Posted by no spam on September 8, 2007, 10:42 am
>-> BTW, I did a little research and calculating on the impact of the
>aircraft.
> -> Taking just the mass and speed of the aircraft, i.e. not counting the
> -> burning jet fuel, the force of the aircraft hitting each tower was
> -> equivalent to about 40,000 pounds of TNT. I didn't know the exact
> numbers
> -> for a couple of things so I had to make a few assumptions. With that
> said
> -> you can check my work. FYI, unless other wise stated all info found by
> -> searching internet and all conversions were done using
> -> www.onlineconversion.com to cut down on human error.
> -> E=1/2 mv^2 ---- Basic kinetic energy formula
> -> 240000 lbs - - - assumed weight of aircraft at impact. ([max t.o. wt +
> -> empty wt]/2)
> -> (max takeoff weight 315,000lbs, empty
> weight
> -> 164,800lbs)
> -> 470 mph - - - - assumed speed at impact (averaged from a few
> estimates)
> -> 689 fps - - - - mph converted to fps
> -> E = (240000 lbs * 689 fps * 689 fps) / 2 = 56966520000 lb-ft^2/sec^2
> -> Using the website to convert that to tons of TNT gives:
> -> 56966520000 lb-ft^2/sec^2 = 18.459 tons of TNT
> -> I'm not sure which tons are used so it could equal either:
> -> 41,348 lbs (long tons), 40,695 lbs(metric tons) or 36,918 lbs(short
> tons)
> -> With those numbers in mind it is amazing that the buildings withstood
> the
> -> impact much less stood long enough for anyone to get out.
> Amazing indeed. Let's try again, without the gobbledygook units.
I used the units I found.
> Suppose the mass of the aircraft was 100 tons (1e5 kg), and it was
> travelling at 200 metres per second. Its kinetic energy would have been
> 0.5 x 1e5 x 200^2, which comes to 2e9 joules. TNT reaches a temperature
> around 1000 C, or maybe a bit more, when it explodes, so its energy
> production must be somewhere around 5000 joules per gram. So the mass
> of TNT that would produce the same energy as the aircraft's would be
> 2e9/5000 grams, which is 4e5 grams, or 0.4 tons. That is, I feel, a
> much more credible amount than your estimate of nearly 20 tons - fifty
> times as much as I've just calculated.
> I have absolutely no idea where the mistake is...
I was surprised at the number myself. But I did the math and showed my work
if I made a mistake please let me know where. One reason I used the website
for the conversions was to remove the chance I would make a math error. I
also used mid-range numbers for the weight and speed at impact to keep from
being accused of trying to hype something.
Posted by daestrom on September 8, 2007, 4:37 pm
>>-> BTW, I did a little research and calculating on the impact of the
>>aircraft.
>> -> Taking just the mass and speed of the aircraft, i.e. not counting the
>> -> burning jet fuel, the force of the aircraft hitting each tower was
>> -> equivalent to about 40,000 pounds of TNT. I didn't know the exact
>> numbers
>> -> for a couple of things so I had to make a few assumptions. With that
>> said
>> -> you can check my work. FYI, unless other wise stated all info found
>> by
>> -> searching internet and all conversions were done using
>> -> www.onlineconversion.com to cut down on human error.
>>
>> -> E=1/2 mv^2 ---- Basic kinetic energy formula
>>
>> -> 240000 lbs - - - assumed weight of aircraft at impact. ([max t.o. wt
>> +
>> -> empty wt]/2)
>> -> (max takeoff weight 315,000lbs, empty
>> weight
>> -> 164,800lbs)
>> -> 470 mph - - - - assumed speed at impact (averaged from a few
>> estimates)
>> -> 689 fps - - - - mph converted to fps
>>
>> -> E = (240000 lbs * 689 fps * 689 fps) / 2 = 56966520000 lb-ft^2/sec^2
>>
>> -> Using the website to convert that to tons of TNT gives:
>>
>> -> 56966520000 lb-ft^2/sec^2 = 18.459 tons of TNT
>>
>> -> I'm not sure which tons are used so it could equal either:
>>
>> -> 41,348 lbs (long tons), 40,695 lbs(metric tons) or 36,918 lbs(short
>> tons)
>>
>> -> With those numbers in mind it is amazing that the buildings withstood
>> the
>> -> impact much less stood long enough for anyone to get out.
