@BillRM,
This is my first post here. I am impressed with DrewDad who got it exactly right in only the sixth post after the start of the thread. Personally I was a skeptic and managed to put out one embarrassing post before I got it (with many more embarrassing posts since).
JB is right that the psychology of the responses to the brainteaser about as interesting as the device.
I see on this thread that BillRM is apparently the Humber (i.e. JB's tar baby;-):
Quote:The wind along the ground is not the issue the wind in relationship to the car is the issue.
and
Quote:Once the car reach the speed and is traveling in the same direction of the wind then as far as it is concern the wind is zero. You can not get energy from a wind who speed is zero as far as the car is concern.
and
Quote:the force is zero when the relative wind velocity is zero so no need to work a F*D equation as that would also be zero.
[emphases added]
Dear BillRM:
The correction to one of the fundamental flaws (emphasized above) in your thinking is that the issue is
not the windspeed wrt the
fixed parts of the
cart; everyone can see that at windspeed the force of the wind on the
fixed cart parts is zero, and at DDWFTTW the wind on the
fixed cart parts produces only drag. The only significance there is that the drag can be minimized by design. By focusing on the
fixed parts of the cart you are treating the cart as if it were a
fixed-sail craft moving directly downwind - it most certainly and
obviously is
not - and as a result your reasoning is faulty.
The relevant issue
is the wind
velocity wrt the
moving blades of the prop. Specifically, consider the point of intersection of a single streamline of the wind with a blade as the blade passes across that streamline. As for any prop-driven craft going directly downwind the relevant issue is that a wind streamline hits the
back of the blades; this is obviously and only possible with adequate prop speed and pitch (again, design parameters). If the wind streamline does hit the back of the blades, then the wind is slowed (pushed back) by the blades, and by Newton 3 ("equal and opposite") provides a force forward on the back of the blade which is transmitted to the cart through the hub. Consider a 10-knot wind from the north and a prop-driven ultralight going south with 20kt airspeed and with 30kt speed over the ground. Unless the
prop pushes
back on the wind the craft cannot stay aloft; the force of the wind on the fuselage and wings only affects fuel consumption, not the ability of the craft to move forward and fly.
That settles the available force issue; the available energy issue (yes, I know the ultralight has an internal power source) is dealt with below.
If you don't get that, or if you think there is a flaw in it, then just retire from the field because you don't have the chops to be here. Oh yeah, and don't ever try to exceed the ground-relative windspeed downwind in an ultralight or take a flight from the West to the East Coast in the jetstream.
Seriously, until you get what I say above about forces don't bother reading any further.
If you do get it, then you should suspect that, since forward force can be provided by the wind on the
prop, it is then possible to extract energy from that wind. As many have pointed out before me, the energy is available in the non-zero relative velocity between two media: the wind and the ground. Lo and behold, the prop is part of a drive train of chains, gears and axles between those same two media!
The final hindrance to understanding is only whether there is a gearing and prop pitch combination that makes this work. There are many demonstrations that this is possible, the oft repeated treadmill videos being the best and far more convincing than the trials at Lake Ivanpaugh and El Mirage, but perhaps the simplest is the "under the ruler faster than the ruler" video on YouTube. It is equivalent to pulling a yo-yo on a flat surface with a string coming from the bottom of the axle: without slip the yo-yo moves faster than the string is pulled. Simply put the cart is a Class 3 lever (the arrows indicate velocities):
Code:
+------> 30kt, LOAD, cart axle
|
|
|
|
+--> 10kt, FORCE, effective (zero-slip) wind point by design
|
+ 0kt, FULCRUM, circumference of cart wheel on ground
where the gearing and the prop pitch place the
effective (i.e. zero-slip) force of the wind between the ground and the cart axle; this point makes the wind analogous to the string in the yo-yo example. If you put the right kite on the string of the yo-yo, then the center of mass of the yo-yo+kite might go DDWFTTW until the system runs out of string.
The equations for the steady-state force and energy (Power = Force dot Velocity) balances are left as an exercise to the reader. Simply put, the only forward force is provided by the prop, and the only energy input is provided by the ground force on the wheels. So
1) to make up for drag and friction forces, the forward prop force (thrust) must be greater than the backward ground force at the wheels, and
2) to make up for drag and friction power losses, the power input at the higher groundspeed at the wheels must be greater than the prop power output at the lower prop-apparent-windspeed.
So both force and energy are available for the cart go DDWFTTW; no conservation or thermodynamic laws are in jeopardy by this cart working as advertised. The upper limit on speed, as with all wind-driven craft, is set by efficiency, specifically one minus normalized drag and friction between the craft and the media.
