Wind Power Vehicle Traveling Down Wind Faster Than The Wind

[A.T.]

Thanks. That's what I'm hoping for (on the optimistic side). What prop efficiency did you use, and what speed ratio (i.e. gearing)?

I used a polar that Llyricist created for NACA6412 @450000 Re, so it not quite accurate. I took the gearing that gives 150RPM at 20mph. The inverted prop efficiency at 2xWS given by JavaProp was 81%.

Just a quick test, I will play around more when i have time.

 

[Llyricist]

I used a polar that Llyricist created for NACA6412 @450000 Re, so it not quite accurate. I took the gearing that gives 150RPM at 20mph. The inverted prop efficiency at 2xWS given by JavaProp was 81%.

Just a quick test, I will play around more when i have time.

If you go here:

https://skydrive.live.com/redir.aspx?cid=27579d7d745f6b79&resid=27579D7D745F6B79!103&authkey=qc!eaR1FyTA%24

You can get AF_6.xml, which is the 6412 at Re 350,000

Change the number after the underscore to match the next higher that you actually have.

 

[A.T.]

If you go here:

https://skydrive.live.com/redir.aspx?cid=27579d7d745f6b79&resid=27579D7D745F6B79!103&authkey=qc!eaR1FyTA%24

You can get AF_6.xml, which is the 6412 at Re 350,000

Thanks. It didn't change the results much though. But lowering the Cd to 0.2 and Crr to 0.006 brings you to 2.17 x windspeed.

 

[rcgldr]

The inverted prop efficiency at 2xWS given by JavaProp was 81%.

Isn't the new "prop" going to be used as a turbine to drive the BB upwind? If so, wouldn't the efficiency be limited by Betz law to about 59%? I'm thinking more like 50% overall.

 

[spork]

Isn't the new "prop" going to be used as a turbine to drive the BB upwind? If so, wouldn't the efficiency be limited by Betz law to about 59%? I'm thinking more like 50% overall.

The new "prop" is indeed going to be a turbine - but the Betz limit really doesn't pertain to efficiency per-se. Of course efficiency can be defined a million different ways, but for our purpose I think it makes sense to look at how much wind energy is converted to useful work (torque x rotary speed of turbine) divided by the total energy lost by the wind.

What Betz tells us is that a stream-tube of air of the same diameter as the turbine, can only give up 59% of it's energy to the turbine. This is because the capture area is smaller than the diameter of the turbine (i.e. some of the air ends up going around rather than through), and you can't bring the wind to a full-stop at the turbine (so the air in the wake of the turbine still has some energy).

 

[rcgldr]

The new "prop" is indeed going to be a turbine - but the Betz limit really doesn't pertain to efficiency per-se. Of course efficiency can be defined a million different ways, but for our purpose I think it makes sense to look at how much wind energy is converted to useful work (torque x rotary speed of turbine) divided by the total energy lost by the wind.

As mentioned in a previous post, I'm thinking of efficiency in terms of power output versus power input, and power as force times speed. Using the cart as a frame of reference, power input = relative air speed x force, power output = relative ground speed x force. If overall efficiency was 55%, then with a 2:1 air:ground effective gear ratio, then output force would be (.55 x 2 =) 1.1 x input force, so 0.1 x force factor left over to compensate for rolling resistance and aerodynamic drag with the BB cart moving upwind at 1 x wind speed.

I was thinking that Betz law applied even to open wind mill generators, which would be similar to the turbine usage on the BB cart, but perhaps I'm wrong on this.

 

[spork]

I was thinking that Betz law applied even to open wind mill generators, which would be similar to the turbine usage on the BB cart, but perhaps I'm wrong on this.

It does apply to open windmill generators, and does apply to the cart. But it's really not a measurement of turbine "efficiency" - or at least not a relevant measure of efficiency (since I suppose we can define it as a sort of efficiency if we choose to).

Betz law says that we can't get all the energy out of a specific reference volume of air. It doesn't limit how much of the extracted energy can be put to good use. The latter is the measure of efficiency that matters to us.

 

[rcgldr]

Betz law says that we can't get all the energy out of a specific reference volume of air. It doesn't limit how much of the extracted energy can be put to good use.

I'm wondering how relatively large the turbine will need to be in order to achieve 1x or greater upwind speed with the BB cart. The "efficiency" I'm wondering about is the power the turbine applies to the wheels to drive the cart and turbine against the wind, versus the turbine drag force times the relative (wrt cart) head wind speed.

 

[A.T.]

The inverted prop efficiency at 2xWS given by JavaProp was 81%.

Isn't the new "prop" going to be used as a turbine to drive the BB upwind?

