The Wind Powered Sail-less Boat

I'm pretty sure an auto-gyro always has air moving "vertically" through the disk. I believe the disk is simply canted a bit aft.

But a parachute only acts as a bluff body. The rotor blade act as the wing of a glider and provide lift through laminar flow. But now you have me thinking. What if I had two sail-planes circling a common point. They each have 50:1 L/D. Would they now descend more slowly than an annular parachute would carry them down if it covered their same flight path (with a giant hole in the center)?

Well, by definition your "glide ratio" in a vertical descent is zero - so I don't know how to comment on that aspect. But to say the vertical option is drag only isn't right at all. I can auto my R/C heli down to a vertical feather soft landing after a long steady state vertical descent (in which the blades are providing lift all the way down).

I don't think that analogy is fair at all. A frisbee dropped vertically (even spinning) cannot develop lift through laminar flow.

 

I think I was too much thinking of marine propellers which do not autorotate in the correct direction due to worse efficiency of the blades.

If you compare a stationary sailing boat sails up and having motor on reverse, it is quite similar to a helicopter staying stationary. If you now put both propellers free spinning, the sailboat propeller will slow down and eventually start to rotate to the other direction when the boat accelerated unless the pitch is reversed. It is not able to maintain such a good L/D and AoA that it would have a positive moment. A heli rotor is able to keep the moment with some optimal pitch even though the velocity through the rotor plane changes from downwards to upwards. This isn't an easy thing to understand, if you think of the propeller using pitch, which would mean that the rotating direction comes from the sign of the pitch and sign of the flow direction through the plane in free spinning mode.

Here is a nice explanation, which I read several years ago, but apparently forgot.
http://www.w-p.dds.nl/bookaut/scblelth.htm

Still there needs to be upward overall (falling velocity - induced velocity) velocity through the rotor plane and thus the lift can not be larger than the parachute unless there is horizontal flow.

Joakim

 

Rotor blade gets it's lift by accelerating air downwards. It is very effective in that, but since we need to get the moment to spin the rotor, the velocity through the rotor plane needs to be upwards. Thus the rotor can not accelerate the flow downwards more than the falling velocity (actually much less). A parachute is not limited to that and thus it can have a full benefit of dragging all the air with it (= Cd of about 2).

Joakim

 

Finite element analysis;

Comparing Upwards force of equivalent parachute

dFpara = 0.5rho*(2pi*r)*Cd*Vs^2 dr

To force upwards by auto-rotating blades


dFauto = 0.5rho*S*(2pi*r)*Cl*((L/D)*Vs)^2 dr

Vs is sink speed, S is the solidity

dFauto/dFpara = S*Cl*(L/D)^2/ Cd

where Cd is coeff of drag of parachute and Cl is coeff lift of autoroatating prop

For the auto prop to sink slower we just need S*Cl*(L/D)^2 to be greater than Cd.

All this is assuming we can ignore the effect of wake feedback.

With wake feedback it becomes nescessarry to descend at a slight angle in order to keep entering "fresh air" . This does not affect greatly the analysis provided the horizontal speed is small as Omega is much greater than Vs. (ie provided L/D of the prop blades is high)

 

I can address this one.

Any logical system with enough expressive power to talk about engineering (more precisely: to express peano arithmetic) is not complete in this sense. Is this remark a joke? It's certainly not relevant.

EDIT: Actually, to be precise, such a logical system can be complete only if it is inconsistent, which renders it not very useful.

 

I assume by this you mean the prop under water is equated with the rotor of the hovering heli, and the sail plays the role of gravity - yes?

Agreed.

I don't follow. Are you saying the water prop would cease to autorotate?

On a heli we definitely do reduce pitch to autorotate. On models we go anywhere from -3 to -12 degrees in an auto. Full scale helis can auto with slightly positive pitch, but not such a positive angle that the heli would hover with that same pitch under engine power.

Agreed.

That logic has a certain appeal, but I don't think it's true. I'd have to think about your claim and look at Tcube's analysis more closely, but I'm inclined to agree with his result showing that the autorotating rotor can be more effective than a parachute - final answer withheld until after I wake up.

 

Yes you understood what I meant by my analogy.

Marine propellers do autorotate, but they always change the direction when the flow direction changes and they do not "brake" efficieciently. Variable pitch might enable better "braking".

Joakim

 

Might I suppose that DDWFTTW will never work on a boat because there is slip in the drive prop and slip in the driven prop, and the resistance to rotation of the driven prop will cause the drive prop to slip, reducing the driving force to the driven prop, which.. you see where I am going? There is no slip in the wheels of the cart, so the slip in the prop allows it to come up to speed.

 

Nope. It's all a matter of efficiency. Given sufficiently efficient props in both the air and water there's no question at all that it could work. It's not 100% clear to me that it would be practical to build one (if there's any meaning to "practical" as it relates to such a useless toy).

 

Well, you might suppose that due to additional inefficiencies and drags it will be more difficult to succeed with DDWFTTW on water. I'm certainly not willing to say that it will never work -- in fact I'll say that a clever person may well succeed and it would be great fun if it happened.

JB

 

God, haven't these last few pages of "thug spamming" just been sooo much fun?

Interesting and unantagonistic theoretical discussions breaking out all over the place.

JB

PS: Sorry ... couldn't resist.

 

JB, yeah

yeah well we should resist and keep the discussion on the topic and try to keep the drama away. Its already almost 30 pages and the "you said, I said" discussion is useless.

 

Just a correction here. The Betz limit is not related to efficiency; rather it is the limit, in percentage terms, of the amount of energy an unducted turbine can extract from a fluid stream.

Both propellers and turbines can achieve very high efficiency. Of the order of 90% for those that are well designed operating at reasonable Re# of say > 100,000.

Rick W

 

I guess it all depends on how you look at it. I certainly understand your point, but it's often expressed as an "efficiency" limit.

This is the second sentence from Wikipedia regarding Betz' law:

http://en.wikipedia.org/wiki/Betz'_law

Because some modern wind turbines approach this potential maximum efficiency, once practical engineering obstacles are considered, Betz' Law shows a limiting factor for this form of renewable energy. Engineering constraints, energy storage and transmission losses and other factors mean that even the best modern turbines operate at efficiencies substantially below the Betz Limit.

And I'm well aware that wikipedia isn't the final word on these things, but just pointing out that it's common to express the Betz limit as an "efficiency".


Also, from http://www.reuk.co.uk/Betz-Limit.htm

The theoretical maximum power efficiency of any design of wind turbine is 0.59 (i.e. no more than 59% of the energy carried by the wind can be extracted by a wind turbine).

 

Mark
Nice work. It is helpful to have knowledgeable input.

I considered building a "model" boat based on one of my pedal boats. Main hull would be 7.2m long with 230mm beam. I would have small outriggers to stabilise it. These would likely be set forward to resist the thrust/drag moment. The whole boat would weigh around 20kg.

My plan was to use a 3m diameter prop I am in the process of making for another use as a wind turbine but I determined it would be really too small for this boat.

To get anything that will work on water needs a very large prop to get prop efficiency up around 60%. I had no difficulty getting water turbine efficiency above 80%. The turbine does NOT need to be massive. Around 600mm would work on the model boat.

If you want to do more analysis I can provide a low drag hull for given design conditions.

I would be interested in your prop design for model boat with 10N of total drag.

Rick W