.I'm fixing an my calculations to include the energy involved in the fuel reaction with the air. This calculation is more involved and more accurate than the assumptions I had about raising the fuel to the boiling point. Since the fuel would have burned in reaction long before all of the fuel was raised to the boiling point in the event of ignition, this seemed to be the more appropriate model. Note however that the conclusions are the same, since now the gases of the reaction absorb a signifigant portion of the heat. I will have the finalized version ASAP. Probably by this weekend if not sooner.
Right now, you are reading the original version.
If the plane that hit the pentagon truly vaporized, then we can do a calculation to determine how fast the plane would have to be traveling for this to occur. For the purposes of simplicity I will assume the plane is an object of pure aluminum, with a Boiling point of 2519° C. The people, the luggage, and the seats will be ignored. This should not present a problem since these materials have a very low specific heat, and also constitute only about 15% of the total weight of the aircraft.
When an object is moving through the air it has a certain amount of kinetic energy. When the object collides with a stationary building, this kinetic energy is converted to other forms of energy, mostly heat. We will assume all the kinetic energy is converted into heat.
If the heat is all then converted to vaporizing the Aluminum, then the heat caused the temperature to reach the boiling point. Thus, we have the kinetic energy equal to the heat necessary to make the aluminum vaporize.
.
m = the mass in kilograms
v = the velocity in meters per second
△T = change in temperature, in Celsius degrees (or Kelvin)
S = Specific Heat , in Joules / kg*C°
Since the equation has the same variable “m” on both sides we can divide by m. Then multiply by 2 and take the square root to solve for the necessary velocity. Or,
Now the Specific Heat of Aluminum (S) is 900, and the change of temperature from 25° C to 2519° C is about 2500° C. So calculating the meters per second, we get
In order to convert the speed of meters per second to miles per hour, we will multiply the miles per meter (to cross-cancel meters and convert to miles) and then multiply 3600 seconds per hour (to cross-cancel seconds and convert to hours.) This results in the conversion factor of 2.236.
And so after multiplying 2.236, our final answer is 4743.2722 miles per hour.
Now if all of the Kinetic Energy could not have been converted to heat, that 747 passenger plane that hit the pentagon would have had to been able to travel well over 5000 miles per hour ?
Newsflash! The top speed of a Boeing 767 is 680 miles per hour. In other words, it is impossible for a plane to fly at full speed into anything and become instantly vaporized because the plane cannot fly at the very high speeds that would be necessary to generate that kind of heat.
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Now, lets assume that some of the heat could have come from the exploding of jet fuel. Note that not all of the heat created from the jet fuel would have gone to the melting of the aluminum, but we will nevertheless make that assumption. So this time the Kinetic Energy of the plane PLUS the heat created from exploding fuel will equal the heat necessary to vaporize the aluminum.
I will assume that the jet fuel has similar characteristics of kerosene. There were about 10,000 gallons of jet fuel which has a density of 3.068 kg/gal . So the mass of 10,000 gallons would be 30,680kg. The specific heat of jet fuel 2100 J/kg*C°. The boiling point of jet fuel is 162.77° C – or about 150 degrees change from room temperature.
You can go to http://www.uscrusade.com/forum/config.pl/read/1064 if you want a more detailed look at the chemistry and energy involved from a kerosene based fuel reaction with oxygen. I will however avoid this discussion. I will merely assume all of the fuel is converted to heat by raising the temperature to the boiling point since the plane vaporized almost immediately upon impact, so the heat from burning fires will not be included.
As for the math, this time when we divide by the mass “m” of the plane, we get the ratio of the fuel mass to the plane mass in the 2nd term on the left side of the equation. A fully loaded 767 Boeing aircraft weighs 159,200 kg. Thus the ratio of fuel mass to plane mass is
Or about 20%. Now solving the above equation for the velocity “v” of the plane, we get
After multiplying by 2.236, this becomes 4676.395 miles per hour. Even if you assume the fuel burned at 1400 degrees , the result is still 4076.63 miles per hour, which is still quite impossible of a speed for a 767 Boeing jet to attain. And even this speed is under the extreme assumption that all of the kinetic energy and all of the energy created from the jet fuel was converted into the heat that vaporized the Aluminum.
