ETSO-C117b

AIRBORNE WIND SHEAR WARNING AND ESCAPE GUIDANCE SYSTEMS (REACTIVE TYPE) FOR TRANSPORT AEROPLANES

1 Applicability

This ETSO provides the requirements that airborne wind shear warning and escape guidance systems (reactive type) for transport aeroplanes that are designed and manufactured on or after the date of this ETSO, must meet in order to be identified with the applicable ETSO marking. It is not applicable to systems that look ahead to sense wind shear conditions before the phenomenon is encountered, nor to systems that use atmospheric and/or other data to predict the likelihood of a wind shear alert.

Appendix 1 to this ETSO describes the MPS for the airborne wind shear warning and escape guidance systems for transport category aeroplanes.

Appendix 2 to this ETSO describes the wind field models used to evaluate the performance of a wind shear warning and escape guidance system.

Appendix 3 to this ETSO describes the conversion of the velocity equations in Appendix 2 to rectangular coordinates.

Appendix 4 to this ETSO contains data that defines the Dryden turbulence model and the discrete gust model used in conducting the required wind shear alert tests.

Appendix 5 to this ETSO describes shear intensity.

Appendix 6 to this ETSO provides a sample computer listing for a simplified aeroplane simulation model for evaluating the effectiveness of various guidance schemes.

2 Procedures

- 2.1 General

The applicable procedures are detailed in CS-ETSO, Subpart A

- 2.2 Specific

None.

3 Technical Conditions

3.1 General

- 3.1.1 Minimum Performance Standard

The applicable standards are provided in the attached Appendix 1.

- 3.1.2 Environmental Standard

See CS-ETSO, Subpart A, paragraph 2.1

- 3.1.3 Computer Software

See CS-ETSO, Subpart A, paragraph 2.2.

- 3.1.4 Airborne Electronic Hardware

See CS-ETSO, Subpart A, paragraph 2.3.

- 3.2 Specific

- 3.2.1 Failure Condition Classification

See CS-ETSO, Subpart A, paragraph 2.4.

A failure of the function defined in 3.1.1 above that results in an unannunciated malfunction or a missed wind shear detection is a major failure condition.

A loss of the function defined in 3.1.1 above is a minor failure condition.

4 Marking

- 4.1 General

See CS-ETSO, Subpart A, paragraph 1.2.

- 4.2 Specific

None.

5 Availability of Referenced Documents

See CS-ETSO, Subpart A, paragraph 3.

[Amdt ETSO/16]

APPENDIX 1 TO ETSO-C117B -EASA PERFORMANCE STANDARD FOR AIRBORNE WIND SHEAR WARNING AND ESCAPE GUIDANCE SYSTEMS FOR TRANSPORT AEROPLANES

ED Decision 2020/011/R

1.PURPOSE

This Appendix establishes the minimum performance standard (MPS) for airborne wind shear warning and escape guidance systems for transport category aeroplanes.

2.SCOPE

The scope of this Appendix is to provide MPS for airborne wind shear warning and escape guidance systems for transport category aeroplanes. All the paragraph references cited herein are in reference to this Appendix only.

This performance standard applies only to wind shear warning systems which identify wind shear phenomena by sensing an encounter with conditions that exceed the threshold values contained in this performance standard. In addition to wind shear warning criteria, this performance standard provides criteria that are applicable to systems that provide optional wind shear caution alert capabilities. Wind shear escape guidance is provided to assist the pilot in obtaining the desired flight path during such an encounter.

3.DEFINITION OF TERMS

a. Airborne wind shear warning system

A device or system which uses various sensor inputs to identify the presence of wind shear once the phenomenon is encountered, and provides the pilot with a timely warning. The system may include both wind shear warning and wind shear caution alerts. A warning device of this type does not provide escape guidance information to the pilot to satisfy the criteria for warning and flight guidance systems.

b. Airborne wind shear warning and escape guidance system

A device or system which uses various sensor inputs to identify the presence of wind shear once the phenomenon is encountered, and provides the pilot with a timely warning and adequate flight guidance to improve the probability of recovery from the wind shear encounter. This system may include both wind shear warning and wind shear caution alerts.

c. Airborne wind shear auto recovery system

A device or system which integrates or couples autopilot and/or autothrottle systems of the aeroplanes with an airborne wind shear flight guidance system.

d. Airborne wind shear escape guidance system

A system which provides the crew with flight guidance information to improve the probability of recovery once a wind shear phenomenon is encountered.

e. Failure

The inability of a system, subsystem, unit, or part to perform within the previously specified limits.

f. False warning or caution

A warning or caution which occurs when the wind shear warning or caution threshold of the system is not exceeded.

g. Nuisance warning or caution

A warning or caution which occurs when a phenomenon is encountered, such as turbulence, which does not, in fact, endanger the aeroplane because of the duration of the subsequent change in the magnitude of the wind shear.

h. Recovery procedure

A vertical flight path control technique that is used to maximise the potential for a recovery from an inadvertent encounter with wind shear.

i. Severe wind shear

A wind shear of sufficient intensity and duration that it exceeds the performance capability of a particular aeroplane type. This would be likely to cause an inadvertent loss of control or ground contact if the pilot did not have information available from an airborne wind shear warning and escape guidance system which meets the criteria of this ETSO.

j. Wind shear caution alert

An alert that is triggered by increasing performance conditions, which is set at a wind shear level that requires immediate crew awareness and probably subsequent corrective action by the pilot.

k. Wind shear warning alert

An alert that is triggered by decreasing performance conditions, which is set at a wind shear level that requires immediate corrective action by the pilot.

4.GENERAL REQUIREMENTS

In addition to the performance requirements provided in the main text of this Performance Standard and in the Appendices to ETSO-C117b, the following general requirements and equipment characteristics are defined below:

a. General standards

The following general requirements shall be met by all wind shear warning and escape guidance systems:

(1)Airworthiness

The design and manufacture of the airborne equipment shall provide for installation so as not to impair the airworthiness of the aeroplane The material shall be of a quality which experience and/or tests have demonstrated to be suitable and dependable for use in aeroplane systems. The workmanship shall be consistent with high-quality aeroplane electromechanical and electronic component manufacturing practices.

(2)General performance

The equipment shall perform its intended function, as defined by the manufacturer.

(3)Fire resistance

Except for small parts (such as knobs, fasteners, seals, grommets and small electrical parts) that would not significantly contribute to the propagation of fire, all the materials that are used shall be self-extinguishing. One means to show compliance with this requirement is contained in Part 25, Appendix F.

(4)Operation of controls

Controls that are intended for use during flight shall be designed to minimise errors, and when operated in any possible combinations and sequences, shall not result in a condition whose presence or continuation would be detrimental to the continued performance of the equipment.

(5)Accessibility of controls

Controls that are not normally adjusted in flight shall not be readily accessible to the operator.

- (6) Interfaces

The interfaces with other aeroplane equipment shall be designed such that the normal or abnormal operation of the wind shear warning and escape guidance equipment does not adversely affect the operation of other equipment.

- (7) Compatibility of components

If a system component is individually acceptable but requires calibration adjustments or matching to other components in the aeroplane for its proper operation, it shall be identified in a manner that will ensure its performance to the requirements specified in this ETSO.

(8)Interchangeability

System components which are identified with the same manufactured part number shall be completely interchangeable.

(9)Control/display capability

A suitable interface shall be provided to allow data input, data output, and control of the operation of the equipment. The control/display shall be operable by one person with the use of only one hand.

(10)Control/display readability

The equipment shall be designed so that all the displays and controls are readable under all cockpit ambient light conditions, ranging from total darkness to reflected sunlight, and are arranged to facilitate the use of the equipment. If limitations are necessary on equipment installations to ensure that the displays are readable, they shall be included in the installation instructions.

(11)Effects of test procedures

The design of the equipment shall be such that the application of the specified test procedures does not produce a condition that is detrimental to the performance of the equipment, except as specifically allowed.

- (12) Equipment computational response time

The equipment shall employ suitable update rates for the computation and display of detection and guidance information.

- (13) Supplemental heating or cooling

If supplemental heating or cooling is required by system components to ensure that the requirements of this ETSO are met, they shall be specified by the equipment manufacturer in the installation instructions.

(14)Self-test capability

The equipment shall employ a self-test capability to verify the proper operation of the system.

- (i) Any manually initiated self-test mode of operation shall automatically return the system to the normal operating mode upon completion of a successful test. - (ii) Any automatically activated self-test feature shall annunciate this mode of operation to the pilot if this feature activates annunciation lights, aural messages, or displaces the guidance commands in any way. - (iii) Use of the system self-test feature shall not adversely affect the performance of operation of other aeroplane systems. - (iv) A failure of the system to successfully pass the self-test shall be annunciated. - (15) Independence of warning and escape guidance functions

Irrespective of whether the warning and escape guidance functions are in a combined system or are separate systems, they should be sufficiently independent such that a failure of either system does not necessarily preclude or inhibit the presentation of information from the other. A warning system failure shall not result in any ambiguous or erroneous guidance system mode annunciations.

- (16) System reliability

(i)The probability of a false warning being generated within the wind shear warning system or the wind shear warning and escape guidance system shall be 1E-4 or less per flight hour.

(ii)The probability of an unannunciated failure of the wind shear warning system or the wind shear warning and escape guidance system shall be 1E 5 or less per flight hour (reserved).

b. Equipment functional requirements -standard conditions

The equipment shall meet the following functional requirements:

(1)Mode annunciation

The mode of operation of the wind shear escape guidance display shall be annunciated to the pilot upon activation of the escape guidance during a wind shear encounter, and upon reversion to a different flight guidance mode.

