Science & Nature Archive

Monday, January 9, 2012

How Much Gas to Charge an iPhone?

iPhone GasI got a link to an interesting article recently, How many gallons of gasoline would it take to charge an iPhone?. The article was published on ExxonMobil's Perspectives blog. It was an attempt to put into perspective just how much energy there is in gasoline, and why it's so useful as a fuel.

Early on, the article presented a 'fact', without any rationale to back it up:

All of the energy concentrated in one gallon of gasoline is enough to charge an iPhone once a day for almost 20 years.

So, I thought I'd run some numbers to see just how reasonable this was.

First, what's the energy content of a gallon of gas? According to Wikipedia's Energy densities page, the energy density of gasoline is 47.2 megajoules per kilogram. A gallon of gas weighs about 6 lbs, for a mass of about 13.2 kg 2.73 kg. Multiplying by the energy density gives 623.04 MJ 128.73 MJ in a gallon of gas.

Now, for something that took a little more work, what's the energy content of the iPhone battery. According to Wikipedia's iPhone 4 page, the battery is 3.7V at 1420 mAh. (An Ah is the "the electric charge transferred by a steady current of one ampere for one hour" - Wikipedia). So, doing a simple calculation on that, let's figure out the power the battery is putting out, and then how much energy that would be after the one hour for the Ah:

P = IV
P = 1.42A * 3.7V
P = 5.254W

As a sanity check, that's in line with what some random guy on the Internet claimed on Yahoo Answers, according to his kill-a-watt power meter.

And since energy is equal to Power times time:

E = Pt
E = 5.254W * 3600s
E = 18,914.4J

So, if we simply divide the energy content of the gas by the energy content of the battery, we get 32,940 charges 6806 charges. Assuming a charge every day for a year, that's 90.2 years 18.6 years. Now, of course, there are inefficiencies in the systems, so that's not right. Gasoline engines in cars are typically on the order of 25% - 30% efficient (per Wikipedia), and their alternators are typically on the order of 50% - 60% efficient. However, permanent alternators run optimally can have efficiencies in the high 90%'s (again, per Wikipedia).

So, the claim that there's enough energy in a gallon of gas to charge an iPhone every day for 20 years seems pretty reasonable (in reality, when you look at the efficiencies, you won't be able to put all that energy into charging the phone).

An iPhone may not be huge, but 20 years is a pretty long time. It really just goes to show how much energy gasoline contains, and why it's so useful for powering vehicles.


As a side note, this is why I personally think that biofuels offer so much hope. If a way can be found to efficiently convert biomass into a gasoline like fuel (such as some of the studies on algae), we'd have a high density energy source that could take advantage of existing infrastructure. No waiting overnight to charge batteries - just a quick 10 minute stop at the pump to fill up with dead algae.

Update 2012-05-08 As a reader pointed out, I made a boneheaded error in my conversion from pounds to kilograms (stupid metric system). I corrected it, striking through the wrong numbers and replacing them with the correct ones.

Friday, July 29, 2011

Is Archaeopteryx Still a Bird?

Archaeopteryx - Berlin SpecimenAround a year ago, I read Peter Wellnhofer's book, Archaeopteryx: The Icon of Evolution. I learned quite a bit, but a new paper on Xiaotingia zhengi throws a kink into archaeopteryx's relative importance in understanding bird evolution.

Here are some typical examples of the coverage the paper has received:

Okay, first thing is to clear up some misconceptions. Paleontologists have not been suggesting that archaeopteryx was the first bird - only that it was the oldest known bird. In fact, if you go look at that review I wrote and look at the family tree from Wellnhofer's book, archaeopteryx is clearly shown on a side branch that went extinct, so nobody's even been arguing that archaeopteryx was a direct ancestor of modern birds. In fact, I'll just copy that family tree here:

Avian Family Tree

What the new paper does call into question is how closely related archaeopteryx is to modern birds. First of all, it's clear that birds are a type of dinosaur, and archaeopteryx was obviously a fairly closely related dinosaur. But new fossils have been found of other closely related dinosaurs - some that could probably fly, and some that probably couldn't. Whereas previously it was assumed that flight probably only evolved once, and therefore archaeopteryx was a bird, all these new fossils are calling that into question.

