Wind powered cart traveling directly down wind faster than the wind

Excellent. Next step... instead of using a chain and sprockets for a transmission, we're going to use a generator on the wheels and an electric motor to turn the prop. This will make it easier to follow the energy flow. OK?


So let's assume we have a tailwind of 5 meters/second (around 10 mph) and we tow the cart up to 10 meters/second.

The cart is being towed, and the wheels are turning our generator. So there's some drag on the wheels. How much drag depends on how much load we put on the generator. So let's load the generator up until the drag at the wheels is 200 Newtons. OK?

So we want to know how much power the generator is putting out. The amount of power we're putting into the generator by turning its shaft is given by force x velocity. The power out will be the same as the power in multiplied by the generator's efficiency. Let's say the generator is 90% efficient.

So I claim we'll get this much power out of our generator in the form of electricity:

electric_power = force * velocity * generator_efficiency
electric_power = 200 Newtons * 10 meter/sec * 0.90
electric_power = 1800 Newton * meters / sec (or Watts)

So far so good?

Just to recap so we can move forward without searching through posts if all is good so far, I'll keep a running list of our agreed quantities:

Tailwind 5 meters/sec
Ground speed: 10 meters/sec
Retarding force on wheels: 200 Newtons
Generator efficiency: 90%
Electrical output from generator: 1800 Watts
 
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I'm losing you on the tailwind and ground speed. In the beginning of your post it says 5 and 10 m/s respectively but the running tally indicates 10 and 20 m/s.
 
ebacon said:
I'm losing you on the tailwind and ground speed. In the beginning of your post it says 5 and 10 m/s respectively but the running tally indicates 10 and 20 m/s.
Click to expand...


Good catch - you caught me in a mistake. I went back and edited it. Now using the original numbers throughout. Check me again and let me know if we're good.

Updated numbers:

Tailwind 5 meters/sec
Ground speed: 10 meters/sec
Retarding force on wheels: 200 Newtons
Generator efficiency: 90%
Electrical output from generator: 1800 Watts
 
ebacon said:
OK, I'm with you so far.
Click to expand...

Great. Now let's take that 1800 watts and use it to turn the electric motor that's turning the prop. And let's make that motor 90% efficient as well.

That means the shaft power on that motor will be given by:

output_power = input_power x motor_efficiency
output_power = 1800 watts * 0.90
output_power = 1620 watts

But we'll lose some efficiency because the prop is not perfect either. Let's make our prop 90% efficient as well. So the effective power we actually get out of the prop will be given by:

effective_prop_power = motor_output_power x prop_efficiency
effective_prop_power = 1620 watts * 0.90
effective_prop_power = 1458 watts

Agreed?

Updated numbers:

Tailwind 5 meters/sec
Ground speed: 10 meters/sec
Retarding force on wheels: 200 Newtons
Generator efficiency: 90%
Electrical output from generator: 1800 Watts
Electric motor output power: 1620 watts
effective_prop_power = 1458 watts
 
spork said:
But we'll lose some efficiency because the prop is not perfect either. Let's make our prop 90% efficient as well. So the effective power we actually get out of the prop will be given by:
Click to expand...
Is that realistic? Under what conditions?
 
spork said:
Great. Now let's take that 1800 watts and use it to turn the electric motor that's turning the prop. And let's make that motor 90% efficient as well.

That means the shaft power on that motor will be given by:

output_power = input_power x motor_efficiency
output_power = 1800 watts * 0.90
output_power = 1620 watts

But we'll lose some efficiency because the prop is not perfect either. Let's make our prop 90% efficient as well. So the effective power we actually get out of the prop will be given by:

effective_prop_power = motor_output_power x prop_efficiency
effective_prop_power = 1620 watts * 0.90
effective_prop_power = 1458 watts

Agreed?

Updated numbers:

Tailwind 5 meters/sec
Ground speed: 10 meters/sec
Retarding force on wheels: 200 Newtons
Generator efficiency: 90%
Electrical output from generator: 1800 Watts
Electric motor output power: 1620 watts
effective_prop_power = 1458 watts
Click to expand...