(2)Malfunction/failure indications

The equipment shall indicate:

- (i) any inadequacy or absence of primary power; - (ii) equipment failures; - (iii) inadequate or invalid warning or guidance displays or output signals; and - (iv) inadequate or invalid sensor signals or sources.

These malfunction/failure indications shall occur independently of any operator actions. The lack of adequate warning displays, escape guidance information, or sensor signals or sources shall be annunciated when compliance with the requirements of this ETSO cannot be assured.

(3)Wind shear caution alert

If the equipment includes a wind shear caution:

- (i) it shall provide an annunciation of increasing performance shear (updraft, increasing headwind, or decreasing tailwind) in accordance with the shear intensity curve shown in Figure 1; - (ii) this caution alert shall display or provide an appropriate output for display of an amber caution annunciation dedicated for this purpose. An aural alert may be provided as an option. The caution display (or output) should remain until the threshold wind shear condition no longer exists (not less than 3 seconds) or a wind shear warning alert occurs; and - (iii) gust conditions shall not cause a nuisance caution alert. Turbulence shall not cause more than one nuisance caution alert per 250 hours (or 3 000 flight cycles based on 1 hour/flight cycle) of system operation.

(4)Wind shear warning alert

- (i) A wind shear warning alert shall provide an annunciation of decreasing performance shear (downdraft, decreasing headwind, or increasing tailwind) with a magnitude that is greater than or equal to that shown in the shear intensity curve shown in Figure 1. - (ii) This warning alert shall display or provide an appropriate output for display of a red warning annunciation labelled 'wind shear' dedicated for this purpose. The visual alert should remain at least until the threshold wind shear condition no longer exists, or for a minimum of 3 seconds, whichever is greater. An aural alert shall be provided that annunciates 'wind shear' for 3 aural cycles. The aural alert need not be repeated for subsequent wind shear warning alerts within the same mode of operation. - (iii) Gust conditions shall not cause a nuisance warning alert. Turbulence shall not cause more than 1 nuisance warning alert per 250 hours (or 3 000 flight cycles based on 1 hour/flight) of system operation.

- (5) Wind shear alert with increased approach sensitivity and reduced take-off sensitivity modes

(i)Increased approach sensitivity mode. If the system separates the approach and take-off scenarios, the crew may reduce the shear intensity level in the approach mode to increase the probability of providing timely wind shear alerts. They may lower the floo r of the shear intensity curve 'must alert' curve in Figure 1 from 0.105 to 0.090. If they lower the floor, they may also modify the turbulence rejection tests in paragraph 4(d)(7)(ii) such that an alert in this region is not a failure of the turbulence rejection test.

(ii)Reduced take-off sensitivity mode. If the system separates the approach and take-off scenarios, the crew may desensitise the take-off mode to reduce the probability of unwanted alerts. They may raise the floor of the shear intensity 'must alert' curve in Figure 1 from 0.105 to 0.120.

(iii)Additional reduced take-off sensitivity mode. Some high performance jet aeroplanes receive unwanted wind shear alerts after take-off when climbing at high rates through atmospheric wind gradients. If these unwanted alerts risk desensitising pilots to wind shear alerting, the crew may tailor the floor of the shear intensity 'must alert' curve in Figure 1 to reduce these unwanted alerts under the following conditions:

(a)The airborne wind shear warning and escape guidance system can determine that the aeroplane is in the take-off versus approach phase.

(b)The aeroplane is climbing at a high rate of climb, the aeroplane continues to climb at a high rate, and the rate of climb is known to create unwanted wind shear alerts.

(c)The aeroplane power setting is at or near a level that is representative of the maximum for the segment of the take-off; for example, maximum take-off thrust.

(d)The Figure 1 shear intensity 'must alert' curve shall be complied with after take-off.

(6)Alerting prioritisation

If alerting is prioritised in the presentation for a wind shear warning and escape guidance system (reactive wind shear), forward-looking wind shear system, terrain awareness and warning system, ground proximity warning system, traffic collision avoidance system, or when a simultaneous aural annunciation could occur, sequencing shall be implemented that ensures that reactive wind shear warning alerts are presented or annunciated first. Reactive wind shear alerts that are cautions have a lower priority than all terrain awareness and warning or ground proximity warning system alerts.

- (7) The reactive wind shear systems caution alert should be disabled if a forward looking wind shear system is in operation. It is acceptable to issue reactive wind shear caution alerts if the forward-looking wind shear system is inoperative. - (8) Operating altitude range

The system shall be designed to function from at least 50 feet above ground level (AGL) to at least 1 000 feet AGL.

(9)Wind shear escape guidance

Flight guidance algorithms shall incorporate the following design considerations:

- (i) At the point of the system warning threshold, the available energy of the aeroplane shall be properly managed through a representative number of wind field conditions. These conditions shall take into account significant shear components in both the horizontal and vertical axes, individually and in combination. - (ii) The flight path guidance commands shall be suitable for the dynamic response of aeroplane of the type on which the system is intended for installation. The applicant shall demonstrate that the flight guidance commands during a dynamic wind shear encounter can be followed without resulting in pilot induced oscillations. - (iii) If the magnitude of the shear components is such as to overcome the performance capability of the aeroplane, guidance commands shall be such that a ground impact will occur in the absence of the ability to produce additional lift, an absence of excessive kinetic energy, and without putting the aeroplane into a stalled condition. - (iv) Flight guidance command information shall be provided for presentation on the primary flight display/attitude direction indicator (PFD/ADI) and any available head-up display (HUD). - (v) Flight guidance displays which command the flight path and pitch attitude should be limited to an angle of attack that is equivalent to the onset of a stall warning or a maximum pitch command of 27°, whichever is less. - (vi) Flight guidance commands and any auto recovery mode (if included) may be automatically activated concurrently with or after the wind shear warning alert occurs, or may be manually selected. If manual selection is utilised, it shall only be via the take-off/go-around (TOGA) switch or equivalent means (i.e. a function of the throttle position, other engine parameters, etc.). - (vii) Manual deselection of wind shear flight guidance and any auto recovery mode (if included) shall be possible by means other than the TOGA switches. - (viii) Systems that incorporate the automatic reversion of flight guidance commands from wind shear escape guidance to another flight guidance mode should provide a smooth transition between the modes. Flight guidance commands shall not be removed from the flight guidance display until either they are manually deselected or until the aeroplane, following the end of the warning conditions, has maintained a positive rate of climb and speed above 1.3 Vs1 for at least 30 seconds.

MEASA

0.25-

0.20

f

av,x

0.15-

0.10-

0.05

0.00

0

FIGURE 1 - SHEAR INTENSITY CURVE

20 knot windspeed

FIGURE 1 -SHEAR INTENSITY CURVE

f av,x = average shear intensity to cause a warning at time tx (resulting in a 20-knot wind speed change, bounded as shown; applies to horizontal, vertical, and combination shear intensities),

<!-- formula-not-decoded -->

- 𝑡 𝑥 , whereby f( t ) = instantaneous shear intensity at time t

.

- 1 A nuisance warning test that utilises the Dryden turbulence model and discrete gust model is conducted independently from the alert threshold tests to verify the acceptability of potential nuisance warnings due to turbulence or gusts.

- c. Equipment performance -environmental conditions - (1) The environmental tests and performance requirements described in this subsection are intended to provide a laboratory means to determine the overall performance characteristics of the equipment under conditions that are representative of those that may be encountered in actual operations. Table 1 defines the environmental tests that are required for the equipment. It shows the section numbers in ED-14G that describe the individual environmental tests. Some of the environmental tests contained in this subsection do not need to be performed unless the manufacturer wishes to qualify the equipment for that particular environmental condition. These tests are identified by the phrase 'When required' in Table 1. If the manufacturer wishes to qualify the equipm ent to these additional environmental conditions, then these 'When required' tests shall be performed. - (2) Environmental requirements. The following subset of performance requirements shall be met under the environmental conditions required by paragraph 3.1.2 of this ETSO. Additionally, all the system controls, displays, inputs and outputs shall perform their intended functions when subjected to the ED-14G environmental conditions.

(i)Section 4.b(1) -Mode Annunciation

(ii)Section 4.b(2) -Malfunction/Failure Indications

(iii)Section 4.b(3) -Wind Shear Caution Alert, except paragraph 4.b(3)(iii)

(iv)Section 4.b(4) -Wind Shear Warning Alert, except paragraph 4.b(4)(iii)

(v)Section 4.b(5) -Wind Shear Alert with Increased Approach Sensitivity and Reduced Take-off Sensitivity Modes

(vi)Section 4.b(9) -Wind Shear Escape Guidance - (3) The applicant shall conduct environmental qualification tests for the following shear intensity (fav,x) and exposure time (s) in Figure 1: 0.1050, 10; 0.1748, 6; and 0.2100, 5; and ensure that the system generates and displays alerts when required. A single representative wind shear waveform may be used for all the environmental tests if the system design is such that different waveforms will not affect the performance under environmental conditions. Gust and turbulence rejection tests are not required under environmental conditions.

Table 1 -Required EUROCAE ED-14G Testing by Category

d. Equipment test procedures

- (1) Definitions of terms and conditions of tests. The following definitions of terms and conditions of tests are applicable to the equipment tests specified herein:

(i)Power input voltage. Unless otherwise specified, all the tests shall be conducted with the power input voltage adjusted to the design voltage ± 2 per cent. The input voltage shall be measured at the input terminals of the equipment under test.

(ii)Power input frequency

(a)In the case of equipment that is designed for operation from an AC power source of essentially constant frequency (e.g. 400 Hz), the input frequency shall be adjusted to the design frequency ± 2 per cent.

