August 2015

NASA/CR–2015-218793

PTM Along Track Algorithm to Maintain 

Spacing During Same Direction Pair-Wise 

Trajectory Management Operations

Victor A. Carreno

National Institute of Aerospace, Hampton, Virginia
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August 2015

NASA/CR–2015-218793

PTM Along Track Algorithm to Maintain 

Spacing During Same Direction Pair-Wise 

Trajectory Management Operations

Victor A. Carreno

National Institute of Aerospace, Hampton, Virginia
Available from:

NASA STI Program / Mail Stop 148

NASA Langley Research Center

Hampton, VA 23681-2199

Fax: 757-864-6500
1. Introduction 

Pair-wise Trajectory Management (PTM) is a cockpit based operation where the 

controller clears an aircraft to maintain spacing from one or more designated 

aircraft. On-board PTM tools will aid the flight crew in implementing the PTM 

spacing. The tools are expected to consist of a traffic display, decision support to 

accept or reject a PTM clearance, speed guidance to maintain spacing, conflict 

detection, alerting and resolution logic, ADS-B in capabilities, and CPDLC 

communications. 

There are two types of PTM operations: 

1. One-dimensional in-trail where the PTM aircraft maintains spacing from aircraft 

in front and/or behind; 

2. Two-dimensional where the PTM aircraft maintains spacing from crossing 

aircraft and can maneuver laterally or longitudinally. 

This paper describes an algorithm that will generate speed guidance for the flight 

crew to maintain spacing from a designated aircraft during one-dimension, same 

direction1, PTM operations. The speed guidance will be in the form of a range of 

Mach speeds. 

2. Algorithm 

The algorithm takes the following parameters as input: 

 Latitude and Longitude of the PTM aircraft (ownship) 

 Velocity vector of the PTM aircraft (ownship) 

 Latitude and Longitude of the Designated aircraft 

 Velocity vector of the Designated aircraft 

 Flight level or altitude of the ownship 

 Velocity vector of the wind 

 Base Mach of the pair, string or chain operation2

 Air temperature 

 The order (leading or trailing) of the PTM aircraft with respect to the 

Designated aircraft 

 Whether or not the ownship is a designated aircraft for another PTM 

operation 

 

1 Same direction means aircraft with headings whose angular difference is less than 45 

degrees. Same course is defined in FAA JO 7110.65 and same track is defined ICAO Doc. 

4444 ATM/501. For the purposes of the algorithm in this paper, same direction, same 

course and same track are synonymous. 

2 PTM aircraft can operate in sequences of aircraft, which are following the same route. 

These sequences are called pairs, strings, and chains depending on the rules they are 

following. See reference [1] for more details.

1
The algorithm produces the following output: 

 Lower and upper range Mach guidance. 

2.1. Coordinates Mapping 

The first step in the PTM along track algorithm is to map the latitude and longitude 

coordinates into Cartesian coordinates. The latitude is mapped to the y-axis and the 

longitude to the x-axis. Figure 2.1 shows an example of two locations with aircraft 

ac1 at 44 degrees north, 43 degrees east and aircraft ac2 at 45 degrees north and 45 

degrees east. 

Figure 2.1. Example Coordinate Positions 

In the example shown in Figure 2.1, aircraft ac1 is defined as the PTM aircraft 

(ownship) and aircraft ac2 as the designated aircraft (traffic). The ownship is set at 

the origin of the Cartesian coordinate system, as shown in Figure 2.2. 

2
Figure 2.2. Location of aircraft in Cartesian Coordinates 

The location of aircraft ac2 is relative to ac1. The y component of the location of ac2 

is the difference in latitude between the two aircraft. The x component of the 

location of ac2 is the difference in longitude of the two aircraft at the average 

latitude. That is, the distance for the y component is the distance between longitude 

43 degrees east and 45 degrees east at the average latitude of 44.5 degrees north. 

The distance for the latitude is calculated by determining the difference in latitude 

angle between the aircraft and multiplying the angle by the radius from the center of 

the earth. The radius is the average radius of the earth plus the aircraft altitude. For 

the example shown in Figure 2.1, the latitude difference in distance is given by, 

 nautical miles (1) 

where, 

3437.74677 is the average radius of the earth in nautical miles, 

4.93746 is an altitude of 30,000 feet in nautical miles. 

