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A simple formula, familiar to high school students, can be used to refute the official account of American Airlines Flight 77 -- alleged to have struck the Pentagon on September 11, 2001.

Force = Mass X Velocity Squared / Radius

This formula approximates the force that would be exerted on an aircraft when it transitions from its downward path to level flight.

First we determine the mass of the aircraft.

Flight 77, a Boeing 757, had taken off from Washington Dulles International airport, and was bound for Los Angeles. Assuming its fuel tanks were full, and ignoring the weight of the 64 passengers, and cargo (which should be available if one wants to include them), the weight of the plane would be about 255,000 pounds (Boeing Technical Specifications).

For our calculation we'll assume that weight and mass are equal, i.e. 255,000 pounds.

For velocity we turn to the official account that Flight 77 struck the Pentagon at "530 miles per hour" (The 9/11 Commission Report, p10).

For our calculation we'll assume that speed and velocity are equal, i.e. 530 mph (speed is a scalar and velocity is a vector).

To calculate the radius, we could begin with a statement in The 9/11 Commission Report (p9): Flight 77 was "5 miles west-southwest of the Pentagon" when it "began a 330-degree turn. At the end of turn, it was descending through 2,200 feet".

Next we need to calculate the maximum radius (the most conservative case) of the arc that would allow the aircraft to transition from its downward path to level flight (while clearing obstacles in its path), and strike the Pentagon at the point described in official reports.

We chose instead to use the radius calculated by Pilots for 9/11 Truth.

Pilots for 9/11 Truth base their calculation on the Flight Data Recorder (FDR) data obtained pursuant to a Freedom of Information Act request filed with the National Transportation Safety Board, and carefully constructed topography of the area below the flight path.

Leaving aside the discrepancies between the official account of Flight 77, and the Flight Data Recorder (which NTSB refuses to answer), Pilots for 9/11 Truth calculated a radius equal to about 579 feet.

From this they calculated the force on the Boeing 757 at 34 Gs, i.e. 34 times the force due to gravity.

There has been some criticism of the calculations performed by Pilots for 9/11 Truth, and they have answered their critics.

With mass, velocity, and radius equal to 255,000 lbs, 530 mph, and 579 feet respectively, the preceding formula yields force equal to 8,276,850 lbs, i.e. the Boeing 757 would act as if it had increased its weight by 8,276,850 lbs, or more than 32 times its normal weight.

With a virtual weight of about 8.5 million pounds, Flight 77 could not have levelled off before striking the Pentagon. It would have crashed before it reached the Pentagon.

This fact alone is sufficient to refute the official account of "Flight 77."

Neither Hani Hanjour -- the alleged pilot trainee "noted for incompetence", nor the Boeing 757, would have been in any condition to fly with "the top of the fuselage of the aircraft no more than 20 ft above the ground" (Pentagon Building Performance Report, p14).

Pilots for 9/11 Truth did another calculation by lowering the height of "Flight 77" below that shown by the FDR. They lowered it to to the top of the Virginia Department of Transportation communications antenna that sits below the alleged flight path.

With this very conservative case, they calculated the force on the Boeing 757 at 11.2 Gs. "11.2 Gs was never recorded in the FDR. 11.2 Gs would rip the aircraft apart" they state.

Calculations by Frank Legge and David Chandler, Scientists for 9/11 Truth, do not take into account the 4-storey Navy Annex on the north side of Columbia Pike (its southeast corner is at an elevation of 124 feet) and the gas station and electric power line west of the Pentagon. These appear to be higher than the flight path calculated by Legge and Chandler, which even if theoretically possible, is at least an order of magnitude more difficult than striking the Pentagon from the east. Stiking from the east is likely to inflict more damage to top military commanders whose offices overlook the Potomac River on the eastern side of the Pentagon.

Frank Legge and David Chandler ignore the overwhelming evidence against their conclusion. Their analysis requires one more step: calculating the probability that Hani Hanjour could fly a Boeing 757 in a spiral turn from 7000 feet along their calculated flight path to strike the western wall of the Pentagon between the first and second floor as described in the Pentagon Building Performance Report.