A commenter (Joe) suggested I look at vehicles powered by the wind that can move faster than the wind. This also came up on Swans on Tea. One of Joe’s points was that I should do this BEFORE MythBuster’s gets to it. And so I shall. I know this is one of those topics that can never really be won – like “the moon landings were fake” or “you can run your car on water”. I will try anyway. If you are not sure what this “faster than wind” thing is all about, check the Swans on Tea link or this boing boing link.
There has been a ton of stuff posted about DWFTTW vehicles. Literally a ton. If you took all the electrons used to transmit data regarding DWFTTW over the internet, it would add up to one ton. So, what I am going to say may have already been said (I can’t look through the whole internet). But you know me, I like to give my own spin on stuff. This one was difficult to start because I wasn’t sure what “angle” to take. Clearly, there is a problem if a vehicle is wind powered and travels faster than the wind. You see it, I see it. But there are many that do not see this as a problem. Really, the reasoning in this area is the same as for most perpetual motion machines. Energy for nothing. Free energy – it’s not the 70’s. Stuff isn’t free.
So, where to start? Start with the basics. There are two important ideas that are useful in this discussion. The momentum principle and the work-energy principle. Both of these ideas are very solid. If someone found a situation where these were violated, it would be a pretty big deal (so, basically we can take them as true).
I talked about the work-energy principle before. Check it out if you want a more in depth tutorial. The basic idea is that we (you and I both) can define work as:
The energy part of the work-energy principle says that the work done on an object changes its energy
At the most fundamental level, energy is either particle energy or field energy. When looking at macroscopic things (like cars) we can make up other energies – like chemical potential energy, thermal energy, electric energy and stuff. Again, this work energy idea is very successful.
The most basic form of this is the same as Newton’s third law. It says:
In this situation, the most useful way to use this is to say that if the net force is zero(vector) on a system (whatever that system may be) then the total change in momentum of that system is zero(vector). Or, if there is a net force, there will be a change in momentum. So, back to the first case of no change in momentum of the system. If there are two particles in the system, and initially both objects have an x-momentum of 5 kg m/s, then after something happens one could have 8 kg m/s and the other could have 2 kg m/s.
Happy? Ok, I am not going to start with a DWFTTW vehicle. Are you disappointed? Instead, I am going to start with a wind generator (is that the correct term?). Here is a simple diagram:
First, in terms of work and energy, the air coming into the generator has a greater kinetic energy than the air leaving. This means that the air decreases in kinetic energy. Where does this energy go? Well, the moving air pushes on the blades of the generator and do work. This increases the “electric energy” of the generator (yes, electric energy is very vague, but it serves the purpose). So, in short the generator gets energy by slowing down the air. It’s not free energy.
In terms of momentum, the air has a change in momentum to the right in the picture above. If I think of the generator plus air as the system, then it also has a change in momentum to the right. This means there must be a force exerted on the system to the right. This force is the force from the ground holding the generator in place. If you want to think about just the air, it has a force exerted on it from the blades of the generator.
Wait. You thought I was going to talk about wind powered vehicles. Well, I am. I think the above case is a great place to start because it uses some of the same ideas as a wind powered vehicle. After all, that is a wind powered device. It just isn’t a vehicle.
Next, some type of sail powered vehicle thingy
I know sail boats are complicated, but I am going to pretend they are simple. Imagine an ice-car sail boat. There is no friction and it has a plain flat sail. The wind is blowing directly behind the ice-car. Here is a picture.
Again, this is simplified. However, in this case the air both changes direction and decreases in speed (and kinetic energy). The car increases in momentum and kinetic energy. I left off the air in front of the car that also collides with it (air resistance), but hopefully you get the idea. The car “gets” energy from the air, which loses energy. Will this car keep speeding up forever? No. If there were no air in front of the car (and no friction from the ice), the car would speed up until it reached the speed of the air. At that point, the air from behind would not hit the sail and interact with it. Obviously, a real ice-car in this case would not even get that fast because of air resistance and ground friction. I have ignored the cases where the wind is coming from the side (because that is more complicated).
How about a jet engine? Or something like that.
Here is a diagram of a jet engine initially at rest (maybe on the runway or something):
So, air comes in from the left. Stuff happens (like a turbine or fuel burning stuff – not really sure). Then air leaves going faster than it was initially. Clearly the air increased in momentum to the right. If I take the air plus engine as my system (ignoring gravity and the force of something holding it up) then the engine must increase in momentum to the left in order for the total momentum to stay the same. What about energy? Well, the air leaving the engine is moving faster than the entering air (increases in kinetic energy). Also, the engine will increase in kinetic energy. Where did this energy come from? It can from burning fuel. Even if the engine is moving, basically, the same thing happens.
Are we ready for the DWFTTW vehicle?
Using the ideas above, couldn’t I put a wind generator on a cart and attach that to an electric motor? Then I could push the cart to get it moving, the wind would turn the generator and power the electric motor. If this was true, then the vehicle should be able to move without any wind at all – or into the wind (whichever you like). I am sure some people will say driving into the wind is different than faster than the wind, but for the purposes of this argument it is not.
One simplification is the wheels. If this is a wind-powered vehicle, you would like the wheels to be as low friction as possible. I am going to go all the way and say that (for this argument) the wheels have ZERO friction. This will make things easier in that I can just talk about the air and the car as the system with no net external forces. Yes, there will be the force of gravity pulling it down, but there will also be the force of the ground pushing up. These forces are equal and thus do not contribute to any change in momentum. Ignoring the friction of the wheels also lets me choose any frame of reference I want. A car moving into a wind is equivalent to a car moving with the wind, but faster than the wind.
Now for my diagram of the DWFTTW car (but I will start with it going INTO the wind):
In this case, I put the wind leaving the “car” going slower than it was before. I did this to match the generator from before. Also, if the air slows down, it can “give” some energy to the car by decreasing its kinetic energy. Why is this a problem? Well, compare this to the jet engine. In the engine, the air was going FASTER afterwards. This resulted in a change in momentum in the direction of desired travel. For this car, the change in momentum of the air is to the left. This would mean (with no external forces) that the car would have to change momentum to the right (oops – that would be the wrong way to go).
Ok – what if I made the air going FASTER after it goes through the wind generator? Well, then momentum would be ok – but not energy. The air would gain energy, where did it come from? Magic? Do you see why this is a problem?
This is the same situation as people trying to make energy from nothing. Clearly the ideas of momentum and energy are very well tested. Still some people think that if just maybe something was different…. Well, I don’t know what else to say. If some supporter of DWFTTW vehicles wanted to reply, he or she would probably make some claim about going faster than the wind is different than going into the wind. If the wheels do not matter, then neither does that. A DWFTTWer may also say something about a purely mechanical means to power the vehicle. Although I discussed a wind generator hooked to a motor, I will still considering the system of the car plus air. So, there you go. That is my take on this subject.
Dear MythBusters. When you do an episode on this topic, please mention my blog. It will make my kids think I am cool.