Wind Power Vehicle Traveling Down Wind Faster Than The Wind

[A.T.]

5 and infinity are not quite the same.

"5 x windspeed" referred to a cart with a certain effective gearing (transmission ratio & pitch)

"tend to infinity" simply means that there is no upper bound on the windspeed multiple if effective gearing is not fixed.

Consistency people! Consistency!

Reference #2 shot down.

Not quite. You have quoted rcgldr out of context, to compare apples & oranges, so that you can falsely claim "inconsistency".

And even if some forum post would contradict the reference, how is that "inconsistency" that shoots down the reference?

But just imagine if equation #9 were correct!

It is correct

Equation #9
(Vehicle Velocity) / (Velocity Difference between wind and ground) = 1/((1/efficiency)-1)

solving for Vehicle Velocity and a cart efficiency of 95% we get:
95% efficiency --> 19x multiplier

So with a 40.42 mph wind, we have a theoretical vehicle velocity of 768mph = mach 1

Yes, IF you can achieve 95% overall efficiency at mach 1. But that's a big IF. The equation doesn't say anything about what overall efficiency is possible at which speed. It just says that there is no upper bound on windspeed multiple IF there is no lower bound (> 0) on losses.

 

[rcgldr]

One thing I don't remember seeing is an explanation of the offset rear wheels which they claim is to counter the effect of prop torque.

To summarize the explanation that ended up in a few posts spread out through this thread:

Note that if a vehicle is at rest in a no-wind condition on a level surface, offset wheels do not produce any net torque. The BB just needed a wider wheelbase to prevent rolling over due to the torque at the propeller, but the BB was too close to the legal width limitation for a towed vehicle to extend the wheelbase equally, so they only extended the left axle.

But just imagine if equation #9 were correct! Equation #9:
(Vehicle Velocity) / (Velocity Difference between wind and ground) = 1/((1/efficiency)-1)

From a previous post:

Assuming a sailcraft holds a constant heading θ relative to the true wind (θ = zero means in the direction of the true wind), then the apparent wind can be split into two components:

apparent_crosswind = wind_speed x sin(θ)
apparent_headwind = sailcraft_speed - (wind_speed x cos(θ))

Note the crosswind component is constant, regardless of the speed of the sailcraft. Only the apparent headwind is related to the sailcraft speed.

All of the thrust from the sail on a sailcraft is due to diversion of the apparent crosswind.

In the case of vehicles that get their power from two media moving respect to each other, power input is ideally independent of the vehicles speed, and with some finite amount of power input, and power consumption that approaches zero as a vehicle's efficiency goes to 100% (no losses, no drag), then it makes sense that there is no mathematical limitation on speed for a theorectial vehicle in a theoretical situation (one where supersonic speeds don't affect the outcome).

 

[ThinAirDesign]

... the BB was too close to the legal width limitation for a towed vehicle to extend the wheelbase equally, so they only extended the left axle.

Not really -- we didn't extend both sides because it was only productive to extend one side. Extending the other side would have been a waste of time, money, materials.

JB

 

[OmCheeto]

Not really -- we didn't extend both sides because it was only productive to extend one side. Extending the other side would have been a waste of time, money, materials.

JB

Very smart indeed.

But I am still trying to calculate the torque on the vehicle, and the assumed angle of attack of the prop that I ran in my simulation were pointed out to be wrong. I've gone back and tried to figure out what the effective AOA of the Blackbirds prop is but I seem to get conflicting data now.

From A.T.'s images on https://www.physicsforums.com/showpost.php?p=3352297&postcount=51", there is the following graph:

It shows a blade_angle(deg) of from ~17 to ~26 degrees
It also lists a blade_AOA(deg) of from ~9 to ~4 degrees

Not being an aeronautical engineer, I do not understand the difference.

Also, Llyricist listed two sets of prop data:

Post #208 seemed to have some very strange data. The radius went up, and then the radius went down, whilst the incidence went down.
Post #230 seemed to make more sense, as the angle of incidence minimized at ~20.6 degrees. More in line with A.T.'s "blade angle".

As I recall, I simplified this problem in my simulation to have a single AOA for the prop.

I don't know if that was proper, but it made for much easier maths, given I'd never heard of Javaprop at the time.

The image of the prop on the Discover Channel (post #75) makes it look as there is almost no twist at all, which seems to contradict Llyricist's numbers of from 80 to 20 degrees from axis to tip end.

I've decided that there is a torque on the vehicle due to the prop, (Yes, there is hope for me yet.), just not the value.

btw, did I mention this was a very fun problem?

 

[Llyricist]

The first numbers I posted were indeed messed up, like I said.

The prop IS twisted, like all well designed props, and it is twisted to keep the angle of attack more or less constant at design speed.