Yes, it's the inverse propeller efficiency:

shaft_power / (turbine_drag * airspeed)

If so, wouldn't the efficiency be limited by Betz law to about 59%?

That's the limit for turbine efficiency defined in the in rest frame of the turbine:

shaft_power / total_kinetic_energy_flow_through_disc

I'm thinking more like 50% overall.

Actually the turbine efficiency of this rotor is much lower, around 12%. But this is not the relevant efficiency for an upwind cart. They are not trying to extract as much energy as possible from a certain volume of air, but rather to achieve the maximal speed. They want as much shaft_power as possible with as little turbine_drag as possible, while for a stationary turbine producing power the turbine_drag is irrelevant.

Imagine you could achieve 100% turbine efficiency and stop the air relative to the turbine. For an upwind car that means you would have not only slowed down the air relative to the ground, but accelerated it in the opposite direction, wasting energy on this. So maximal turbine efficiency is not your goal here. The inverse propeller efficiency is a better indicator, but the cart performance also depends on the other efficiency parameters.

 

[rcgldr]

It's the inverse propeller efficiency:
shaft_power / (turbine_drag * airspeed)

versus Betz law:
shaft_power / total_kinetic_energy_flow_through_disc

This is what I was wondering, if the power to the wheels versus the drag x airspeed could be greater than Betz's 59% factor. If the efficiency is 70% or higher, then greater than 1x wind speed upwind should be achievable with the BB cart.

 

[A.T.]

This is what I was wondering, if the power to the wheels versus the drag x airspeed could be greater than Betz's 59% factor.

Yes sure. For a very slow rotating turbine the inverse propeller eff. is mainly a function of the L/D ratio of the blades. But there are practical limits and minimum power requirements that have to be balanced against this.

 

[chingel]

If I were in a motorglider and gliding directly downwind, would you say the tailwind pushes harder on the propeller when the prop is engaged? How about if I were gliding upwind when I engaged the prop?

The motorglider and its prop would see no difference at all (tailwind, headwind, or no wind).

Our cart operates exactly as the motorglider in a tailwind. Th spinning prop interacts with the air it's in in exactly the same way as an airplane prop in flight interacts with the air it's in.

I'm not sure how a motorglider works, how does it make it's propeller spin?

With the cart that has a screw in a wooden block, when you push the wooden block and the screw isn't turning, you only push a certain amount, but if the screw is turning, you also have to push on the turning parts if the screw isn't slipping in the wood, basically you will be pushing harder when you want to keep the block at the same speed. I think it's the same way with the wind cart. The extra energy to go faster than the wind when you engage the propeller at windspeed doesn't come from multiplying the force, it just makes sure the propeller keeps turning the right way, but because the wind starts pushing harder, ie it also has to work on the rotating parts.

 

[A.T.]

I'm not sure how a motorglider works,

Neither does the air, that interacts with its propeller.

The extra energy to go faster than the wind when you engage the propeller at windspeed doesn't come from multiplying the force, it just makes sure the propeller keeps turning the right way, .

The gearing (multiplying the force) is not only making the propeller turn the right way, it makes the entire cart accelerate the right way. What is "extra energy" anyway? And why do you keep taking about engaging the propeller at windspeed? It is engaged all the time.

 

[Redbelly98]

Betz law says that we can't get all the energy out of a specific reference volume of air. It doesn't limit how much of the extracted energy can be put to good use. The latter is the measure of efficiency that matters to us.

I've been following this discussion as much as I can. Put another way:

• A certain volume of air contains an amount of energy x.
• That air loses an amount of energy y in the turbine.
• An amount of energy z gets converted to mechanical energy.
• z ≤ y ≤ x

Betz law says that y/x (or z/x for that matter) can't be more than 59%. However, z/y is the measure of efficiency used here.

 

[A.T.]

I've been following this discussion as much as I can. Put another way:

• A certain volume of air contains an amount of energy x.
• That air loses an amount of energy y in the turbine.
• An amount of energy z gets converted to mechanical energy.
• z ≤ y ≤ x

All those kinetic energies depend on the reference frame. They are some frames where the turbine puts energy into the air. Your z ≤ y ≤ x is valid only in some reference frames.

Betz law says that y/x (or z/x for that matter) can't be more than 59%.

Betz law applies only in the rest frame of the turbine, which is the rest frame of the upwind cart. In that accelerating frame the kinetic energy contained in a volume of air is not constant. So you can stay well below that 59% at a constant turbine efficiency (around 12%), and still get more and more shaft_power, because the air moves faster and faster. However, that increase in turbine power is countered by the increasing power demand at the wheels, so the theoretical net power is approximately constant and depends mainly on the true wind velocity.

