DDWFTTW - Directly Downwind Faster Than The Wind

[Rick Willoughby]

The figures at the back of the papers provide the areas. He compares them with sail area actually used on the boat he based the calculations on. Figure 7 gives the DDWFTTW case. You should look more closely - like all engineering papers of the time the drawings/figures were provided at the back of the report. Took me a second read to realise he actually did calculations for the DDWFTTW. I can do better than reference it I have attached the figure. If you actually read the entire paper you will find it.

My initial impression of the DDWFTTW principle was that it would need a continuously variable transmission to get the best result. This may be true but for any given windspeed I find the cart, at least, has no problem accelerating up to the set design condition. I have not looked at all possibilities but seems to work fine with fixed pitch and fixed gearing. One thing that can be overlooked is that the prop speed is linked to vehicle speed. The angle of attack is higher at low speed than at the design condition but if the prop is big enough to achieve DDWFTTW then it will have ample thrust to accelerate up to this speed. There is no dead-spot in the range.

Likewise with the boat the turbine and prop are linked so their operating regimes at any speed are similar - the prop is never in a really good regime for a boat of pleasure craft proportions and even worse for a model to demonstrate it. A manned boat needs a very large prop even for a slender hull like a rowing scull. Admittedly my design speed is a higher ratio of windspeed than Bauer has used but he is discussing a 2.5t boat of only moderate length.

Rick W

[sailor2]

Originally Posted by Rick Willoughby

The figures at the back of the papers provide the areas. He compares them with sail area actually used on the boat he based the calculations on. Figure 7 gives the DDWFTTW case.
Rick W

Sorry you are very wrong. The areas in that figure are blade areas not swept areas. He uses that definition in just about every page.
Please read it again and see for youself, he is very clear on this issue, no place for misunderstandings.
A headline taken from page 110

3.5 Windmill Performance at heading of 180 degrees.

Third sentence below heading reads:

Such angles could be used at gamma=180degs, but this would result in much larger blade areas than given in figure 7.

Also see page 112 equation (A-15)
That's a standard equ. relating Cl & lift_force using Blade area, flow speed, density just like for a solid wing used on aeroplane. Nothing to do with swept areas.

[Rick Willoughby]

Originally Posted by sailor2

Sorry you are very wrong. The areas in that figure are blade areas not swept areas. He uses that definition in just about every page.
Please read it again and see for youself, he is very clear on this issue, no place for misunderstandings.
A headline taken from page 110 Third sentence below heading reads:
Also see page 112 equation (A-15)
That's a standard equ. relating Cl & lift_force using Blade area, flow speed, density just like for a solid wing used on aeroplane. Nothing to do with swept areas.

I see. This means his figures are now at least closer to what I would expect. Glad you cleared that up. I still think the areas are small for such a heavy boat exceeding the hull speed.

I have a swept area of 201sq.m and a blade area of 3.2sq.m for a single person craft 7.2m long displacing 100kg. These are high aspect blades with average L/D well over 20 in most conditions.

You could work out the swept area for a given foil section by taking the lift to drag ratio that he provides. There will be differences based on number of blades of course but at least you could determine if he is in the ball park. I personally think it would be exceedingly difficult to get his Gimcrack above windspeed of 11kts in DDWFTTW mode but I have not done any calculation on this.

Rick W

[Rick Willoughby]

If you take the DDWFTTW case shown in figure 7 Bauer determines a blade area of 100sq.ft with the L/D of 12 to do 12kts.

A 10% cambered foil to achieve this at low Re# needs to have a blade aspect up around 4. So prop radius is determined to be 20ft. Swept area is hence a little over 1200sq.ft.

I have grave doubts that a prop of these proportions would drive that heavy boat with a far field velocity of 1kt.

Rick W

[sailor2]

Originally Posted by Rick Willoughby

If you take the DDWFTTW case shown in figure 7 Bauer determines a blade area of 100sq.ft with the L/D of 12 to do 12kts.

A 10% cambered foil to achieve this at low Re# needs to have a blade aspect up around 4. So prop radius is determined to be 20ft. Swept area is hence a little over 1200sq.ft.

I have grave doubts that a prop of these proportions would drive that heavy boat with a far field velocity of 1kt.