If you go to fasterthanthewind.org, and scroll down on the right to get to the older blogs, for the end of 2009 and the beginning of 2010, you can see the construction process of the propeller blades and get a better idea of the twist.

 

[spork]

To first order approximation we run about 5 degrees angle of attack at all stations of the blade at our design point.

 

[Llyricist]

The two posts were automatically put in moderation, meaning they were not visible except to forum Mentors -- we're not sure why this happened.

I have made the posts visible again, here are direct links:

Post # 208
https://www.physicsforums.com/showthread.php?p=3427707"

Thank you.

 

[Llyricist]

Llyricist did a beautiful job with his posts.



Ron

Thanks, I have to admit, I had a tough learning curve for the energy accounting in a frame of reference where the ground is stationary. I knew it worked, and could do it in other frames, but that negative work thing gave me a hard time.

 

[Llyricist]

Yes he did. He's also done some great analysis and some really nice animations.

And if anyone is interested, and you have flash player installed, they are animations of all the runs they did on July 3, 2010, showing the wind direction and relative wind direction, cart speed, wind speed, apparent wind speed, and wind speed multiple. And they can be viewed here:

Runs 1 and 2: http://megaswf.com/serve/1146662/"

Runs 3 and 4: http://megaswf.com/serve/1146664/"

Runs 5 and 6: http://megaswf.com/serve/1146723/"

Runs 7 and 8: http://megaswf.com/serve/1147000/"

I had to split them up because of Flash's Total frames limitation.

 

[A.T.]

From A.T.'s images on https://www.physicsforums.com/showpost.php?p=3352297&postcount=51", there is the following graph:

It shows a blade_angle(deg) of from ~17 to ~26 degrees
It also lists a blade_AOA(deg) of from ~9 to ~4 degrees

This numbers came from JavaProp when I automatically chose the best prop pitch stetting for every given speed, and estimated efficiencies.

blade_angle : the angle between airfoil cord and propeller disc at 75% propeller radius
blade_AOA : is the angle between airfoil cord and the relative airflow at 75% propeller radius

Post #208 seemed to have some very strange data. The radius went up, and then the radius went down, whilst the incidence went down.
Post #230 seemed to make more sense, as the angle of incidence minimized at ~20.6 degrees. More in line with A.T.'s "blade angle".

Yes, in the propeller geometry the angle of incidence (deg) at 0.75 radius corresponds to my blade_angle. But the variable propeller pitch can offset the angle of incidence along the blade by some number.

The image of the prop on the Discover Channel (post #75) makes it look as there is almost no twist at all, which seems to contradict Llyricist's numbers of from 80 to 20 degrees from axis to tip end.

Better perspective:
http://www.fasterthanthewind.org/2009/12/checking-alignment.html

 

[rcgldr]

variable propeller pitch

A propeller uses an AOA versus prop disk that decreases as radius increases, normally set so that the propeller pitch (the effective advanced distance per revolution) is the same at all radius (except for the hub).

It might be easier to figure the math out if you knew the pitch numbers for the BB propeller. There's a physical pitch based on geometry, and the effective pitch based on air flow. Some props have the pitch measured in a static flow (no headwind) situation, but there is an induced headwind in the vicinity of the prop. Some simplified static thrust calculators ignore the geometrical pitch of a prop. If there was a headwind speed that corresponded to the geometric pitch times revolutions per unit of time, then the propeller would not increase the air speed except for the twisting (torque) of the air flow.

- - -

In the meantime, I've run into a math problem trying to determine a limit. For an ideal (no losses) sailcraft that diverts apparent wind directly aft of the sailcraft (diverting it to become an apparent headwind), the limit of the flow aft of the sailcraft wrt ground approaches wind speed x cos(θ) as the sailcraft speed approaches infinity.

Here are the formulas:

θ = sailcraft heading wrt wind. θ = zero means directly downwind.
v = sailcraft speed
w = true wind speed
aw = apparent wind speed (wrt sailcraft)
da = diverted apparent wind (the wind flow off the aft end of the ideal sail) wrt sailcraft
dw = diverted apparent wind wrt ground

ac = apparent cross wind = w sin(θ)
ah = apparent head wind = v - w cos(θ)

aw = sqrt(ac² + ah²)
aw = sqrt((w sin(θ))² + (v - w cos(θ))²)
aw = sqrt( w² + v² - 2 w v cos(θ) )

after the idealized sail diverts the apparent wind, it is in the same direction as the sailcraft, so da has the same magnitude as aw, just a different direction.

da = sqrt( w² + v² - 2 w v cos(θ) )

The speed of the diverted wind relative to ground is

dw = v - da = v - sqrt( w² + v² - 2 w v cos(θ) )

using a spreadsheet to test the formula, it turns out that

limit v -> ∞ of dw = w cos(θ)

However I'm not able to directly solve this limit.