(b)In the case of equipment designed for operation from an AC power source of variable frequency (e.g. 300 to 1 000 Hz), unless otherwise specified, the test shall be conducted with the input frequency adjusted to within 5 % of a selected frequency and within the range for which the equipment is designed.

(iii)Wind field models. Unless otherwise specified, the wind field models used for the tests shall be those specified in Appendix 2 to ETSO-C117b.

(iv)Adjustment of equipment. The circuits of the equipment under test shall be aligned and adjusted in accordance with the manufacturer's recommended practices prior to the application of the specified tests.

- (v) Test instrument precautions. Due precautions shall be taken during the execution of the tests to prevent the introduction of errors that result from the connection of voltmeters, oscilloscopes, and other test instruments across the input and output impedances of the equipment under test. - (vi) Ambient conditions. Unless otherwise specified, all the tests shall be made within the following ambient conditions: - -Temperature: + 15 to + 35 °C (+ 59 to + 95 °F) - -Relative humidity: Not greater than 85 % - -Ambient pressure: 84 -107 kPa (equivalent to + 5 000 to -1 500 ft) (+ 1 525 to -460 m) - (vii) Warm-up period. Unless otherwise specified, all the tests shall be conducted after the manufacturer's specified warm -up period. - (viii) Connected loads. Unless otherwise specified, all the tests shall be performed with the equipment connected to loads which have the impedance values for which it is designed. - (2) Test procedures. The equipment shall be tested in all the modes of operation that allow different combinations of sensor inputs to show that it meets both the functional and accuracy criteria.

Dynamic testing provides quantitative data regarding the performance of wind shear warning and escape guidance equipment using a simplified simulation of flight conditions. This testing, when properly performed and documented, may serve to minimise the flight test requirements.

It shall be the responsibility of the equipment manufacturer to determine that the sensor inputs, when presented to the wind shear warning and escape guidance equipment, will produce performance that is commensurate with the requirements of this standard. Additional sensor inputs may be optionally provided to enhance the capability and/or performance of the equipment.

The equipment required to perform these tests shall be defined by the equipment manufacturer as a function of the specific sensor configuration of the equipment. Since these tests may be accomplished in more than one way, alternative test equipment set ups may be used where equivalent test functions can be accomplished. Combinations of tests may be used wherever appropriate.

The signal sources of the test equipment shall provide the appropriate signal formats for input to the specific system under test without contributing to the error values that are being measured. Tests need only be performed once, unless it is otherwise indicated.

The scenarios that are established for testing wind shear warning and escape guidance systems represent realistic operating environments to properly evaluate such systems. The wind field models contained in Appendix 2 to ETSO C117b should be used to evaluate the performance of the wind shear warning and escape guidance systems. The manufacturer may propose different wind field models provided that it is shown that they represent conditions that are at least as severe as those contained in this ETSO.

Note: The test waveform parameters provided in this ETSO are sufficiently broad to cover the wind field parameters that were observed in the known accident cases. However, the manufacturer is encouraged to verify that the detection systems will actually detect these wind shears by subjecting them to the wind field conditions specified for use in evaluating guidance commands.

- (3) Test set-up. Simulator tests shall be used to demonstrate the performance capability of the wind shear warning and escape guidance equipment. A suitable equipment interface shall be provided for recording the relevant parameters that are necessary to evaluate the particular system under test. The aeroplane simulator shall be capable of appropriate dynamic modelling of a representative aeroplane and of the wind field and turbulence conditions contained in Appendices 2 and 3 to this ETSO, or other wind field/turbulence models that are found to be acceptable by the administrator.

Note: This section requires testing in a single representative aeroplane simulator. Approval of the installation will require system testing in an aeroplane simulator that is representative of the aeroplane. Thus, we recommend you to accomplish the paragraph 4(d)(3) simulator testing in as many representative simulators as are necessary to cover all the intended installations.

- (4) Functional performance (paragraphs 4(b)(1) through 4(b)(5), 4(b)(8) and 4(b)(9)). Each of the functional capabilities identified in paragraphs 4(b)(1) through 4(b)(5), 4(b)(7) and 4(b)(8) shall be demonstrated with the wind shear warning and escape guidance equipment powered. These capabilities shall be evaluated either by inspection or in conjunction with the tests described in paragraphs 4(d)(5) through 4(d)(10). - (5) Mode annunciation (paragraph 4(b)(1)). With the equipment operating, verify that the wind shear escape guidance display mode of operation is annunciated to the pilot upon activation of the escape guidance and upon reversion to a different flight guidance mode. - (6) Malfunction/failure indications (paragraph 4(b)(2)). Configure the equipment for simulation tests as defined in paragraph 4(d)(3).

(i)With the system active (within the operating altitude range) and inactive (outside the operating altitude range), remove one at a time each required electrical power input to the equipment. There shall be a failure indication by the equipment of each simulated failure condition.

(ii)With the system active (within the operating altitude range) and inactive (outside the operating altitude range), cause each sensor or other signal input to become inadequate or invalid. There shall be a failure indication by the equipment of each simulated failure condition. - (7) Wind shear caution alert (paragraphs 4(b)(3) and 4(b)(5)(i)). For equipment that incorporates a wind shear caution alert function, accomplish the following tests:

(i)Configure the equipment for a simulation test as defined in paragraph 4(d)(3). Subject the equipment to acceleration waveform values that meet the following conditions (reference Figure 2). The system shall generate an appropriate caution alert (or no alert) within the time intervals specified when subjected to the following average shear intensity (fav,x) values:

Notes:

- (1) The average shear intensity which shall result in a caution alert after a time tx or less meets the definition of fav,x in Figure 1. The maximum instantaneous shear intensity of the test waveform is restricted to 0.075 or 100 % of fav,x above the average shear value fav,x, whichever is less. The minimum instantaneous shear intensity of the test waveform is zero. The test waveform rise and fall rates shall be limited to a maximum of 0.1 per second. The shear intensity before time 0 is zero for a sufficiently long time to allow the system to settle to stable conditions. - (2) In order to achieve the test condition with the shear intensity fav,x equal to or greater than 0.270, it is necessary to have an initial rise of sufficient rate to achieve a shear intensity f value that will allow subsequent rise and fall rates that are limited to 0.1 per second to achieve the required fav,x value. - (3) Account for latency due to the alert calculation and alert annunciation display functionality when measuring the alert time

The test conditions specified above shall be repeated 5 times for each axis (horizontal and vertical). A total of 90 runs are required for verification of the detection (9 conditions × 5 for each axis) for both performance increasing and performance decreasing wind shears. A different waveform for fav,x will be utilised for each of the 5 runs. An appropriate alert (or no alert) shall be generated for each test condition.

Verify that the system displays or provides an appropriate output for display of an amber caution annunciation that is dedicated for this purpose. Verify that the visual caution display (or output) remains at least until the threshold wind shear condition no longer exists, or a minimum of 3 seconds (whichever is greater), or until a wind shear warning occurs.

- (ii) Subject the equipment to wind speeds that are defined by the Dryden turbulence model contained in Appendix 4 to ETSO C117b. The system shall be exposed to these conditions for a minimum of 50 hours (or 600 flight cycles) at each altitude specified in Appendix 4 to ETSO C117b for a minimum total test duration of 250 hours (or 3 000 flight cycles based on 1 hour/flight cycle).

No more than 1 nuisance caution shall be generated during this test.

An alternative test equipment set-up may be used to accomplish the equivalent test function for the turbulence testing. A combination of analysis, simulation and testing may be used to demonstrate the performance of the equipment.

- (iii) Subject the equipment to the wind speeds that are defined by the discrete gust rejection model contained in Appendix 4 to ETSO C-117b. No alert shall be generated as a result of this test. - (8) Wind shear warning alert (paragraphs 4(b)(4) and 4(b)(5)(ii)). - (i) Configure the equipment for simulation tests as defined in paragraph 4(d)(3). Subject the equipment to acceleration waveform values that meet the following conditions (reference Figure 2). The system shall generate an appropriate warning alert (or no alert) within the time intervals that are specified when it is subjected to the following average shear intensity (fav,x) values:

Notes:

- (1) The average shear intensity which shall result in a warning alert after a time tx or less meets the definition of fav,x in Figure 1. The maximum instantaneous shear intensity of the test waveform is restricted to 0.075 or 100 % of fav,x above the average shear value fav,x , whichever is less. The minimum instantaneous shear intensity of the test waveform is zero. The test waveform rise and fall rates shall be limited to a maximum of 0.1 per second. The shear intensity before time 0 is zero for a sufficiently long time to allow the system to settle to stable conditions. - (2) In order to achieve the test condition with the shear intensity fav,x equal to or greater than 0.270, it is necessary to have an initial rise of a sufficient rate to achieve a shear intensity f value that will allow the subsequent rise and fall rates that are limited to 0.1 per second to achieve the required fav,x value. - (3) Account for any latency due to the alert calculation and alert annunciation display functionality when measuring the alert time.

The test conditions specified above shall be repeated 5 times for each axis (horizontal and vertical). A total of 90 runs are required for verification of the detection (9 conditions × 5 for each axis) for both performance increasing and performance decreasing wind shears. A different waveform for fav,x will be utilised for each of the 5 runs. An appropriate alert (or no alert) shall be generated for each test condition.

Verify that the system displays or provides an appropriate output for display of a red warning annunciation labelled 'wind shear' that is dedicated for this purpose. Verify that the visual warning display (or output) remains until the threshold wind shear condition no longer exists, or a minimum of 3 seconds, whichever is greater. Verify that an aural alert is provided that annunciates 'wind shear' for 3 aural cycles.

