The book Geekspeak: A Guide to Answering the Unanswerable, Making Sense of the Insensible, and Solving the Unsolvable by Dr. Graham Tattersall poses, and answers, those questions that no one else seems to address -until now. Can you tell how heavy a bus is by looking at it? What size wings does an angel need to fly? What are the best words to use in a personal ad? How much could sea levels rise?
This is one of those books that makes being a geek fun (which geeks already knew) and makes real-world math accessible to those who might avoid it otherwise. To give you a taste of Geekspeak, we have obtained permission to reprint a chapter for your perusal. Fly Wheels looks at measuring biological power in mechanical terms in order to compare the two.
One of the key technologies for personal transportation is a way of storing energy in something that doesn't weigh very much. A gallon of gas will keep your car going for about an hour, with the engine developing an average power of, say, 30hp (20kW). The gas effectively stores 20 kilowatt-hours of energy in each gallon.
Gasoline is an amazingly compact way of carrying a lot of energy. A gallon of it weighs only about 6 pounds. A figure of merit for gasoline as a portable fuel might be the amount of useful energy for each pound of fuel-its energy density. On this count gasoline is rated at nearly 2 kilowatt-hours per pound (kWh/pound).
I once made an electric bike powered by a pair of lead-acid car batteries carried in baskets. Together they weighed about 50 pounds and could deliver a total energy of only 2kWh. That's a puny energy density of 0.04kWh/lb, just one-fiftieth as effective as gasoline.
This, of course, is the curse of electric cars. There is no cheap battery technology that allows anywhere near as much energy to be stored per pound of battery as per pound of gas.
Pedaling the bike, plus its 50 pounds of batteries, back from work yet another day when the charge had run out, I made a calculation: 2 pounds of sugar digested by a human would give more muscle energy than both batteries combined.
The energy in a 2-pound bag of sugar is almost 4kWh. Muscles can convert that energy into mechanical work with an efficiency of up to 20 percent. That's an output energy density of 0.4kWh/lb-not as good as gasoline, but, amazingly, in the same ballpark.
A muscle engine in a car would be a winner; the emissions would be just carbon dioxide, water, and maybe a bit of wind, depending on the food of the engine. And this may not be just the science-fiction dream that it sounds. There is a lot of academic research into so-called molecular motors, the power source of our muscles.
The molecular motors inside your body are built from a particular kind of protein molecule, the shape of which can be distorted, rather like scrunching up a piece of rubber band in your fist. The scrunching is done by a chemical called adenosine triphosphate (ATP), which is supplied to the muscle in the bloodstream. ATP is itself synthesized from the sugars in your food.
At a signal from your brain, the chemical fist of the ATP is unclenched-the molecule rearranges its shape into a more relaxed form, providing mechanical force as it goes. There are billions of these molecules acting together, making the muscle pull. Synthetic proteins, which act in a similar way, might provide the basis of future power plants.
Flying insects can do even better. They use similar molecular motors to make the wing beat repetitively with a very high energy efficiency, up to 40 percent. But could harnessing the power of houseflies be the way forward for car travel? If so, how many would you need to pull your car along at, say, a respectable 40 miles per hour?
First you need an idea of how much power a single fly can generate. A very rough estimate of 1 fly-power can be made if you know the fly's weight and how long it takes to rise a certain distance into the air after taking off from a tabletop.
When the fly takes off, it uses energy to lift its weight. Some of that energy is used to accelerate its body and lift it into the air, and some will go into heating its body and warming the air. But as the fly rises, it also increases its energy in another way. This newly acquired energy is called potential energy. The higher the fly flies, the more potential energy it gains.
The energy is "potential" because it doesn't come into play until something happens. If a fly stopped moving its wings, its potential energy would change into speed energy as it fell back down and would finally be released as a small amount of heat energy when it crash-landed on the table.
It's a fair approximation to say that the energy expended by the fly in rising to its cruising height is the same as the potential energy it will have once it's there. (It's actually a bit more, but for the purpose of our armchair arithmetic we can let that go.) So if we can work out our fly's potential energy, we can work out the value of 1 fly-power. We just need to divide this energy by the time it takes the fly to reach cruising height, and we have its power in watts.