Continuing, the downwind component of dw = dw cos(θ), so

limit v -> ∞ for dw cos(θ) = w cos²(θ)

The true wind is slowed down by w - dw cos(θ), so

limit v -> ∞ for w - dw cos(θ) = w - w cos²(θ) = w sin²(θ)

This limit is approached from above, with slightly higher numbers at lower speeds. The point of this is that the true wind is slowed by at least wind speed x sin²(θ) regardless of the idealized sailcraft speed. This is getting back to the point that for an ideal sailcraft, there is some finite power input but zero power consumption, so there's no mathematical limit to the sailcrafts speed.

 

[RonL]

If it has not already been considered, the building of counter rotating props will eliminate some torque problems, double the math fun and maybe add just a little more efficiency. Make the lead prop about 10% smaller than the following prop, then consider a slightly adjustable mast that let's angle be adjusted (a little like timing a brushed electric motor). Just a couple of quick thoughts.

Ron

 

[OmCheeto]

If it has not already been considered, the building of counter rotating props will eliminate some torque problems, double the math fun and maybe add just a little more efficiency. Make the lead prop about 10% smaller than the following prop, then consider a slightly adjustable mast that let's angle be adjusted (a little like timing a brushed electric motor). Just a couple of quick thoughts.

Ron

Oh dear hey-Zeus...

Dear Ron,

I'm trying to simplify the math, not make it more complicated.​

sincerely,

Om

 

[RonL]

Oh dear hey-Zeus...

Dear Ron,

I'm trying to simplify the math, not make it more complicated.​

sincerely,

Om

Sorry Om, I was trying to not get carried away. Could have mentioned what has already been said about leverage of energy and suggested use of transfer to a center opening in the prop(s) where a high speed impeller produces a high velocity air discharge which en-trains air flow from the larger prop area, giving it a more low pressure zone to move into. The thrust through the system would not meet resistance from the surroundings as quickly.

Some people love math wish I could do better at it, but I am making some progress

I better quit

Ron

 

[RonL]

I designed and built the thing, and you've lost me. What heat is being converted to work?
Yes he did. He's also done some great analysis and some really nice animations.

Sorry to not answer sooner, I have a hard time converting my thoughts into words that make sense to most people. Here is what my mind is seeing, the weight of the cart and it's motion is converted into energy to drive the propeller, the air resistance in front of the propeller is reduced in an increasing lower value as RPM's go higher (in my mind a slight vacuum), the thrust generated by the propeller into the forward moving wind is in a slightly compressed state (warmer) and by some standard a more solid mass and as it moves away from the spinning propeller it should start to appear somewhat like a mushroom (if it could be seen) this increases the area of applied force by some amount.
In my thoughts (within reason) a heavier cart might actually produce a stronger energy transfer, provided wind friction area can be held to a minimum, resulting in a faster speed.

Hope this makes some sense to someone, would it fall into a (Non-Equalibrium Thermodynamic system) ?

Ron

 

[rcgldr]

Here is what my mind is seeing, the weight of the cart and it's motion is converted into energy to drive the propeller.

A summary of earlier posts.

From a ground frame of reference, the thrust from the propeller is slowing down the wind, and slowing down the wind is the source of power that propels the cart. When the cart is accelerating, the increase in it's kinetic energy is part of the power consumed from the power sourced by slowing down the wind.

A backwards force exerted from the ground to the wheels creates a torque that the wheels use to drive the propeller. There's an effective gearing between wheels and propeller that multiplies force and divides speed. This only works if there's a tailwind since the propeller thrust speed is less than the ground speed, relative to the cart.

 

[ThinAirDesign]

In my thoughts (within reason) a heavier cart might actually produce a stronger energy transfer, ...

Nope. All other things being the same, a heavier cart would be slower.

JB

 

[OmCheeto]

Ok, I simplified the FBD to the point where I hope those like me* can see where the offset wheelbase comes from:

the left up arrow indicates the force imparted onto propeller by the wind.

the right down arrow indicates the reaction force of the wheel-propeller interface which has to be resisted.

ergo, there is a counterclockwise torque on the vehicle.

this is why no one should take me seriously when I only have about 30 minutes to put together diagrams and thoughts.

*idiot!

 

[rcgldr]

Ok, I simplified the FBD to the point where I hope those like me can see where the offset wheelbase comes from.