>>
>> Amazing indeed. Let's try again, without the gobbledygook units.
> I used the units I found.
>> Suppose the mass of the aircraft was 100 tons (1e5 kg), and it was
>> travelling at 200 metres per second. Its kinetic energy would have been
>> 0.5 x 1e5 x 200^2, which comes to 2e9 joules. TNT reaches a temperature
>> around 1000 C, or maybe a bit more, when it explodes, so its energy
>> production must be somewhere around 5000 joules per gram. So the mass
>> of TNT that would produce the same energy as the aircraft's would be
>> 2e9/5000 grams, which is 4e5 grams, or 0.4 tons. That is, I feel, a
>> much more credible amount than your estimate of nearly 20 tons - fifty
>> times as much as I've just calculated.
>>
>> I have absolutely no idea where the mistake is...
> I was surprised at the number myself. But I did the math and showed my
> work if I made a mistake please let me know where. One reason I used the
> website for the conversions was to remove the chance I would make a math
> error. I also used mid-range numbers for the weight and speed at impact
> to keep from being accused of trying to hype something.
One of the many problems using 'English' units is that a pound-mass is not
the same thing as a pound-force. If you always use the complete terms, you
can easily spot where you need a 'conversion'.
Take for example a one pound-mass object that is allowed to free-fall in
'normal' gravity. It accelerates at 32.2 ft/sec^2. Yet if that same mass
rests on a scale, it exerts a downward force of just one pound-force. In
order to make Newton's "F=MA" work out, you have...
1 pound-force = 1 pound-mass * 32.2 feet/s^2 / <conversion constant>
The conversion constant is often called gc (g-sub-c) and has a value of 32.2
lbm-ft/ (lbf-sec^2). This conversion between pound-mass and pound-force
goes back more than a century when man didn't always have a good
understanding of the two. Pressure measurements and guages were often
calibrated with 'dead-weight' testers that simply put a certain number of
pounds mass on a piston with a known area to create a pressure (pound-force
per unit area). A lot of times when people (or web pages) use the term
'pound', you have to be careful to figure out if they mean pound-mass or
pound-force. Some places will use terms like 'slug' or 'poundal' to try and
avoid confusion with pound-force, but I've always used 'pound-mass' and
'pound-force'.
In your formula for KE you have...
KE = 1/2 * 240000 lbm * (689 ft/s)^2 = 5.69e10 lbm-ft^2/sec^2
But that isn't the same as 5.69e10 lbf-ft of energy. It's the wrong units.
To convert from lbm-ft/sec^2 to lbf-ft we must divide by g-sub-c and that
gives us 1.77e9 lbf-ft of energy. Converting that to Joules is about 2.40e9
Joules.
This site says a ton of TNT is about 4.0e9 Joules, so we have about 0.6 ton
of TNT equivalent.
http://hypertextbook.com/facts/2002/AlexRoslyakov.shtml
Still a sizeable explosion.
daestrom
P.S. Metric is easier, but here in the US I've always had to work through
the 'English' units. But even some common usage in the metric system can
confuse mass and force (e.g. a 'kilogram-force')
Posted by no spam on September 8, 2007, 9:58 pm
>>>-> BTW, I did a little research and calculating on the impact of the
>>>aircraft.
>>> -> Taking just the mass and speed of the aircraft, i.e. not counting the
>>> -> burning jet fuel, the force of the aircraft hitting each tower was
>>> -> equivalent to about 40,000 pounds of TNT. I didn't know the exact
>>> numbers
>>> -> for a couple of things so I had to make a few assumptions. With that
>>> said
>>> -> you can check my work. FYI, unless other wise stated all info found
>>> by
>>> -> searching internet and all conversions were done using
>>> -> www.onlineconversion.com to cut down on human error.
