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Mess with your minds: A wind powered craft going faster than a tail wind speed.

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bdunham7:

--- Quote from: electrodacus on December 27, 2021, 04:23:04 am ---OK then why that second formula that should represent the same thing provide a different value ?

--- End quote ---

Because it doesn't represent the same thing.  You are 'intuiting' (assuming wrongly) what the result should be and then assuming the formula is wrong when it doesn't match  your preconceived notion.  The result of the formula, which is correct,  is that it takes more power to go 20km/h in still air than it does to go 10km/h against a 10km/h headwind. 

electrodacus:

--- Quote from: bdunham7 on December 27, 2021, 04:28:49 am ---Because it doesn't represent the same thing.  You are 'intuiting' (assuming wrongly) what the result should be and then assuming the formula is wrong when it doesn't match  your preconceived notion.  The result of the formula, which is correct,  is that it takes more power to go 20km/h in still air than it does to go 10km/h against a 10km/h headwind.

--- End quote ---

We are only talking about power needed to counter drag not the other things like rolling resistance and friction in the internal mechanism.
And whatever you have in front of the vehicle as an area or a sail or a wind turbine it will not be able to see a difference between you traveling at 20m/s or traveling at just 10m/s with 10m/s head wind it will still see the same equivalent 20m/s air relative to vehicle.
It is irrelevant if air moves or vehicle moves.
This is true for a vehicle, for a sail or for a wind turbine.
This is not a question of general knowledge is a question of logic alone. So you did not need to learn this in school to understand the two cases are the same as far as drag is concerned.

bdunham7:

--- Quote from: electrodacus on December 27, 2021, 04:36:41 am ---This is not a question of general knowledge is a question of logic alone. So you did not need to learn this in school to understand the two cases are the same as far as drag is concerned.

--- End quote ---

I don't know what you should and shouldn't learn in school, but I do agree that the question is extremely simple.  And you have simply gotten it wrong.  The drag is the same, the power is not.  Drag is a force and is the same in each case.  Thus when I pedal the bicycle, I will have to apply a certain amount of force to the pedals to counter that drag.  If I'm going 20km/h in still air however, I have to pedal twice as fast with the same force as I do pedaling an identical bicycle at 10km/h into a 10km/h wind.  Same force, twice as fast.  Twice the power.  Extremely simple.  No calculus.  Everybody understands it except you.

electrodacus:

--- Quote from: bdunham7 on December 27, 2021, 04:51:55 am ---
--- Quote from: electrodacus on December 27, 2021, 04:36:41 am ---This is not a question of general knowledge is a question of logic alone. So you did not need to learn this in school to understand the two cases are the same as far as drag is concerned.

--- End quote ---

I don't know what you should and shouldn't learn in school, but I do agree that the question is extremely simple.  And you have simply gotten it wrong.  The drag is the same, the power is not.  Drag is a force and is the same in each case.  Thus when I pedal the bicycle, I will have to apply a certain amount of force to the pedals to counter that drag.  If I'm going 20km/h in still air however, I have to pedal twice as fast with the same force as I do pedaling an identical bicycle at 10km/h into a 10km/h wind.  Same force, twice as fast.  Twice the power.  Extremely simple.  No calculus.  Everybody understands it except you.

--- End quote ---

The power needed to overcome that drag is the same.
When you drive at 20km/h with no wind you experience an apparent headwind of 20km/h
When you drive at 10km/h with no wind you experience an apparent headwind of 10km/h but if to that you add a 10km/h headwind then you have an apparent head wind of 20km/h.
Also if you double the speed drag power increases 8x not 2x or even 4x

IanB:

--- Quote from: electrodacus on December 27, 2021, 01:10:09 am ---Thus this sort of wrong understanding is fairly common as it ended up in Wikipedia.

--- End quote ---

But every physicist in the world, every engineer in the world, every textbook in the world, agrees with that formula in Wikipedia. So are you going to tell the whole world they have been getting it wrong for the past 200 years and re-write all the physics textbooks?


--- Quote from: electrodacus on December 27, 2021, 04:36:41 am ---This is not a question of general knowledge is a question of logic alone. So you did not need to learn this in school to understand the two cases are the same as far as drag is concerned.

--- End quote ---

This is interesting. That formula that appears in Wikipedia is not derived from logic. It is derived from experiment. Many experiments. Over the years, scientists and experimenters measured the amount of power required in different situations, and they found that all of their experiments match the formula given by Wikipedia. What is more, you can repeat those experiments yourself, and if you do so, you will also obtain results matching that formula.

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