Wednesday, July 22, 2009

Two exciting things (DII and DWFTTW)


The first thing I got excited about recently is the news announcement that roughly 20 big German companies are talking about investing €400 billion in the Desertec Industrial Initiative. What is thrilling about this announcement is that it involves a sum of money that is in the right ballpark for a genuine plan to get off fossil fuels. So often, government announcements have involved 1 million here, 10 million there, and (rarely) 100 million. I reckon the cost of putting together a new energy system for the UK must be roughly 400 billion pounds, or 10 billion pounds per year from today to 2050. This is much more than millions; but it is still perfectly affordable, given that we already spend 80+ billion per year on energy and 80+ billion per year on insurance. I'd love to see details of what the German companies think they could buy for their 400 billion euro.
The second exciting thing was to discover, thanks to James from Isentropic, what I now consider to be the two best videos on ther internet. Namely: Downwind Faster than the Wind (DWFTTW) [which demonstrates that it is possible to make a wind-powered vehicle that goes directly downwind faster than the wind] and Under the ruler faster than the ruler [which explains with a nice simple model how faster-than-wind travel works].
What intrigues me philosophically about the wind-powered-travel expositions is that it reveals how fragile and weak "understanding" can be: I thought I understood wind-powered travel, and I already knew about wind-powered vessels that can sail directly upwind (eg, Revelation II, pictured). But I got the answer to the question "is DWFTTW possible?" wrong! - even though the principle by which upwind travel works is just the same as the principle of DWFTTW travel. So it seems that when I "understood" upwind travel, what I really did was append to my stack of physics heuristics another heuristic, permitting upwind travel; I didn't add a piece of knowledge that was capable of working in new situations.

12 comments:

dave said...

This is all about frames of references isn't it? However, I'm still a bit confused about DWFTTW. Let's say I'm moving from left to right in a DWFTTW vehicle at 12m/s. The wind is blowing from left to right at 10m/s. This is equivalent to me at standstill with a 2m/s wind from right to left? I am then extracting energy from the 2m/s wind in order to power my vehicle. Is that what is going on? So-- on that premise am I right in thinking it is impossible to build a wind powered vehicle which moves at the same speed as the wind? It would either have to be extracting energy from a tailwind or a headwind, as seen from the frame of reference moving with the vehicle? Another question here: is the 'propellor' behaving like a turbine, or a compressor/fan? I imagine the former because otherwise it would be putting energy into the wind rather than extracting energy from the wind.

Milan said...

As reported in The Economist, Munich Re has invited 20 large companies to form a consortium, intended to build concentrating solar power stations in Africa and the Middle East, as well as the high voltage direct current (HVDC) lines required to bring that power to Europe. The stations will use molten salt heat storage, so as to be able to generate power day and night. Munich Re, the world’s largest reinsurer, is motivated by concern about its exposure to climate change. Fully implemented, the scheme would cost $560 billion and provide 15% of Europe’s projected energy demand in 2050. The complete system would cover 17,000 square kilometres of territory.

All told, the plan is very promising. It is refreshing to see companies thinking strategically about the long-term harm climate change could do to them, as well as the long-term opportunities associated with renewable energy. A report produced by the Wuppertal Institute for Climate, Environment and Energy and the Club of Rome determined that the project could produce 240,000 jobs in Germany, as well as €2 trillion worth of electricity by 2050.

Even more importantly, it could demonstrate the feasibility of the desert concentrating solar / HVDC option, which could be extended to the Southern US and elsewhere. As SEWTHA explains, this is one of the renewable options where the figures add up, and it could be possible to generate the kind of energy societies demand. Here’s hoping the Desertec plan helps lead the way.

David MacKay said...

dave said "This is all about frames of references isn't it?"... well, maybe, if that helps you! "However, I'm still a bit confused about DWFTTW. Let's say I'm moving from left to right in a DWFTTW vehicle at 12m/s. The wind is blowing from left to right at 10m/s. This is equivalent to me at standstill with a 2m/s wind from right to left?" Yes, as long as you say you are at a standstill on a treadmill that is zooming past your stationary self (and thus your wheels are spinning!) "I am then extracting energy from the 2m/s wind in order to power my vehicle. Is that what is going on?" No, not in this frame of reference. In the frame you specified, you are extracting energy from the ground and using it to chuck the slowly moving wind backwards, faster! (relative to you). "So-- on that premise am I right in thinking it is impossible to build a wind powered vehicle which moves at the same speed as the wind? It would either have to be extracting energy from a tailwind or a headwind, as seen from the frame of reference moving with the vehicle?" You are actually incorrect - go and watch the videos! Under those conditions you can extract energy from the moving ground and use it to hurl air backwards and thus accelerate to faster-than-wind speed. "Another question here: is the 'propellor' behaving like a turbine, or a compressor/fan? I imagine the former because otherwise it would be putting energy into the wind rather than extracting energy from the wind." Definitely the right question to ask! It is working like a compressor/fan, from the point of view of you sitting on the car. From the point of view of an onlooker at the roadside who notices the speed of wind particles, he'll notice that the wind is being chased and guzzled up by your propellor and slowed down a little. So from his point of view, you are extracting kinetic energy from the wind.

Thomas said...

New huristics: anywhere there is relative motion, there is energy to be had by opposing it. What you do with that energy is "just" a matter of gearing.