The new paper suggests that archaeopteryx was more closely related to deinonychosaurs* than to modern birds. The problem is that deinonychosaurs can't fly. So, there are basically two possibilites:

  1. Flight evolved multiple times in the maniraptorans. The common ancestor of archaeopteryx and modern birds was flightless, and each lineage evolved flight on its own. It's possible that powered or gliding flight evolved in other closely related lineages (such as Microraptor)
  2. Flight evolved once in the maniraptorans. The common ancestor of archaeopteryx and modern birds could fly, but then some lineages, such as the deinonychosaurs, lost that ability (like ostriches with teeth).
  3. Okay, I guess there's a third possibility. It's possible that the common ancestor of archaeopteryx and modern birds could fly, but that flight also evolved in another lineage of maniraptorans.
  4. Well, I suppose there's a fourth possibility, as well - that the proposed phylogeny by Xing Xu et al is incorrect, and that archaeopteryx should still be considered a member of avialae.
  5. I can't actually think of a fifth possibility, but I'm sure thre are some more possibilities I haven't thought of.

Here's the cladogram from the paper with the new proposed phylogeny:


(Click for larger image)

(Source: Pharyngula)

Paraves is the group that contains both archaeopteryx and modern birds. It also includes the deinonychosaurs, which couldn't fly. But in the avialae branch, it includes epidexipteryx, which also couldn't fly. We know from modern birds that losing the ability to fly has occured multiple times (ostriches, penguins, kiwis, dodos, etc.), so it's possible that the common ancestor for Paraves could fly and the deinonychosaurs and epidexipteryx both lost that ability. But it's also possible, like I wrote above, that flight evolved independently in the archaeopterygidae and the avialae.

So why doe this matter? Aside from trying to sort out the evolutionary relationships, I would think that this is relevant to the trees down vs. ground up debate on the origins of flight. As Wellnhofer pointed out, archaeopteryx was a terrestrial animal, not adapted for life in the trees. And it looked like its terrestrial characteristics were primitive, not secondarily derived from an arboreal ancestor. That was strong evidence in favor of the ground up hypothesis. But if flight evolved independently in archaeopteryx and modern birds, then archaeopteryx doesn't really tell us much about that evolution in birds. The trees down vs. ground up debate is back on.

So, what we have now are a bunch of fossils of very closely related dinosaurs, but it's not quite clear how they all fit together, and especially how the origin of flight fits in. I know what I would like for the truth to be, but reality doesn't care about my feelings. It's just going to take finding more fossils to fill in the family tree and make the picture more clear. Get to work on it paleontologists.**

For more information, here's a very good blog entry describing the new paper:
Pharyngula - Xiaotingia zhengi


*Okay, my nomenclature's not exactly right, but rather than re-type the whole thing, I'm just going to add this note. When I wrote 'deinonychosaurs' in this article, I was mostly referring to the dromeosaurs and troodontids, since this new analysis places archaeopteryx and related animals in with the deinonychosaurs.

**Actually, a comment from Tom Holtz in that Pharyngula thread (Holtz is a paleontologist at the University of Maryland) indicates that there are some new fossils that were recently discovered that should be coming to light fairly soon.

Updated 2011-07-31 - Added the fourth and fifth possibilities in the list, and added the note on my misuse of the nomenclature.

Monday, June 13, 2011

Directly Downwind Faster Than the Wind (DDWFTTW)

DWFTTW BlackbirdThere's an interesting topic that stirs quite a bit of debate in certain circles these days - whether or not a wind powered cart can travel directly downwind faster than the wind, itself. This concept is generally known by one of two acronyms, Down Wind Faster Than The Wind, DWFTTW, or the slightly longer Directly Down Wind Faster Than The Wind, DDWFTTW.

The cart in the concept has a propeller connected to wheels through a driveshaft and transmission. You might intuitively think that this is impossible. I know I did. It sounds too much like a perpetual motion machine, with the wheels powering the propeller which pushes the wheels. So, I thought I would set out to prove it impossible with a few free body diagrams, but now that I've studied the diagrams, I find myself thinking that it might actually work.