The distance for the longitude is calculated by determining the difference in 

longitude angle between the aircraft and multiplying by the radius of a plane normal 

to the earth axis that dissects the earth at the average latitude, as shown in Figure 

2.3. For the example shown in Figure 2.1, the longitude difference in distance is 

given by, 

nautical miles (2) 

y =1 ́

2p

360

 ́ (3437.74677 + 4.93746)

x = 2  ́

2p

360

 ́ (3437.74677 + 4.93746)sin(90 - ave_ latitude)

3
Figure 2.3. Calculation of Longitudinal distance at Average Latitude 

2.2. Velocity Vectors 

The velocity vectors of the aircraft are mapped to the Cartesian coordinates system 

with the north component to the y-axis and the east component to the x-axis. 

Figure 2.4 shows an example of velocity vectors and utilizes the position of the 

example of Figure 2.2. The velocity vector for aircraft ac1 is 333.75 knots north and 

333.75 knots east. The velocity vector for aircraft ac2 is 286.08 knots north and 

381.43 knots east. Aircraft ac1 and ac2 speeds are 472.0 knots and 476.79 knots, 

respectively. 

4
Figure 2.4. Example of Velocity Vectors on the Cartesian Plane 

2.3. Intersection and Parallel Routes 

The one dimensional PTM operations are based on “along track” distance. To 

determine the along track distance between the aircraft, the intersecting point of the 

aircraft tracks is determined. Figure 2.5 shows the intersecting point for the 

position and velocity vector example. 

Figure 2.5. Intersecting Point of the Tracks 

5
There are 4 cases when determining the relative location of the intersecting point 

with respect to the aircraft: 

 Aircraft ac1 is after the intersection and ac2 is before 

 Aircraft ac2 is after the intersection and ac1 is before (Example of Figure 2.5) 

 Both aircraft are after the intersection point 

 Both aircraft are before the intersection point 

There is a possibility that there is no intersecting point between the tracks. This 

occurs when the velocity vectors are parallel. 

2.4. Leading and Trailing Aircraft and Along Track Distance 

Using the intersecting point of the tracks, the leading and trailing aircraft and the 

along track distance can be calculated. 

Case 1. Aircraft ac1 is after the intersection and ac2 is before 

When aircraft ac1 is after the intersecting point and ac2 is before, ac1 is the leading 

aircraft. The along track distance is the sum of the distances from each aircraft to 

the intersecting point. 

Case 2. Aircraft ac2 is after the intersection and ac1 is before 

When aircraft ac2 is after the intersecting point and ac1 is before, ac2 is the leading 

aircraft. The along track distance is the sum of the distances from each aircraft to 

the intersecting point. 

Case 3. Both aircraft are after the intersection point 

When both aircraft are after the intersection point, the aircraft with the longest 

distance to the intersection point is the leading aircraft. The along track distance is 

the difference of the leading aircraft distance minus the trailing aircraft distance to 

the intersection point. 

Case 4. Both aircraft are before the intersection point 

When both aircraft are before the intersection point, the aircraft with the shortest 

distance to the intersection point is the leading aircraft. The along track distance is 

the difference of the trailing aircraft distance minus the leading aircraft distance to 

the intersection point. 

6
Parallel tracks 

When the velocity vectors are parallel, there is no intersection point. A 

perpendicular vector to the velocity vector of ac2 to is calculated as shown in 

Figure 2.6. 

Figure 2.6. Aircraft on Parallel Tracks 

The intersection point for the parallel tracks scenario is the point a-beam of aircraft 

ac2. When aircraft ac1 is before the projected intersection point, aircraft ac2 is the 

leading aircraft. When aircraft ac1 is ahead of the intersection point, ac1 is the 

leading aircraft. The along track distance is the distance between aircraft ac1 and 

the projected intersection point. 

2.5. Speed Guidance for the PTM (ownship) Aircraft 

The objective of the algorithm is for the PTM (ownship) aircraft to maintain spacing 

from the designated aircraft in a safe and efficient manner. The spacing is the sum of 

a separation standard and buffer distance. The algorithm gives speed guidance to 

achieve the spacing. That is, if the along track distance is greater than the spacing, 

the algorithm will give speed guidance such that the along track distance can be 

reduced. When the along track distance is at or near the spacing, the algorithm will 

give speed guidance to maintain the spacing. The algorithm will give speed guidance 

such that the PTM aircraft can increase the along track distance if the PTM aircraft is 

not a designated aircraft for another PTM aircraft in a string. See examples 1 and 2 

which illustrate a PTM pair and a PTM string and the speed guidance associated 

with these operations. 