OK so far. I have the same question as Gary F wrt to 90% efficiency, but as long as the efficiency < 1 I'm still in the plausible camp.
 
Gary F said:
Is that realistic? Under what conditions?
Click to expand...

You guys are used to short props at high RPM, putting out lots of thrust. That is inefficient for the same reason stubby wings are inefficient. That's why sailplanes have such long skinny wings, and also why we have a 17.5 foot prop on the blackbird spinning 1/10th as fast as the props on your Cessna, and putting out only a fraction of the thrust.

Yes, under those conditions I believe we're right in the ballpark of 90% efficiency with our prop. But if you don't like it I can go back when we're done and reduce prop efficiency to 75%. I won't be able to get the same multiple of wind speed, but it'll still go directly downwind faster than the wind.

ebacon said:
OK so far. I have the same question as Gary F wrt to 90% efficiency, but as long as the efficiency < 1 I'm still in the plausible camp.
Click to expand...

Excellent. So now we have the prop putting out an effective 1458 watts. The cart is going over the ground at 10 meters/sec, but it's only going through the air at 5 meters/sec, because of the tailwind. And this is what makes the magic work as you'll see.

Again we use the fact that:
power = force x velocity

In this case that means:

effective_prop_power = thrust x velocity_of_prop_through_air
1458 watts = thrust x 5 meters/sec
thrust = (1458 joules/sec) / (5 meters/sec)
thrust = 291.6 joules/meter = 291 Newtons

Good so far?

We're not quite done, but almost there. We still have to account for aerodynamic drag and rolling resistance in the real world.

Updated numbers:


Tailwind 5 meters/sec
Ground speed: 10 meters/sec
Retarding force on wheels: 200 Newtons
Generator efficiency: 90%
Electrical output from generator: 1800 Watts
Electric motor output power: 1620 watts
effective_prop_power = 1458 watts
Prop thrust = 291.6 Newtons
 
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ebacon said:
OK, I'm with you so far.
Click to expand...

OK. So we're towing the Blackbird downwind at twice wind speed. We've got 200 Newtons of drag because the wheels are turning a generator. After generator losses, electric motor losses, and prop losses, we're getting 291.6 Newtons of thrust.

Now we have to consider rolling resistance...

The cart weighs about 650 lbs with my butt in it. Our rolling resistance is approximately 0.01. This gives us about 6.5 lbs of rolling resistance (28.9 Newtons).

That leaves just one more drag source - aerodynamic drag.

So I've got 291.6 Newtons of thrust minus 200 Newtons retarding force, and another 28.9 Newtons of rolling resistance. That gives me a surplus of thrust of 62.7 Newtons. So the question is whether I can make a chassis that yields less than 62.7 Newtons of drag when moving through the air at 5 meters/sec.

Without going into the drag equation, can we agree that I could in theory make this thing as slippery as need be? We can certainly do the drag equation if necessary.

But assuming I can achieve an aero drag of less than 62.7 Newtons, it means the tension in my tow rope is less than 0 while going downwind at twice wind speed. In other words, I can lose the rope and the cart will still accelerate.



Latest numbers:

Tailwind 5 meters/sec
Ground speed: 10 meters/sec
Retarding force on wheels: 200 Newtons
Generator efficiency: 90%
Electrical output from generator: 1800 Watts
Electric motor output power: 1620 watts
effective_prop_power = 1458 watts
Prop thrust = 291.6 Newtons
rolling resistance = 28.9 Newtons
 
OK, let's do the aerodynamic drag...

Drag = 1/2 * rho * V^2 x Cd * reference_area

Rho is air density: 1.2 kg/m^3
V is airspeed: 5 meters/sec
Cd is our coefficient of drag: 0.25
reference area = 2 meter^2

So:

Drag = 1/2 x 1.2 x 5^2 * .25 * 2.0
Drag = 7.5 Newtons.

Therefore...

