# Calculation of radius of turn

## Presentation on theme: "Calculation of radius of turn"— Presentation transcript:

The method used to calculate turn radii are applicable to aircraft performing a constant radius turn. The material has been derived from the turn performance criteria developed for RNP 1 ATS routes and can be used in the construction of the required additional protected airspace on the inside of turns also for ATS routes other than those defined by VOR. Turn performance is dependent on two parameters ground speed and bank angle. Due to the effect of the wind component changing with the change of heading, the ground speed and hence bank angle will change during a constant radius turn. However, for turns not greater than approximately 90 degrees and for the speed values considered below, the following formula can be used to calculate the achievable constant radius of turn, where the ground speed is the sum of the true airspeed and the wind speed: Radius of turn = (Ground Speed)2 Constant ‘G’ * TAN(bank angle)

The greater the ground speed, the greater will be the required bank angle. To ensure that the turn radius is representative for all foreseeable conditions, it is necessary to consider extreme parameters. A true airspeed of km/h (550 kt) is considered probably the greatest to be encountered in the upper levels. Combined with maximum anticipated wind speeds in the medium and upper flight levels of 370 km/h (200 kt) [99.5 per cent values based on meteorological data], a maximum ground speed of km/h (750 kt) should be considered. Maximum bank angle is very much a function of individual aircraft. Aircraft with high wing loadings flying at or near their maximum flight level are highly intolerant of extreme angles Most transport aircraft are certified to fly no slower than 1.3 times their stall speed for any given configuration. Because the stall speed rises with TAN(bank angle), many operators try not to cruise below 1.4 times the stall speed to protect against gusts or turbulence. For the same reason, many transport aircraft fly at reduced maximum angles of bank in cruise conditions. Hence, it can be assumed that the highest bank angle which can be tolerated by all aircraft types is in the order of 20 degrees.

By calculation, the radius of turn of an aircraft flying at km/h (750 kt) ground speed, with a bank angle of 20 degrees, is NM (41.69 km). For purposes of expediency, this has been reduced to 22.5 NM (41.6 km). Following the same logic for the lower airspace, it is considered that up to FL 200 (6 100 m) the maximum figures to be encountered are a true airspeed of 740 km/h (400 kt), with a tailwind of 370 km/h (200 kt). Keeping the maximum bank angle of 20 degrees, and following the same formula, the turn would be defined along a radius of NM (26.76 km). For expediency, this figure may be rounded up to 15 NM (27.8 km). Given the above, the most logical break point between the two ground speed conditions is between FL 190 (5 800 m) and FL 200 (6 100 m). In order to encompass the range of turn anticipation algorithms used in current flight management systems (FMS) under all foreseeable conditions, the turn radius at FL 200 and above should be defined as 22.5 NM (41.6 km) and at FL 190 and below as 15 NM (27.8 km).

The Special Committee on Future Air Navigation Systems (FANS) identified that the method most commonly used over the years to indicate required navigation capability was to prescribe mandatory carriage of certain equipment. The committee developed the concept of required navigation performance capability (RNPC). FANS defined RNPC as a parameter describing lateral deviations from assigned or selected track as well as along track position fixing accuracy on the basis of an appropriate containment level The RNPC concept was approved by the ICAO Council and was assigned to the Review of the General Concept of Separation Panel (RGCSP) for further elaboration. The RGCSP, in 1990, noting that capability and performance were distinctively different and that airspace planning is dependent on measured performance rather than designed-in capability, changed RNPC to required navigation performance (RNP).

The RGCSP then developed the concept of RNP further by expanding it to be a statement of the navigation performance necessary for operation within a defined airspace. System use accuracy is based on the combination of the navigation sensor error, airborne receiver error, display error and flight technical error. This combination is also known as navigation performance accuracy The RNP types specify the navigation performance accuracy of all the user and navigation system combinations within an airspace. RNP types can be used by airspace planners to determine airspace utilization potential and as an input in defining route widths and traffic separation requirements, although RNP by itself is not sufficient basis for setting a separation standard.

RNP as a concept applies to navigation performance within an airspace and therefore affects both the airspace and the aircraft. RNP is intended to characterize an airspace through a statement of the navigation performance accuracy (RNP type) to be achieved within the airspace. The RNP type is based on a navigation performance accuracy value that is expected to be achieved at least 95 per cent of the time by the population of aircraft operating within the airspace.

The application of RNAV techniques in various parts of the world has already been shown to provide a number of advantages over more conventional forms of navigation and to provide a number of benefits, including: a) establishment of more direct routes permitting a reduction in flight distances; b) establishment of dual or parallel routes to accommodate a greater flow of en-route traffic; c) establishment of bypass routes for aircraft over flying high-density terminal areas; d) establishment of alternatives or contingency routes on either a planned or an ad hoc basis; e) establishment of optimum locations for holding patterns; and f) reduction in the number of ground navigation facilities.

RNP may be specified for a route, a number of
Defining RNP airspace RNP may be specified for a route, a number of routes, an area, volume of airspace or any airspace of defined dimensions that an airspace planner or authority chooses. Potential applications of RNP include:* a) a defined airspace, such as North Atlantic minimum navigation performance specifications (MNPS) airspace; b) a fixed ATS route, such as between Sydney, Australia and Auckland, New Zealand; c) random track operations, such as between Hawaiiand Japan; and d) a volume of airspace, such as a block altitude on a specified route.