The following parameters are used in the computation of the speed guidance: 

 Separation standard distance – a minimum distance that shall never be 

infringed upon. The range between the aircraft shall never be less than the 

separation standard distance. 

 Buffer distance – a distance used to achieve the operational goal of the 

separation standard 

 Spacing – the sum of the separation standard distance and the buffer 

distance. 

 Along track distance – The distance between the aircraft along the flight path 

of the aircraft over segments that might include turns at waypoints. 

7
 Wind velocity – the velocity vector of the wind at the ownship location. 

 Base Mach – the speed that has been assigned to the designated aircraft. 

 Time to achieve spacing – the time used to calculate the speed guidance and 

to achieve spacing. 

 Time to achieve spacing when loss of spacing – the time used to calculate the 

speed guidance to achieve spacing when the along track distance is less than 

the spacing. 

 Maximum Mach – The maximum Mach that the algorithm will give as an 

upper bound. This value depends on the type of the aircraft. This maximum 

Mach does not mean that the aircraft can actually achieve this speed. It is a 

bound put on the algorithm guidance output. 

 Minimum Mach – The minimum Mach that the algorithm will give as the 

lower bound. This value depends on the type of the aircraft. This minimum 

Mach does not mean that the aircraft can actually achieve this speed. It is a 

bound put on the algorithm guidance output. 

The speed guidance is calculated starting with the ground speed of the aircraft. A 

new ground speed is calculated for the PTM aircraft. When the PTM aircraft is 

leading, the new ground speed is, 

 knots (3) 

where, 

 is the ground speed of the designated aircraft, 

 is the along track distance between the aircraft, 

 is the time to achieve spacing. 

When the PTM aircraft is trailing, the new ground speed is, 

 knots (4) 

From the new ground speed, a new True Air Speed (TAS) is calculated taking into 

account the wind velocity vector at the ownship location. The vectorial components 

of the TAS are calculated from the new ground speed. 

tasx= new_ gs ́sin(heading) -windx

 (5) 

tasy= new_ gs ́cos(heading) - windy

 (6) 

The magnitude of the TAS is calculated from the vectorial components. 

new_ gs = gsd -

DAT - spacing

Ts

gsd

DAT Ts

new_ gs = gsd +

DAT - spacing

Ts

8
TAS = tasx

2

+ tasy

2

 (7) 

In order to calculate the Mach speed, the speed of sound is calculated by, 

 knots (8) 

where temp is the temperature of the air in degrees Celsius. 

The new Mach number is the new True Air Speed divided by the speed of sound at 

altitude, 

new_ Mach =

TAS

ssound

 (9) 

The new Mach speed is rounded to the nearest one hundredth of a Mach. The speed 

guidance is determined from the new Mach speed, the maximum and minimum 

Mach, whether the ownship is leading or trailing the designated aircraft, and 

whether the ownship is a designated aircraft for another PTM operation. 

When the ownship is leading and not the designated aircraft for another PTM 

operation, the guidance is, 

Lower Mach = New Mach 

Upper Mach = Maximum Mach

When the ownship is leading and is designated aircraft for another PTM operation, 

the guidance is, 

Lower Mach = New Mach 

Upper Mach = max(Base Mach, New Mach) 

When the ownship is trailing and not the designated aircraft for another PTM 

operation, the guidance is, 

Lower Mach = Min Mach 

Upper Mach = New Mach 

When the ownship is trailing and is the designated aircraft for another PTM 

operation, the guidance is, 

Lower Mach = min(Base Mach, New Mach) 

Upper Mach = New Mach 

ssound =

3600

1852

 ́ 331.3  ́ 1+

temp

273.15

9
Where the function max(a, b) gives the greater of the two numbers a and b and the 

function min(a,b) gives the lesser of the two numbers a and b. 

