The Wind Powered Sail-less Boat

A prop or rotor-head in autorotation is quite different from the case of the prop-cart. In autorotation the prop acts as a turbine (i.e. it's being powered by the wind), and is subject to the Betz efficiency limitation (about 60% max). On the cart, the prop is actually acting as a prop. Rather than driving the wheels, the wheels are driving the prop (yes it can be counterintuitive). As such it is not subject to this lower efficiency limit. More importantly perhaps is that in autorotation the theoretical limit would take us to the speed of the wind - not greater.


EDIT: seems you have to be quick on the draw here. I see two others already addressed the autorotation issue.

 

Okey dokey. The energy analysis for this vehicle at steady state faster than the wind is quite straightforward. We'll start with the theoretical case in which the thrust produced by the prop must exactly equal the tangential braking force of the road on the wheels.

Working from the reference frame of the steady-state cart, the road is putting energy into the system as given here:

Er = Vc * F (basically: power = force x velocity)

In which:
Er is the energy delivered by the road to the cart
Vc is the velocity of the cart relative to the road
F is the braking force of the road against the wheels

The energy needed to produce the necessary thrust is given by:

Et = (Vc - Vw) * F (again: power = force x velocity)

In this case:
Et is the energy needed to produce the necessary thrust
Vc is again the velocity of the cart relative to the road
Vw is the velocity of the wind relative to the road
F is again the thrust or braking force (they're equal in our theoretical case).

So we can see some interesting things.

- With a tail wind we have extra energy given by:

Ee = F * Vw

Where Ee is the excess energy above that which is needed to maintain steady state.

For the cart to exactly match the wind speed would require zero-energy and zero force/thrust for our theoretical case.

Interestingly, we will have any number of losses in the real world. The propeller efficiency is likely to be in the 80% range. The transmission efficiency might be 90-95% efficient. There will be rolling resistance, and aerodynamic drag on the frame. The rolling resistance can be made arbitrarily small, and the aero drag will be arbitrarily small for a speed just barely in excess of the wind speed.

However, what we have to do is show that F x Vw (our excess energy) is sufficient to overcome the real-world losses. Clearly Vw (the wind speed) can be made arbitrarily large, and F can be made small through the use of efficient propeller and transmission. Our calculations suggest we can achieve 2X wind speed with easily available parts and design considerations in a 15 mph wind (full-scale cart) and 2.3 times the wind speed with that same cart in 30 mph wind (which I won't be trying).

Sorry, can't do that. I've already drafted an article for publication, and that would keep me from submitting it. I'll be happy to answer any questions and provide any analysis I can however.

 

OK. See attached analysis. The last equation should be useful for quickly playing around with the few important parameters to see if a DDWFTTW boat is hydrodynamically feasible. I just worked this out, so there may be typos or algebra hacks.

In any case, the key question is whether the turbine/prop thrust moment can be overcome by a vehicle whose drag does not exceed the net available thrust (estimated by the last equation). It's obvious this can be done on land with wheels, but it's not so clear it can be done on water with hulls. My first guess is that you want a three-hull vessel. A catamaran well ahead of the CG to provide most of the buoyancy and the nose-up moment, and to give roll stability. Then add a small central ama-type hull in the back just big enough to keep the tail afloat when sitting still.

 

Mark:
>It's obvious this can be done on land with wheels, but it's
>not so clear it can be done on water with hulls.

I would love to see it done on water, but I too have my doubts. I certainly know I don't have the boat design expertise to pull it off.

Thanks for the .pdf.

JB

 

Well, nuts. I thought I had it there for a minute. In his article, Goodman claims that the key to understanding DDWFTTW is that "the wheels are turning the propeller and the propeller need only produce enough lift in still air to overcome the forces required to turn it." I can understand the wheels turning the propeller if we are talking about a car on a treadmill, but I fail to see how the wheels can turn the propeller of a car that is sitting still in the middle of the road. Goodman himself said that it took 4mph of wind to start the prop (and wheels) turning. He goes on to say that at greater wind speeds the prop is producing more lift than the wheels are drag. He gives figures of 552 grams of prop lift vs. 402 grams of wheel drag at 10 mph wind speed. This sounds very much like it is the prop rotation that continues to drive the wheels. This sounds reasonable to me because it allows me to believe that the car would come to a halt if the wind died, thus preserving my faith in Newton. As far as a boat powered the same way, one would have to find a water propeller that approached the efficiency of wheels on tarmac.

 

Many thanks Mark for your attachment. One valuable input from you can actually make it worth wading through pages and pages of tedious shouting matches. You even took into consideration the inappropriateness of the classically defined eta which goes to zero at zero airspeed.



The whole thing of "which drives which" can be a bit misleading.

Think; The axial thrust of the air prop is what drives the water turbine through the water which in turn provides the power to sustain the air prop 's rotation against its resistance to rotation.



Another thing, the betz limit is how much is the maximum energy that can be extracted from a cylindrical stream tube by a turbine, not how much energy you get back from moving a turbine through a fluid. There is a fundamental difference.

 

To produce propeller thrust at any speed, the prop requires shaft power. Therefore, one cannot explain or analyze DDWFTTW without looking at the power flow from the wheels to the prop, or from the water turbine to the prop. Perhaps the simplest way to say it is:
Using its provided shaft power, the prop needs to generate enough thrust to overcome the sum of two aft forces:
1) the wheel traction force (or turbine drag force) which provides the prop's power, plus
2) the vehicle drag.

 

Don't feel bad -- it's one screwy little problem. There are several on this thread that understand it well and perhaps with a bit of back and forth you'll come up with something that works for you.

First, by "still air", I quite certain he means when the cart is going the same speed as the wind rather than a "no wind" day -- "still air" relative to the chassis of the cart.