>>>
>>> -> E=1/2 mv^2 ---- Basic kinetic energy formula
>>>
>>> -> 240000 lbs - - - assumed weight of aircraft at impact. ([max t.o. wt
>>> +
>>> -> empty wt]/2)
>>> -> (max takeoff weight 315,000lbs, empty
>>> weight
>>> -> 164,800lbs)
>>> -> 470 mph - - - - assumed speed at impact (averaged from a few
>>> estimates)
>>> -> 689 fps - - - - mph converted to fps
>>>
>>> -> E = (240000 lbs * 689 fps * 689 fps) / 2 = 56966520000 lb-ft^2/sec^2
>>>
>>> -> Using the website to convert that to tons of TNT gives:
>>>
>>> -> 56966520000 lb-ft^2/sec^2 = 18.459 tons of TNT
>>>
>>> -> I'm not sure which tons are used so it could equal either:
>>>
>>> -> 41,348 lbs (long tons), 40,695 lbs(metric tons) or 36,918 lbs(short
>>> tons)
>>>
>>> -> With those numbers in mind it is amazing that the buildings withstood
>>> the
>>> -> impact much less stood long enough for anyone to get out.
>>>
>>> Amazing indeed. Let's try again, without the gobbledygook units.
>>
>> I used the units I found.
>>
>>
>>> Suppose the mass of the aircraft was 100 tons (1e5 kg), and it was
>>> travelling at 200 metres per second. Its kinetic energy would have been
>>> 0.5 x 1e5 x 200^2, which comes to 2e9 joules. TNT reaches a temperature
>>> around 1000 C, or maybe a bit more, when it explodes, so its energy
>>> production must be somewhere around 5000 joules per gram. So the mass
>>> of TNT that would produce the same energy as the aircraft's would be
>>> 2e9/5000 grams, which is 4e5 grams, or 0.4 tons. That is, I feel, a
>>> much more credible amount than your estimate of nearly 20 tons - fifty
>>> times as much as I've just calculated.
>>>
>>> I have absolutely no idea where the mistake is...
>>
>> I was surprised at the number myself. But I did the math and showed my
>> work if I made a mistake please let me know where. One reason I used the
>> website for the conversions was to remove the chance I would make a math
>> error. I also used mid-range numbers for the weight and speed at impact
>> to keep from being accused of trying to hype something.
>>
> One of the many problems using 'English' units is that a pound-mass is not
> the same thing as a pound-force. If you always use the complete terms,
> you can easily spot where you need a 'conversion'.
> Take for example a one pound-mass object that is allowed to free-fall in
> 'normal' gravity. It accelerates at 32.2 ft/sec^2. Yet if that same mass
> rests on a scale, it exerts a downward force of just one pound-force. In
> order to make Newton's "F=MA" work out, you have...
> 1 pound-force = 1 pound-mass * 32.2 feet/s^2 / <conversion constant>
> The conversion constant is often called gc (g-sub-c) and has a value of
> 32.2 lbm-ft/ (lbf-sec^2). This conversion between pound-mass and
> pound-force goes back more than a century when man didn't always have a
> good understanding of the two. Pressure measurements and guages were
> often calibrated with 'dead-weight' testers that simply put a certain
> number of pounds mass on a piston with a known area to create a pressure
> (pound-force per unit area). A lot of times when people (or web pages)
> use the term 'pound', you have to be careful to figure out if they mean
> pound-mass or pound-force. Some places will use terms like 'slug' or
> 'poundal' to try and avoid confusion with pound-force, but I've always
> used 'pound-mass' and 'pound-force'.
> In your formula for KE you have...
> KE = 1/2 * 240000 lbm * (689 ft/s)^2 = 5.69e10 lbm-ft^2/sec^2
> But that isn't the same as 5.69e10 lbf-ft of energy. It's the wrong
> units. To convert from lbm-ft/sec^2 to lbf-ft we must divide by g-sub-c
> and that gives us 1.77e9 lbf-ft of energy. Converting that to Joules is
> about 2.40e9 Joules.
Well duh!!!! I should have caught it myself with the units. After having
it driven into my head that one of the reasons you leave the units in the
equations was to make sure you wind up with the correct units you'd think
I'd would have seen that. Thanks.
I though the number was way off but 'it all added up'. As I also have been
told you can't proofread your own work, I guess that applies to me and MY
math as well.
> This site says a ton of TNT is about 4.0e9 Joules, so we have about 0.6
> ton of TNT equivalent.