2.6. Non linearity to account for Incremental Nature of 

Guidance 

The speed guidance in units of Mach speed is given to the flight crew in 0.01 Mach 

increments. This is the typical resolution of the Mach command in the flight control 

panel. That is, Mach guidance in thousandth of Mach increments cannot be selected 

in the flight control panel of the aircraft. For example, a Mach guidance of 0.834 

would not be possible to implement in a typical aircraft flight control panel. 

To be able to achieve spacing closer to the desired spacing objective, a non-linear 

characteristic is designed into the algorithm. 

The non-linearity is added into the algorithm by determining if the along track 

distance is less than the spacing requirement or more than the spacing requirement 

plus a hysteresis parameter. If the along track distance is less than the spacing 

requirement, the Mach guidance is adjusted by 0.01 Mach to increase the distance 

between the aircraft. If the along track distance is more than the spacing 

requirement plus the hysteresis parameter, the Mach guidance is adjusted by 0.01 

Mach to decrease the distance between the aircraft. 

3. Performance of the Algorithm and Examples 

This section presents three examples and what speed guidance is produced for a 

given set of parameters. The parameters used for the examples are shown in 

Table 3-1.

Table 3.1. Parameters Used for the Examples 

Parameter Value

Separation Standard distance 5 nautical miles

Buffer 1.5 nautical miles

Spacing 6.5 nautical miles

Hysteresis 0.2 nautical miles

Base Mach 0.82

Time to achieve spacing 30 minutes

Time to achieve spacing when 

loss of spacing exists

10 minutes

Minimum Mach 0.77

Maximum Mach 0.86

10
Example 1 

Example 1 is a PTM pair where the PTM aircraft is trailing the designated aircraft as 

shown in Figure 3-1. In this figure, the black aircraft (A) is the PTM aircraft and the 

white aircraft (B) is the designated aircraft. Aircraft A is maintaining spacing from B. 

Figure 3-1. Example 1, PTM pair with PTM Aircraft Trailing 

The speed guidance as a function of along track distance is shown in Figure 3-2.

Figure 3-2. Mach Guidance for Aircraft A as a Function of Along Track Distance 

When the along track distance is 6.4 NM, the algorithm gives a guidance of 0.77 to 

0.81 Mach. The upper guidance is less than the base Mach which will increase the 

along track distance to achieve the desired spacing of 6.5 NM. When the along track 

distance is 6.6 NM, the algorithm gives a guidance of 0.77 to 0.82 Mach which will 

increase or maintain the present distance. When the along track distance is 6.8 NM, 

the algorithm gives a guidance of 0.77 to 0.83 Mach which allows for the PTM 

aircraft to go faster than the designated aircraft and reduce the along track distance. 

The flight crew also has the option of going slower than 0.83 Mach to maintain or 

increase the distance. When the along track distance is 14 NM, the algorithm gives a 

11
guidance of 0.77 to 0.85. The flight crew can decrease, maintain, or increase the 

along track distance. 

Example 2 

Example 2 is a PTM string where 2 PTM aircraft are in trail of the designated aircraft 

as shown in Figure 3-3. Aircraft B is the designated aircraft for aircraft A and aircraft 

A is the designated aircraft for aircraft C. Aircraft A is maintaining spacing from 

aircraft B and aircraft C is maintaining spacing from aircraft A. 

Figure 3-3. Example 2, PTM String with PTM aircraft Trailing 

The speed guidance for PTM aircraft A as a function of along track distance between 

aircraft A and B is shown in Figure 3-4. 

Figure 3-4. Mach Guidance for Aircraft A as a Function of Along Track Distance 

12
Table 3.2 shows the distances and times for Example 1 when the PTM aircraft 

follows the upper guidance speed and the Time to Achieve Spacing parameter is set 

to 30 minutes. When the initial distance is 14 NM and the PTM aircraft follows the 

upper guidance, the aircraft will achieve spacing in 57.4 minutes.

Table 3.2. Time and Distance Between the PTM and Designated Aircraft, with Time to 

Achieve Spacing set at 30 minutes 

Time Distance PTM aircraft 

speed

Closure rate

0 minutes 14 NM 0.85 Mach 17.3 knots

1.4 minutes 13.6 NM 0.84 Mach 11.5 knots

17.1 minutes 10.6 NM 0.83 Mach 5.8 knots

57.4 minutes 6.7 NM 0.82 Mach 0 knots

Table 3.3 shows the distance and times for Example 1 when the PTM aircraft follows 

the upper guidance speed and the Time to Achieve Spacing parameter is set to 15 

minutes. When the initial distance is 14 NM and the PTM aircraft follows the upper 

guidance, the aircraft will achieve spacing in 38.6 minutes. 