- (ii) Subject the equipment to the wind speeds that are defined by the Dryden turbulence model contained in Appendix 4 to ETSO C117b. The system shall be exposed to these conditions for a minimum of 50 hours (or 600 flight cycles) at each altitude specified in Appendix 4 to ETSO C117b for a minimum total test duration of 250 hours (or 3 000 flight cycles based on 1 hour/flight cycle). No more than 1 nuisance warning shall be generated during this test.

An alternative test equipment set-up may be used to accomplish the equivalent test function for the turbulence testing. A combination of analysis, simulation, and testing may be used to demonstrate the performance of the equipment specified in this paragraph 4(d)(8)(ii).

- (iii) Subject the equipment to the wind speeds that are defined by the discrete gust rejection model contained in Appendix 4 to ETSO-C117b. No alerts shall be generated as a result of this test.

MEASA

Intensity

Shear

0.301

0.25 -

0.201

0.15 1

0.10-

0.05-

0

Sample waveforms for 10 sec test point

zero

time 0

before

FIGURE 2 -WIND SHEAR ALERT TEST

- waveform 2

The average of all waveforms

from 0 to 10 sec is 0.105.

- (9) Operating altitude range (paragraph 4.b(8)). Configure the equipment for the simulation tests as defined in paragraph 4(d)(3). Simulate a take-off to an altitude of at least 1 500 feet AGL. Verify the wind shear warning and escape guidance system is operational from at least 50 feet AGL to at least 1 000 feet AGL. Simulate an approach to landing from 1 500 feet AGL to touchdown. Verify the wind shear warning and escape guidance system is operational from at least 1 000 feet AGL to at least 50 feet AGL.

- (10) Wind shear escape guidance (paragraph 4.b(9)). Configure the equipment for simulation tests as defined in paragraph 4(d)(3). Subject the equipment to each of the wind field conditions contained in Appendix 2 to ETSO C117b for each operating mode (take-off, approach, landing, etc.) that is available. Each test condition shall be repeated 5 times. Recovery actions for the fixed pitch method comparison shall be initiated immediately upon entering the shear condition.

Notes:

- (1) Evaluate wind shear escape guidance commands using a simulation that incorporates the necessary dynamic modelling of the representative aeroplane (more than 1 representative aeroplane model may be necessary) in which installation of the equipment is intended. Dynamic modelling of the representative aeroplane should include consideration of all the relevant effects, including but not limited to pitch and roll rates, control authority, delays between control inputs and aeroplane responses, display system leads and lags, etc. - (2) The simulator should provide for a pilot in the loop evaluation of guidance flyability during simulated wind shear encounters. The guidance command gains should be consistent with those incorporated in the flight guidance system. While 'fine -tuning' of th e guidance commands to obtain the optimum performance for a specific aeroplane may be accomplished, the use of unique tailoring for a specific aeroplane may not be necessary. Evaluation through means of a suitable engineering simulation may be acceptable to demonstrate the suitability of the guidance commands for a representative aeroplane. However, the equipment manufacturer should demonstrate that the flight guidance commands during a dynamic wind shear encounter can be followed without resulting in pilot-induced oscillations.

(i)Verify that the flight path guidance commands manage the available energy of the aeroplane to achieve the desired trajectory through the shear encounter. These tests shall be performed with vertical only, horizontal only, and a combination of vertical and horizontal shear conditions. You may reduce the number of times you repeat each of these tests conditions to less than 5. To reduce the number of repetitions to less than 5, you shall have gathered sufficient data to demonstrate that the flight path guidance commands meet these requirements. You should also include aeroplane weight and centre of gravity variations if applicable.

- a. For the take-off case, verify that the flight guidance commands produce a trajectory that provides a resultant flight path that is at least as good (when considered over the entire spectrum of test cases) as that obtained by establishing a 15° pitch attitude (at an approximate rate of 1.5° per second) until the onset of a stall warning, and then reducing the pitch attitude to remain at the onset of a stall warning until the shear condition is exited. Evidence of a significant decrement (considered over the entire spectrum of test cases) below the flight path that is provided by the fixed pitch method that results from the use of the guidance commands provided by the system shall be adequately substantiated.

- b. For the approach/landing case, verify that the flight guidance commands produce a trajectory that provides a resultant flight path that is at least as good (when considered over the entire spectrum of test cases) as that obtained by establishing the maximum available thrust and a 15° pitch attitude (at an approximate rate of 1.5° per second) until the onset of stall warning, and then reducing the pitch attitude to remain at the onset of stall warning until the shear condition is exited. Evidence of a significant decrement (considered over the entire spectrum of test cases) below the flight path that is provided by the fixed pitch method that results from the use of the guidance commands that are provided by the system shall be adequately substantiated.

- c. For shear conditions that exceed the available performance capability of the aeroplane, verify that the flight guidance commands result in a ground impact in the absence of the ability to produce additional lift, an absence of excessive kinetic energy, and without putting the aeroplane into a stalled condition.

Note: There is no requirement to perform the tests described in paragraphs 4(d)(10)(ii) through (vii) with horizontal only, vertical only, and a combination of vertical and horizontal shear conditions. You may perform the tests described in paragraphs 4(d)(10)(ii) through (vii) with only the combination vertical and horizontal shear conditions.

- (ii) Verify that the flight guidance command outputs are capable of display on the associated flight displays. The interface specifications shall be verified and determined to be appropriate for the systems that are identified in the equipment installation instructions. - (iii) Verify that the pitch attitude commands do not result in an angle of attack that exceeds the onset of a stall warning or a maximum pitch command of 27°, whichever is less.

[Amdt ETSO/16]

- (iv) For systems that incorporate manual activation of recovery flight guidance commands, verify that the system is activated only by the TOGA switches (or equivalent means). For systems that provide automatic activation of recovery guidance, verify that the system is activated concurrently with the wind shear warning alert. - (v) Verify that the wind shear recovery guidance commands and any automatic recovery mode can be deselected by a means other than the TOGA switches. - (vi) For systems that incorporate automatic reversion of flight guidance commands from wind shear escape guidance to another flight guidance mode, verify that the transition between the flight guidance modes provides smooth guidance information. - (vii) Verify that flight guidance commands are not removed from the flight guidance display until either they are manually deselected or until the aeroplane, following the exit of the warning conditions, has maintained a positive rate of climb and speed above 1.3 Vs1 for at least 30 seconds.

APPENDIX 2 TO ETSO-C117B -WIND FIELD MODELS AND DATA

ED Decision 2020/011/R

This Appendix contains data that defines the wind field models to be used in conducting the tests specified in paragraph 4(d)(10) of this ETSO. This material was developed by the National Aeronautics And Space Administration (NASA), reference NASA Technical Memorandum 100632 [ref. 1].

The downburst model parameters below provide the variables to be used to obtain the representative test conditions: (1) and (2)

- (1) From analytic microburst model documented in NASA TM-100632. These parameters are based on data from Proctor's Terminal Area Simulation System (TASS) model. - (2) For the takeoff case, the downburst centre is positioned at the point the aeroplane lifts off the runway for all test cases. - (3) For the approach/landing case, the downburst centre is positioned as stated. The test is begun with the aeroplane at an initial altitude of 1 500 feet on a 3° glideslope (touchdown point approximately 29 000 feet away). The distance from the starting point indicates where the centre of the downburst shaft is located relative to the starting point. The number in parentheses next to it indicates the relative distance of the microburst centre from the touchdown point (not the end of the runway). A negative number indicates that the microburst centre is located before the touchdown point, positive indicates it is past the touchdown point.

SUMMARY

A simple downburst model has been developed for use in batch and real-time piloted simulation studies of guidance strategies for terminal area transport aeroplane operations in wind shear conditions. The model represents an axisymmetric stagnation point flow, based on velocity profiles from the Terminal Area Simulation System (TASS) model developed by Proctor [ref. 3,4] and satisfies the mass continuity equation in cylindrical coordinates. Altitude dependence, including boundary layer effects near the ground, closely matches real-world measurements, as do the increase, peak, and decay of outflow and downflow with increasing distance from the downburst centre. Equations for horizontal and vertical winds were derived, and found to be infinitely differentiable, with no singular points existent in the flow field. In addition, a simple relationship exists among the ratio of maximum horizontal to vertical velocities, the downdraft radius, depth of outflow, and altitude of maximum outflow. In use, a microburst can be modelled by specifying four characteristic parameters. Velocity components in the x, y, and z directions, and the corresponding nine partial derivatives are obtained easily from the velocity equations.

INTRODUCTION

Terminal area operation of transport aircraft in a wind shear environment has been recognised as a serious problem. Studies of aeroplanes trajectories through downbursts show that specific guidance strategies are needed for aeroplanes to survive inadvertent downburst encounters. In order for guidance strategies to perform in simulations as in actual encounters, a realistic set of conditions must be present during development of the strategies. Thus, aeroplane and wind models that closely simulate real-world conditions are essential in obtaining useful information from the studies.

Wind models for use on personal computers, or for simulators with limited memory space availability, have been difficult to obtain because variability of downburst characteristics makes analytical models unrealistic, and large memory requirements make the use of numerical models impossible on any except very large capacity computers.

Bray [ref. 2] developed a method for analytic modelling of wind shear conditions in flight simulators, and applied his method in modelling a multiple downburst scenario from Joint Airport Weather Studies (JAWS) data. However, the altitude dependence of his model is not consistent with observed data and, although flexibility in sizing the downbursts is built into the model, it does not maintain the physical relationships which are seen in real-world data among the sizing parameters. In particular, boundary layer effects should cause the radial velocity to decay vertically to zero at the ground, as does the vertical velocity.

