# Discussion: Vector And Turn Analysis Of Observed And Measured Flight Paths Of 9/11 WTC Aircraft

**Abstract Aidan Monaghan 3-27-2010 911blogger.com**

The observed speeds of the attack aircraft of September 11, 2001 in New York City were extreme by comparison to the typical speeds of similar aircraft traveling at similar altitudes. The calculated speed for United Airlines Flight 175 (UA 175) is three times greater than the speed recommended for landing approaches of such wide-body airliners toward airport runways that are comparable in width to each World Trade Center tower. The calculated speed for American Airlines Flight 11 (AA 11) was two and one half times greater than the speed recommended for landing approaches of such wide-body airliners. While creating significantly less response time for possible human hijacker pilot course corrections during final target approaches that would demand superior control surface operation, a general vector analysis of the course and speed for these two aircraft demonstrate that the unusually high speeds observed generated greater accuracy of the aircraft while enroute to their targets, as a result of smaller deflection angles and ground track displacements in feet per second, created by existing crosswinds and potential wind shear. **A coupling of these two factors suggests superior navigation of AA 11 and UA 175, consistent with an unreported use augmented GPS guided aircraft autopilot systems available circa 2001, which also seem to be in evidence during analysis of UA 175’s final turning approach toward WTC 2[1].**

`UA 175’s 20 Degree Banking Turn On 9/11 From 1.2 Miles Distant`

`UA 175’s Final 18 Degrees Of Banking Turn`

**UA 175 Turn Analysis**

Video of United Airlines flight 175 (UA 175) on September 11, 2001 while enroute to World Trade Center tower 2 (WTC 2) reveals how it’s next-to-final, stable, descending and approximately 20 degree banked turn toward WTC 2 that alone would have resulted in UA 175’s impact with the south face of WTC 2, begins from a distance of 1.2 miles before impact.[2] While intercepting a 200 foot wide target during a constant radius turn beginning over one mile before impact apparently provides significant challenges for an inexperienced human pilot, such descending constant radius turns designed to intercept plotted waypoints during commercial aviation approach operations are supported by augmented GPS navigation service and related commercial flight management systems available circa 2001. Aircraft distances are based on reported aircraft speed for UA 175 of 799 feet per second at impact and measured times to impact[3].

UA 175 eight seconds and 1.2 miles before impact:

UA 175 seven seconds before impact:

UA 175 six seconds before impact:

UA 175 five seconds before impact:

UA 175 four seconds before impact:

UA 175 three seconds before impact:

It can determined that UA 175’s unwavering next-to-final banked turn toward WTC 2 alone without correction, would apparently have lead to the impact of UA 175 with the south face of WTC 2. At approximately 2.5 seconds prior to its impact with WTC 2, UA 175 banks an additional 18 degrees to its left, apparently generating an estimated lateral movement of approximately 21 feet closer to the center of the south face of WTC 2.[4] This approximation of an additional 18 degrees of bank is arrived at by subtracting the approximately 20 degree observed bank angle of UA 175 while enroute to WTC 2 during five of its final eight seconds of flight, from the 38 degree angle of impact created by UA 175’s impact with WTC 2.

`UA 175’s 38 Degree Angle Of Impact With WTC 2`

Because UA 175 impacted WTC 2 approximately 23 feet to the right of the center of its south face, it can be determined that even without the observed final 18 degrees of additional banking turn initiated by UA 175 approximately 2.5 seconds prior to its impact with WTC 2, that UA 175 would still have impacted WTC 2 at approximately 44 feet to the right of the center of its south face. This conclusion is arrived at by calculation of the distance between the groundtrack created by the final 18 degree banking turn performed by UA 175 2.5 seconds before its impact with WTC 2 and what would have been the remainder of the approximately 20 degree next-to-final banking turn that was already underway. As will be demonstrated, UA 175’s final turn spanning 18 degrees of bank beginning 2.5 seconds prior to its impact with WTC 2, generated only 21 feet of lateral displacement from the groundtrack created by the prior turn.