Table 3.3. Time and Distance Between the PTM and Designated Aircraft, with Time to 

Achieve Spacing set at 15 minutes 

Time Distance PTM aircraft 

speed

Closure rate

0 minutes 14 NM 0.86 Mach 23.1 knots

6.8 minutes 11.4 NM 0.85 Mach 17.3 knots

11.6 minutes 10.0 NM 0.84 Mach 11.5 knots

18.9 minutes 8.6 NM 0.83 Mach 5.8 knots

38.6 minutes 6.7 NM 0.82 Mach 0 knots

Example 3 

Example 3 is a PTM chain where a PTM aircraft is between two designated aircraft 

as shown in Figure 3-5. Aircraft B and C are the designated aircraft for aircraft A. 

Aircraft A is maintaining spacing from aircraft B and C. 

Figure 3-5. Example 3, PTM Chain 

13
The speed guidance for PTM aircraft A as a function of along track distance between 

aircraft A and B and between aircraft A and C is shown in Figure 3-6.

Figure 3-6. Mach Guidance for Aircraft A as a Function of Along Track Distance 

between Aircraft A and B, lower x axis, and Aircraft A and C, upper x axis 

4. Accuracy, Errors, and other Considerations 

Radius of the Earth 

The calculations of distances from one position to another are performed using the 

average radius of the Earth. Because the Earth is not a perfect sphere, this can result 

in calculation errors of distance. The radius of the Earth at the equator is taken for 

WGS84 as 3,443.918466 nautical miles. The radius at the pole is 3,432.371660 for 

WGS84. The average radius used in the calculation of along track distance is 

3437.746771. When calculating the distance between two aircraft, which are 

approximately 15 nautical miles apart, an error of up to 0.0269 nautical miles or 

49.87 meters could result. The error increases as the distance between the aircraft 

increases and decreases as the distance between the aircraft decreases, where it is 

more critical. At 5 nautical miles apart, the maximum error will be 0.00898 nautical 

miles or 16.62 meters. A function to estimate the Earth radius as a function of 

latitude has been added which makes this error negligible. 

14
Coordinates Transformation 

The transformation from latitude and longitude to Cartesian coordinates could 

result in a distance error. To map the east-west longitude to the x-axis, the average 

latitude is used. When the aircraft are 15 nautical miles apart, the worst error is 

0.00006265 nautical miles or 0.116 meters. This error is negligible. 

Range vs. Along Track Distance 

A requirement for 1-dimensional PTM operations is that aircraft are same direction. 

Same direction aircraft are aircraft with headings whose angular difference is less 

than 45 degrees. The objective of the algorithm described in this paper is to 

maintain along track spacing. For separation standards and safety, the range 

between the aircraft is considered the metric of importance rather that the along 

track distance. 

When the along track distance is, for example, 6.5 nautical miles and the leading 

aircraft turns 45 degrees at a waypoint, the range between the aircraft will become 

6.005 nautical miles at the closes point of approach. 

Round of Mach Guidance 

The PTM Along Track algorithm will calculate Mach guidance to many digits of 

precision. However, it is not practical to give to the flight crew Mach guidance that is 

more than one hundredth of a Mach. For example, a Mach guidance of 0.82 to 

0.823176 cannot be implemented in the flight control panel. The need for giving 

guidance no more precise than hundredths of a Mach results in the optimal spacing 

not being achieved. Table 3.1 shows that when the aircraft have an along track 

distance of 8.0 nautical miles, the base Mach is 0.82, and the spacing is 6.5 nautical 

miles, the guidance is 0.82 to 0.82. That means that with this guidance, the spacing 

of 6.5 nautical miles will not be achieved. On the other hand, if the along track 

distance is 6.0 nautical miles, which is less than the desired spacing of 6.5 nautical 

miles, the guidance is also 0.82 to 0.82. If the along track distance gets reduced to 

5.9 nautical miles, and using the parameters of Table 3.1, then the guidance will be 

0.81 to 0.81 to increase the distance. 

