Directly UPWIND faster than the wind

[A.T.]

The Blackbird Landyacht which went 2.8x faster than the wind directly downwind, has been outfitted with a turbine and is now going directly upwind, faster than the wind. The official numbers are not in yet, but estimates are 1.5 - 2x windspeed.

The DUWFTTW blog:
https://fasterthanthewind.wordpress.com

For comparison: At the http://en.wikipedia.org/wiki/Racing_Aeolus the upwind vechicles achieve max upwind speeds of 0.75 windspeed. But their rotor size is limited by the rules:


The old threads about directly downwind:
https://www.physicsforums.com/showthread.php?t=421733
https://www.physicsforums.com/showthread.php?t=562993

 

[sophiecentaur]

Very humbling when I am struggling to make any distance at all when 45 degrees off the wind in my dear ol' Westerly Centaur sailing cruiser, 'Sophie'. But you can't go below in that machine above and make a cup of tea!

 

[A.T.]

Very humbling when I am struggling to make any distance at all when 45 degrees off the wind in my dear ol' Westerly Centaur sailing cruiser, 'Sophie'. But you can't go below in that machine above and make a cup of tea!

Some made boats like this. They also go directly upwind, but not as fast:

 

[sophiecentaur]

Not available on eBay yet?

 

[spork]

Some raw video from the runs. It looks like we'll be submitting data for a run at 2.1X wind speed directly upwind.

http://www.metacafe.com/watch/8679238/blackbird_going_directly_upwind_faster_than_the_wind/

 

[CWatters]

Nice work.

It's amazing how many people still don't think it's possible to sail directly up wind. Even when videos are available.

 

[cosmik debris]

Nice work.

It's amazing how many people still don't think it's possible to sail directly up wind. Even when videos are available.

Yes, no one can fake a video, right? BTW I'm not saying that these are fakes only that a video is not the best of proofs.

 

[spork]

I'm not saying that these are fakes only that a video is not the best of proofs.

That's why we documented everything about the project to the best of our ability and posted it in our build blog. We also set a record - not because we wanted a record, but because it would necessarily involve a trusted and disinterested 3rd party scrutinizing our efforts.

Finally, I posted a set of build videos so anyone could make their own working model for just a few bucks and demonstrate it for themselves on a treadmill in their own living room.

I tried to do everything but go door-to-door. Some people find that creepy.

 

[A.T.]

It's amazing how many people still don't think it's possible to sail directly up wind. Even when videos are available.

In Australia ME students have to build DUW carts in introduction courses:

https://www.youtube.com/watch?v=WH9Qnf8fwBo

One can also buy build sets:

https://www.youtube.com/watch?v=zmC2BaL0KOk

However, going 2.1x windspeed directly upwind would be significant. A paper by Blackford from 1978 claimed that 2x directly upwind would be the absolute theoretical limit. The response by Ruina was never published:
http://ruina.tam.cornell.edu/research/topics/miscellaneous/push-me_pull-you.pdf

 

[spork]

The response by Ruina was never published:
http://ruina.tam.cornell.edu/research/topics/miscellaneous/push-me_pull-you.pdf

Andy Ruina and I have become friendly acquaintances over the last couple of years. Interestingly, he's done some really good work on another topic that I've debated hotly on internet forums - namely bicycle dynamics (and particularly the need to counter-steer at all speeds). He's a very very sharp, friendly, and interesting guy.

Don't be too surprised if you see a paper on wind powered vehicles from him published after all.

 

[rcgldr]

I seem to recall something in one of the previous threads that with similar efficiency, upwind would be about 1x slower than downwind, so if 3x downwind, then about 2x upwind.

 

[A.T.]

