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The top of descent is usually calculated by an on-board flight management system, and is designed to provide the most economical descent to approach altitude, or to meet some other objective (fastest descent, greatest range, etc.). The top of descent may be calculated manually as long as distance, air speed, and current altitude are known. This ...
In aviation, the rule of three or "3:1 rule of descent" is a rule of thumb that 3 nautical miles (5.6 km) of travel should be allowed for every 1,000 feet (300 m) of descent. [1] [2] For example, a descent from flight level 350 would require approximately 35x3=105 nautical miles. This would have to be adjusted for headwind or tailwind, [1] and ...
So, for example, if a route is 20 kilometres (12 mi) with 1600 metres of climb (as is the case on leg 1 of the Bob Graham Round, Keswick to Threlkeld), the equivalent flat distance of this route is 20+(1.6×8)=32.8 kilometres (20.4 mi). Assuming an individual can maintain a speed on the flat of 5 km/h, the route will take 6 hours and 34 minutes.
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...
The top of climb may be calculated manually with considerable effort. [ 1 ] Alternatively, when manual planning and monitoring a VFR flight, TOC is an elegant and efficient way for a pilot to eliminate all the vaguery and variability of departing any airport (the turns assigned, changes of runway the pilot cannot control).
In optimization, a descent direction is a vector that points towards a local minimum of an objective function :.. Computing by an iterative method, such as line search defines a descent direction at the th iterate to be any such that , <, where , denotes the inner product.
However, Newton's method fails to converge on problems that have non-differentiable kinks. In recent years, some interior-point methods have been suggested for convex minimization problems, but subgradient projection methods and related bundle methods of descent remain competitive. For convex minimization problems with very large number of ...
The adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. [1] It has applications in geophysics, seismic imaging, photonics and more recently in neural networks. [2] The adjoint state space is chosen to simplify the physical interpretation of equation ...
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