`UA 175’s Impact Approximately 23 Feet Right Of Center Of WTC 2`

`Relationship Between Two Differing Rates Of Turn Beginning At Common Point`

`Augmented GPS, Autopilot Controlled Radius-To-Fix Turn`

Estimates for aircraft turn radius and turn circumference are derived from the following calculations:

Aircraft turn radiuses (R) are provided by: R = True Airspeed^2/11.26Tan(Angle of Bank)

Aircraft turn circumferences (C) are provided by: C = 2(Pi)R.

The proportions of each constant radius turn completed is provided by: T = Speed*Time/Circumference of Turn.

Turn proportions are then multiplied by 360 degrees to determine the number of degrees of each turn completed:

UA 175’s Final Turn Radius = 799^2/11.26Tan(30 degrees). This 30 degree AoB is an approximated average for a span of 21-38 degrees during the 2.5 seconds prior to impact with WTC 2.

UA 175’s Final Turn Angle: [(799f/s)2.5/217,059]*360 = 3.31 degrees of turn.

UA 175’s Next-to-Final Turn Radius = 799^2/11.26Tan(20 degrees) This 20 degree AoB is based on observed approximations.

UA 175’s Next-to-Final Turn Angle: [(799f/s)2.5/344,287]*360 = 2.09 degrees of turn

Angles of turn completed and turn radiuses are then utilized in order to obtain ordered pairs for use in a Cartesian coordinate system:

X(for Turns A and B) = R – [R * Cos (Degrees of Turn)]

Y(for Turns A and B) = R * Sin (Degrees of Turn)

Aircraft Turn A (final turn):

Xa = 34,546 – (34,546 * Cos (3.31)) = 57.63

Ya = 34,546 * Sin (3.31) = 1,994.6

Aircraft Turn B (next-to-final turn):

Xb = 54,795 – (54,795 * Cos (2.09)) = 36.45

Yb = 54,795 * Sin 2.09 = 1,998.3

Individual aircraft X and Y components are combined:

X-separation = Xa – Xb

Y-separation = Ya – Yb

X-separation = 57.6 – 36.4 = 21.2

Y-separation = 1,994.6 – 1,998.3 = -3.7

The approximate final distance between UA 175’s next-to-final turn and its final turn at impact with WTC 2, is obtained by Pythagorean’s theorem:

[(X-separation^2) + (Y-separation^2)] =21.2^2 + -3.7^2 = 463.13^1/2 = 21.5 feet.

Given that UA 175’s unchanging next-to-final banked turn of 20 degrees maintained until approximately 2.5 seconds before its impact with WTC 2, would alone have apparently resulted in UA 175’s impact with WTC 2, it would seem that UA 175’s inability to impact more accurately with the center of WTC 2’s south face was a result of the lateral deflection that would be caused by the 11-22mph crosswinds experienced while enroute to WTC 2, which was earlier demonstrated to generate a maximum of 14 feet per second (f/s) of lateral groundtrack displacement by using the upper estimate of 22mph. At a rate of uncorrected lateral displacement of 14f/s multiplied by 8 seconds, a tracking error of 112 feet wide right of the center WTC 2’s south face is apparently generated. This magnitude of displacement generally correlates with the estimated displacement of 44 feet from the center of the south face of WTC, that would have resulted from UA 175’s next-to-final turn if not corrected. UA 175’s final 18 degrees of final banking turn to its left, which would generate an estimated lateral movement of approximately 21 feet closer to the center of the south face of WTC 2 than the groundtrack created by its next-to-final turn, may suggest an autoflight system under augmented GPS guidance attempting to correct a trajectory for interception of a geographic waypoint located at the center of WTC 2.

Adding or subtracting a mere 5 degrees of bank angle with respect to the observed 20 degrees of banking next-to-final turn of UA 175, beginning from a distance of 1.2 miles prior to UA 175’s impact with WTC 2, results in displacements of 108 feet and 119 feet respectfully, to the left and right of the groundtrack created by the observed 20 degrees of banking next-to-final turn of UA 175.

Estimates for aircraft turn radius and turn circumference are derived from the following calculations:

Aircraft turn radiuses (R) are provided by: R = True Airspeed^2/11.26Tan(Angle of Bank)

Aircraft turn circumferences (C) are provided by: C = 2(Pi)R.

The proportions of each constant radius turn completed is provided by: T = Speed*Time/Circumference of Turn.

Turn proportions are then multiplied by 360 degrees to determine the number of degrees of each turn completed.