North Atlantic regional planning body established under the auspices of the International Civil Aviation Organisation (ICAO). This Group is responsible for developing the required operational procedures; specifying the necessary services and facilities and; defining the aircraft and operator approval standards employed in the NAT Region. NORTH ATLANTIC MINIMUM NAVIGATION PERFORMANCE SPECIFICATIONS AIRSPACE The vertical dimension of MNPS Airspace is between FL285 and FL420 (i.e. in terms of normally used cruising levels, from FL290 to FL410 inclusive). The lateral dimensions include the following Control Areas (CTAs): REYKJAVIK, SHANWICK, GANDER and SANTA MARIA OCEANIC plus the portion of NEW YORK OCEANIC which is North of 27°N but excluding the area which is west of 60°W & south of 38°30'N

In the MNPS Airspace an aircraft must be equipped with the following:
a) two fully serviceable Long Range Navigation Systems (LRNSs). A LRNS may be one of following • one Inertial Navigation System (INS); • one Global Navigation Satellite System (GNSS); or • one navigation system using the inputs from one or more Inertial Reference System (IRS) or any other sensor system complying with the MNPS requirement. Note 1: Currently the only GNSS system fully operational and for which approval material is available, is GPS. b) each LRNS must be capable of providing to the flight crew a continuous indication of the aircraft position relative to desired track. c) it is highly desirable that the navigation system employed for the provision of steering guidance is capable of being coupled to the autopilot.

PERFORMANCE MONITORING
The horizontal (i.e. latitudinal and longitudinal) and vertical navigation performance of operators within NAT MNPS Airspace is monitored on a continual basis. If a deviation is identified, follow-up action after flight is taken, both with the operator and the State of Registry of the aircraft involved, to establish the cause of the deviation and to confirm the approval of the flight to operate in NAT MNPS and/or RVSM Airspace.

The Organised Track System (OTS
As a result of passenger demand, time zone differences and airport noise restrictions, much of the North Atlantic (NAT) air traffic contributes to two major alternating flows: a westbound flow departing Europe in the morning, and an eastbound flow departing North America in the evening. The effect of these flows is to concentrate most of the traffic unidirectionally, with peak westbound traffic crossing the 30W longitude between 1130 UTC and 1900 UTC and peak eastbound traffic crossing the 30W longitude between 0100 UTC and 0800 UTC.

Due to the energetic nature of the NAT weather patterns, including the presence of jet streams, consecutive eastbound and westbound minimum time tracks are seldom identical. The creation of a different organised track system is therefore necessary for each of the major flows. Separate organised track structures are published each day for eastbound and westbound flows. These track structures are refered to as the Organised Track System or OTS. It should be appreciated, however, that use of OTS tracks is not mandatory. Currently about half of NAT flights utilise the OTS. Aircraft may fly on random routes which remain clear of the OTS or may fly on any route that joins or leaves an outer track of the OTS. There is also nothing to prevent an operator from planning a route which crosses the OTS. However, in this case, operators must be aware that whilst ATC will make every effort to clear random traffic across the OTS at published levels, re-routes or significant changes in flight level from those planned are very likely to be necessary during most of the OTS traffic periods

Applying RNP in an airspace
Ideally, airspace should have a single RNP type; however, RNP types may be mixed within a given airspace. An example would be a more stringent RNP type (DMEDME) being applied to a specific route in a very high frequency (VHF) omni directional radio range (VOR)/DME airspace or a less stringent RNP type applied to a specific airspace. RNP can apply from take-off to landing with the different phases of flight requiring different RNP types. As an example, an RNP type for take-off and landing may be very stringent whereas the RNP type for en-route may be less demanding

Relation of RNP to separation minima
RNP is a navigation requirement and is only one factor to be used in the determination of required separation minima. RNP alone cannot and should not imply or express any separation standard or minima. Before any State makes a decision to establish route spacing and aircraft separation minima, the State must also consider the airspace infrastructure which includes Surveillance and communications. In addition, the State must take into account other parameters such as intervention capability, capacity, airspace structure and occupancy or passing frequency

RNP is a fundamental parameter in the determination of safe separation standards.
The risk of collision is a function of navigation performance, aircraft exposure, and the airspace system’s ability to intervene to prevent a collision or maintain an acceptable level of navigation performance. An increase in traffic in a particular airspace can result in airspace planners considering a change in airspace utilization (e.g. separation minima,route configuration) while maintaining an acceptable level of risk. In collision risk analysis, this acceptable level of risk is referred to as the target level of safety (TLS)

Airspace characteristics that affect separation standards
EXPOSURE Intervention NAVIGATION Route Configuration ATC Traffic Density Surveillance Communication Risk Collision=F(navigation+route Configuration+survelliance+communication+ATC)

AIRCRAFT PERFORMANCE The concept of RNP is based on the expected navigation performance accuracy of the population of aircraft using the airspace. This in turn places demands on individual aircraft, manufacturers of aircraft and aircraft operators to achieve the navigation performance required for a specific RNP type airspace on each flight. The RNP concept may also require different aircraft functional capabilities in different types of RNP airspaces. As an example, an RNP airspace with a high accuracy requirement may have functional requirements for parallel offset capability, whereas a less accurate RNP airspace may only require point-to-point navigation capability

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