In a study conducted at NASA Langley Research Center, three different guidance strategies for a Boeing 737-100 aeroplane encountering a microburst on take-off were developed [ref. 3-4]. These strategies were first developed using a personal computer, and then implemented in a pilot-in-theloop simulation using a very simple wind model in both efforts. The wind velocities used are depicted in Figure 1. This model consisted of a constant outflow outside of the downburst radius and a constant slope headwind to tailwind shear across the diameter of the downburst.

Wx =-KW

MEASA

H

+KW

Wx

- KW

X1

Wh =-4 KW°h

Figure 1 -Wind Model Used in Guidance Studies

It was recognised that a more realistic wind model could significantly alter the outcome of the trajectory. For the subsequent part of this study, which involves altering the aeroplane model to simulate approach to landing and escape manoeuvres and additional take-off cases, a more realistic wind model was preferred. The simple analytical model outlined in this report was developed for this purpose.

SYMBOLS

DEVELOPMENT OF VELOCITY EQUATIONS

Beginning with the full set of Euler and mass continuity equations, some simplifying assumptions about the downburst flow conditions were made. Effects of viscosity were parameterised explicitly, and the flow was assumed to be invariant with time. The downburst is axisymmetric in cylindrical coordinates, and characterized by a stagnation point at the ground along the axis of the downflow column. The flow is incompressible, with no external forces or moments acting on it.

The resulting mass conservation equation is

<!-- formula-not-decoded -->

<!-- formula-not-decoded -->

This equation is satisfied by solutions of the form

<!-- formula-not-decoded -->

<!-- formula-not-decoded -->

<!-- formula-not-decoded -->

<!-- formula-not-decoded -->

Note that 𝑓 ′ (𝑟 2 ) = 𝜕𝑓(𝑟 2 ) 𝜕𝑟 2 . To solve this system of equations, solutions were assumed for two of the functions and the other two were obtained from equations 4a and 4b.

It was desired that the velocity profiles of this analytic model exhibit the altitude and radial dependence shown in the large-scale numerical TASS (Terminal Area Simulation System) weather model [ref. 6-9]. The TASS model is based on data from the Joint Airport Weather Studies (JAWS) [ref. 10], and provides a three- dimensional velocity field, frozen in time, for given locations of an aeroplane within the shear [ref. 11-12].

Written out in full, equation 2 is

provided that SITIVITY TO RADIUS OF PRECIPITATION S

2.0

1.8

MEASA

1.6

1.4

B= 3000M

1.2

1.0

Z/y

.8

.6

.4

.2

- 15

L

1000

700

600

500

400

300

200

100

- 10

R=5000M\_ \_

- 5

-.50.25 0 .25.50.751.00

(M/S)

U/U

max

. . .

0550

LABORATORY

NIMROD

Figure 2 -Vertical Profile of Microburst Outflow (Non-dimensional)

Figure 2 shows dimensionless vertical profiles of horizontal velocity, u, for TASS data, laboratory data obtained by impingement of a jet on a flat plate, and data from NIMROD (Northern Illinois Meteorological Research on Downbursts) [ref. 13-21]. Specific points of interest are the maximum horizontal velocity (located 100-200 metres above the ground), below which is a decay region due to boundary layer effects, zero velocity at the stagnation point on the ground, and an exponential decay with altitude above the maximum velocity altitude. Vertical velocity profiles from TASS data are shown in Figure 3, also exhibiting a decay to zero at the stagnation point.

VERTICAL PROFILES OF VERTICAL VELOCITY FOR 30 JUN 82 CASE: SENSITIVITY TO RADIUS OF PRECIPITATION SHAFT

Figure 3 -Vertical Profile of Microburst Downflow

- 20

R= 1500M

MEASA

Shaping Function g(r 2)

The radially varying characteristics desired for the horizontal wind were two peaks of equal magnitude and opposite direction located at a given radius, with a smooth, nearly linear transition between the two. Beyond the peaks, the velocity should show an exponential decay to zero. The vertical velocity was required to have a peak along the axis of symmetry (r = 0), and to decay exponentially as the radius increases.

A pair of shaping functions that gave velocity profiles matching the TASS data as required are given below.

· Increasing Radius →

<!-- formula-not-decoded -->

<!-- formula-not-decoded -->

<!-- formula-not-decoded -->

The remaining solutions were found by integrating equations 4a and 4b, yielding:

<!-- formula-not-decoded -->

Figures 4 and 5 show plots of these shaping functions.

Figure 4 -Characteristic Variation of Horizontal Shaping Functions

· 1(r 2)

MEASA

· Increasing Altitude p(z)

Shaping Function

Figure 5 -Characteristic Variation of Vertical Shaping Functions

Combining the functions as in equation 3, the horizontal and vertical velocities are expressed as

<!-- formula-not-decoded -->

<!-- formula-not-decoded -->

By taking derivatives of equations 5 and 6 with respect to r and z, respectively, and substituting in equation 2, it can be shown that the velocity distributions satisfy continuity.

The parameters z* and ε were defined as characteristic scale lengths associated with 'out of boundary layer' and 'in boundary layer' behaviour, respectively. Analysis of TASS data indicated that z* = z m2, the altitude at which the magnitude of the horizontal velocity is half the maximum value.

It was also noted that the ratio

<!-- formula-not-decoded -->

To determine the location of the maximum horizontal velocity, the partial derivatives of u with respect to r and z were set equal to zero. The resulting equation for the r-derivative is

<!-- formula-not-decoded -->

The resulting equation for the z-derivative is

<!-- formula-not-decoded -->

Recalling that zm/z* = 0.22, the values 1.1212 and 12.5 were obtained from iteration for the ratios r/R and z*/ ε , respectively.

Altitude (ft)

1000

MEASA

Using these values, the maximum horizontal velocity can be expressed as umax = 0.2357 λ R. The maximum vertical wind is located at r = 0 and z = zh, by definition, and is given by

<!-- formula-not-decoded -->

A ratio of maximum outflow and downflow velocities can be formed

<!-- formula-not-decoded -->

The Scaling factor, λ , was determined by using either of equations 5 or 6 for horizontal or vertical velocity, and setting it equal to the maximum velocity, umax or wmax, respectively. Solving for λ results in:

<!-- formula-not-decoded -->

The velocity equations were easily converted to rectangular coordinates, as shown in the Appendix. Partial derivatives with respect to x, y, and z were obtained by differentiating the velocity equations, and are also listed in this Appendix.

DISCUSSION AND RESULTS

€

Vertical and horizontal velocity profiles for u and w are shown in Figures 6 and 7.

40

Figure 6 -Vertical Velocity Profiles for the Analytical Model

580

40

MEASA

40

20

Velocity (kts)

- 20

- 16000

Radial Velocity Profiles wx.h =Zm

Figure 7 -Radial Velocity Profiles for the Analytical Model

Four profiles are shown for each component. The horizontal wind profiles in figure 6 were taken at the radios of peak outflow (r = 1.1212 R) and at about one-fourth that radius (r = 0.3 R), where the maximum outflow is approximately half the value at the peak outflow radius. The vertical wind profiles were taken at the radius of peak downflow (r = 0) and at r = 0.3 R. Horizontal wind and vertical wind profiles in figure 7 were taken at altitudes of h = zm (maximum outflow), h = z* (half-maximum outflow), and h = zh (depth of outflow).

This analytical model is compared with TASS, laboratory, and NIMROD data in figure 8. The figure shows that, when non-dimensionalised by the altitude of half-maximum outflow (z*) and by the maximum outflow (u = umax), the analytical model agrees closely with the other data.

MEASA

2.0

1.8

1.6

1.4

1.2

1.0

.8

.6

·4

.2

Z/y

.....

1

-.50-.25 0 .25.50 .751.00

U /Umax ANALYTICAL

Figure 8 -Comparison of Wind Model Vertical Profiles

Different shears can be modelled by specifying four parameters, and the location of the downburst centre relative to the aeroplane flying through it. The four parameters are: 1) a characteristic horizontal dimension; 2) the maximum wind velocity; 3) the altitude of maximum outflow; and 4) the depth of outflow. The characteristic horizontal dimension specified is the radius of the downdraft column, noting that this is about 89 % of the radius of the peak outflow. The maximum wind velocity can be either horizontal or vertical.

CONCLUDING REMARKS

The analytic microburst model developed for use in real-time and batch simulation studies was shown to agree well with real-world measurements for the cases studied. The functions chosen for the model showed boundary-layer effects near the ground, as well as the peak and decay of outflow at increasing altitudes, and increasing downflow with altitude. The exponential increase and decay of the downflow and outflow (in the radial direction) are also characterised by the model. Equations for horizontal and vertical winds are simple and continuously differentiable, and partial derivatives in rectangular or cylindrical coordinates can be easily obtained by direct differentiation of the velocity equations. The governing equation for this system is the mass conservation law, and the analytic velocity functions developed here satisfied this condition. The model is sustained by a strong physical basis and yields high fidelity results, within the limitations of maintaining simplicity in the model, and variability of the microburst phenomenon. Parameterization of some of the characteristic dimensions allows flexibility in selecting the size and intensity of the microburst.

-

REFERENCES

- 1 Oseguera, M. and Bowles R. L.: A Simple, Analytic 3-Dimensional Downburst Model Based on Boundary Layer Stagnation Flow, Rosa, July 1988.

- 2 Bray, R. S.: Application of Data to Piloted Simulations. Wind Shear/Turbulence Inputs To Flight Simulation and Systems Certification, NASA CP-2474, 1987, pp. 97-115.