I seem to recall something in one of the previous threads that with similar efficiency, upwind would be about 1x slower than downwind,

[STRIKE]That is true for low total efficiency. The difference gets smaller for higher total efficiencies.[/STRIKE]

Check out equation 9 (upwind) and 20 (downwind)

http://orbit.dtu.dk/fedora/objects/orbit:55484/datastreams/file_3748519/content

Total efficiency -> wind-speed multiple:

I assume the Blackbird reaches around 0.7 total efficiency at max. speed. Note that his total efficiency already includes aero-drag and rolling resistance.

 

[harrylin]

The Blackbird Landyacht which went 2.8x faster than the wind directly downwind, has been outfitted with a turbine and is now going directly upwind, faster than the wind. The official numbers are not in yet, but estimates are 1.5 - 2x windspeed.[..]

When I heard about these things I first though" no way", based on wrong (simplistic) intuition - and it took me some time to figure out how/why it can work. :tongue2:

[.] I posted a set of build videos so anyone could make their own working model for just a few bucks and demonstrate it for themselves on a treadmill in their own living room. [..]

Link please?

 

[rcgldr]

I seem to recall something in one of the previous threads that with similar efficiency, upwind would be about 1x slower than downwind ...

downwind = 1 / (1-x) ... upwind = 1 / ((1/x) - 1)

Doing the math for (downwind - upwind):

1 / (1-x) - 1 / (1/x - 1) =
1 / (1-x) - 1 / (1/x - x/x) =
1 / (1-x) - 1 / ((1-x) / x) =
1 / (1-x) - x / (1-x) =
(1-x) / (1-x) =
1

 

[A.T.]

Doing the math for (downwind - upwind):
1 / (1-x) - 1 / (1/x - 1) = 1

Indeed.

However as mentioned before, the lower ground speed in the upwind case should result in lower ground speed related losses, so maybe a bit less than 1x wind speed difference.

On the other hand: for 2x upwind you have 1.5 times the relative headwind, of 3x downwind, so 2.25 times the drag. This is why that total efficiency is tricky, because it not only affects max. speed but also depends on the speed.

It is also not clear if the 2.8x (3.4x unofficial) was the Blackbird's limit for downwind. In stronger winds it might have gone even faster efficiency-wise, but was prevented by transmission power limits (chain broke).

 

[A.T.]

Link please?

http://www.instructables.com/id/Downwind-Faster-Than-The-Wind-Cart/

 

[rcgldr]

However as mentioned before, the lower ground speed in the upwind case should result in lower ground speed related losses, so maybe a bit less than 1x wind speed difference.

On the other hand: for 2x upwind you have 1.5 times the relative headwind.

I thought I already removed that part from my previous post. You have less ground speed but more wind speed for the upwind case, but I assume the formulas in that pdf article already took that into account, so I removed the comment about ground speed in the upwind case.

It is also not clear if the 2.8x (3.4x unofficial) was the Blackbird's limit for downwind. In stronger winds it might have gone even faster efficiency-wise, but was prevented by transmission power limits (chain broke).

I'm thinking that 3.4x was closer to it's limits. I'm not sure if a stronger wind helps. There's probably an ideal wind speed, above which reduces efficiency, perhaps due to drag being related to speed². The ice boats seem to get their best ratio of boat speed VMG (the directly downwind component) versus wind speed with a wind speed around 10 to 16 mph (16 to 26 kph), or at least the ratio at 10 to 16 mph is better than the ratio above 30 mph. Maybe the issue is the wind tends to be more gusty if the average wind speed is over 30 mph.

 

[Llyricist]

The ice boats seem to get their best ratio of boat speed versus wind speed with a wind speed around 10 mph == 16 kph.

I don't know if that is true in the absolute sense, but in the case of their downwind VMG, the multiple definitely does get higher with higher wind speeds. And their limit is also determined by their structural strength.

 

[harrylin]

http://www.instructables.com/id/Downwind-Faster-Than-The-Wind-Cart/

Ah thanks - that looks not too difficult indeed!

 

[spork]

Ah thanks - that looks not too difficult indeed!