The formula for potential energy is this:
But what about mass-what does a fly weigh? Think of something of a similar weight that you can conveniently measure. For example, suppose that a housefly weighs about the same as a grain of rice. It could be half as much, or twice as much, but it is unlikely to be either a tenth, or ten times as much. A grain of rice will do nicely.
Count how many grains of rice you can scoop up with a teaspoon, and put ten teaspoonfuls of rice onto the kitchen scales. Divide the weight by ten, and then by the number of grains per teaspoonful. You now have the weight of one rice grain-and the approximate weight of a fly. It'll come out as about 50 mg. That's fifty-thousandths of a gram, which is the same as fifty-millionths of a kilogram.
Next, have a look at some flies as they take off. How long do they take to rise to their cruising height? That's a tricky one.
You can make several rough timings and average them to get a more accurate final value. But even one timing is hard, because the time is so short. One way if to hold a ticking clock against your ear as you watch the flies rise. Older clocks have a tick-tock time of one second, but the ticks on some modern clocks are much more rapid. Count the number of ticks per second from your clock to calibrate your "audio timer".
My clock does five ticks per second, and the fly rises to about 1 meter in the time of one tick-that's one-fifth of a second. Now the fly-power can be calculated. So, to put into the formula above we have values 10 (for g), 0.00005 kg and 1 meter:
A typical car engine running on the flat at 40 mph will be generating around 20,000 watts, or 200 million fly-power. So 200 million flies, attached by silken threads to the front of your car and suitably trained, could pull it along at up to 40 mph. Whether that's a green alternative depends on the flies.
Geekspeak is an essential tool that will help you exercise your brain and solve the unsolvable, make you sound intelligent so you can impress your friends, and enable you to better understand the fascinating world in which we live in ways never thought possible before.
This is one of those books that makes being a geek fun (which geeks already knew) and makes real-world math accessible to those who might avoid it otherwise. To give you a taste of Geekspeak, we have obtained permission to reprint a chapter for your perusal. Fly Wheels looks at measuring biological power in mechanical terms in order to compare the two.
One of the key technologies for personal transportation is a way of storing energy in something that doesn't weigh very much. A gallon of gas will keep your car going for about an hour, with the engine developing an average power of, say, 30hp (20kW). The gas effectively stores 20 kilowatt-hours of energy in each gallon.
Gasoline is an amazingly compact way of carrying a lot of energy. A gallon of it weighs only about 6 pounds. A figure of merit for gasoline as a portable fuel might be the amount of useful energy for each pound of fuel-its energy density. On this count gasoline is rated at nearly 2 kilowatt-hours per pound (kWh/pound).
I once made an electric bike powered by a pair of lead-acid car batteries carried in baskets. Together they weighed about 50 pounds and could deliver a total energy of only 2kWh. That's a puny energy density of 0.04kWh/lb, just one-fiftieth as effective as gasoline.
This, of course, is the curse of electric cars. There is no cheap battery technology that allows anywhere near as much energy to be stored per pound of battery as per pound of gas.
Pedaling the bike, plus its 50 pounds of batteries, back from work yet another day when the charge had run out, I made a calculation: 2 pounds of sugar digested by a human would give more muscle energy than both batteries combined.
The energy in a 2-pound bag of sugar is almost 4kWh. Muscles can convert that energy into mechanical work with an efficiency of up to 20 percent. That's an output energy density of 0.4kWh/lb-not as good as gasoline, but, amazingly, in the same ballpark.
A muscle engine in a car would be a winner; the emissions would be just carbon dioxide, water, and maybe a bit of wind, depending on the food of the engine. And this may not be just the science-fiction dream that it sounds. There is a lot of academic research into so-called molecular motors, the power source of our muscles.
The molecular motors inside your body are built from a particular kind of protein molecule, the shape of which can be distorted, rather like scrunching up a piece of rubber band in your fist. The scrunching is done by a chemical called adenosine triphosphate (ATP), which is supplied to the muscle in the bloodstream. ATP is itself synthesized from the sugars in your food.