The algorithm currently rounds the guidance to the nearest hundredth of a Mach. It 

is possible to modify the algorithm to round up or round down (truncate) to the 

nearest hundredth of the Mach. This modification will change the algorithm 

performance. If rounding up, the guidance will allow the aircraft to get closer 

together when the PTM aircraft is trailing and maintain the aircraft farther apart 

when the PTM aircraft is leading. When rounding up, the opposite effect will occur. 

The algorithm could also round depending on whether the PTM aircraft is trailing or 

leading and be designed such that the guidance will allow for the distances to be 

reduced further or the distances to remain longer. 

15
Pressure Altitude vs. Geometric Altitude 

The mapping of latitude and longitude to Cartesian coordinates take into account 

the aircraft altitude. The altitude is added to the radius of the Earth to determine 

distances. If the altitude used as input to the algorithm is the flight level of the 

aircraft rather than the geometric altitude, then an error will result. When the sea 

level barometric pressure is 29.92 inches of mercury (1013 hPa), the flight level is 

approximately the geometric altitude. Variations in atmospheric pressure will make 

the flight level and geometric altitude differ. To estimate the error, a lower 

atmospheric pressure than average is assumed. A lower atmospheric pressure will 

cause the aircraft to fly at lower geometric altitudes for a given pressure altitude. 

This in turn will result in a larger calculated distance than the actual distance. 

Assuming a barometric pressure of 25.10 inches of mercury (850 hPa), which is the 

lowest barometric pressure recorded on Earth, and the aircraft at FL350, the 

geometric altitude will be approximately 30,500 feet. 

When the aircraft are at a distance of 15 nautical miles, the difference between flight 

level and geometric altitude for this worst case condition will result in an error of 

0.003231 nautical miles or 5.98 meters. 

GPS and ADS-B Position Errors 

The algorithm accuracy will depend in the accuracy of the data being provided by 

the GPS data of the PTM (ownship) aircraft and the ADS-B data of the Reference 

aircraft. The source data of the ADS-B data of the designated aircraft is expected to 

also be GPS. 

The distance calculation errors resulting from position errors will depend on the 

magnitude of the position errors and whether the errors are correlated between the 

PTM and designated aircraft (correlated bias errors) or independent errors. 

The provision of 5 nautical miles separation in the U.S. National Airspace System 

using ADS-B requires a Navigation Accuracy Category for position of 7. This NACp 

level correspond to an accuracy of 0.1 nautical miles or 185.2 meters at a 95% level. 

5. Summary and Conclusion 

The PTM Along Track algorithm gives guidance to the flight crew of a PTM aircraft 

to maintain spacing from a designated aircraft during PTM operations. The spacing 

is the sum of a separation standard minimum distance and a distance buffer. The 

objective of the algorithm is to maintain safe and efficient PTM operations. Safe 

operations entail the range between the aircraft to never be less than the separation 

standard minimum. For efficient operations, it is desired that the along track 

distance is reduced as much as possible. 

16
Due to the rounding of the Mach guidance given to the flight crew and other 

operational considerations, an exact spacing cannot be achieved. The algorithm 

must establish an optimal balance between maintaining high aircraft density during 

PTM operations and achieving the safety requirements. 

6. References 

[1] Carreño, V. and Graff, T.; Definitions, Theory and Operational Rules for Chains 

and Strings in the PTM Application, version 6, 2 September 2013.

17
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PTM Along Track Algorithm to Maintain Spacing During Same Direction 

Pair-wise Trajectory Management Operations 

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NNL13AA08B

 6. AUTHOR(S)

Carreno, Victor A.

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 NASA Langley Research Center

 Hampton, Virginia 23681-2199 

 

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14. ABSTRACT

Pair-wise Trajectory Management (PTM) is a cockpit based delegated responsibility separation standard. When an air traffic 

service provider gives a PTM clearance to an aircraft and the flight crew accepts the clearance, the flight crew will maintain 

spacing and separation from a designated aircraft. A PTM along track algorithm will receive state information from the 

designated aircraft and from the own ship to produce speed guidance for the flight crew to maintain spacing and separation. 

15. SUBJECT TERMS

Avionics; Delegated responsibility; Separation standard; Traffic management

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collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and 

Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person 

shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

01- 08 - 2015