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Mess with your minds: A wind powered craft going faster than a tail wind speed.
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electrodacus:
I will try to add more to the example maybe that will help.

Vehicle wants to drive against wind direction so upwind at 0.001m/s

Power needed is 60N * (10+0.001) = 600.06W

Vehicle wants to drive down wind it can waste the excess as heat in brake pads or generate

60N * (10-0.001) = 599.94W

This Is just simplified as I kept the force the same 60N but force will be slightly different just did not wanted to use the more complex looking formula as this is a good enough approximation. 
Kleinstein:
One needs to include the speed of the wind in the power, when you calculate the power the wind is loosing, but not in the energy the vehicle with the sail is gaining.  A sail is not 100% efficient and quite some of the power taken from the wind is just converted to heat, warming up the wind.
fourfathom:
I don't see much point arguing about efficiencies, when the electrodacus model only applies to drag-propulsion (a sail DDW), and his equation insists that available force is a function of AWS (Apparent Wind Speed), or  (wind speed - vehicle speed)^3.  This is not the case with the spinning propeller.  The model with a generator being driven by AWS does not represent the wheel/propeller vehicle.  Of course electrodacus can "prove" that the vehicle can't indefinitely exceed windspeed DDW, but his proof doesn't apply to the actual vehicles in question.
tom66:

--- Quote from: bdunham7 on December 14, 2021, 10:44:28 pm ---
--- Quote from: electrodacus on December 14, 2021, 10:29:35 pm ---No motion of the vehicle means zero power can be generated at the wheel.

--- End quote ---

Let's stick with that for a moment.

So you say that for any non-zero speed, the power is (whatever your formula is) or about 60N * (wind speed - vehicle speed), but right at zero the power goes to zero?

So if I'm sitting there and the vehicle is stopped with brakes, there's no energy being dissipated by the brake, but if I allow the vehicle to creep forward at 1mm/s, now the brakes are dissipating almost 600W?

--- End quote ---

Same idea as a short circuited solar panel dissipating almost no power as the voltage across the panel is effectively zero.  Or open circuit where current is effectively zero.
CatalinaWOW:
Electrodacus is in love with his model.  A common problem with simulation people.  Simulations are wonderful things.  They can provide insight that is hard to obtain with actual physical tests, allow measurements that are literally impossible with physical tests and often save tremendous amounts of time and money.

But simulations have two fundamental flaws, that are often difficult to recognize.  First, they are all approximations and do not provide comprehensive information on when the omissions are important.  Second, usually a small problem but huge here, is that simulations no matter how large and wonderful do not inherently match the problem being simulated.  The math is all correct but doesn't represent the physics of the situation. 

In Electrodacus case there is a pretty obvious problem which he is overlooking.  He is not intrinsically wrong with his (10m/s -0.001m/s) formulation.  That is one way of presenting the problem.  But he is overlooking the fact that 0.001 m/s second of incremental velocity requires only a trivial amount of power.  Regardless of source.  In his own thought process there is zero drag in the condition of interest since the vehicle is moving at wind speed.  So the only consumer of power is the increase of momentum due to making the vehicle move faster.  The flawed thinking is ignoring the power required to maintain the initial 10 m/s velocity.

Having said all of that, it has been regularly asserted that a sailboat can tack downwind faster than a balloon blown down wind.  If this is indeed true the advantage must be small and dependent on perfect execution and perhaps on boat configurations which perform poorly in other conditions.  I say this because racing yachts consistently set spinnakers and run nearly directly downwind rather than tacking to get there faster.  These people spend millions of dollars to win, they wouldn't ignore any consistent advantage.
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