**Turn Separation Between 15 and 20 Degrees of Bank**

Aircraft Turn A: 15 degrees: (r: 74,430); [(799)8/467,657]*360 = 4.9

Aircraft Turn B: 20 degrees: (r: 54,795); [(799)8/344,287]*360 = 6.7

Aircraft Turn A:

Xa (15 degrees)= 74,430 – [74,430 * Cos (4.9)] = 272

Ya (15 degrees) = 74,430 * Sin 4.9 = 6,357.5

Aircraft Turn B:

Xb (20 degrees)= 54,795 – [54,795 * Cos (6.7)] = 374

Yb (20 degrees) = 54,795 * Sin 6.7 = 6393

X-separation = Xa – Xb

Y-separation = Ya – Yb

X-separation = 272 – 374 = -102

Y-separation = 6,357.5 – 6,393 = -35.5

Separation = square root of [(X-separation^2) + (Y-separation^2)]

(-35.5)^2 + (-102)^2 = 11,664^1/2 = 108 feet feet

**Turn Separation Between 20 and 25 Degrees of Bank**

Aircraft Turn A: 20 degrees: (r: 54,795); [(799)8/344,287]*360 = 6.7

Aircraft Turn B: 25 degrees: (r: 42,771); [(799)8/268,738]*360 = 8.5

Aircraft Turn A:

Xa (20 degrees)= 54,795 – [54,795 * Cos (6.7)] = 374

Ya (20 degrees) = 54,795 * Sin 6.7 = 6393

Aircraft Turn B:

Xb (25 degrees)= 42,771 – [42,771* Cos (8.5)] = 469.8

Yb (25 degrees) = 42,771 * Sin 8.5 = 6,321.9

X-separation = Xa – Xb

Y-separation = Ya – Yb

X-separation = 374 – 469.8 = -95.8

Y-separation = 6,393 – 6,321.9 = 71.1

Separation = square root of [(X-separation^2) + (Y-separation^2)]

(-95.8)^2 + (71.1)^2 = 14,232.8^1/2 = 119 feet

For the morning of September 11, 2001, wind speed and direction for the altitude of the aircraft impacts with each WTC tower were reported to be between 11 mph and 22mph, from the direction of true north[1] For this analysis, the upper estimate of 22mph (32 f/s) is used. Wind speeds near coastlines like those on Manhattan at the Hudson River and Upper New York Bay, can often be double those recorded on shore. Wind direction near such coastlines are also known to be less predictable than on shore winds. [2] The north faces of each WTC tower were oriented 29 degrees clockwise from true north. [3] The impact of AA 11 with WTC 1 was perpendicular to its north face. The impact of UA 175 was approximately 9 degrees clockwise of perpendicular to its south face. At its time of impact with WTC 1, AA 11 is estimated to have been traveling at a speed of 683 feet per second (466 mph) [4]. At its time of impact with WTC 2, UA 175 is estimated to have been traveling at a speed of 799 feet per second (545 mph)[5] Analysis of adjusted hypothetical speeds for AA 11 and UA 175 (185 mph) is based on recommended Airbus landing approach speed.[6] Calculations are rounded to the nearest integer.

**Vector Calculations for American Airlines Flight 11**

P (plane): approximate compass bearing 210° (traveling approximately southwest) at 655 f/s (446 mph); W (wind): traveling south at 32 f/s (22 mph).

Plane and wind vector components represented by ordered pairs:

P = [655 f/s cos(240°), 655 f/s sin(240°)] = -328, -567

W = [32 f/s cos(270°), 32 f/s sin(270°)] = 0, -32

-328 + 0 = -328

-567 + (-32) = -599

Resolved components substituted into Pythagoreans theorem for resultant speed:

||P + W|| = 328² + 599² = 466, 3851/2 = 683 f/s (466 mph)

Resolved components substituted for resultant bearing:

tan ?1(599/328) = 61°; (90° – 61°) + 180° = 209°

Deflection angle = 210° – 209° = 1°

Groundtrack displacement = 1°tan(683f/s) = 12f/s

**Vector Calculations For Adjusted Speed For American Airlines Flight 11**

P (plane): approximate compass bearing 210° (traveling approximately southwest) at 272 f/s (185 mph); W (wind): traveling south at 32 f/s (22 mph).