Excess thrust = 291.6 - 200 - 28.9 - 7.5
Excess thrust =

Latest numbers:

Tailwind 5 meters/sec
Ground speed: 10 meters/sec
Retarding force on wheels: 200 Newtons
Generator efficiency: 90%
Electrical output from generator: 1800 Watts
Electric motor output power: 1620 watts
effective_prop_power = 1458 watts
Prop thrust = 291.6 Newtons
rolling resistance = 28.9 Newtons[/QUOTE]
Aero drag = 7.5 Newtons
Excess thrust = 55.2 Newtons (about 12.5 lbs)

DISCLAIMER: I'm on a conference call while doing this. Double check my math.
 
OK. No need to do a drag equation for the cart at such slow speed. I agree that the drag force would be/could be small.

I'm dumbfounded.

Is there more?
 
ebacon said:
OK. No need to do a drag equation for the cart at such slow speed. I agree that the drag force would be/could be small.
Click to expand...

See above. I decided to knock out the drag equation while wasting time on a conference call.

Incidentally, 5 meters/sec is about 11.2 mph (through the air), or 22.4 mph over the ground. Not screaming fast by any means, but not all that much slower than our record run. Our fastest run was about 54 mph (in about 20 mph wind).

I'm dumbfounded.
Click to expand...

Exactly the reaction we were going for with this brain-teaser! :D

Is there more?
Click to expand...

Much more. We'll be going directly UP wind faster than the wind soon. There's also the very interesting result that says we can harvest MUCH more energy from the wind if we use a moving windmill vs. one that's fixed to the ground.
 
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spork said:
Much more. We'll be going directly UP wind faster than the wind soon. There's also the very interesting result that says we can harvest MUCH more energy from the wind if we use a moving windmill vs. one that's fixed to the ground.
Click to expand...

Spork:

Got to give you credit... I also had difficulty getting my arms around this... not at all intuitive. Appreciate you taking the time to break it down in easier to understand parts and giving an explaination. The upwind part should be interesting as well.

Gary
 
Gary said:
Spork:

Got to give you credit... I also had difficulty getting my arms around this... not at all intuitive. Appreciate you taking the time to break it down in easier to understand parts and giving an explaination. The upwind part should be interesting as well.

Gary
Click to expand...


Thanks. We can do a similar analysis for the upwind run if you want. The real difference is that we lose the prop and replace it with a turbine. Now instead of the wheels turning the prop, the turbine turns the wheels. The interesting thing is that the turbine is constrained by the Betz limit, while the prop is not.
 
Spork,

Do you know if it is true that a sailboat or iceboat can beat a balloon that is drifting downwind? I read that in some of the DDWFTTW arguments and saw it in a video, but I still have trouble believing that one. It seems that the best a sailboat could do is the downwind component of the wind vector.

I agree that the apparent wind and hull speed routinely exceed the true wind speed but that's a different issue.
 
ebacon said:
Spork,

Do you know if it is true that a sailboat or iceboat can beat a balloon that is drifting downwind? I read that in some of the DDWFTTW arguments and saw it in a video, but I still have trouble believing that one. It seems that the best a sailboat could do is the downwind component of the wind vector.

I agree that the apparent wind and hull speed routinely exceed the true wind speed but that's a different issue.
Click to expand...


It is true. In the last Americas Cup race Ellison's downwind leg beat the wind by a factor of about 2X. Ice boats and land yachts do it absolutely routinely. I understand they can achieve a downwind VMG (velocity made good) up to 4X or 5X.

It's easy to show how that works with a quick vector analysis. I can post it if you like.

If you consider one of the blades of our prop, it's doing exactly the same thing. It's simply on a continuous downwind tack (a "broad reach") in which it's downwind speed component is greater than wind speed.

ETA: Yesterday I was invited to watch two of Ellison's 45' cats practicing on the bay for the upcoming America's Cup. We were aboard a 130' schooner, and they were screaming by us at about 35 mph - just feet from us at times. I'm sure they were beating the wind on their downwind tacks.
 
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If it's not too much work I would like to see the vector analysis.

You've been more than gracious with your time and I don't want to be a bother.
 
ebacon said:
If it's not too much work I would like to see the vector analysis.

You've been more than gracious with your time and I don't want to be a bother.
Click to expand...

Yes you do. It's the pilot in us. LOL
 
spork said:
. . .