- 3 Hinton, D. A.: Aircraft Trajectory Guidance During Wind Shear Encounters. Master's Thesis, George Washington University, January 1988.

- 4 Hinton, D.A.: Flight management strategies for escape from microburst encounters, NASA TR 4057, 29, pp. 1988.

- 5 Hinton, D.A.: Relative merits of reactive and forward-look detection for wind shear encounters during landing approach for various microburst escape strategies, NASA TM-4158, DOT/FAA/DS-89/35, 1990.

- 6 Proctor, F.H.: The Terminal Area Simulation System, Volume I: Theoretical Formulation, NASA Contractor Report 4046, April 1987.

- 7 Proctor, F. H.: Numerical simulations of an isolated microburst. Part I: Dynamics and structure, J. Atmos. Sci., 45, pp. 3137-3160, 1988.

- 8 Proctor, F.H.: The Terminal Area Simulation System, Volume II: Verification Cases. NASA Contractor Report 4047, April 1987.

- 9 Proctor, F. H., 1989: Numerical simulations of an isolated microburst. Part II: Sensitivity experiments, J. Atmos. Sci., 46, pp. 2143-2165.

- 10 Frost, W.: Modeling and Implementation of Wind Shear Data. Wind Shear/ Turbulence Inputs to Flight Simulation and Systems Verification, NASA CP-2474, 1987, pp. 49-66.

- 11 Proctor, F. H.: NASA Wind Shear Model -- Summary of Model Analysis. Airborne Wind Shear Detection and Warning Systems, NASA CP-10006, 1988, pp. 29-66.

- 12 Proctor, F. H., and Bowles, R. L.: Three-dimensional simulation of the Denver 11 July 1988 microburst-producing storm, Meteorol. and Atmos. Phys., 49, 1992, pp. 107-124.

- 13 Fujita, T. T.: Tornadoes and Downbursts in the Context of Generalized Planetary Scales. Journal of Atmospheric Sciences, vol. 38, no. 8, August 1981, pp. 1511-1534.

- 14 Oseguera, R. M.; Bowles, R. L.; and Robinson, P. A., 1992: Airborne In Situ Computation of the Wind Shear Hazard Index, AIAA Paper 92-0291, 1992.

- 15 Lewis M. S., Robinson P. A., Hinton D. A., Bowles R. L.: The relationship of an integral wind shear hazard to aircraft performance limitations, NASA TM-109080, 1994.

- 16 Arbuckle, P. D., Lewis M. S., Hinton D. A.: Airborne systems technology application to the windshear threat, 20th Congress of the International Council of the Aeronautical Sciences, ICAS Paper No. 96-5.7.1, pp. 1640-1650, 1996.

- 17 Airborne Windshear Detection and Warning Systems. First Combined Manufacturers' and Technologists' Conference, NASA CP -10006, DOT/FAA/PS-88/7, 1988.

- 18 Airborne Windshear Detection and Warning Systems, Second Combined Manufacturers' and Technologists' Conference, NASA CP -10050, 1990.

- 19 Airborne Windshear Detection and Warning Systems, Third Combined Manufacturers' and Technologists' Conference, NASA CP -10060, DOT/FAA/RD-91/2-1, 1991.

- 20 Airborne Windshear Detection and Warning Systems, Fourth Combined Manufacturers' and Technologists' Conference, NASA CP -10105, DOT/FAA/RD-92/19-1, 1992.

- 21 Airborne Windshear Detection and Warning Systems, Fifth and Final Combined Manufacturers' and Technologists' Conference, NASA CP -10139, DOT/FAA/RD-94/14-1, 1994.

[Amdt ETSO/16]

APPENDIX 3 TO ETSO-C117B -WIND FIELD MODEL COORDINATE SYSTEM TRANSFORMATION

ED Decision 2020/011/R

This Appendix describes the conversion of the velocity equations in Appendix 2 to rectangular coordinates.

Define intermediate variables to simplify written equations:

<!-- formula-not-decoded -->

Horizontal and Vertical Velocities

<!-- formula-not-decoded -->

Partial Derivatives

<!-- formula-not-decoded -->

Other Relationships

<!-- formula-not-decoded -->

<!-- formula-not-decoded -->

(λ is determined from the above relationships)

<!-- formula-not-decoded -->

Variable List

z*

= altitude where wx is half the value of wx max (ft)

ε

= characteristic height of boundary layer effects (ft)

zh

= depth of outflow (ft)

zm

= altitude of maximum outflow (ft)

λ

= scaling parameter (s -1 )

r

= radial distance from aeroplane to downburst (ft)

h

= altitude of aeroplane (ft)

R = radius of downdraft (ft)

xad, yad = x, y coordinates, aeroplane to microburst (ft)

wx max, wy max, wh max maximum winds, x, y, and h directions [Amdt ETSO/16]

Easy Access Rules for European Technical Standard Orders (CS-ETSO) (Amendment 16)

APPENDIX 4 TO ETSO-C117B -DRYDEN TURBULENCE AND DISCRETE GUST MODEL

ED Decision 2020/011/R

This Appendix contains data that defines the Dryden turbulence and discrete gust model to be used in conducting the tests specified in paragraphs 4(d)(7)(ii), 4(d)(7)(iii), 4(d)(8)(ii), and 4(d)(8)(iii) of Appendix 1 to this ETSO.

Dryden Turbulence Model

<!-- formula-not-decoded -->

where:

SIGMAu, SIGMAv, SIGMAw are the RMS intensities;

TAUu = Lu/VA;

TAUv = Lv/VA;

TAUw = Lw/VA;

Lu, Lv, Lw are the turbulence scale lengths; VA is the aircraft's true airspeed (ft/sec);

PI = 3.1415926535;

PI2 = 6.2831853070 (2 times PI);

SQRT3 = 1.732050808 (square root of 3); and

S is the Laplace transform variable.

The following table lists SIGMAu, SIGMAv, SIGMAw, Lu, Lv, and Lw versus altitude. Extrapolation will not be used, and simulator altitudes outside the bounds of the turbulence list will use the data at the boundary.

The applicant shall demonstrate that the variance of their turbulence implementation is adequate.

<!-- formula-not-decoded -->

Discrete Gust Rejection

Discrete gusts (in the horizontal axis) with ranges of amplitude and frequency (A and OMEGA) of the form [A(1 -cos OMEGAt)] shall be used.

The following table lists the values of A and OMEGA to be used (this simulates an approximate 15knot gust condition):

[Amdt ETSO/16]

APPENDIX 5 TO ETSO-C117B -SHEAR INTENSITY

<!-- formula-not-decoded -->

where

wx = Horizontal component of the wind rate of change expressed in g units (1.91 kt/s = 0.1 g) (positive for increasing headwind).

•

Wh

= Vertical component of the wind vector w (ft/s) (positive for downdraft).

V

= True airspeed (ft/s).

g

= Gravitational acceleration (ft/sec2).

[Amdt ETSO/16]

ED Decision 2020/011/R

APPENDIX 6 TO ETSO-C117B -WIND SHEAR SIMULATION MODEL

ED Decision 2020/011/R

The following computer listing (written in QuickBasic) provides a simplified aircraft simulation model for evaluating the effectiveness of various guidance schemes. This simulation runs on a personal computer, and the results obtained using it have been found to be comparable to those obtained on a full six-degrees-of-freedom simulator. This model was developed by J. Rene Barrios of the Honeywell Company.

The Wind Shear Simulation Model (WSSM) is a point mass three-degrees-of-freedom mathematical model which simulates the motion of an aeroplane in a vertical plane. The equations of motion, which are described in the wind axes, include the wind components of velocity and acceleration so that the aeroplane dynamics during a wind shear encounter are accurately modelled. This model has been used by several investigators to study the behaviour of an aeroplane during wind shear encounters.

Note: The Wind Shear Simulation Model provided at the end of this Appendix is an example written in Microsoft QuickBasic. Other programming languages such as Microsoft FORTRAN, C, or assembly language are also acceptable.

The Equations of Motion

The motion of a constant mass point in the vertical plane may be described by four equations of state and a control variable. For an aeroplane, it is convenient to use an orthogonal reference frame which is attached to the frame of the aeroplane, and its x-direction points in the direction of motion. Such a reference frame is the relative wind reference frame.

The following equations model the states of the aeroplane in the wind axes:

$$Vdt = g[(T.csalf) - D)/W - sngam] - Wxdt.csgam - Wzdt.sngam (1)$$

$$Gdt = {g[(T.snalf + L)/W - csgam] + Wxdt.sngam - Wzdt.csgam}/V (2)$$

$$Hdt = V.sngam + Wz (3)$$

$$Xdt = V.csgam + Wx (4)$$

where:

Vdt

Rate of change of true airspeed in knots/second

G

Gravitational constant in knots/second

T

Total engine thrust in lb

csalf

cos (alpha)

alpha

Angle of attack in radians

D

Total drag in lb.

W

Gross weight in lb

sngam

sin (gamma)

gamma

Flight path angle in radians

Wxdt

Inertial wind shear x-component in knots/second

Gdt

Rate of change of gamma in rad/second

snalf

sin (alpha)

L

Total lift in lb

V

True airspeed in knots

Hdt

Altitude rate in knots

Wz

Inertial wind z-component in knots

Xdt

Ground speed in knots

In the above equations, the positive directions are upwards and forwards. This implies that tailwinds and updrafts are positive, while headwinds and downdrafts are negative. All the states can be determined from a given alpha; therefore, alpha is the control variable.

