DDWFTTW - Directly Downwind Faster Than The Wind

rob
To give you an idea of what the challenge is I looked at a NACA0010 profile on a bicycle type vehicle weighing 30kg plus 75kg rider. I assumed drag equivalent to an upright bike. This is probably optimistic given the size of the prop.

This vehicle is intended to really perform. The design objective was to do 10m/s (say 22mph) in 5m/s wind (say 10kts). This wind should be reasonably easy to come across. The vehicle drag at this speed is 17N when apparent wind is 5m/s.

The check condition is zero apparent wind and vehicle moving at 5m/s. The vehicle drag is 6N.

The prop needs to 5m (16ft) in diameter and 3-bladed with 190mm chord (almost 8 inches) operating at 100rpm. (Will need to be made from CF to keep the weight down of course). Efficiency at design condition is 76%.

The design point requires a prop input power of 390W. This will be a bit over 400W required at the wheels allowing for transmission losses. So extra drag with a bit of wheel slip is say 42W to drive the prop when vehicle is at 10m/s. Total drag is now 59W. The prop will generate thrust of 60N in 5m/s wind with 400W. So it does the job.

When the vehicle is doing 5m/s the apparent wind is zero and prop is doing 50rpm if the gearing is fixed. The prop power absorbed is 96W - say 100 at the wheels. This will add about 21N extra drag at the wheels so total drag is 27N. The prop will be producing 37N so the vehicle will be accelerating - no problem here.

If you were to use an asymmetrical blade - eg NACA16-610. The diameter can be reduced to 3.5m. Prop power reduces to 310W running at 110rpm. Still 3-bladed but with slightly larger chord. It also gets through the zero apparent wind condition. This prop would probably be OK for going upwind as well and would automatically depower because it would stall early if it was loaded up when working as a turbine.

So for a duel function prop/turbine I think something like a 3.5m asymmetric prop/turbine would work OK.

 

Perspective.

The seeming impossible has been overcome, how ? - perspective. Opens the next small door to the next invention that can be usefull in a sensable way.

Would the same apply when you are floating down a current using hydrodynamics ?

 

Assuming you're floating down a current, and you have an apparent wind, then yes, you could use the same principles to go DDCFTTC. Assuming, of course, that you can achieve the necessary efficiency.
At that point, you'd be using an air turbine, and a water prop. ... and it's actually the exact same thing as a current boat going DUW, just from a different frame of reference. (Imagine there is no current, but there is wind; or there is no wind but there is current...same idea, just looking at it from a diff. perspective)

 

Thanks Rick, I'm gonna stew on that for a little while before I respond...very useful (for solving this problem at least) information.

 

The relativity is reversible however most currents would be too slow. A bit like operating the cart on a treadmill.

 

That and the differential in speed between the vessel and the liquid. Liquid is not compressable, and you won't be able to use it as the wind.

 

Under the conditions required to achieve DDWFTTW the air is not compressible either. It is operating at very low pressure differential. The pressure difference to achieve 60N of thrust from a 5m or even 3.5m diameter disc is minute.

Rick W

 

Fanie, if you're trying to go downstream faster than the stream, just go directly upwind once & think about the relativity of it:
When you're going directly upwind in a turbine (windmill) boat, you're actually already going downstream faster than the water flow, relative to the wind. So there's really no difference at all there.

 

I thought I should post this link here to give Goodman proper recognition for the treadmill demonstration. It was this video that enabled me to grasp the physics behind DDWFTTW:
http://www.ayrs.org/MOV05703.mpg

The fact that it is on the ayrs web site lends credence to its scientific merit so encouraged me to spend time to understand it.

This video was done well before any of the cart on treadmill videos appeared on YouTube.

 

Let's hope this gets through to those frenetic ********* on Sailing Anarchy.

 

To add to the reference sources I have attached a couple of scientific papers that spork posted on another thread on this topic. You will see the physics involved was well documented 40 years ago although these two papers concentrate on the upwind boat. Credit to Dr Bauer for his efforts.

 

I think there's only one ******** left on S/A that has a problem. It took years, and cost lives, but it seems everyone there has now been convinced, or at least wandered off shaking their heads.

Indeed. I wish though that I could find the paper that inspired Bauer to build his cart

 

In the second pdf on your post:
And in page 112 on Bauers paper in formulas (A-2) & (A-3)
Assumed air- & water- speeds related to blades in air & water respectively, is calculated ignoring any induced velocities at the actuator disk in any direction.
This assumption doesn't seem to hold water with any realistic swepted areas for the rotating part in air. This causes a major overestimation of the gained speeds for the vessel compared to the traditional boat.
Trying to use lower L/D to compensate this is not easy task at all and don't think it as a good idea anyway.
If one interprates the results on page 115 with water- & air- speeds related to swept areas rather than as those related to real wind & boatspeed related to water, the graphs don't necessarily extend to ddwfttw at all in my opinion.

That of course does't mean acheaving ddwfttw would be impossible on the water, quite the contrary, just not so easily as those papers estimate.

 

The swept areas I get are larger than Bauer calculates but then he makes simplifying assumptions that he notes. Remember when this study was done the availability of computers was limited and engineers of his vintage were usually not trained in their use at that time. I did not get my first programmable calculator until I started work and I am a generation after Bauer.

I believe his analysis at least highlights the similarities between props/turbines and sails

 

I have downloaded that pdf years ago, and certainly haven't find any indication on Bauers assumed swept areas. How can you compare yours to something that isn't defined at all ? If you think it is, please state the page number and quote a few lines in the neighborhood so I can find it.
I think this is the biggest simplification by far and is not notified at all as far as I can see. I sure hope I'm wrong in this one, but can't see how.

Sure, no computers back then, but momentum theory is much older than Bauers' papers on this subject. So involving swept areas & at least axial induced velocities from momentum theory should have been there as vital part of the analyses. It can easily be done by hand calc at least for one case, if not for all speeds & gear ratios & ...

I believe his analysis at least highlights the similarities between props/turbines and sails. Agreed. But leaves out most of the differencies.
Like in a normal sailboat whole appendage has same aoa, while in a turbine what do you do if it converts too much shaftpower from linear forces & flow ?
If you reduce pitch, the blade-element near hub goes quickly aoa=0 in soon after becomes an inefficient prop if pitch is changed anymore. Having blade_elements at tip on different aoa than those near hub reduces efficiency.
If you dimension turbine for max speed case so this doesn't happen, the turbine tips will stall easily at lower boat speeds by overloading. This kills efficiency very suddenly. Stalling blades near hub like props do has much less effect on efficiency. If avoided by suitable gear ratio, power level is way below the optimum as required for max excess thrust according the ddw2.pdf Drela posted and my test runs with it.
I guess one could use more than one turbine and put them on drive legs like outboards and lift one of them completely off water once max speed with 2 of them has been accheaved. This would cut too much power off, so over all power level could increase at more suitable rate with boatspeed instead as a third power of Vb.