{"id":640,"date":"2008-05-13T20:59:59","date_gmt":"2008-05-13T20:59:59","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2008\/05\/13\/bad-gas-math\/"},"modified":"2008-05-13T20:59:59","modified_gmt":"2008-05-13T20:59:59","slug":"bad-gas-math","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2008\/05\/13\/bad-gas-math\/","title":{"rendered":"Bad Gas Math"},"content":{"rendered":"

This has been mentioned elsewhere – like on the Machinist blog on Salon<\/a> (where I first saw it) – but I can’t resist saying something about it myself. And I’ll also chip in a little bit of originality, by also criticizing some of the people that I’ve seen criticizing it.<\/p>\n

The story is, there’s a scammy company that sells a rather expensive device that allegedly increases your gas mileage. The way that it (supposedly) works
\nis that it uses electricity from the alternator to get hydrogen by splitting
\nwater, and then adding that hydrogen to the air that gets mixed in the engine. The argument is that the hydrogen causes the gasoline to burn more completely and more cleanly, thus increasing the efficiently of the engine, which allows it to go further on a gallon of gasoline.<\/p>\n

A local TV station in Florida claims to have tested the device. They tested the mileage of their news van using a dynamometer; then they mounted the device on the engine of their news van, and after giving it time to break in, put the
\nvan back on the dynamometer, and tested its mileage again.<\/p>\n

Here’s where the pathetic part comes in. They reported that before mounting the hydrogen generator on their van, they got an average mileage of 9.4 miles per gallon. After mounting it, they claim that they got 23.2 miles per gallon. Ok so far? Now, they go on to say that increasing their mileage from 9.4 to 23.2 mpg is a 61% improvement in mileage.<\/p>\n

<\/p>\n

So, our intrepid reporters don’t have a clue of what percentages mean or how to compute them. You might<\/em> think that perhaps they misreported the
\n“23.2” number – maybe it was supposed to be something like “13.2”? Nope, that
\ndoesn’t work. In fact, no plausible typo for either 9.4 or 23.2 gives you anything
\nclose to 60%. So where on earth did they get the number from?<\/p>\n

Being a math geek, I saw it pretty quickly; hopefully, some of you out there
\ndid as well. 9.4 is almost exact 4\/10ths of 23.2. If you take 9.4, divide it by 23.2, and then subtract that from 1, you get about 0.60. That’s how they did it – they took 9.4; figured out what percent it was of 23.2, and then took the difference as the percentage improvement.<\/p>\n

That’s spectacular innumeracy. It’s incredibly stupid. It’s stupid in that
\nthat’s a mind-bogglingly idiotic way of trying to compute a percentage
\nimprovement. And it’s stupid in that anyone who had the slightest understanding
\nof just what percentage change means<\/em> would immediately notice that doubling<\/em> something means a 100% improvement; since 23.2 is well over
\ndouble 9.4, that means that it’s got to be more than 100%. Anyone who’d say that 25 is less that 100% larger that 10 is an idiot.<\/p>\n

What about the other side of things? Lots of people are (justifiably) skeptical of whether the hydrogen generator could possibly improve mileage. One comment which I saw (but unfortunately can’t recall where I saw it now) said: “It’s idiotic: it violates the laws of thermodynamics. You can’t possible generate
\nany more power by adding hydrogen to the mix than you spent splitting the water.”<\/p>\n

Bzzt. Sorry, no.<\/p>\n

If you were arguing that the improvement comes about because of the additional energy of burning the hydrogen, then that would be true. Burning hydrogen produces a bunch of energy and creates water; splitting water consumes a bunch of energy
\nin order to break the water molecules. Recombining hydrogen and oxygen to produce
\nwater can’t produce more energy than it takes to split them – that would, indeed, violate thermodynamics.<\/p>\n

But that’s not what the proponents of the hydrogen generator say. Their
\nargument is that the process of burning gasoline in an engine is extremely
\ninefficient. There’s a fair bit of gasoline that doesn’t get burned; the part that
\ndoes get burned doesn’t always burn in the ideal way to convert the energy from
\nburning it into mechanical force. The hydrogen augmentation argument isn’t that
\nyou’re adding energy by burning hydrogen, but that adding extra hydrogen to the
\nmix increases the efficiency of how the engine burns gasoline – that a larger
\nportion of the gasoline gets burned in the engine cylinder, and that it burns in a
\nclean sustained burn that maximizes the mechanical energy extracted from that
\nburn. There’s no thermodynamic reason why that couldn’t work: separated the
\nhydrogen and oxygen in water isn’t cheap, energy-wise, but gasoline contains a
\nhell of a lot of chemical energy, and a moderate improvement in the efficiency of
\nhow we extract that energy could outweigh the cost of splitting a small quantity
\nof water.<\/p>\n

Mathematically, it’s a stupid error – not as stupid as the percentage
\nmiscalculation, but still pretty stupid. We can write out a simple equation that
\nestimates energy production from burning gasoline.<\/p>\n

Suppose that a gram of gasoline produces a maximum of J joules when burnt.
\nWe want to convert that from heat energy to mechanical energy. A standard engine
\nwill do that with an efficiency, Eg<\/sub>, where Eg<\/sub> > 0 and < 1. So the engine will
\nproduce Eg<\/sub>×J joules of mechanical energy per gram.<\/p>\n

Now, suppose we add hydrogen to the mix.<\/p>\n

Hydrogen produces H joules per gram, and in an engine, the energy of burning
\nit can be converted to mechanical energy with an efficiency of EH<\/sub>.
\nFurther, splitting enough water to produce a gram of hydrogen has an energy cost
\nof C, where C>H. So even if you could burn hydrogen with perfect efficiency,
\nit would still be a loser energy-wise.<\/p>\n

If<\/em> burning hydrogen and burning gasoline in the engine are
\nindependent – which is the basis of the erroneous argument – then the energy
\ngenerated by burning N grams of gasoline + M grams of hydrogen in a hydrogen
\ngenerator-augmented engine N×Eg<\/sub>×J + M×Eh<\/sub>×H – M×C. <\/p>\n

Since C>H, the second quantity (the hydrogen-augmented one) is clearly smaller than the first (the pure gas one). But the problem is, Eg<\/sub>
\nisn’t a fixed constant over all mixtures of gases in the engine. Add more nitrogen and less oxygen to the fuel mix, and it goes down. What happens to that efficiency when you add hydrogen?<\/p>\n

I don’t know. But I do know that treating it as a constant is wrong – obviously<\/em> wrong.<\/p>\n

I’m not trying to defend the hydrogen generator. I still very much doubt that
\nthe hydrogen generator works as advertised. I’m very skeptical of it. (If it
\nworked, I think we’d see companies like Honda and Toyota, which make lots of money
\nselling extra-efficient hybrids adding it to their cars – if you could boost the
\nefficiency of simple gasoline engine by as much as the hydrogen generator claims,
\nyou’d have pretty much the efficiency of the hybrid without needing to go to the huge amount of engineering effort needed to produce an effective hybrid.) But
\nbad math is bad math.<\/p>\n","protected":false},"excerpt":{"rendered":"

This has been mentioned elsewhere – like on the Machinist blog on Salon (where I first saw it) – but I can’t resist saying something about it myself. And I’ll also chip in a little bit of originality, by also criticizing some of the people that I’ve seen criticizing it. The story is, there’s a […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[5],"tags":[],"class_list":["post-640","post","type-post","status-publish","format-standard","hentry","category-bad-physics"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-ak","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/640","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=640"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/640\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=640"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=640"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=640"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}