Flight Path Characteristics ===================================== .. sectionauthor:: Luke Frisken .. contents:: Table of Contents :depth: 3 Standard Rate Turn ---------------------- According to the FAA Aeronautical Information Manual :cite:`AIM2015`, a standard rate turn is defined as: A turn of three degrees per second From this information, and the airspeed of the aircraft, a number of parameters can be derived for an aircraft undergoing a turn as descussed by Luiz Monteiro :cite:`Monteiro`. As a side node, the following parameters ignore slip, and are therefore at least marginally inaccurate. Turn Radius ^^^^^^^^^^^^^^^^^^^^ :math:`v = Velocity` :math:`\omega = AngularVelocity` :math:`r = TurnRadius` :math:`r = \frac{v}{\omega}` For a standard rate turn, the Angular Velocity is: :math:`\omega = \frac{d\phi}{dt} = \frac{3^{\circ} \times \frac{\pi}{180^{\circ}}}{1}` :math:`\omega = \frac{\pi}{60}` Therefore the turn radius for a standard rate turn would be: :math:`r = \frac{v * 60}{\pi}` Bank Angle ^^^^^^^^^^^^^^^^^^^^ :math:`\alpha = tan^{-1}(\frac{v^2}{g \times r})` :cite:`Monteiro` Holding Patterns ------------------------ Holding patterns are planned flight paths involving a series of turns which are designed to keep an aircraft at a certain location. Some Example Situations from AIM: .. figure:: Holding_Pattern_1.png :align: center Holding Patterns :cite:`AIM2015` .. figure:: Holding_Pattern_2.png :align: center Holding Pattern Terms :cite:`AIM2015` Below 14,000 feet, both the inbound and outbound legs are supposed to take 1 minute. Above 14,000 feet this increases to 1.5 minutes. :cite:`AIM2015` Turns during a holding pattern are typically at a standard rate and have a maximum bank angle of 30 degrees. :cite:`AIM2015` Pattern Entry ^^^^^^^^^^^^^^^^^^^^ The choice of entry procedure into a holding pattern is determined by the relative aproach direction to the direction of the hold. .. figure:: Holding_Pattern_4.png :align: center Entry Procedures :cite:`HoldingWikipedia` .. figure:: Holding_Pattern_3.png :align: center Entry Procedures :cite:`AIM2015` Adhering to Airways or Routes ------------------------------ The FAA is expecting pilots to take actions necessary to remain within route boundary. This could take the form of leading turns. :cite:`AIM2015` .. figure:: Adhering_To_Routes.png :align: center Adhering to Airways or Routes :cite:`AIM2015` Bibliography ------------------------- .. bibliography:: /references/SoftwareFinalYear.bib :style: unsrtalpha :filter: docname in docnames