If you build one you definitely have to let us know how it goes. You too can play a part in the grand hoax. :)

 

[ozone]

Can someone link me to where I can learn more about the physics behind this.. I find this quite intriguing.

 

[A.T.]

Can someone link me to where I can learn more about the physics behind this.. I find this quite intriguing.

This paper handles both cases directly up & down wind faster than the wind:
http://orbit.dtu.dk/fedora/objects/orbit:55484/datastreams/file_3748519/content

This video explains the basic mechanical principle, also for both directions:

https://www.youtube.com/watch?v=pw_B2MnMqZs

 

[r-j]

These may be silly questions, but that never stopped me before.

When going upwind, is the speed measured in multiples of the wind? So if you are doing twice the wind speed, the ground speed is twice the wind? So does that mean the wind felt by the craft is three times wind speed?

10mph wind. 20 mph up wind. Wind from the crafts POV is 30 mph?

 

[jduffy77]

These may be silly questions, but that never stopped me before.

When going upwind, is the speed measured in multiples of the wind? So if you are doing twice the wind speed, the ground speed is twice the wind? So does that mean the wind felt by the craft is three times wind speed?

10mph wind. 20 mph up wind. Wind from the crafts POV is 30 mph?

You are correct.

 

[CWatters]

Google "Apparent wind"

 

[spork]

Some questions were posed via PM that I'd like to respond to on the thread (I've already responded by PM as well)...

First I had to make sense of what a propeller even does, and from what I gather it produces propulsion by pulling the vehicle into the air in front of it.

That's essentially correct. It's basically a couple of wings swung around an axis. The lift generated pulls the vehicle forward.

The wheel/propeller are connected through some sort of transmission.

That's correct. There is a fixed ratio transmission between the propeller and wheels in the downwind case, or between the turbine and wheels in the upwind case.

In both cases we use ratchets to let the prop or turbine spin freely if it gets ahead of the wheels. This relates to practical matters and allows us to prove we're not using stored energy. Ratchets are not a necessary part of the design.

Next the gearing is set so that the propeller has to spin faster than the wheels turn (not too sure of the exact ratio here but I think it needs to be greater than 2).

Not exactly. It's less about the rotational rate of the wheels and propeller, and more about the rate each advances through (or on) its medium. For the downwind cart, the prop needs to advance through the air more slowly than the wheels advance over the ground. It's exactly the opposite for the upwind vehicle.

In the initial accelerating phase i.e. when the cart is slower than the wind you are simply drawing power from the wind until you reach some cutoff point.

In the downwind case, the whole vehicle (prop included) is simply a bluff body being pushed by the wind initially. As it begins to move, the prop starts to turn (since it's geared to the wheels). This of course begins to produce thrust. There's a smooth transition between the bluff body phase and the thrust phase. Prop thrust is the sole contributor by the time we reach wind speed.

In the upwind case, the turbine is turned by the wind, and that in turn turns the wheels. There is no change in phase in this case.

Once you hit this cutoff point the cart then actually begins to draw power from its own forward movement...

Yes and no. We have to consider the relative wind over the vehicle when doing the analysis, but we never use any stored energy or momentum of the vehicle to our advantage.

Whether a wind powered vehicle can "make its own wind" is a bit more of a philosophical question, but my inclination (without going into a lot of detail) is to say that it really can't. You could argue either side of this, but you don't get something for nothing as it might otherwise imply.

...and the potential difference between the velocity of the wind at the propeller and the wind speed at ground level (this part is probably the most confusing aspect of the whole machine, and I am not entirely sure how this process works).

It sounds like you're talking about wind gradient. While it's possible to design a vehicle that exploits wind gradient, this one does not. This vehicle exploits the energy available from the relative velocity of the two media (ground and air).

 

[rcgldr]

In the initial accelerating phase i.e. when the cart is slower than the wind you are simply drawing power from the wind until you reach some cutoff point. Once you hit this cutoff point the cart then actually begins to draw power from its own forward movement.