> http://hypertextbook.com/facts/2002/AlexRoslyakov.shtml
> Still a sizeable explosion.
> daestrom
> P.S. Metric is easier, but here in the US I've always had to work through
> the 'English' units. But even some common usage in the metric system can
> confuse mass and force (e.g. a 'kilogram-force')
One of the reasons I used English units was to advoid conversion errors
because all of my data was already in English units. Well I guess I did
that, I didn't have a conversion error. Just a major brain fart on matching
units.
FYI, my site says 4.184e9 joules per ton but what 1.84e8 between friends :)
Posted by no spam on September 8, 2007, 9:58 pm
>-> > Suppose the mass of the aircraft was 100 tons (1e5 kg), and it was
> -> > travelling at 200 metres per second. Its kinetic energy would have
> been
> -> > 0.5 x 1e5 x 200^2, which comes to 2e9 joules. TNT reaches a
> temperature
> -> > around 1000 C, or maybe a bit more, when it explodes, so its energy
> -> > production must be somewhere around 5000 joules per gram. So the mass
> -> > of TNT that would produce the same energy as the aircraft's would be
> -> > 2e9/5000 grams, which is 4e5 grams, or 0.4 tons. That is, I feel, a
> -> > much more credible amount than your estimate of nearly 20 tons -
> fifty
> -> > times as much as I've just calculated.
> -> >
> -> > I have absolutely no idea where the mistake is...
> -> I was surprised at the number myself. But I did the math and showed my
> work
> -> if I made a mistake please let me know where. One reason I used the
> website
> -> for the conversions was to remove the chance I would make a math error.
> I
> -> also used mid-range numbers for the weight and speed at impact to keep
> from
> -> being accused of trying to hype something.
> As I said, I have no idea where the error is. Maybe the website got the
> conversion factor wrong. Websites are very fallible. Or maybe you
> somehow did the arithmetic wrongly. Frankly, I have no intention of
> trying to wade through all those bafflegab units to try to find the
> problem.
> Of one thing I am certain. A 100-ton plane, flying fairly slowly, does
> not have anything like the same energy as 20 tons of TNT!
> The metric numbers I used, 1e5 kg and 200 m/s, were pretty close to the
> values you used. And I'm sure that the value of 5000 J/g for the energy
> of TNT is right, at least to within a factor of 2 or so. So our two
> results should have been the same, to within the factor of 2. The fact
> that they differed by a factor of 50 mens that one of us (or maybe
> both) was wrong. I am much more confident in my result than I am in
> yours...
It is strange. I'll check into it. All I know it that website has been
dead on for every over thing I've ever needed to convert.
XML site map
>aircraft.
> -> Taking just the mass and speed of the aircraft, i.e. not counting the
> -> burning jet fuel, the force of the aircraft hitting each tower was
> -> equivalent to about 40,000 pounds of TNT. I didn't know the exact
> numbers
> -> for a couple of things so I had to make a few assumptions. With that
> said
> -> you can check my work. FYI, unless other wise stated all info found by
> -> searching internet and all conversions were done using
> -> www.onlineconversion.com to cut down on human error.
> -> E=1/2 mv^2 ---- Basic kinetic energy formula
> -> 240000 lbs - - - assumed weight of aircraft at impact. ([max t.o. wt +
> -> empty wt]/2)
> -> (max takeoff weight 315,000lbs, empty
> weight
> -> 164,800lbs)
> -> 470 mph - - - - assumed speed at impact (averaged from a few
> estimates)
> -> 689 fps - - - - mph converted to fps
> -> E = (240000 lbs * 689 fps * 689 fps) / 2 = 56966520000 lb-ft^2/sec^2
> -> Using the website to convert that to tons of TNT gives:
> -> 56966520000 lb-ft^2/sec^2 = 18.459 tons of TNT
> -> I'm not sure which tons are used so it could equal either:
> -> 41,348 lbs (long tons), 40,695 lbs(metric tons) or 36,918 lbs(short
> tons)
> -> With those numbers in mind it is amazing that the buildings withstood
> the
> -> impact much less stood long enough for anyone to get out.
> Amazing indeed. Let's try again, without the gobbledygook units.