This problem seems like a really good example of how energy flows vary depending on reference frame.

The ruler thing is cool, but isn't the whole of the picture for DWFTTW, as unlike the ruler, the air is not a solid. I've tried to think through what the air would do as a cart starts off from stopped and accelerates up to faster than the wind, but i'm not sure i've guessed the flow patterns right:

With the cart stopped, drag on the cart and its propeller try to push the cart forwards. The air passing the propeller also tries to turn the propeller like a turbine, but the direction of the gearing is chosen so that this would turn the wheels backwards. If the ratio of the gearing reduces the force from the propeller to the wheels, then the cart starts to move forwards and the propeller turns the wrong way against the wind. (If the gearing increased the force from the prop to the wheels, the cart would go backwards upwind using the prop as a turbine.)

With the cart moving slower than the wind:
In the road's reference frame, there is a trail of slowed-down air ahead of the craft, from which it has drawn its energy. From the air's point of view, the craft is being dragged backwards by the road, pulling a trail of sped-up, backwards moving air in front of it.

At first the propeller will probably be stalled, but as the cart accelerates the apparent tail-wind decreases, the propeller spins faster, and it begins to blow air backwards relative to the cart (at a slower speed than the road is going backwards underneath it, due to the gearing). Air in this backwards jet will slow down, spread out and then be turned forwards by the tail-wind. It will pass around the outside of the propeller before turning again and being sucked back through it. The apparent tail wind will blow around this bubble of circulating air, dragging on it and so being slowed.

In the cart's frame, as it accelerates the tail wind fades, the jet intensifies, and the stagnation point where the jet is turned forwards by the tail wind is pushed ever further behind the cart. When the cart matches speed with the wind, the jet grows backwards without limit and the airflow in the cart's frame is like that around a fan in otherwise still air.

In the road's frame, the trail of slowed-down air ahead of the cart fades away while the jet of slowed down air behind it extends ever further behind. Then, as the cart overtakes the wind, the back of the jet of slowed down air can no longer keep up, so a tube of slowed down air grows behind the cart.

As the cart accelerates, the amount by which it is slowing the air decreases, so a frictionless cart has a maximum speed set by its gearing. If, with the road going back under it at speed v, the cart pushes air back at speed v/r, then with wind speed a it will not slow the wind if a = v - v/r, or v = a(r-1).

It still bothers me that lines of flow converge through a propeller and diverge through a turbine, but from the road the cart's propeller seems to be a turbine when it's overtaking the wind, while in the cart's frame it's pushing air, and i can't see how a change of frame can make a diverging flow look like a converging flow.

David MacKay said...

@thomas: yes, very well put. I like your new heuristic.
You said "It still bothers me that lines of flow converge through a propeller and diverge through a turbine, but from the road the cart seems to have a turbine when it's overtaking the wind, while in the cart's frame it has a propeller, and I can't see how a change of frame can make a diverging flow look like a converging flow." I agree. This issue is still bothering me too. Perhaps we need to put cart and treadmill in a nice wind-tunnel with smoke to help us understand!

dave said...

The reason the flow lines diverge behind a (stationary) wind turbine is because of conservation of mass: the air is slowed down by the turbine (in order to extract energy), and since rho.A.v is constant, A (cross sectional area) must increase as v decreases. Vice versa for a propellor/fan/compressor.

dave said...

ps with this in mind, one simple way to model a turbine (I have used this in 2D CFD) is just as a semi-porous disc.

R said...

I wonder if we could solve the intermittency problem with wind power by engineering the equivalent of a wind turbine atop a giant treadmill? I don't understand the physics well enough to tell whether there is some net energy gained through the gearing (and of course it would have to be a lot to outweigh the other frictions in the system).

Jimmy said...

Does the energy balance work? ie. Can the car harvest enough energy from its apparent wind to overcome friction?

I am at a loss to comprehend how if the car and wind were both travelling from left to right at say 12 m/s, the car can extract any more energy from the wind bearing in mind that the apparent wind speed in the car is 0m/s and hence there is no available energy for it to accelerate

David MacKay said...

Jimmy: yes, the energy balance works fine. In the frame in which the car and wind are both stationary, yes, the car cannot get any energy from the wind -- all it can do is do work on the air by grabbing it and pushing it. But in that frame there is another source of energy: the road, roaring by! You can use your wheels to hold back the roaring road a little, and get energy from it (which you then use to shove the air around).

The Faster Than the Wind Team said...

San Jose State University Aero Professor and Stanford Phd Dr. Nikos Mourtos along with a team of students and advisors have taken on a project to construct and document DDWFTTW in a more thorough way than ever before. Their goal is to achieve a documented 2x windspeed DDW.

Follow their blog at www.fasterthanthewind.org

Remember that in the blog format the latest posts show up on top. To view the entries from the start, click on the "2009" link on the right (below the list of followers) and scroll to the bottom.

Enjoy.

JB

LG said...

Not sure I understand the problem actually. An ice yacht will do 70kts in 15kts of wind. The actual air-speed is irrelevant (once there is a significant amount of it) only the apparent wind matters (always you travel at an angle to the wind, not directly parallel with it, so apparent wind speeds can get beyond actual wind speed).

This looks like it works in basically the same way as far as I can see, just that instead of a single fixed airfoil (sail) you use a different type of airfoil (turbine blades) driving screw or wheels. Such a cool idea!