In both cases, the cart draws power from the wind by slowing the wind, extracting kinetic energy from the wind (using the Earth as a frame of reference). Even when the cart itself is moving faster than the wind, the thrust from the prop is slowing the wind (wrt earth).

 

[spork]

In both cases, the cart draws power from the wind by slowing the wind, extracting kinetic energy from the wind (using the Earth as a frame of reference). Even when the cart itself is moving faster than the wind, the thrust from the prop is slowing the wind (wrt earth).

Absolutely right. It's also worth mentioning that, while there's a sort of change in operation mode for the downwind cart, the change is not fundamental. For the downwind cart, the wheels turn the propeller - always - at all speeds both above and below wind speed.

For the upwind cart, the turbine always turns the wheels.

 

[CWatters]

There is an easy way to understand the feasibility of the upwind cart.. That's to understand that individual blades of the prop do not move directly upwind. They are "tacking" in 3D.

 

[azizlwl]

Just wishful thinking. Then all the physics laws will violated by Youtube.

 

[spork]

There is an easy way to understand the feasibility of the upwind cart.. That's to understand that individual blades of the prop do not move directly upwind. They are "tacking" in 3D.

This is true as well - and is true of both the upwind and downwind cart. In fact this is how I originally conceived of the downwind cart (though it turns out I was not the first to do so).

To understand that the blades are on a continuous helical tack, it's of course important to understand that their gearing to the wheels replaces the constraint that would otherwise be provided by the keel of a sailboat.

 

[r-j]

You are correct.

There's something I rarely see. ;)

What causes the cart to reach a maximum speed? If the faster it goes the more wind it 'feels', is there a limit to how fast a craft could eventually reach?

 

[Llyricist]

There's something I rarely see. ;)

What causes the cart to reach a maximum speed? If the faster it goes the more wind it 'feels', is there a limit to how fast a craft could eventually reach?

The advance ratio between the rotor and the wheels sets the hard theoretical limit.

For instance, in the downwind case, a propeller pitched and geared to advance half as far through the air as the wheels go over the ground, will be limited by that to twice wind speed. Of course, since a propeller can never achieve "hard gearing" with the air to do that (there will always be "slip"), the limit will be less than that. An example of a very similar situation is:

But in real terms, it is mostly aerodynamic drag force, as well as the other efficiencies, that catches up to the the thrust force and prevents further acceleration.

 

[spork]

There's something I rarely see. ;)

What causes the cart to reach a maximum speed? If the faster it goes the more wind it 'feels', is there a limit to how fast a craft could eventually reach?

The vehicle has a "design speed" given by the turbine pitch and gearing. This is what we call the "vehicle speed ratio" (VSR). It's the rate at which the turbine would advance through the air divided by the rate at which the wheels advance over the ground - keeping in mind the two are connected by a transmission.

If that number is greater than 1.0, you have a vehicle that can theoretically go directly into the wind faster than the wind. If it's less than 1.0, you have a vehicle that can go directly downwind faster than the wind. The closer you get to 1.0 from either side, the greater a multiple of wind speed you can theoretically achieve (this can be worked out through simple kinematics).

But... the closer you get to 1.0, the greater the required efficiency needed to make the vehicle work at all at that VSR. You can change the VSR by changing the gearing or the prop/turbine pitch. With the Blackbird, we do have the ability to change the prop/turbine pitch on the fly. We can change the gearing, but only while stopped.

That being said, there is no theoretical limitation on maximum multiple of wind speed. It's just a matter of building a vehicle with high enough efficiency - and operating in a low enough wind.

The reason you need to operate in a low wind if you want to achieve very high multiple of wind speed is that you start fighting compressibility effects of air at higher speeds. This will inherently reduce your efficiency, and therefore limit your multiple of wind speed.

 

[Llyricist]

I see that the term has changed from "Advance Ratio", which also refers to something else related to props, to vehicle speed ratio. Fair enough :)