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March 1st, 2006

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04:27 pm - And in other news....
I found out today that the yield of a ton of TNT is approximately 999331.231489 Calories (as opposed to calories).

This realization led me to some quick calculations:
1) there's 31.2291009 Calories per ounce of TNT.
2) the RDA for your average 6 foot human who exercises somewhat is 2000 Calories (or 2 megacalories).

Some quick divison implies that you should consume just over 4 lbs. of TNT a day (approx. 64.0428300 ounces). I don't think I eat 4 lbs. of food a day, therefore the food I eat has a higher energy density than TNT.

Moreover, a can of Cherry Coke (not my drink of choice, but one immediately nearby) is 150 Calories (or 12.5 Calories per fluid ounce). This implies that some 2.4983280 fluid ounces of Cherry Coke is equivalent to an ounce of TNT. Now if only I had a digital scale to translate fluid ounces.

testing4l: What trips me out is that I don't think I eat >4 lbs of food a day
zweeb: ah, so the energy content of a bacon double chese burger is higher per gram than TNT
testing4l: That doesn't seem right to me.
zweeb: its revelations like these that make my friendship with you rewarding =)
testing4l: I mean, at the nuclear level, sure
testing4l: Umm....thanks, I think?
zweeb: hahaha
zweeb: lets face it, who else that i know is going to come up with that kind of conclusion?

(LJ-ify your IMs before pasting!)

The Tsar Bomba was the largest yield fusion bomb built in the days where "megaton lag" meant something. It achieved some 2 MT output per metric ton, though in theory could have achieved approximately double had there not been fallout concerns (thus the third stage was made of lead instead of depleted uranium). The Mk-41 wasn't as large, though it achieved a much better output of 5.2 MT per metric ton. In theory, though the fusion weapons have an upper limit of 6 MT per metric ton.

So, in Calories per ounce (1 MT = 1000000 tons of TNT = 999331231489.4 Calories and 1 metric ton = 2240 lbs. = 35840 oz.):
The Tsar Bomba achieved 55766251.7572209 Calories per ounce (or ~56 gigacalories)
The Mk-41 achieved 144992254.5687745 Calories per ounce (or ~145 gigacalories)
The theoretical yield would achieve 167298755.2716629 Calories per ounce (or ~167 gigacalories)

Using that measure, as little as .0000119 oz. up to .0000358 oz. would deliver your daily amount of Calories, though I'm pretty sure that a fusion bomb of that size would most likely be the last thing you ate that day...or ever.

(7 comments | Leave a comment)


[User Picture]
Date:March 2nd, 2006 12:59 am (UTC)
Bored, are we? Interestingly, I mostly have already done these sort of calculations during moments of extreme boredom. I don't find it honestly very surprising, seeing how inefficient chemical reactions actually are. It's not like even a fraction of a percentage of actual energy content in a stick of TNT is exhausted when it blows up. Take into consideration that even if your right arm were to inexplicably turn into pure energy the resulting explosion would be well above your average yield nuclear bomb. Chemical power has about two times nine to the tenth power energy yield compared to its mass, nuclear power is about two times thirteen to the tenth, and raw energy, by comparison, is about two times seventeen to the tenth -- that's 10000x more efficient than nuclear power is. Food energy conversion, as such, is only marginally more efficient than conventional chemical reactions.

Oops. Now excuse me, you've just distracted me and I'm late for my Star Thugs game!
[User Picture]
Date:March 2nd, 2006 04:36 am (UTC)
Forgive me, my friend, but I laughed aloud. You have twelve significant digits -- including six past the decimal point -- and you're off by about 15 percent. ];-)

===|==============/ Level Head
[User Picture]
Date:March 2nd, 2006 05:35 pm (UTC)
My source for the conversion was this site which makes some notes about unusual rounding, but I had assumed (apparenty incorrectly) that a basic conversion wouldn't be subject to error.

Having sniffed around, I find wikipedia has an entry saying that a ton of TNT is equivalent to a billion thermochemical calories (or a million Calories). I'd think that's the error in question, but that'd mean that I'm <1% off.
[User Picture]
Date:March 2nd, 2006 07:32 pm (UTC)
You're confusing (understandably) the "standard measurement used as a convention for megaton" and the energy actually contained in TNT, which is the context you seemed to be using above.

There are also differences in the different flavors of calories, but these are in the fraction of a percent range.

Actual measured TNT explosions produce around 1.16 billion calories (thermochemical) per megaton. (This is different from (and higher than) simply burning the stuff.) That value is about 16% higher than the old "standard measure" -- hence my use of "about 15%". No sense using more digits than the situation called for. ];-)

Ah -- even Wikipedia has this. And it's a reasonable writeup, as this topic is not political nor controversial. ];-)

Best wishes.

===|==============/ Level Head
[User Picture]
Date:March 2nd, 2006 08:04 pm (UTC)
While I can appreciate estimations in a practical setting, there's nothing I like more than a nice, long precise number. You may have noticed this with any of the incarnations of my time script. This obviously was just numbers for the sake of numbers and strange comparisons.

I almost tempted to run the numbers again, but I think I'll allow it to stand. Much in the same way that we don't update the value of a horsepower.
[User Picture]
Date:March 2nd, 2006 08:19 pm (UTC)
That's fine -- though I would note a flaw in the analogy:

There is no actual "standard horse" available for measuring; they are creatures of biology with uncountable variations between them, and in their ability to deliver power at any given moment. Picking the value for "horsepower" was somewhat arbitrary.

Trinitrotoluene is a substance with an exact, and exactly reproduciable, chemical formulation. Under standard conditions, it will (and does) support repeatable measurements.

===|==============/ Level Head
[User Picture]
Date:December 8th, 2006 08:43 pm (UTC)
Oh, I was picking on James Watt, not the determination of the energy in TNT. James Watt had a bit of an interest in underestimating the amount of work a horse could do. He also played a bit loose on the calculation, figuring arbitrarily that a horse was about 50% more powerful than a pony.

As my physics teacher put it, it would have to be a very sick horse to only manage 1 horsepower. I recall reading somewhere that on average, a horse could manage about 15 horsepower at peak output.

(It really is amazing which comments slip by when you postpone replying to one immediately!)

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