Plane and wind vector components represented by ordered pairs:

P = [272 f/s cos(240°), 272 f/s sin(240°)] = -136, -236

W = [32 f/s cos(270°), 32 f/s sin(270°)] = 0, -32

-136 + 0 = -136

-236 + (-32) = -268

Resolved components substituted into Pythagoreans theorem for resultant speed:

||P + W|| = 136² + 268² = 90,3201/2 = 301 f/s (205 mph)

Resolved components substituted for resultant bearing:

tan ?1(268/136) = 63°; ( 90° – 63°) + 180° = 207°

Deflection angle = 210° – 207° = 3°

Groundtrack displacement = 3°tan(301 f/s) = 16 f/s

**Vector Calculations for United Airlines Flight 175**

P (plane): approximate compass bearing 38° (traveling approximately northeast) at 823 f/s (561 mph); W (wind): traveling south) at 32 f/s (22 mph).

Plane and wind vector components represented by ordered pairs:

P = [823 f/s cos(52°), 823 f/s sin(52°)] = 507, 649

W = [32 f/s cos(270°), 32 f/s sin(270°)] = 0, -32

507 + 0 = 507

649 + (-32) = 617

Resolved components substituted into Pythagoreans theorem for resultant speed:

||P + W|| = 507² + 617² = 637,7381/2 = 799 f/s (545mph)

Resolved components substituted for resultant bearing:

tan ?1(617/507) = 51°; ( 90° – 51°) = 39°

Deflection angle = 39° – 38° = 1°

Groundtrack displacement = 1°tan(799 f/s) = 14f/s

**Vector Calculations For Adjusted Speed For United Airlines Flight 175**

P (plane): approximate compass bearing 38° (traveling approximately northeast) at speed 272 f/s (185 mph); W (wind): traveling south) at 32 f/s (22 mph).

Plane and wind vector components represented by ordered pairs:

P = [272 f/s cos(52°), 272 f/s sin(52°)] = 167, 214

W = [32 f/s cos(270°), 32 f/s sin(270°)] = 0, -32

167 + 0 = 167

214 + (-32) = 182

Resolved components substituted into Pythagoreans theorem for resultant speed:

||P + W|| = 167² + 182² = 61,0131/2 = 247 f/s (168 mph)

Resolved components substituted for resultant bearing:

tan ?1(182/167) = 47°; ( 90° – 47°) = 43°

Deflection angle = 43° – 38° = 5°

Groundtrack displacement = 5°tan(247 f/s) = 22 f/s

References:

[1]Plausibility Of 9/11 Aircraft Attacks Generated By GPS-Guided Aircraft Autopilot Systems

http://www.journalof911studies.com/volume/2008/AutopilotSystemsMonaghan.pdf

[2] NIST NCSTAR 1-5A (PDF page 124)

http://wtc.nist.gov/NCSTAR1/PDF/NCSTAR%201-5A%20Ch%201-8.pdf

[3] The Use of Land and Sea Based Wind Data in a Simple Circulation Model

http://ams.allenpress.com/archive/1520-0485/14/1/pdf/i1520-0485-14-1-193…

[4] UA 175’s 20 Degree Banking Turn On 9/11

http://www.youtube.com/watch?v=FZi7TiXWcC4

[5] NIST NCSTAR 1-5A (PDF page 97)

http://wtc.nist.gov/NCSTAR1/PDF/NCSTAR%201-5A%20Ch%201-8.pdf

[6] UA 175’s Final 18 Degrees Of Banking Turn

http://www.youtube.com/watch?v=i_aQK0fAMOA

[7] NIST NCSTAR 1-5A (PDF page 121)

http://wtc.nist.gov/NCSTAR1/PDF/NCSTAR%201-5A%20Ch%201-8.pdf

[8] NIST NCSTAR 1-5A (PDF page 61)

http://wtc.nist.gov/NCSTAR1/PDF/NCSTAR%201-5A%20Ch%201-8.pdf

[9] NIST NCSTAR 1-5A (PDF page 97)

http://wtc.nist.gov/NCSTAR1/PDF/NCSTAR%201-5A%20Ch%201-8.pdf

[10] Flight Operations Briefing Notes: Approach Techniques (PDF page 3)

http://www.mediafire.com/?2mn3hcymyig