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

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fourfathom:

--- Quote from: CatalinaWOW on December 15, 2021, 06:00:28 pm ---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.

--- End quote ---

It wasn't until recently that sailboats have been able to reduce drag sufficiently to be able to beat a balloon DDW.  Iceboats can easily do this, but traditional "displacement" sailboats (such as mine) just can't overcome the drag to be able to do it.  When I fly a spinnaker in heavy wind my best angle is DDW, not jibing, because I am limited by my "hull speed".  In lighter wind I will jibe back and forth, using the spinnaker, and make better progress than I would by sailing DDW.  The more modern "ultralight" boats have reduced drag to where they can beat the balloon by jibing.  Foiling boats (such as the Americas Cup catamarans that I posted the polars for) have even less drag and can very comfortably beat that balloon, and not by a small margin.  These boats don't even carry spinnakers as, even downwind jibing, the AWA is so far forward that the spinnaker would not be an efficient sail shape.

(AWA = Apparent Wind Angle, DDW = Dead Down Wind)

electrodacus:

--- Quote from: CatalinaWOW on December 15, 2021, 06:00:28 pm ---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.

--- End quote ---

Not quite sure you understood the conditions of the problem.
There is no 10m/s vehicle speed condition that is the wind speed relative to ground the vehicle speed relative to ground is zero.
So question was how much such a vehicle can generate when driving directly downwind (relative to ground) at 0.001m/s and the other question how much power the vehicle requires to be able to drive upwind at 0.001m/s relative to ground.

So vehicle in the problem was not at same speed as wind speed.  With this information corrected what do you think ?

electrodacus:

--- Quote from: fourfathom on December 15, 2021, 06:31:59 pm ---
--- Quote from: CatalinaWOW on December 15, 2021, 06:00:28 pm ---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.

--- End quote ---

It wasn't until recently that sailboats have been able to reduce drag sufficiently to be able to beat a balloon DDW.  Iceboats can easily do this, but traditional "displacement" sailboats (such as mine) just can't overcome the drag to be able to do it.  When I fly a spinnaker in heavy wind my best angle is DDW, not jibing, because I am limited by my "hull speed".  In lighter wind I will jibe back and forth, using the spinnaker, and make better progress than I would by sailing DDW.  The more modern "ultralight" boats have reduced drag to where they can beat the balloon by jibing.  Foiling boats (such as the Americas Cup catamarans that I posted the polars for) have even less drag and can very comfortably beat that balloon, and not by a small margin.  These boats don't even carry spinnakers as, even downwind jibing, the AWA is so far forward that the spinnaker would not be an efficient sail shape.

(AWA = Apparent Wind Angle, DDW = Dead Down Wind)

--- End quote ---

In this particular conditions kinetic energy is used as energy storage device.
Thinks about ideal case where say you accelerate at 2x wind speed at an angle thus you can now change direction directly downwind and since there is no friction losses you can maintain 2x direct downwind forever.
A vehicle always driving directly downwind can not take advantage of the kinetic energy storage. So a vehicle always driving directly downwind requires some other form of energy storage and in the case of Blackbird that is the pressure differential created by the propeller.

There are many ways to prove that energy storage is used including driving until you get to peak speed and see how speed will decrease all the way down below wind speed. But the easiest way to prove if with the correct equations that show clearly there is no wind power available to any type of wind powered vehicle when that vehicle is at wind speed direct down wind or above (for above there is but that is negative meaning deceleration not acceleration).

Derek's proof was done using (vehicle speed - wind speed) and that is just demonstrably wrong as correct equation will have (wind speed - vehicle speed).
Same equation will need to apply to all conditions meaning when vehicle below wind speed and when vehicle above wind speed as you can not just change the equation when vehicle is at a different speed.

Kleinstein:

--- Quote from: electrodacus on December 15, 2021, 07:19:31 pm ---
Derek's proof was done using (vehicle speed - wind speed) and that is just demonstrably wrong as correct equation will have (wind speed - vehicle speed).
Same equation will need to apply to all conditions meaning when vehicle below wind speed and when vehicle above wind speed as you can not just change the equation when vehicle is at a different speed.

--- End quote ---
Recongnizing that the equation should conver different cases without changing the equation is a good point: this also applies to looking at the vehicle moving a snails speed aroung zero. The correct equation incudes this case.

The slow speed case does not directly apply to the vehicle going faster that the wind. However it clearly shows the the equation proposed by electrodacus is flawed and leads to obvious problems there. Looking at this point may also help him correcting his understanding of force and power.  Doing the calculations only with power can be tricky if there are processes with less than 100% efficiency (e.g. like the sail).

Having an equation with (w-v) or (v-w) is not such a big difference, it is just the sign and this may be different depending on how one defines the direction of force or an axis.  One has to look not just at the one line with the formula, but also the explaination fo the symbols.

I don't think Derek's proof has a major mistake in the equations, as it leads to the right conclusion - just getting a result that is not obvious to everybody is no proof that there is an error. Usually math is way more reliable than intuition.

fourfathom:

--- Quote from: CatalinaWOW on December 15, 2021, 06:00:28 pm ---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.
--- End quote ---

Just to emphasize this, racing yachts do *not* generally run nearly dead downwind.  Unless limited by hull-speed (iceboats, ultralight boats, and foiling boats are not hull-speed limited), a sailboat trying to get directly downwind will jibe back and forth for a better "speed to mark" or "speed made good" (which is the boat speed times the cosine of the angle of the course sailed relative to the course directly to the mark).

This doesn't apply to the land-vehicle, but if you're interested the only time a racing boat will sail directly downwind is when it is limited by hull-speed, which is approximately [1.34 * sqrt(boat waterline length in feet)] (speed result in knots)  This isn't a brick-wall limit, but above hull-speed it requires dramatically more power to move the boat.  I don't know the curve, but it's extremely steep.  When sailing at hull-speed there is no longer an advantage to sailing a longer course (jibing back and forth), since you can't go any faster.

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