Since the model is that of a point mass, it is necessary to introduce the concept of alpha\_command and actual alpha to account for the effect of the horizontal tail/elevator. This is done by introducing a lag between the alpha\_command and the actual alpha. Therefore, any command that is given to the elevator or stabiliser can be interpreted as an alpha\_command, which will cause a change in the angle of attack.

From equations 1, 2, 3 and 4, it can be seen that any change in alpha will produce a change in the longitudinal and normal accelerations, which in turn will change the states of the aeroplane.

The Path Control Function

The different segments of the trajectory flown by the WSSM are described by a series of alpha\_commands, which are generated by the procedure explained below.

1.The aeroplane is trimmed for the initial conditions specified by the user. The initial conditions are usually specified as the altitude, gross weight, flaps, speed, flight path angle, and wind characteristics. The trimming operation consists in finding the angle of attack that satisfies the equations of state and will result in an unaccelerated motion.

2.After the initial trim, alpha\_command must be specified for each segment of the trajectory, which usually consists of a climb or descent segment at constant speed or constant path angle, and guidance through wind disturbances. The wind disturbance is provided by wind models that can be selected at initialisation time.

3.In order to specify an alpha\_command, the user must supply a subroutine where a quadratic function is defined in such a way that when minimised with respect to alpha, and constrained by the equations of state, the minimising alpha will produce the desired path in an optimal manner. For example, if we want to fly initially at a constant path angle, say 8 degrees, then the quadratic function may be defined by the expression:

<!-- formula-not-decoded -->

where:

cst

Function to be minimised w.r.t alpha

dt

Gdt*dt

Time increment used in simulation in sec.

A predictive term which anticipates the change in gamma

Other expressions follow:

<!-- formula-not-decoded -->

<!-- formula-not-decoded -->

The minimisation of the function cst is performed by a subroutine at each time frame and is totally transparent to the user, who has to supply only the objective function cst.

4.Each expression defining a different value of the objective function cst is called a 'LAW'. The user selects the guidance law to be used during the wind shear encounter at the time the menu is displayed. This method allows the user to compare different guidance laws under the exact same conditions.

The Wind Models

The WSSM has two types of wind models: the Dallas-Ft Worth accident wind field, simulated by a quad\_vortex model, and the constant shear model, which is user defined via the initial conditions menu.

Plotting Capabilities

The WSSM can plot up to 3 runs with 10 parameters per run. The length of each run should be kept under 60 seconds. This feature allows the user to compare different trajectories by overlaying the results.

The Programme

The WSSM is written in Microsoft QuickBasic, which is a highly structured language with a very friendly full-page editor. QuickBasic is very convenient for development, since it allows the user to stop execution, change the programme and continue executing. It also interfaces with Microsoft FORTRAN, C, or assembly language.

The procedure suggested for this application is that the WSSM be compiled without subroutines DETECT and GUIDE. DETECT and GUIDE can be separately compiled and put in a library called WNDSHR.QLB. These external subroutines may be written in Microsoft FORTRAN, C, or assembly language.

Listing of Programme '************ AIRCRAFT FLIGHT PROFILE SIMULATION ********** DECLARE SUB PLOT ( ) DECLARE SUB TAKEOFF ( ) DECLARE SUB EULER ( ) DECLARE SUB MCRBRST ( ) DECLARE SUB WINDS ( ) DECLARE SUB OPT ( ) DECLARE SUB MIN (DM, M2, C1, C2, C3, M) DECLARE SUB BEGIN ( ) DECLARE SUB VSHAKER ( ) DECLARE SUB COST ( ) DECLARE SUB LIMIT ( ) DECLARE SUB RATES ( ) DECLARE SUB THRUST ( ) DECLARE SUB ATMOS ( ) DECLARE SUB PRINTS ( ) DECLARE SUB DRAGS ( ) COMMON SHARED FLPS%, GEAR%, GEAR$, CL, CD, LIFT, DRAG, ALPHA COMMON SHARED SEC, ALT, DST, HDOT, ALF, GAM, GAMREF, GREF, G COMMON SHARED WSALERT%, WXO, WL, WX, WXDT, WZ, WZDT, DFW COMMON SHARED WV, LC%, GM, GREFF, NOSAVE, GMO COMMON SHARED DELTA, ISA, T0, SPDSND, VT, VC, MACH, A0, TAT, TAMF COMMON SHARED THRST, EPR, TFCT, APPFLG% COMMON SHARED SNGM, CSGM, CSAL, SNAL, VDOT, WG, GDOT, XDOT COMMON SHARED AWX, AWZ, AU, AZ, VG, GRND, KF1, GMIN, KF2 COMMON SHARED ACMD, OLDALF, DT, HP, LP, ALFLIM COMMON SHARED LAW%, GMR, ASS, CST, VTO, GCMD COMMON SHARED OUTFILE$, DM, ALT1, PL$, TTT, WXDTO, TDX, TSH, WZO, TDZ, TSV COMMON SHARED GM1, VTP, THETA COMMON SHARED ALFRTE, PLMFLG% '******************************************* ' MAIN PROGRAM * '******************************************* START: '&lt; ----------------&lt;&lt; RE-RUNS START HERE

``` CLOSE : CLEAR COLOR 15, 1: CLS : VIEW PRINT LOCATE 8, 23: PRINT "WINDSHEAR SIMULATION" LOCATE 10, 23: PRINT "FOR " LOCATE 12, 23: PRINT "BOEING 737/200 " LOCATE 23, 23: PRINT "TYPE " + CHR$(&H22) + "I" + CHR$(&H22) + " FOR INFORMATION" DO WHILE a$ = "" a$ = INKEY$ LOOP IF a$ = "I" OR a$ = "i" THEN a$ = "": CLS '---------------------- INFORMATION PAGE----------------------------------------LOCATE 2, 2: PRINT "BOEING 737/200 INFORMATON" LOCATE 3, 2: PRINT "JT8D-17 ENGINES" LOCATE 5, 2: PRINT "-------------------------------------------------------------------------" LOCATE 7, 2: PRINT "ALLOWABLE WEIGHT RANGES..................: 75,000 TO 120,000 POUNDS" LOCATE 9, 2: PRINT "ALLOWABLE TAKEOFF FLAP SETTINGS.........: 1, 2, 5, 15, 20, 25 DEGREES" LOCATE 11, 2: PRINT "ALLOWABLE LANDING FLAP SETTINGS.........: 30, 40 DEGREES" LOCATE 13, 2: PRINT "TAKEOFF EPR AT SEA LEVEL, STD. DAY...: 2.1 " LOCATE 15, 2: PRINT "REFERENCE WING AREA.......................: 980 SQUARE FEET" LOCATE 17, 2: PRINT "REFERENCE TAKEOFF SPEED..................: V2 + 10" LOCATE 19, 2: PRINT "REFERENCE LANDING SPEED..................: 1.3 Vs" LOCATE 23, 2: PRINT "Press Any Key to Continue..." DO: LOOP WHILE INKEY$ = "" END IF ANS$ = "2" CLS WHILE (ANS$ = "2") LOCATE 10, 30: PRINT "Fly ..... 1" LOCATE 12, 30: PRINT "Plot ..... 2" LOCATE 14, 30: PRINT "Exit ..... 3" LOCATE 18, 30: INPUT "Selection ....."; ANS$ IF ANS$ = "2" THEN CALL PLOT COLOR 15, 1 ```

CLS END IF WEND IF ANS$ = "3" THEN END CALL BEGIN 'GET DATA/INITIALIZE VARIABLES CALL THRUST 'INITALIZE THRUST CALL TAKEOFF 'INITALIZE TAKEOFF CALL COST 'SUBROUTINE COST CALL PRINTS 'SUBROUTINE PRINT FOR ICL% = 1 TO TTT ' TTT IS THE RUN TIME IN SECONDS CALL THRUST ' SUBROUTINE EPR/THRUST CALL WINDS ' SUBROUTINE WINDS ' CALL DETECT ' SUBROUTINE WINDSHEAR DETECTION ' SUPPLIED BY USER ' MUST RESIDE IN LIBRARY WNDSHR.QLB CALL OPT ' SUBROUTINE OPTIMIZE CALL LIMIT ' SUBROUTINE ALPHA RATE CALL EULER ' SUBROUTINE INTEGRATE CALL ATMOS ' SUBROUTINE ATMOSPHERE CALL PRINTS ' SUBROUTINE PRINT IF ALT &lt; 0 THEN EXIT FOR NEXT ICL% PRINT "RUN IS COMPLETE" PRINT "TYPE " + CHR$(&amp;H22) + "D" + CHR$(&amp;H22) + " FOR RUN DATA" a$ = "" DO WHILE a$ = "" ' Wait for key to be pressed a$ = INKEY$ LOOP VIEW PRINT: COLOR 15, 4: CLS IF a$ = "D" OR a$ = "d" THEN a$ = "" LOCATE 2, 2: PRINT "DATA FROM CURRENT RUN" LOCATE 4, 2: PRINT "--------------------------------------------------------------" LOCATE 6, 2: PRINT "GROSS WEIGHT: "; WG; " POUNDS" LOCATE 7, 2: PRINT "ISA DEVIATION: "; ISA; " DEG C"

LOCATE 8, 2: PRINT "FLAP POSITION: "; FLPS%; " DEGREES" LOCATE 9, 2: PRINT "GEAR POSITION: "; GEAR$ LOCATE 11, 2: PRINT "CONTROL LAW: "; LAW% LOCATE 12, 2: PRINT "GAMMA REFERENCE: "; GAMREF LOCATE 13, 2: PRINT "PITCH LIMITING: "; PL$ IF PL$ = "YES" THEN LOCATE 14, 2: PRINT "MAXIMUM PITCH: "; HP * 57.3; " DEGREES" LOCATE 15, 2: PRINT "MINIMUM PITCH: "; LP * 57.3; " DEGREES" END IF LOCATE 16, 2: PRINT "TIME OF RUN: "; TTT * DT; " SECONDS" IF DFW = 1 THEN LOCATE 17, 2: PRINT "DALLAS/FW Wind Model" ELSE LOCATE 17, 2: PRINT "HORIZ. WIND MAGNITUDE "; WXO; " KNOTS" LOCATE 18, 2: PRINT "HORIZ. SHEAR MAGNITUDE: "; WXDTO; " KNOTS/SECOND" LOCATE 19, 2: PRINT "HORIZ. SHEAR DURATION: "; TDX; " SECONDS" LOCATE 20, 2: PRINT "VERT. WIND MAGNITUDE: "; WZO * 1.689; " FT/SECOND" LOCATE 21, 2: PRINT "VERT. WIND DURATION: "; TDZ; " SECONDS" LOCATE 22, 2: PRINT "--------------------------------------------------------------" END IF IF LEN(OUTFILE$) = 0 THEN OUTFILE$ = "NONE" LOCATE 23, 2: PRINT "OUTPUT FILE: "; OUTFILE$ LOCATE 24, 2: PRINT "Press Any Key to Continue...." DO: LOOP WHILE INKEY$ = "" 'Wait for key to be pressed END IF GOTO START END SUB ATMOS STATIC '****************************************************** ' SUBROUTINE ATMOSPHERE * '****************************************************** STATIC THETA L% = ALT &gt; 36089! FISA = 1.8 * ISA

- IF ALT &gt; 36089 THEN