The offset wheelbase was done to widen the wheelbase on the left as roll prevention from the counter clockwise torque from the air. The wheelbase could have been extended equally on both sides and would provide the same roll prevention (actually a tiny bit more due to the small amount of mass in the wheel moved to the right). One of the posts mentioned that the wheelbase was too close to the legal limit on width for a towed vehicle, and another post mentioned that the right axle wasn't extended simply because it wasn't needed.

Any torque from the wheelbase, whether offset or equal, is a reaction to a torque applied to the wheelbase from the vehicle. The reason for a widened wheelbase is to prevent the vehicle from rolling over onto it's side due to the vehicle torque.

 

[mender]

I thought that one of the main reasons was to equalize the dynamic load on the rear tires for better traction and more even wear.

 

[RonL]

I thought that one of the main reasons was to equalize the dynamic load on the rear tires for better traction and more even wear.

I think things are going on that may not have been considered, weight is key to traction, and energy transfer is taking place between traction and propeller resistance. This torque resistance will tend to lift one side and add pressure to the other and at speed, I suspect if some way to measure each wheel for turns, you will find they will all have a different reading.
Because of energy transfer the drive wheels will slip just a little during each turn, based on how much actual force is pushing down on them.
Omcheeto's drawing has the qualities of a true Professor.

Ron

 

[ThinAirDesign]

I thought that one of the main reasons was to equalize the dynamic load on the rear tires for better traction and more even wear.

While those were side bennies, the sole reason was with our higher than expected efficiencies (and thus speeds) we almost tipped it over in Ivanpah.

JB

 

[ThinAirDesign]

Omcheeto's drawing has the qualities of a true Professor.

Ron

Perhaps -- but it's still quite nebulous at best and most likely just plain wrong.

JB

 

[mender]

While those were side bennies, the sole reason was with our higher than expected efficiencies (and thus speeds) we almost tipped it over in Ivanpah.

JB

Must have missed that!

(edit)

 

[ThinAirDesign]

Must have missed that!

(edit)

http://www.fasterthanthewind.org/2010/04/so-heres-short-version-of-story-behind.html

 

[OmCheeto]

Perhaps -- but it's still quite nebulous at best and most likely just plain wrong.

JB

I agree. Kind of.

 

[RonL]

Perhaps -- but it's still quite nebulous at best and most likely just plain wrong.

JB

Before I say anything else, I must make it clear that to an extreme, I am IMPRESSED and RESPECTFUL of what has been done here and say well done to all involved.

If it sounded as if I was implying a lack of thought by all or anyone involved, please forgive, it was in no way intended. The attention to wheel hub design, shows clearly a very high level of thought processing.

My nebulous thoughts may be wrong and out of context, they are for the most part based on 40 years of contract jobs and sales of skid steer loaders, where spinning, sliding, skidding and hydraulic levered load increase to eliminate slippage, have all been put to use in making a machine utilize a maximum efficiency of energy transfer.

I'll ease out now and return to my own compressed air/electric build and research.
Thanks for the u-tube releases, they have confirmed many of the things I could never say in good descriptive wording.

Best wishes

Ron

 

[ThinAirDesign]

Best wishes

Ron

Ron, no offense was taken and I apologize if it appeared so. I was merely commenting on the fact that without clearer definitions, Om's drawing was rather ambiguous.

As to the wheel RPMs that you mentioned, there is no differential in the BB and thus under most normal circumstances the RPMs will match exactly. There are ratchets on the drive axle which allow us to maneuver the cart around without lockup, but again this in straight operation will not allow one driving wheel to rotate faster than the other.

I love skid steers (I own a tracked version - ASV RC-85).

JB

 

[RonL]

Ron, no offense was taken and I apologize if it appeared so. I was merely commenting on the fact that without clearer definitions, Om's drawing was rather ambiguous.

As to the wheel RPMs that you mentioned, there is no differential in the BB and thus under most normal circumstances the RPMs will match exactly. There are ratchets on the drive axle which allow us to maneuver the cart around without lockup, but again this in straight operation will not allow one driving wheel to rotate faster than the other.

I love skid steers (I own a tracked version - ASV RC-85).

JB

Thanks, I wasn't sure as I thought the drawing was more clear than my comments If everything is OK I'll leave well enough alone.

I left equipment sales about the time mini-excavators started showing up in the US with rubber tracks, the rubber tracks caught on quickly with the skidders.
I made a move into heavier equipment, but can never think of being without a small do almost anything machine, my motto, "being without a Bobcat, is like working with a broken arm", at least if one is outside doing more than simple yardwork. (guess I'm still a "black and white" guy). I did look up the machine you mentioned, it looks like a really productive unit.

I'll keep a watch for new and improved progress in the wind machines.

Ron

 

[Llyricist]

One more of the many esoteric things I learn from this discussion. I had never heard of a skid steer before, now I know what one is.