 

[spork]

That's the limit for turbine efficiency defined in the in rest frame of the turbine:

shaft_power / total_kinetic_energy_flow_through_disc

I believe the Betz limit doesn't look at the actual energy flow through the disk, but rather the energy that would flow through the disk if that flow were not disturbed by the disk. I think it uses the disk reference area applied to the free-stream. In reality, some of the energy from the reference area ends up flowing around the disk due to the high pressure upstream of the disk.

I'm not sure how a motorglider works, how does it make it's propeller spin?

That's where the motor comes in.

 

[chingel]

The gearing (multiplying the force) is not only making the propeller turn the right way, it makes the entire cart accelerate the right way. What is "extra energy" anyway? And why do you keep taking about engaging the propeller at windspeed? It is engaged all the time.

Yes you are right the gearing also determines the speed at which the propeller and also the cart will go. It has to have an advantage so that the wind pushing on the propeller wouldn't make it go the other way.

With the extra energy I meant the energy to go faster than windspeed once you are already at windspeed. If you just multiply force by levers, there is no extra energy, but the extra energy comes from the wind which I think starts to push more.

I talked about engaging the propeller at windspeed, because I wanted to understand what happens in such a situation. The only difference I think compared to when it is engaged all the time, is that the propeller already has some momentum at windpseed. The cart should still work when you engage the propeller at windspeed, the propeller just needs some time to speed up, maybe making the cart slow down a little until the propeller is up to speed.

 

[Redbelly98]

All those kinetic energies depend on the reference frame.
.
.
.
Betz law applies only in the rest frame of the turbine...

D'oh, of course!

 

[A.T.]

With the extra energy I meant the energy to go faster than windspeed once you are already at windspeed.

That's not "extra energy". Thats the same energy that is used below wind speed.

but the extra energy comes from the wind which I think starts to push more.

There is no "extra energy". All the energy comes from the true wind being reduced.

 

[chingel]

I mean extra energy compared to when the propeller is not spinning. When you engage the propeller, the wind also works on the propeller blade that is turning, acting like a screw in a wooden block.

 

[A.T.]

I mean extra energy compared to when the propeller is not spinning. When you engage the propeller, the wind also works on the propeller blade that is turning.

When you engage the propeller the wheels also start braking. To get any "extra energy" by engaging the propeller you have to multiply the wheel force, to get a greater prop thrust. It's the net force resulting from the gearing that determines if you accelerate (gain energy).

 

[RonL]

Unless I missed it, I do not see mention of the, different energy rate changes, as speeds increase.
Wind energy to the turbine will be a cube factor.
Friction losses to body and frame parts increase by a square factor.
The KE of all things that are in motion, increase exponentially.

I looked at the rules (just a quick look) and all energy storage methods are ruled out, but could the transmission system be electric ? Wheel generators, sending electric energy straight to a motor in the turbine ?

Ron

 

[spork]

The KE of all things that are in motion, increase exponentially.

It raises as the square of the velocity. I don't think that's technically "exponentially".

I looked at the rules (just a quick look) and all energy storage methods are ruled out, but could the transmission system be electric ?

I don't recall whether the current rules allow it, but we've certainly discussed that approach. I think it's fine as long as we demonstrate that we have no way of accelerating by using stored energy.

 

[Llyricist]

Unless I missed it, I do not see mention of the, different energy rate changes, as speeds increase.
Wind energy to the turbine will be a cube factor.
Friction losses to body and frame parts increase by a square factor.
The KE of all things that are in motion, increase exponentially.

I looked at the rules (just a quick look) and all energy storage methods are ruled out, but could the transmission system be electric ? Wheel generators, sending electric energy straight to a motor in the turbine ?

Ron

Just to nitpick, the first half appears to be talking about the upwind turbine cart, but then you talk about putting the motor on the turbine and the generators on the wheels, which would be the reverse of what you would want to do with the upwind cart.

 

[RonL]

Just to nitpick, the first half appears to be talking about the upwind turbine cart, but then you talk about putting the motor on the turbine and the generators on the wheels, which would be the reverse of what you would want to do with the upwind cart.

I am going to need to back off a little, this where I start getting in trouble. This is an area that starts over lapping into electric aviation possibilities in my mind.
You are correct,...but if...
Motor/generator actions can be switched almost instantly changing which and where resistance is lost or applied, as energy,... does this give some amount of micro tweaking of that leverage effect mentioned before?

Ron

 

[spork]

Motor/generator actions can be switched almost instantly changing which and where resistance is lost or applied, as energy,... does this give some amount of micro tweaking of that leverage effect mentioned before?

I don't think so. The most we can ask of the transmission is to transmit the power with as near as possible 100% efficiency. The leverage we take advantage of comes from the difference in velocity between surface and air.