ETA: Yesterday I was invited to watch two of Ellison's 45' cats practicing on the bay for the upcoming America's Cup. We were aboard a 130' schooner, and they were screaming by us at about 35 mph - just feet from us at times. I'm sure they were beating the wind on their downwind tacks.
Click to expand...

That's insane.

I raced the Bayview Mackinac the first year that the Wahoo! cat ran. We docked next to her at the finish albeit a few days later. :D

What a boat. I think it is also in the 50ish foot range. The crew said it was so fast that they were porpoising across the waves. I can't imagine that ride.

Here she is

http://www.youtube.com/watch?v=aCH7Kr0mzWA
 
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This is the vector diagram for an ice-boat that’s maintaining a course such that its downwind velocity component is faster than the wind. I've assumed a boat going 45 degrees downwind at a speed of twice the wind speed. The ticket is to then compute the necessary L/D of the sail and keel to make this possible (this would have the boat making a downwind velocity component of 1.414 times the wind-speed).

Given the wind velocity and the boat velocity, we can easily compute the apparent wind over the sail. From this we see the direction of lift and drag on the sail. What we need to do to make sure this sailing configuration is possible is to insure that "alpha" is small enough so that the resultant force has a forward pointing component (relative to the boat). In this case alpha would have to be 45 - 16.3 degrees or 28.7 degrees (or less). That relates to a sail whose L/D is 1.83. Obviously this is easily achievable. However, I've assumed a keel with infinite L/D in this case. The drawing gets a little more cluttered if we include the keel's L/D. So I'll try to describe it in words. I'm going to assume an L/D of 10:1 for the keel (easily done with an ice-boat). This will trim 5.7 degrees off of my 28.7 degree budget. That leaves me with an allowable 23 degrees(L/D = 2.35:1) to achieve this configuration. So with a keel that has a 10:1 L/D and a sail/boat that has an overall 2.35:1 or better L/D this configuration can be achieved (we can achieve a downwind component about 40 percent faster than the wind speed).

In each case the vehicle pushes the fluid backward relative to the vehicle itself, but not backward as quickly as the vehicle is moving forward. It’s all about exploiting the energy available at the wind/ground interface. This is why when we compute the energy produced by the prop it is less than the energy harvested by the wheels (on our prop-cart). In the real world this will always be true.
 

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ebacon said:
That's insane.

I raced the Bayview Mackinac the first year that the Wahoo! cat ran. We docked next to her at the finish albeit a few days later. :D

What a boat. I think it is also in the 50ish foot range. The crew said it was so fast that they were porpoising across the waves. I can't imagine that ride.

Here she is

http://www.youtube.com/watch?v=aCH7Kr0mzWA
Click to expand...

Interestingly, as fast as those cats are (about 35 mph), they're not nearly as fast as the overall water speed record for sailing. That record is closer to 60 mph now (it's gone between sailboats, kiteboards, and windsurfers several times now). I'm pretty sure I've hit 35 on my kiteboard many times. I have a friend that's working on the program for Ellison who said the kiteboards on the bay were keeping up with them.
 
spork said:
Interestingly, as fast as those cats are (about 35 mph), they're not nearly as fast as the overall water speed record for sailing. That record is closer to 60 mph now (it's gone between sailboats, kiteboards, and windsurfers several times now). I'm pretty sure I've hit 35 on my kiteboard many times. I have a friend that's working on the program for Ellison who said the kiteboards on the bay were keeping up with them.
Click to expand...

Roger that.

Thanks for the vector diagram. It helps me see what my skipper talked about when we were racing. He always said that the broad reach was the fastest point of sail and I believed that, but I couldn't get my head around the faster than the wind part.

You guys on the west coast know how to sail. Here's a short story.

About fifteen years ago I was taking bids on a software contract in Detroit. Two partners flew in from California to bid. During our conference they showed me their previous projects. At the end of their portfolio presentation was a sailboat racing handicap system. They didn't talk about that slide and let it just flash across the screen.

After we discussed formalities I popped a question -- So which one of you two race sailboats? They laughed and wondered where my question came from. I told them that I noticed their sailboat software and knew that they didn't make any money from it so one of those two must love sailing.

