/or initiate braking actions to prevent runway end excursions. These calculations can be used to create a “landing long” warning and aggressively control braking to make up for the shortened available runway distance if an airplane lands too far along the length of the runway. In keeping with this added functionality, these calculations could be used to warn if sufficient runway is not available even prior to touchdown.
The present invention is a braking system and method utilizing a simplified estimate of a distance between two locations on the earth based on spherical geometry where the distance between the two points is relatively small. A braking system utilizing the aforementioned simplified estimate is more efficient and better equipped to handle rapidly changing estimates for braking needs and variable conditions, making the braking system more robust than prior art systems. In the present invention, geodesics evaluations are replaced with a modified Haversine formula that can include a one-time computation of the cosine of latitude coordinate using, if appropriate, a truncated power series calculation.
These and other features of the present invention will best be understood with reference to the detailed description of the preferred embodiment provided below.
The present invention applies a specific braking force using the aircraft's braking system autobrake functionality. When a pilot preselects a taxiway at which the aircraft will exit the designated runway, the autobrake control manages the deceleration in manner such that the aircraft is moving at a preselected velocity as it reaches the runway exit with the minimal amount of time on the runway, within safety and protocol standards. The invention dynamically determines the brake to exit distance using a modified Haversine formula with a small angle approximation that reduces to an arithmetic calculation.
For any two points on a sphere, the Haversine of the central angle between them is given by
where hav is the Haversine function:
d is the distance between the two points (along a great circle of the sphere; see spherical distance)
r is the radius of the sphere (see
φ1, φ2: latitude of point 1 and latitude of point 2, in radians
λ1, λ2: longitude of point 1 and longitude of point 2, in radians
Solving for d, one can obtain the following formula:
This represents the distance between two points on a sphere having an radius r at the respective latitude and longitudes. Note that in relation to the size of the earth, for applications where the distances are on a runway of an airport then |φ2−φ1|<<1 and |λ2−λ1|<<1. Therefore, the preceding equation can be reduced to
If |φ2−φ1|<<1, then φ2≈φ1 and cos φ2≈cos φ1→cos φ1 cos φ2≈cos2 φ1
This leads to
d=2r sin−1√{square root over ((½(φ2−φ1)2+(cos φ1)2(λ2−λ1)2)})
Here, the term inside the sin−1 function is much smaller than 1 because (φ2−φ1)2 and (λ2−λ1)2 are individually much less than 1, and for any φ1, 0≤cos2 φ1≤1. Therefore, since for small angles, α: α≈sin α≈sin−1 α, then the equation further reduces to
d=2r(½)√{square root over ((φ2−φ1)2+(cos φ1)2(λ2−λ1)2)}
d=r√{square root over ((φ2−φ1)2+(cos φ1)2(λ2−λ1)2)}
Since cos2 φ1=½[1+cos 2 φ1], the equation can also be written as
d=√{square root over ((φ2−φ1)2+½[1+cos 2 φ1](λ2−λ1)2)}
The cosine term in this equation can be evaluated using a look-up table of values stored in a the memory of the braking system's processor, or other known approximations for the trigonometric function. Since this term is a constant throughout the braking run, it only has to be computed or looked up once at or before the beginning of the braking run.
Also, the cosine function can be written as a power series:
cos φ1=1−(½!)[φ12]+(¼!)[φ14]- . . .
Thus, another method for approximating the cosine term in the distance calculation would be to compute it to sufficient accuracy using an appropriate number of terms of this power series. Using a truncated power series approximation for the cosine term (done only once per braking run), the simplified distance equation is therefore reduced to a number of arithmetic calculations that can easily be handled dynamically by a brake control system processor.
The aircraft's navigation system provides longitude and latitude coordinates, φs and λs, as necessary to complete the calculations for the distance estimation. With the simplification described above, there are no iterative computations needed and the distance can be readily determined quickly and without undue computational processing.
To implement an autobraking system that utilizes the foregoing approximations,
While the inventor has described some of the preferred embodiments of the present invention, the invention should not be construed so as to be limited to the embodiments depicted and described herein. Rather, the scope of the invention is governed by the appended claims, without limitation to any specific embodiment or illustration.
This is a continuation based on U.S. Ser. No. 15/852,913, filed Dec. 22, 2017, which claims priority from U.S. Provisional Patent Application No. 62/439,799, filed Dec. 28, 2016, the contents of which are incorporated by reference herein in their entirety.
Number | Date | Country | |
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62439799 | Dec 2016 | US |
Number | Date | Country | |
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Parent | 15852913 | Dec 2017 | US |
Child | 17077262 | US |