Background

First, to get a bit of background on this concept, here are some of the websites of its main proponents:

To get an idea of just how much passion this concept evokes, take a look at some of the discussion threads arguing over it:

As one last link before getting into my own discussion, the Faster Than the Wind Team claims to have built and tested a car that demonstrates the concept. The North American Land Sailing Association (NALSA) witnessed and authenticated the event. While some might think that would be enough to convince doubters, many remain skeptical of the claims and suspect foul play or incompetence (such as not running directly downwind or measuring windspeed incorrectly in the more generous accusations).

Here's some video of the record claiming run.


Main Issues

There are two big discussions in this debate, whether a DWFTTW car is even possible, and second, whether the widely circulated 'Treadmill Experiment' is useful in demonstrating its validity. Since the first claim is more interesting, I'll address that first.

Is DWFTTW Possible?

To address this, I drew up some free body diagrams. All the diagrams are shown in an assumed steady state condition. For simplicity, the vehicles are all simplified as just a single wheel, a prop/turbine, and a transmission connecting them.

Let's start with something that we know works, an upwind vehicle.

Free Body Diagram of Upwind Vehicle

In this case, V_wind will be greater than V_ground. The prop/turbine will be acting as a turbine, so it will be creating drag. The wheel will be driving the vehicle, so F_ground will be in the forward direction. Since the vehicle is in equilibrium:
F_ground = Drag

To calculate the power from the turbine and the power from the wheel:

P_turbine = Drag * V_wind
P_wheel = F_ground * V_ground

Since Drag = F_ground, if V_wind > V_ground, then P_turbine > P_wheel. That's what it needs to be to overcome transmission losses and the vehicle wind drag that I didn't account for. So, the diagram and analysis agree with what we expect from reality.


Next, let's move on to a case that we know doesn't work, a vehicle with no wind.

Free Body Diagram of Vehicle in No Wind

Once again, to maintain equilibrium:
F_ground = Thrust

Since I labeled the forces slightly differently, here are the power equations:

P_prop = Thrust * V_wind
P_wheel = F_ground * V_ground

Since Thrust = F_ground and V_wind = V_ground, then P_prop = P_wheel. That doesn't work, since transmission losses will sap the energy out of that system, as will the air drag. I think it should be obvious enough that if you reverse the drive direction (i.e. a turbine powering the wheels), that it still comes out to P_turbine = P_wheel, which doesn't work. So again, the diagram and analysis agree with what we expect from reality.


Now, let's move on to the DDWFTTW case.

Free Body Diagram of Downwind Vehicle

Once again, to maintain equilibrium:
F_ground = Thrust

The power equations are the same as the previous case:

P_prop = Thrust * V_wind
P_wheel = F_ground * V_ground

Since Thrust = F_ground, if V_ground > V_wind, then P_wheel > P_prop. Like the first case, that's what it needs to be to overcome transmission losses and the vehicle wind drag.

So, it seems counter-intuitive, but unless I've made a mistake somewhere, it looks like it should work. Maybe there is something to what the propenents have been saying, that the differential velocities are the source of energy, and why this isn't a perpetual motion machine. As the diagrams show, if there's no wind at all, then the vehicle doesn't run.


The Treadmill Experiment

An early proof of concept experiment that made its rounds on the Internet was to put one of these carts on a treadmill and see what happened. The video is included in the links I gave at the start of this entry, but I'll embed it here to make it easier for you.

The treadmill experiment prompted two big questions - is it representative of a cart moving downwind over the ground, and does it demonstrate the validity of the DWFTTW concept?

The answer to the first question is a clear yes. The treadmill is an equivalent reference frame. That's how wind tunnels work – it's all about relative velocities. If a treadmill is moving at a steady 10 mph in still air, it's the same as the ground being stationary with a steady 10 mph wind.

Consider this. The Earth's surface is not stationary itself. Given a circumference of approximately 25,000 miles, and a rotation period of 24 hours, the ground is moving at just over 1000 mph at the equator (and that's ignoring the Earth's motion around the Sun, the Sun's motion around the Milky Way, and the Milky Way's motion about the local galactic cluster). In other words, the Earth could be considered a giant treadmill. But we can safely neglect that if we use a frame of reference that moves along with the earth. It's the same thing with the treadmill. As long as all the relative velocities are equivalent, then your reference frames are equivalent.

But, did the experiments in the video demonstrate the validity of DWFTTW? I think the answer is yes to that as well, but I also have an idea for another experiment.