It ends up that both of them loved sailing and brought their gear to Detroit in hopes of hitching a ride on Lake St. Clair. It just happened that our crew was racing a weekly series that night so I called my skipper and got them on our boat. They schooled the heck out of us and put us in second place that evening. That was the best our rag-tag team ever did. They knew how to squeeze performance out of every person, yard of fabric, . . .
 
I used to windsurf, and now mostly kitesurf. I'm not qualified to sail anything much more than a Sunfish. But the guy that hired me into my current job has won more world records than I can count. He recently won two separate "round the world" races, and just won "Yachtsman of the year" (which his wife has won twice! :D )
 
spork said:
I used to windsurf, and now mostly kitesurf. I'm not qualified to sail anything much more than a Sunfish. But the guy that hired me into my current job has won more world records than I can count. He recently won two separate "round the world" races, and just won "Yachtsman of the year" (which his wife has won twice! :D )
Click to expand...

Nice!

The people that do around the world are a different breed. Besides the sailing there's the contingencies for injury at sea and having to stitch yourself up (shudder), dismasting, capsizing, on and on, and knowing that you are out of range of aircraft rescue. That's Rambo stuff.

I'm still in the dinghy camp, too. I have a Snipe and plan to get my daughter into it this year. She's eight years old and getting comfortable with her swimming skills. This year I hope to introduce her to dinghy sailing on an inland lake. She doesn't know that that's all I'm good for yet. :D
 
ebacon said:
The people that do around the world are a different breed. Besides the sailing there's the contingencies for injury at sea and having to stitch yourself up (shudder), dismasting, capsizing, on and on, and knowing that you are out of range of aircraft rescue. That's Rambo stuff.
Click to expand...

No doubt. On the Volvo around the world race, his team had two boats. The partner boat lost a man overboard. They recovered his body (too late), and spent the next two weeks transporting the body to the next port. He's been on board for de-mastings, pitch-poles, and general major mechanical failure. He was once hit by lightning when working on an antenna fixture from below deck.

I'll stick to the safer stuff like hang gliding and paragliding. His stories sound exciting, but not exactly fun.
 
Spork,

If you're still logging in here could you please riddle me one more question?

I think I have enough understanding of how the car works to defend it. I'm trying over at beechtalk.com.

One question that someone could ask and that I still can't answer relates to the following video. Why does the tell-tale on the nose of the cart show a headwind?

http://www.youtube.com/watch?v=5CcgmpBGSCI
 
ebacon said:
Spork,

If you're still logging in here could you please riddle me one more question?

I think I have enough understanding of how the car works to defend it. I'm trying over at beechtalk.com.

One question that someone could ask and that I still can't answer relates to the following video. Why does the tell-tale on the nose of the cart show a headwind?

http://www.youtube.com/watch?v=5CcgmpBGSCI
Click to expand...

What you see on the nose is a sort of home made protractor. We were trying several methods to make sure I kept the cart steered directly downwind. I had a piece of yarn tied at the top of that pole and I used the protractor to make sure it was centered. There was also a camera at the base of that pole looking straight up at the protractor and yarn. I don't think I had either the camera or yarn in place on that particular run. We soon gave up on that method anyway.

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You'll have to let us know how it goes convincing others. Some accept it relatively quickly, and some never will.
 
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spork said:
When it comes to energy bookkeeping, we are very careful to never short change the universe. It's considered very bad form. :D
Click to expand...
Is that like crossing the proton streams (ala Ghostbusters)?
 
gismo said:
Is that like crossing the proton streams (ala Ghostbusters)?
Click to expand...

Sort of. But crossing the proton streams brings the entire universe to a violent end, while short-changing the universe on energy makes the gods focus their anger directly at you.

Now technically, I have diplomatic immunity from the laws of physics, but I still try not to violate them. I figure it's just part of being a good guest during my visit to your universe.
 
I don't get how this is so hard to understand as possible or real by a bunch of pilots. Have the dispbelievers never used the invisible mystery of lift? Sail boats haven't had to rely on the wind pushing them since the Vikings traveled the earth.
 
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