Second, in that statement I believe he is using "lift" to actually mean "thrust". To word it in another way, in a steady state situation the same speed as the wind, the prop only needs to generate enough thrust to overcome the needs of the device that turns it -- which include rolling frictions, transmission losses, and parasitic/induced prop drag. There will be no aero drag on the cart itself to overcome.

In the initial 'start mode' of the cart, it is the simple drag of the air over the entire device that starts moving it downwind -- not thrust from the prop. Once this drag starts turning the wheels against the rolling surface, *then* the prop begins to generate the thrust which propels it to above the speed of the wind.

I can't find that in his .pdf. but it doesn't seem that far off from what we've experienced. If the cart is sitting in the street, there must be enough of a tail wind blowing across the body of the craft to create the force to get it started.

But remember, he says "The key to understanding DWFTTW, is that the wheels are turning the propeller ...". He really is right -- that is absolutely key.

Just as a relevent aside Timothy, take a good look at the prop in both our videos and the Goodman video. Notice that it's twisted the wrong way to be reacting to the tailwind as a turbine. Notice which way it spins when his wife give it a slight push downwind -- if the wind were spinning it directly, it would have to spin the other direction.

When looking at his "lift" and "drag" figures, remember that there are two ways for the "lift" to overcome the drag of the wheels -- by spinning the drive mechanism directly (which doesn't happen as demonstrated by the paragraph above this) or by generating thrust which over comes the wheel drag and moves the chassis forward. It is this second method that is used by the cart.

Newton is safe. If the spinny, pinwheel thingy on the rear of the cart is used as a turbine OR a prop, either way it will stop spinning when the wind dies. The difference in the two lies in the fact that if used as a turbine, the cart will never be able to equal the windspeed, let alone exceed it.

Now the "scholar" thing I get -- the rest of that just leaves me speechless.

JB

 

It's also important to note that you definitely do not want to operate the water turbine at the Betz limit. The goal for the water turbine is max efficiency for a given power requirement, not max power for a given diameter. This means a larger diameter and a smaller solidity than what the Betz limit dictates.

 

Fixed typo in equation (10) of the PDF. New PDF uploaded in message 378.

 

On another forum this discussion took us down the road of human powered flight. One of the members (jjcote) chimed in with some useful knowledge on the topic, and I mentioned that JJ has some first hand experience with one of the legends in the field. Mark is that guy. I had no idea Mark participated in these forums. But I'm guessing you guys already know what a great resource you have on your hands.

Mark, there are certainly sailboats that can achieve and maintain downwind VMG greater than wind speed, so that suggests we can have a DDWFTTW watercraft at least in the trivial case. This could consist of two such sailboats side by side on alternate downwind tacks - attached by a telescoping rod. Clearly this isn't a very practical solution, but it seems it would meet the letter of the law. From there I'm inclined to believe it could be done in practice with a slightly more "conventional" design (if we could call any such vehicle conventional). But as with the prop-cart I don't think it would be of any use beyond proving it could be done.

 

(Mark Drela post # 384) Which brings me to what are the most important factors to increase T/Fx .

Fx is thrust or axial force and T is torque .

It seems to me that the most important consideration is pitch , given that section , radius etc will be optimized for the given case.

This has been studied extensively for propellers and it seems that the envelope has a peak at around 45 - 50 deg although the peak is broad ( not very critical)

In the case of turbines , the overwhelming assumption is that it is rigidly attached to the ground so axial thrust is largely irrelevant ( the thrust bearings might feel differently about this) so there is little information as to how to optimize efficiency in regards to maximizing Torque*Omega whilst minimizing Fx*V

Presumably, it would mirror the best angles found in propellers?

 

Interestingly, the prop on a DDWFTTW cart acts as a propeller and not a turbine both below and above wind speed, but the vehicle itself can be thought of as a non-stationary turbine with some very interesting results. The stationary turbine (i.e. windmill) has a clear maximum energy output based on wind speed and Betz limit. A moving turbine (basically the DDWFTTW prop cart) has a theoretically limitless power output because it moves through the air (rather than simply waiting for the air to move through its blades) and can thus harvest more energy from that air.

Of course this has all sorts of practical limits, and I have serious doubts as to whether such a contraption would ever make sense.

 

Pretty much. You want to increase the turbine diameter to increase its efficiency, until one of several things start to dictate otherwise:
1) The drag of the support strut starts to overcome the turbine efficiency improvement.
2) The blades get too narrow for a) structural requirements, or b) adequate chord Reynolds number

Effect 2) can be counteracted somewhat by reducing the RPM to increase the advance ratio lambda ( = V / Omega R / V ), or coarser pitch, which drives up the solidity requirement. A slower turbine then has the bonus of a smaller required gear-down and hence reduced gearing losses. Whatever the best combination is, the resulting turbine will definitely have a larger lambda than a typical wind turbine. Wind turbines have lambda = 0.12 -- 0.16, while the water turbine will probably want something closer to lambda = 0.25 -- 0.40 or even more. Larger lambda also makes the blade profile drag less critical, which is good for a small machine with small Reynolds numbers.

Conversely, the air prop will want to be designed for efficient operation near the "hover" condition, or lambda = 0.

 

Interesting that you should largely confirm what i was thinking.

In fact the high angles for propellers have always surprised me.

My gut feeling for maximizing power - minimizing axial thrust on a turbine is to take a highly cambered thin section (with high L/D & @ high Cl ) and take the very high lambda to its engineering limit whilst aiming for aspect ratio no lower than 8 or 10.

This would result in a very high torque , low RPM turbine , but with a very favourable T/Fx ratio , i think.


The other thing here is that high RPM actually helps keep the blades straight against the loads (up to reasonable limits) which would work against this .

The strut may be optional for this kind of turbine ( Rick? ) .