Do Hybrids Equal Savings?

May 28, 2008 – 12:14 am

With gas prices going through the roof, many people have contemplated buying a new car, particularly a gas/electric hybrid, to drastically improve their gas mileage and lower their gas bill. But are the savings people are getting really all they're cracked up to be?

Don't get me wrong. I'm all for saving the environment and I've been making some lifestyle changes to help lower my carbon footprint (though you can have my long, hot showers when you pry them from my cold, dead fingers), but this post isn't about what's environmentally or morally or ethically right. It's about what makes economic sense for you and what doesn't. Is getting rid of your old car and buying something new with better gas mileage really going to save you money?

To your right is a calculator that will help you figure out exactly how much money you'd save on gas if you got a car with better mileage. You may have seen some calculators like this before, but mine is different in two ways. First, all the values have sliders, so you can quickly and easily adjust for different annual driving patterns, gas prices, and mileage differences. Second, instead of showing you how much you'll save per year, it shows you how much you'll save per month.

Why does it show your monthly savings?

First, because the yearly figure is going to be 12 times higher and much more impressive, but most people rarely think of things they buy regularly in terms of yearly cost. Do you think of your phone bill in yearly costs? How about your grocery bill? How about how much you're spending on gas? Most people think in more immediate terms.

Second, because it creates a better number for comparing against the costs of that new car. I drive a 7 year old Hyundai that's paid off. It gets around 24 miles to the gallon and right now I'm driving about 280 miles a week or 14,500 a year. Let's say I was going to trade it in on a Toyota Prius. According to Edmunds.com, the 2008 Prius base model with no options is going for $21,549 in my neck of the woods. With a realistic trade-in estimate on my Hyundai, a 5.99% loan for 60 months, tax and license (note: the federal tax credit for hybrids is no longer available for the Prius) and I'm looking at a monthly payment of $368.54 a month.

If we figure I'd get 47 miles per gallon from the Prius, at current prices ($4 a gallon), I'd only be saving $98.55 a month. Now at $1182.60 a year, it might seem more impressive. But when you compare the $98.55 a month savings to the $368.54 a month I'd have to pay for the Prius, it doesn't make sense. As much as my wallet is hurting, it would be hurting $270 more a month. I'd be much happier at the pump, but if I looked at the overall impact on my budget... not so much.

But the sliders are there for you to play with the numbers. If you've got a street-tank that's getting all of 15 miles per gallon, but it has a higher trade-in value, so you could end up in a Prius for $200 a month, it started making economic sense when gas hit $3.65 a gallon. On the other hand, there's always quality of life issues to consider. Maybe you go for the midground and move from that street tank to a crossover, preserving some of that "haul my kids and all their crap in comfort" element. You may have to wait until gas crests $6.50 a gallon before you're in the economic black, but you may consider that extra few bucks a month worth the smaller carbon footprint and lower numbers at the pump.

I'm not saying that you shouldn't dump your Suburban for a Prius if that's what you want to do. But if you're going to have to take on a new car payment or raise your car payment, it's worth using this calculator to see if the monthly savings on gas are going to even come close to the extra money you'll be spending on car payments.

Automatically assuming that a higher mileage car equals saving money is a very Rough Equivalent. Do the math.

Posted in Distance, Monetary Value | 1 Comment »

Dancing On The Head Of a Pin

May 23, 2008 – 12:15 am

Previously I discussed a letter from reader Scott about parts per billion, and we had plenty of fun discovering that the allowable level of lead in drinking water was equal to about a shot glass in an olympic size pool. But reader Scott had brought up parts per billion as part of a larger discussion on how many angels could dance on the head of a pin.

It's a bit difficult to quantify the number of angels on the head of a pin, because first we'd have to quantify the size of an angel. That can range from subatomic to supermassive to no size at all. And the day we can get the world to agree on the size of an angel, we'll have solved a number of problems of much greater importance than how many of them can dance on the head of a pin.

Of course, my answer is "all of them... if we set the pin in the path of a conga line populated by all the angels who each step on the pin as they dance by." All I was asked was "how many angels can dance on the head of a pin?" No one ever defined what "dance on" meant precisely, nor is this modified by any language requiring those angels to dance on it simultaneously, rather than in succession. And yes, I did turn down a scholarship to law school. Why do you ask?

But that doesn't provide any Rough Equivalents and it doesn't mathematically attack the problem of how many very small things can occupy the head of a pin. So I decided to take it seriously (for a very brief moment).

According to Wayne's Word (an encyclopedia of natural history), they use a 1.5 millimeter diameter for the size of the head of a pin whenever they use the head of a pin in comparisons, and that seems reasonable to me. That gives you a surface area on a flat, round pin head of 1.767 square millimeters.

I don't know how big an angel is, but I do know how big a flu virus is. Since we'll measure the flu virus in nanometers, we have to break down the pin head area into nanometers. Since a millimeter is a million nanometers on a side, it would represent a trillion square nanometers. So we've got 1.767 trillion square nanometers of area on the pin head.

With a 70 nanometer diameter, a perfectly round flu virus would take up 3848.5 square nanometers. But they're not perfectly round, and if they were, we couldn't cram them in so all their edges were touching anyway. We'd still have gaps. So, to keep things fair, I'm assigning each virus a square space, 70 nanometers on a side, meaning 4900 square nanometers.