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Yet this speed cannot even be obtained if the plane dropped straight to the ground from the maximum altitude of commercial planes : at 40,000 meters. By letting the kinetic energy equal the potential energy due to gravity we can determine the speed of an object that falls from the sky to the ground.
Or if you solve this equation for the velocity “v” , you get :
, where “h” is the height
and “g” is the gravitational constant. So,
Or 1,979.83 miles per hour. And this is at the maximum height of commercial planes WITHOUT INCLUDING wind resistance and terminal velocity. The plane that hit the pentagon however, did not begin it’s dive towards the Pentagon at 40,000 meters, but at 3,000 meters. So the plane could not have reached speeds greater than 4,000 miles per hour.
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Now let’s assume the plane could have been traveling at 1,000 miles per hour upon impact with the Pentagon. How much more energy “E” would have been necessary to generate the heat required to vaporize the aluminum?
Or,
Let’s assume also that the fuel was burning at 600 ° C in order to include some aspect of heat from the fires of burning fuel . This is 4 times the boiling point of jet fuel. So if we solve for E .
And using the values for the variables that have been earlier described, we get
Joules
Or 2.399432 x 108 kilo-joules. How much more energy is this exactly? One kilo-watt hour is equivalent to 3600 kilo-joules. So this extra energy is equivalent to 66,650.8888 kw-hours, about enough energy to power 100 family residences for an entire month (assuming 750 kw-hrs per month.)
4.184 × 106 kilo-Joules is the energy released by explosion of 1 ton of TNT. So the extra energy would be equivalent to 57.3478 tons of TNT. And this is a very low end limit based on the assumption that the fuel energy was burning at 600 ° C, instead of 150 ° C. ( Note: At the lower temperature, the extra energy would be 64.277 tons of TNT.)
Now the density of TNT is about 1500 kg per m3 , so 57.3478 tons is about 80 cubic meters of TNT, which is the equivalent of 80,000 Liters , 21,134 gallons, or 2.7 million fluid ounces of volume. That's 225,000 cans of 12 oz. Coca-Cola or 9,375 f lat-bed cases of 24 cans each.
Leaving aside other issues, if we are to believe that it was a plane that hit the Pentagon, where did all of this extra energy come from?
There were two 9 ton engines on each wing, each of which constitute 10% of the total weight (20% together.) But how come there was only one hole at the point of impact? The idea that the wings and two 9-ton engines both folded up neatly into the single hole is absurd. According to the laws of physics and the historical experience, if the wings would ever sever from the body, the twin engines and wings would have been left exterior to the building. More likely, the wings should have remained intact upon impact, and there should have been two additional holes where the two 9-ton engines impacted the Pentagon. But there was only one small hole.
The official story of the 767 Boeing passenger plane completely vapoizing inside of the Pentagon defies rational application of the laws of Physics. But the government could clear all of this up by just releasing one of the videos they must have of the event. There are hundreds of video and surveillance equipement surrounding the Pentagon, yet the only video that is released is an entrance gate video that had an obstacle blocking the path of the "plane" that hit the Pentagon. What about the cameras on top of the Pentagon, or the two videos the FBI confiscated from a nearby hotel and gas station video camera? Why not release every single video, if these videos would prove once an for all that what hit the Pentagon was a passenger airplane? What kind of national security could be hurt by the releasing of these videos? Certainly the "crazy notions" of the critics would be forever silenced, so why don't they release every single video.
And the very notion that a plane could be in national air space for nearly 20 minutes without a surface to air missle blowing the plane out of the sky. How could such an inexperienced, incompetent pilot drop 3,000 meters and then suddenly strafe the ground at 100 feet for the last half a mile without bouncing on the ground? When Blue Angels do this air trick they cut their engines and turn them on again just before they hit the ground. The Boeing 767 is a much larger and heavier plane than the Blue Angels. How could this plane drop 7,000 feet out of the sky and then suddenly strafe the ground without crashing? The amount of g-force preventing the plane from making a near 90 degree turn is impossible for a plane with that weight to overcome. This is similar to a Large SUV taking a 90 degree turn at speeds in excess of 100 miles per hour, with the exception that the lift of the air is less forgiving than the friction of the road.