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Newton's third law problem.

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electrodacus:

--- Quote from: Kleinstein on November 29, 2022, 08:42:56 am ---The interaction of the wind with the vehicle is no way close to 100% efficient - with a standing obstacle it is more like 0%. Even a good wind turbine is not close to 100% efficient. So it does not make sense to base the calculation on the power that the wind could provide with 100% efficiency.

So it is not about an energy or power balance, but about the forces.

--- End quote ---

You are correct that a wind turbine is no more than 40 to 45% efficient but a sail is way more efficient approaching ideal.
In any case the reason for using ideal numbers is so that there can be no discussion about improving efficiency as even with ideal case no vehicle can drive upwind without using energy storage and a trigger mechanism.

No sail based vehicle can drive directly upwind not because the wind power is zero at that point is actually maximum is because that power can only be used to accelerate the vehicle direct downwind not direct upwind.
So if a stationary vehicle has 300W of wind power available when stationary it can accelerate down wind using all that but it can not move upwind at all unless it has >300W
Changing the sail for anything else like a less efficient wind turbine will not help things as you still need more than wind turbine power in order to accelerate upwind so what happens is that a very small energy storage is involved and that will be charged then used to move upwind even for a super small distance then energy storage can be recharged and things will repeat many times a second but human brain will translate that as continues motion so you will in most cases need a slow motion video to observe what happens.
And I showed that video many times and it was dismissed. 




--- Quote from: Kleinstein on November 29, 2022, 08:42:56 am ---The power you calculate for  the air drag is coming from the wind and not form vehicle to drive. It gets obvious for a stationary obstacle - not power needed by the obstacle to keep standing. There is no sudden change from stationary objects and very slow moving objects. The air drag power is taken from wind and converted to heat.   A wind turbine could use part of that power for other purposes, like driving the vehicle.

--- End quote ---

Actually the stationary obstacle is moving is just locked to earth so it is moving together with earth. The earth is accelerated by that wind hitting the obstacle but since on the planet wind is moving in multiple direction it all basically cancels out  not to mention the earth mass vs air density.
So you will need to ignore the case where brakes are engaged.
Also thinking in terms of forces gets you much higher chances of making mistakes but in both cases you will get the same result.

A sail vehicle can also drive upwind but in order to do so it will need first to charge the only type of energy storage it has (kinetic energy storage) and so drive at an angle maybe even perpendicular to wind direction and when it has enough stored energy it can just change direction to directly upwind and yes it will slow down as stored energy is used up but it will move significant distance upwind.
This things happen much slower so anyone can observe but the propeller based moves directly upwind at all times is just that it accelerates and stops accelerating multiple times per second as the very small energy storage is charged and discharged at many Hz so human brain perceive/interpret that as smooth motion.

electrodacus:

--- Quote from: PlainName on November 29, 2022, 04:38:11 pm ---
    Pu ∝ (Vw - Vv)

Your premise is that when the vehicle is at wind speed there is no power available. That is, Pu = 0. And that's correct for this simple case. What we're interested in is a case where Vw - Vv = 0 and Pu > 0.

--- End quote ---

That is the same thing with what I say is just that is correct for any case unless it involves energy storage. You may call that stored wind power.




--- Quote from: PlainName on November 29, 2022, 04:38:11 pm ---
Moving on, there's the small problem of the propeller, which is driven by the wheels. The propeller is sucking power, via the wheels, so let's add another term:

   Pv - Vehicle power. This is the power the wheels soak up when driving the propeller.

That changes things thus:

    (Pu + Pv) ∝ (Vw - Vv)


--- End quote ---

All this and what followed is incorrect.

I will try to explain so please read:

This Pu is all that it is so when you take what you call Pv from the wheel you are actually subtracting that from Pu
If that Pu is 1000W that is what is available to accelerate the vehicle in the wind direction and so if you take 700W at the wheel you are left with only 300W to accelerate the vehicle so the vehicle acceleration is reduced.
Now you can take those 700W and send it to propeller that will be used for propulsion and so if this was 100% efficient and air was not a compressible fluid then all this 700W will end up accelerating the vehicle adding to the existing 300W so 1000W in total thus you did nothing compared to original where all 1000W where directly provided by wind.

The reality is that air is a compressible fluid so very little of those 700W you put in propeller will result as net thrust as it pushes against a compressible fluid the equivalent of a spring so most of that is stored so pressure differential is increased.
The more energy you put there the more pressure differential will increase and sometime around when vehicle speed is about 0.3x wind speed direct down wind the power provided by the stored energy matches the power available from wind directly and from that point the stored energy is the main force pushing the vehicle and when vehicle is at wind speed all power comes from this created pressure differential that is also maintained moved along with the vehicle but is more complex to visualize.

This is also what pushes the treadmill vehicle that is indoor with zero wind speed.  The treadmill provide vehicle with power as long as human keeps the vehicle constrained so all energy is used to create the pressure differential then when it is full it will be maintained and so when human releases the vehicle the force pushing the vehicle comes from this stored pressure differential and there is no longer any power coming from the treadmill. 

PlainName:

--- Quote ---This Pu is all that it is so when you take what you call Pv from the wheel you are actually subtracting that from Pu
If that Pu is 1000W that is what is available to accelerate the vehicle in the wind direction and so if you take 700W at the wheel you are left with only 300W to accelerate the vehicle so the vehicle acceleration is reduced.
--- End quote ---

You are missing it still.

Yes, Pv is subtracted from Pu (that's what the equation says after all!) and, no doubt to your vast delight, when Vw-(Vv-Vt) is 0, Pu is 0 so there is nothing to extract from, hence no power to turn the prop. That's why Vv-Vt can never reach wind speed.

So, Vv-Vt must be slower than wind speed because around the point Pu is 0, Pv is still being sucked out leading to an actual negative Pu. The whole thing will slow (although, in reality accelerate1) until Pu = Pv.


--- Quote ---If that Pu is 1000W
--- End quote ---

Stop with the putting in values until you have a proper equation to insert them into, and currently you don't. All you're doing is confusing things by having some arbitrary number you need to distribute somewhere, but you don't really know where.

---
[1] Kind of. As we see from the experiments, it needs a helping had (some models, literally) to get up to speed whereupon the model will take over on its own. This is really just saying that it would slow down if for some reason (wind gust, kick up the pants) it did go overspeed.

electrodacus:

--- Quote from: PlainName on November 29, 2022, 05:35:34 pm ---
Stop with the putting in values until you have a proper equation to insert them into, and currently you don't. All you're doing is confusing things by having some arbitrary number you need to distribute somewhere, but you don't really know where.

--- End quote ---

I use values as people do not see a limit.

There is only wind power as input. There is absolutely nothing else.
There is a single equation describing the amount of power available to any wind powered vehicle and as you started to realize it is proportional with wind speed minus vehicle speed.

This equation alone is proof that no vehicle can exceed wind speed directly downwind as equation shows wind power available is zero.
And also same equation shows that no vehicle can drive directly upwind because in order to move upwind you need more than wind power.

So there is nothing to discuss other than if this equation is the correct one or not. Once you agree with that equation the conclusion is clear.

Now if you want to know how those vehicle work because they work then that is a separate discussion and involves energy storage.

PlainName:

--- Quote ---This equation alone is proof that no vehicle can exceed wind speed directly downwind as equation shows wind power available is zero.
--- End quote ---

You are applying it by ignoring the propeller output and power sink, so the equation is useless for this vehicle. I've shown you how the missing things fit in and you can't even say why that is wrong, other than "it's all incorrect".

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