When we divide 1.76 trillion square nanometers of space on the head of this pin by 4900 nanometers, we find out we can fit 360,612,245 influenza virus cells on the head of a pin. So if we concluded that an angel was the size of a flu virus, the guardian angels for the entire populations of the United States and Canada could fit on the head of a pin, with room to spare.

But let's expand this out. In a square inch, there are 645.16 square millimeters, or 645.16 trillion square nanometers. So, in a square inch, we could pack in 131.6 billion flu viruses. It would be a bit cramped, but it would be close to 20 flu virus cells for every man, woman, and child in the world... in a square inch.

But you know how I like to lay things out for distance. I've done a calculator to get a distance in pennies laid end to end or bologna slices laid end to end. What about influenza virus cells laid end to end? I'm approximately 25,714,260 flu virus cells tall.

Feel like telling the world your height in flu virus or your answer to how many angels can dance on the head of a pin? Post it in the comments below.

Posted in Area, Distance | 1 Comment »

Fred's Measuring Cup

May 21, 2008 – 12:15 am

Over the past few days, friends have been asking me "have you seen this measuring cup?" They were all abuzz about this new gag measuring cup that featured markings on it for things like "20,000 grains of rice" or "volume of half a human brain." I knew I had to feature it. It's like the physical embodiment of this site.

You can see the other side of the Fred Equal Measure measuring cup over at Amazon.com.

Does it seem odd that this measuring cup is suddenly all over the net a month after I launched this blog? It was even on Gizmodo yesterday. Did I somehow enter the forefront of an offbeat measurements zeitgeist that is about to sweep the web? Will I be in the right place at the right time?

Well, maybe next week when I talk about odds (which are different than statistics, and we'll get into why that is next week), we can try to calculate the odds of of that meme going nuclear and that rising tide lifting this boat. Or maybe I'll just compare my odds of winning the lottery to my odds of being attacked by killer bees. Whatever's fun.

Thanks to Cathie for being the first to bring the cup to my attention and Dr. Stone at USC for being the straw that broke the camel's back in deciding to feature this. And yes, if you send me a cool tip or idea that I use, I will mention you and link to your site if you have one.

Posted in Food & Diet, Volume | Post A Comment »

Parts Per Billion

May 19, 2008 – 12:15 am

In the "Molecules of Caffeine" post, I calculated the number of caffeine molecules in a can of Mountain Dew. This lead reader Scott to e-mail me about the concept of parts per billion. For example, the Environmental Protection Agency has set their "action level" for lead in drinking water (the level at which you need to take action to reduce the lead) at 15 parts per billion. But how much is that? Is it 15 atoms of lead for every atom of something else? Is it by weight? Is it by volume?

In a case where it's in solution (dissolved in water or another liquid), it's by weight. If you have one gram of water and 15 parts per billion of lead, that means 15 billionths of that gram's weight would be from lead.

But that still didn't do it for me. I wanted to know how many lead atoms were allowable in a liter of water. Since 15 parts per billion is the point at which you have to do something, we'll conclude that the "allowable" level of lead in drinking water is 14 parts per billion. So in a liter of water, which traditionally weighs 1 kilogram, that's 14 millionths of a gram.

Now we know that a mole of lead weighs 207.2 grams, so we divide 0.000014 by 207.2, which gives us roughly 0.000000067567568. Multiply it by 6.02214179 x 10²³ and we have a mere 40,690,147,229,729,700, or 40.7 million billion atoms of lead in each liter of water.

If we applied 14 parts per billion to the population of the world, it would represent roughly 94 people, or less than 1/12th of the number of billionaires in the world in 2008 according to Forbes (1,125 as of their March 2008 billionaires report). According to Wikipedia, the average lifespan of a human right now is 67 years (this includes developed nations and third world countries averaged together). In 67 years, 14 parts per billion is just under 30 seconds. But in a liter of water, 14 parts per billion of lead is 40.7 million billion atoms.

Of course, that got me thinking, how much lead is in a swimming pool? I already got the figure for the volume of an olympic size pool for the "Pool Full Of Pudding" post, so we know that's 2,500 cubic meters. And since a cubic meter is 1,000 liters, that pool contains 2.5 million liters. If each liter contains 14 millionths of a gram, this is a simple calculation. The millionths on the lead's weight and the million on the number of liters cancel each other out, so it's 35 grams (14 x 2.5), or roughly 1.25 ounces of lead dissolved into an olympic size swimming pool's worth of water.

If we were using a simple liquid like vodka, to get an olympic size pool's vodka level (not the alcohol level, but the vodka level) to 14 parts per billion, we'd pour in around a shot glass of vodka.

Let's look at some parts per billion ratios in some of our favorite foods.

The McDonald's nutrition information chart says that a Big Mac weighs 214 grams and contains roughly 29 grams of fat. So the fat content of a Big Mac could be expressed as 135,514,018 parts per billion, roughly 10 million times higher than the allowable level of lead in drinking water.

According to calorie-count.com, the carb level in a Ho Ho is 642,857,142 parts per billion or just short of 46 million times the allowable lead level in drinking water.

So, now that you know how to express things in parts per billion, what are some Rough Equivalents you can come up with? Post them in the comments section below.

Posted in Content, Volume | 1 Comment »