My initial skeptical thought was that by physically holding the cart stationary on the treadmill before releasing it, they were storing energy by spinning up the propeller on the cart. When they released the cart, it would surge forward using that stored energy. It's just like a toy helicopter where you pull a string to make it take off. There's nothing surprising about that.

But, if you watch the video, once the cart is operating, they aren't holding it against the treadmill, they're holding it back against its own thrust. That, to me, is indicative that the cart wants to run faster than the treadmill. Unfortunately, given the short length of their treadmill, the videos never show the cart reaching a steady state.

My suggestion for a better experiment (aside from the full size human carrying cart) is to build a long treadmill inside a building, and put their cart on that with some guides to keep it from running off track. If it achieved a steady state forward velocity relative to a stationary observer (and was well documented by independent observers), then I'd think most reasonable skeptics would be convinced. Alternatively, the cart could be placed on the treadmill before the treadmill was started in motion, so that it wouldn't be touched by human hands at all once the experiment started. Judging by the Faster Than the Wind Team's human carrying cart, I would think they have the means to carry this out, and all remaining doubts could be put to rest.

Alternate Explanation 1

I think a better way to understand this vehicle, is rather than thinking of it as a ground vehicle powered by the wind, think of it as an aircraft powered by the ground. I have a little thought experiment that might help. Envision the vehicle suspended on some rails, with the prop aligned to propel it down the rails, and with the wheel hanging below on a caster that enables the wheel to face any direction. If you put a conveyor up to the wheel with the conveyor running sideways relative to the vehicle, it's obvious that the conveyor will turn the wheel, which will drive the propeller and push the vehicle down the tracks. Now, if you start rotating the conveyor to more closely align with the tracks, it will continue to drive the wheel. The more closely it aligns with the tracks, the higher the drag load that it will impart, but it will continue driving the wheel.

So, think of the cart as an aircraft that with no other forces acting on it would want to be 'at rest' with zero relative windspeed. But, once the ground starts moving relative to the aircraft, it provides a power source that the aircraft can tap into to propel itself.

Alternate Explanation 2

Consider a cart where one set of wheels is turning a generator used to power another set of wheels driven by motors. This obviously won't work. Since both wheels are moving over the ground at the same speed, if the force at each wheel was of equal magnitude, then the power created by the generating wheel would be equal to the power being used by the driving wheel, which doesn't work when you account for losses.

If a cart with a propeller was moving through still air, then it would be the same thing. That was what I tried to explain with the no wind case. When forces are equal and velocities are equal, then powers are equal.

What makes the downwind case work, is that the wheels and the propeller are operating in two different media at two different speeds. For a propeller, we typically look at the thrust generated for a given power, since that's the way engines operate. It's well understood that for a given power, thrust drops with airspeed. But looking at that a different way, it means that to generate a given thrust, the power requirement goes up with airspeed. So, using the no wind day as a baseline, when the thrust from the prop and the drag from the wheels are the same, the input and output powers are the same (which doesn't work because of losses). Now, if you add a little bit of tail wind, it means the propeller is not travelling through the air as fast. If you maintain it at the same thrust, it means the power requirement goes down. So, now we're getting into a regime where the power generated by the wheels is higher than that required by the prop. With enough of a tail wind, the power differential can get big enough to overcome the inefficiencies and make the system actually work.

Conclusion

So in the end, once I gave this a little thought, I surprised myself. I think my initial gut reaction to this concept was wrong, and that the DDWFTTW proponents are right. That's all part of honest skepticism - knowing when to admit you were wrong and to change your views based on new reasoning and evidence. It's certainly nice to know that the Faster Than the Wind Team is most probably honest, and that the videos probably aren't a hoax. Congratulations to them for their achievement.


Now that I've had my say, and hopefully convinced people that this is possible, here's a good article on it:


I'll also add that the nice thing about this question is that it's testable. If I get a chance, I'll build a little cart myself. If enough people do this and test it, it should be confirmed pretty quickly. If you're one of the people that feels really strongly about this, go do a test for yourself.

Added 2011-06-13

I figured it might be fun to throw in a few real numbers to get a feel for how this would work. So, I pulled some numbers out of the air to see how the calculations come out.

