DDWFTTW - Directly Downwind Faster Than The Wind

If the tailwind cannot transfer energy to the cart then how can it have higher kinetic energy (speed) in a tailwind?

The energy being imparted by the propeller on the air is the same, given we are using the same motor and so on.

Edit: would you say that the propeller generates a fixed thrust at a given velocity of the cart relative to the air that the propeller finds itself in?

 

I just can't give up.
Yes fully agree with the above. This is the frame of reference for the air to cart interface that is relevant. And I am sure we agree that same power can create much higher thrust in slow speed than it could in high speed? right?

Now do the same for the wheels and the ground. Which is the other pair.

 

Kinetic energy and speed are two different quantities. Kinetic energy is a function of velocity and mass.
That is correct the velocity of the air flowing by the blades will generate a fixed thrust. However, since there is a horizontal component to the wind, the angle of incidence will change, with an accompanying change in thrust.

 

Agreed, but if the mass of the cart stays the same then higher velocity must mean higher kinetic energy.

So I reiterate, there must be some mechanism for the tailwind to transfer energy to the fan driven cart, otherwise the cart would not be able to have higher velocity (and so kinetic energy) in a tailwind compared to if it was travelling in still air.

 

Thrust is a function of power input and other variables. More thrust at low speed would indicate a propeller with a low pitch.

The wheels are not a function of air flow on a revolving foil. They use the kinetic energy accumulated in the cart. When the turbine becomes a propeller, it is not inputting power from the environment to the system, but outputting power from the system to the environment. The kinetic energy will eventually be used to turn the propeller and the cart will stop. The turbine/propeller is either inputting power into the system, which will accelerate to some speed below that of the wind, or outputting energy, in which case it will use the accumulated kinetic energy until the cart stops. If the turbine/propeller is inputting and outputting energy simultaneously, there will be a net loss until the cart stops or finds a balance at much below the air speed.

 

That is not correct. The relative velocity is all that matters. The speed over ground is irrelevant.

 

No it doesn't. You keep saying this. It is braking force and mixing energy to the forces is just confusing - most logical is to talk about power (force * speed).

The cart has one force from propeller pushing the cart forward and one pushing the cart back from the wheels. Do you agree with this. (Naturally also drag and other forces like gravity but relevant to the powertrain)
Lets assume we drop the cart at above wind speed to the ground. (disregard acceleration for a bit) Would you agree that the wheels would exert a braking force (ie a force towards the back of the cart) and propeller a pushing force (ie a thrust pushing towards the front of the cart)?

 

btw here is a very clear video of the cart in action.
DDWFTTW - Directly Downwind Faster Than The Wind https://www.boatdesign.net/threads/ddwfttw-directly-downwind-faster-than-the-wind.25527/page-29#post-909117

 

So we agree that for zero rolling resistance at the wheels, an electrically fan driven cart will go at the same relative velocity to the air regardless of whether it is in still air or a tailwind? After all the thrust is the same, and the air resistance from the cart body is the same, and the conditions experienced by the fan (relative velocity of air) are the same.

 

The video shows the taletales briefly hanging limp. There is no steady state where it goes faster than the wind.

 

I agree. As you say, there are losses which result in a maximum steady velocity lesser than that of the wind. It is possible to accumulate energy and have short burst of speed higher than that of the wind though

 

Yes, we agree on that.

 

Well naturally. That is the point where the cart's speed matches the windspeed. Apparent wind goes to zero so naturally the telltales just hang. Then as it accelerates - downwind direction they start to shift backwards.
The telltales act exactly as is predictable.

 

I don't say such thing but it is good that we agree that there are the two forces: one thurst from propeller and two braking force from wheels.

Now let's assume like in my example earlier that the cart is going 6m/s downwind direction in a 5m/s true wind. Let's not worry about how we got here.

Would you agree that the propeller operates in 1m/s airflow (6m/s s peed minus the wind speed of 5m/s)?
And that the wheels touch ground that is passing by at 6 m/s?

agreed?

 

The sign is incorrect. If the cart is the frame of reference the airflow is -1m/s and the ground is moving at -6m/s. Both velocities are to the left in the graph.