At a signal from your brain, the chemical fist of the ATP is unclenched-the molecule rearranges its shape into a more relaxed form, providing mechanical force as it goes. There are billions of these molecules acting together, making the muscle pull. Synthetic proteins, which act in a similar way, might provide the basis of future power plants.
Flying insects can do even better. They use similar molecular motors to make the wing beat repetitively with a very high energy efficiency, up to 40 percent. But could harnessing the power of houseflies be the way forward for car travel? If so, how many would you need to pull your car along at, say, a respectable 40 miles per hour?
First you need an idea of how much power a single fly can generate. A very rough estimate of 1 fly-power can be made if you know the fly's weight and how long it takes to rise a certain distance into the air after taking off from a tabletop.
When the fly takes off, it uses energy to lift its weight. Some of that energy is used to accelerate its body and lift it into the air, and some will go into heating its body and warming the air. But as the fly rises, it also increases its energy in another way. This newly acquired energy is called potential energy. The higher the fly flies, the more potential energy it gains.
The energy is "potential" because it doesn't come into play until something happens. If a fly stopped moving its wings, its potential energy would change into speed energy as it fell back down and would finally be released as a small amount of heat energy when it crash-landed on the table.
It's a fair approximation to say that the energy expended by the fly in rising to its cruising height is the same as the potential energy it will have once it's there. (It's actually a bit more, but for the purpose of our armchair arithmetic we can let that go.) So if we can work out our fly's potential energy, we can work out the value of 1 fly-power. We just need to divide this energy by the time it takes the fly to reach cruising height, and we have its power in watts.
The formula for potential energy is this:
Energy = g x Mass x Height
The g here is the acceleration due to gravity: the rate at which the speed of a falling object increases. Its value is 9.81 meters per second per second. Call it 10 to make life easier.But what about mass-what does a fly weigh? Think of something of a similar weight that you can conveniently measure. For example, suppose that a housefly weighs about the same as a grain of rice. It could be half as much, or twice as much, but it is unlikely to be either a tenth, or ten times as much. A grain of rice will do nicely.
Count how many grains of rice you can scoop up with a teaspoon, and put ten teaspoonfuls of rice onto the kitchen scales. Divide the weight by ten, and then by the number of grains per teaspoonful. You now have the weight of one rice grain-and the approximate weight of a fly. It'll come out as about 50 mg. That's fifty-thousandths of a gram, which is the same as fifty-millionths of a kilogram.
Next, have a look at some flies as they take off. How long do they take to rise to their cruising height? That's a tricky one.
You can make several rough timings and average them to get a more accurate final value. But even one timing is hard, because the time is so short. One way if to hold a ticking clock against your ear as you watch the flies rise. Older clocks have a tick-tock time of one second, but the ticks on some modern clocks are much more rapid. Count the number of ticks per second from your clock to calibrate your "audio timer".
My clock does five ticks per second, and the fly rises to about 1 meter in the time of one tick-that's one-fifth of a second. Now the fly-power can be calculated. So, to put into the formula above we have values 10 (for g), 0.00005 kg and 1 meter:
Energy = 10 x 0.00005 x 1 = 0.0005 joules
Power is energy per second, and our fly has taken 0.2 seconds to rise 1 meter, so its power is 0.0005 divided by 0.2. That makes 0.0001 watts-one-tenth of a milliwatt. That's enough to make an LED glow dimly in the dark. A small battery-powered torch gives out about 1 watt-that's 10,000 fly-power. Flies aren't very bright.A typical car engine running on the flat at 40 mph will be generating around 20,000 watts, or 200 million fly-power. So 200 million flies, attached by silken threads to the front of your car and suitably trained, could pull it along at up to 40 mph. Whether that's a green alternative depends on the flies.
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Geekspeak is available from publisher HarperCollins, at Amazon, and at a bookstore near you.
How one solves the unsolvable is far beyond my
brain.
That made me laugh. Thanks.