I started out with a ground speed of 30 ft/s (~20.5 mph). Assuming 100 pounds of drag on the wheels, this works out to 3000 ft-lb/s of power (~5.5 HP). Assuming a 90% efficient drive train, there's 2700 ft-lb/s going into the prop. Now, the next step requires a little understanding of propellers which I've explained on my static site (Theoretical Max Propeller Efficiency). Assuming a figure of merit of 0.9*, and a propeller diameter of 15', the prop will create 170.5 lbs of static thrust. So, at the state where ground speed matches wind speed, the thrust created by the propeller will be greater than the drag on the wheels - the cart will accelerate forward. And since the cart is at zero relative airspeed at that condition, there's no aerodynamic drag to consider. Also note that there's no stored energy from a flywheel effect in this analysis, so the steady state condition will necessarily be at some speed where the cart is going faster than the wind speed.

You can play around with those numbers if you want to. For the given efficiencies and prop diameter, the break even point where thrust = drag is around 495 lbs (27 HP @ 30 ft/s). If you hold the efficiencies and drag constant, the break even point on thrust & drag occurs for a 6.7 ft diameter propeller. All of these numbers appear to be fairly reasonable, giving me yet further confidence that the Faster Than the Wind Team probably achieved what they stated.

* This figure of merit is a measure of how much of the power is going into accelerating the air. This is a more useful measure than efficiency for low speeds, since by definition, propeller efficiency is equal to zero for static thrust. A figure of merit of 1 is the theoretical limit. The propellers I've designed at work typically achieve figures of merit of 0.92 to 0.94 for static thrust.

Tuesday, March 8, 2011

Book Review - Why Evolution Is True

I've just finished reading Jerry Coyne's book, Why Evolution Is True. This is one of my new favorites for introducing evolution to people who don't currently understand or accept it. It contains a great balance of theory and evidence, or in other words, explaining how evolution works, as well as showing the evidence of how we know that.

The book covered a wide range of topics, and did it well while keeping the book to a manageable length. It started with an explanation of what evolution actually is. This was a pretty important chapter, given how much many people misunderstand evolution. He then moved on to fossil evidence for evolution, followed by discussion of vestigial organs, embryological evidence, evidence from poor 'design', and biogeographical evidence. Following all that was a discussion of natural selection and sexual selection, and then a discussion of speciation. The penultimate chapter focused on recent human evolution (recent as in after the chimp & bonobo lineage diverged from ours). Finally was a chapter to wrap it all up, which also discussed what some people believe to be implications of evolution (i.e. if it says we're just animals, why not act like animals). Of course, by covering such a broad range of topics, Coyne couldn't delve too deeply into any single one, but I think it was very good for an introductory book.

Why Evolution Is True was written not just to explain evolution, but also as a counter to creationism. In many places, he pointed out why evolution was a more reasonable explanation to certain pieces of evidence than creationism. When I read Richard Dawkins' book, The Greatest Show on Earth, I'd mentioned that he hammered too hard on creationists, and that it was a bit of a distraction. In contrast, Coyne seemed to spend just enough time discussing creationism without it becoming too distracting from the far more interesting story of evolution itself.

Coyne was also very balanced in his discussions of controversial areas, or areas where the evidence isn't conclusive. For example, in the discussion of sexual selection, he mentioned both the good genes hypothesis and the perceptual bias hypothesis, as well as studies that provided evidence for both.

In short, this book is a great introduction to people who don't understand evolution. Donald Prothero's Evolution: What the Fossils Say and Why It Matters may have a more detailed discussion of the fossil evidence, and Carl Zimmer's The Tangled Bank may have a more detailed discussion of the mechanisms, but Coyne's book has just the right balance of theory and evidence, especially evidence from a broad range of disciplines.


For a great review from Amazon, go here.

Updated 2011-11-02 Fixed link to Zimmer's The Tangled Bank.

Wednesday, February 16, 2011

The Double Blind Gaze

Skeptic Society UFOI've gotten permission from The Skeptics Society to post one of their old articles on this site. The article is:

The Double-Blind Gaze: How the Double-Blind Experimental Protocol Changed Science.

If you've never read this article before, I highly recommend that you do so now. It focuses mainly on medicine, but also shows how it can be difficult to determine the truth of reality, and why the scientific method is so important.

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