``` TMP = .7519 * T0 DELTA = .2234 * EXP((36089! - ALT) / 20806) ELSE TMP = T0 - .0035662 * ALT DELTA = (TMP / T0) ^ 5.256 END IF TAMB = TMP + FISA 'TAMBient in deg. R TAMF = TAMB - 459.7 ' " " F THETA = TAMB / T0 SQRTH = SQR(THETA) SPDSND = A0 * SQRTH IF VT > 0 THEN MACH = VT / SPDSND VC = A0 * SQR(5 * (((1 + MACH * MACH / 5) ^ 3.5 - 1) * DELTA + 1) ^ .28571 - 5) TAX = (TMP + FISA) * (1 + .2 * MACH * MACH) 'Deg. R TAT = 5 * (TAX - 459.7 - 32) / 9 'Deg. C IF INKEY$ < > "" THEN PRINT : INPUT "Press ENTER to continue...."; XXX END SUB SUB BEGIN STATIC CLS : VIEW PRINT '<--------------------------------- DATA_INPUT ------------------------------> PRINT INPUT "OUTPUT FILE (DEFAULT IS NO FILE) "; OUTFILE$ IF OUTFILE$ = " " THEN NOSAVE = 1 ELSE NOSAVE = 0 END IF ' CONSTANTS USED IN CALCULATIONS: A0 = 661.478599# 'Speed of sound at sea level in knots G = 19.07583 'Gravitational constant in knots/sec T0 = 518.67 'Standard temperature at SL in deg Rankine DT = .25 'Simulation time step in seconds ' ---------------------------------- INITIALIZATION OF VARIABLES-------------------------GMIN = 0 VDOT = 0 ```

``` ALT1 = 0 INPUT "TAKEOFF OR APPROACH (T/A) (Default is T)....."; ANS$ IF ANS$ = "a" OR ANS$ = "A" THEN INPUT "ENTER ALTITUDE IN FEET (Default is 1000' . "; ALT1 IF ALT1 = 0 THEN ALT1 = 1000 APPFLG% = 1 TFCT = 1 END IF ALT = ALT1 ' ----------------------- CONFIGURTATION CONSTANTS-----------------------------------------ASS = 16.5 'Stick Shaker alpha in degrees ASS = ASS / 57.3 ' " " " "radians ' ------------------------------------------- GROSS WEIGHT ENTRY-----------------------------------------PRINT : INPUT "ENTER GROSS WEIGHT IN POUNDS (Default is 110000) "; WG IF WG = 0 THEN WG = 110000! ' DEFAULT SETTING FL% = 0 WHILE (NOT FL%) INPUT "ENTER FLAPS SETTING (Default is 0)............."; FLPS% SELECT CASE FLPS% CASE 0, 1, 2, 5, 15, 20, 25, 30, 40 FL% = -1 CASE ELSE FL% = 0 PRINT "Invalid flaps setting" PRINT "Only 0, 1, 2, 5, 15, 20, 25, 30, & 40 are supported" PRINT END SELECT WEND IF FLPS% < 15 THEN GEAR% = 1 IF FLPS% = 15 THEN INPUT "GEAR UP OR DOWN (1/0) (Default is Down)....."; GEAR% IF GEAR% = 1 THEN GEAR$ = " UP" ELSE GEAR$ = " DOWN" END IF ```

``` INPUT "ENTER ISA DEV. IN DEGREES C (Default is 0)......"; ISA PRINT CALL VSHAKER ' COMPUTE V2+10 FOR FLAPS<33 OR 1.3Vs FOR FLAPS>32 PRINT " CONTROL LAW SELECTION:" PRINT PRINT " Speed = 1.1* V_stall = 1" PRINT " Alpha = Stick Shaker Alpha = 2" PRINT " Horizontal Acceleration = 0 = 3" PRINT " 15_Degree Pitch = 4" PRINT " Theoretical HONEYWELL/SPERRY = 5" PRINT " User Defined = 6" PRINT INPUT " SELECT CONTROL LAW ....................... "; LAW% IF LAW% = 0 THEN LAW% = 5 PRINT : PRINT ' ----------------------------------- GAMMA REFERENCE INPUT--------------------------------IF LAW% > 4 THEN INPUT "ENTER GAMMA REFERENCE IN DEGREES (Default is 0)........."; GMR PRINT GAMREF = GMR GMR = GMR / 57.3: GMIN = GMR END IF ' --------------------------------------- PITCH LIMITING SELECTION--------------------------------------------INPUT "PITCH LIMITING DESIRED (y/n) (Default is NO)..............."; PL$ IF PL$ = "Y" OR PL$ = "y" THEN PL$ = "YES" INPUT " MAXIMUM PITCH ALLOWED IN DEGREES "; HP INPUT " MINIMUM PITCH ALLOWED IN DEGREES "; LP HP = HP / 57.3: LP = LP / 57.3: PL% = 1 ELSE HP = 100 LP = -100 PL% = 0 PL$ = "NO" END IF ```

``` CLS ' ----------------------------------------------- TIME FOR RUN---------------------------------------------------------------- PRINT INPUT "ENTER TIME OF RUN IN SECONDS (Default is 45).............."; TTT TTT = TTT / DT IF TTT = 0 THEN TTT = 45 / DT ' DEFAULT SETTING ' ------------------------------------- WINDSHEAR SET UP---------------------------------------------------- INPUT "DALLAS/FW Wind Model (y/n)...(Default is constant Shear)....."; ANS$ IF ANS$ = "Y" OR ANS$ = "y" THEN DFW = 1 ELSE DFW = 0 PRINT INPUT "MAGNITUED OF HORZ. WIND IN KNOTS......(Head wind < 0)......"; WXO INPUT "MAGNITUED OF HORZ. SHEAR IN KT/SEC. (Dec. Perf. > 0)......"; WXDTO INPUT "DURATION OF HORZ. SHEAR IN SEC.............(Default is 0)......"; TDX INPUT "TIME FOR SHEAR TO START IN SEC..............(Default is 0)......"; TSH PRINT INPUT "MAGNITUED OF VERT. WIND IN FT/SEC. (Down Draft < 0)......"; WZO WZO = WZO / 1.689 'Convert to knots INPUT "DURATION OF VERT. WIND IN SEC...........(Default is 0)........"; TDZ INPUT "TIME FOR SHEAR TO START IN SEC...........(Default is 0)......"; TSV PRINT END IF ' -------------------- OTHER SET UPS---------------------------------------------------- VT = VTO WX = WXO CALL ATMOS ' SUBROUTINE ATMOSPHERE ' ---------------------------------- HEADERS FOR SCREEN DISPLAY---------------------------------------------------- CLS : PRINT PRINT "TIME ALT HDOT VT ALPHA GAMMA PITCH GREF WXDT WZ VDOT ALRT" PRINT "(SEC) (FT) (FPM) (KTS) (DEG) (DEG) (DEG) (DEG) (KT/S) (FPS) (KT/S)" PRINT STRING$(75, "-"): VIEW PRINT 5 TO 25 '************************************** ```

' SUBROUTINE INIT\_OUTPUT FILE *

'**************************************

IF NOSAVE THEN ' CREATE OUTPUT FILE

ELSE

OPEN "O", 2, OUTFILE$

FMT$ = " ###.## ##### ##### #### #### ## ###.## ###.## ###.##"

FMT$ = FMT$ + " ###.## ###.# ###.# ##.## "

END IF

END SUB

SUB COST STATIC

'************************************************************

' SUBROUTINE COST *

'************************************************************

CALL DRAGS ' SUBROUTINE DRAG &amp; LIFT

CALL RATES ' SUBROUTINE RATES

IF LC% = 0 THEN 'Constant gamma segment

FCT = (GM + GDOT * DT - GMO) ^ 2

GREFF = 57.3 * GMO

ELSE 'All guidance laws

SELECT CASE LAW%

CASE 1 ' ---------------------------- 1.1*Vstall-----------------------------------