Rick W

I'm afread I have to disagree with you again.
A 2D l/d from xfoil or similar is one thing and 3D L/D is another with a different meaning. When calculating 3D from2D case you need distribution of lift in addition of span loading. To get your values with blade aspect of 4 your assumed lift distributions are not realistic at all. Do you realise that lift is dependent on flow speed squared and at halfway between tip & root there is just 1/2 of the tangential speed and approximately 1/4 of dynamic pressure if axial flow is neglible compared to tangential. To get same lift there you need 4 times greater chord*Cl halve way in from tip than near tip. That is possible with this very simplified theory, but further closer to axis this approach falls apart. If you would use a more sophisticated theory involving both tangential & axial induced flow in addition of the axial induced flow things get worse, not better. I would be very surprased to have any better than even L/D=6 with aspect of 4 for individual blade if L & D are defined in relation to assumed flow direction (without induced velocities) at r/R = 0.7 as Bauer did in his analyses. If you define L & D related to local flow things are obviously a lot different, but you still overestimated the L/D. Keep in mind L is oriented more towards creating torque near hub than near tip.

[Rick Willoughby]

Originally Posted by sailor2

I'm afread I have to disagree with you again.
A 2D l/d from xfoil or similar is one thing and 3D L/D is another with a different meaning. When calculating 3D from2D case you need distribution of lift in addition of span loading. To get your values with blade aspect of 4 your assumed lift distributions are not realistic at all. Do you realise that lift is dependent on flow speed squared and at halfway between tip & root there is just 1/2 of the tangential speed and approximately 1/4 of dynamic pressure if axial flow is neglible compared to tangential. To get same lift there you need 4 times greater chord*Cl halve way in from tip than near tip. That is possible with this very simplified theory, but further closer to axis this approach falls apart. If you would use a more sophisticated theory involving both tangential & axial induced flow in addition of the axial induced flow things get worse, not better. I would be very surprased to have any better than even L/D=6 with aspect of 4 for individual blade if L & D are defined in relation to assumed flow direction (without induced velocities) at r/R = 0.7 as Bauer did in his analyses. If you define L & D related to local flow things are obviously a lot different, but you still overestimated the L/D. Keep in mind L is oriented more towards creating torque near hub than near tip.

You seem horribly bent in discrediting Bauer's work. I just accept it for what it is - a simplistic approach.

I do my own prop and turbine analysis that I know gives reliable results. I consider his numbers highly optimistic. If you go back through the myriad of pages on this topic on the various threads you will see discussions on the size of the prop and turbine required for specific applications.

If you want to build a boat that will work I can give you a design. I would not rely on Bauer's numbers for design purposes but I do give him credit for his early work on the science.

Rick W

[Rick Willoughby]

Don't be sorry or afraid to disagree with me. It sounds like a put down - intended or otherwise. I don't think you are sorry or afraid at all. Just say what you mean. If I am wrong it won't be the first time. I can remember I was once wrong but it rarely happens.

Rick W

[sailor2]

Originally Posted by sailor2

I would be very surprased to have any better than even L/D=6 with aspect of 4 for individual blade if L & D are defined in relation to assumed flow direction (without induced velocities) at r/R = 0.7 as Bauer did in his analyses. If you define L & D related to local flow things are obviously a lot different, but you still overestimated the L/D. Keep in mind L is oriented more towards creating torque near hub than near tip.

Also keep in mind the use of r/R = 0.7 to represent the all blade_elements is based on assumption that centre of pressure of prop disk is located there. This gives some idea of the lift distribution along span assumed in his analyses.
Also note that by simply using narrower chords & greater revs to get better AR nothing is gained in terms of L/D as span loading doesn't change at all. Only reducing disk loading will have positive effect on that. Using narrower blades might propably do the opposite if RE-numbers are brought down as well. So high blade AR by it self is no solution at all in improving things.

Ps. I'm not any prop- or aero- expert, just an amateour in the field unlike Drela or Speer. I have carefully analysed what is easily available in web on the subject (as widely interprated) with presumably good enough engineering skills thoug.
If you have doubts on any of this due to that, don't hesitate to ask from more knowlidgeable, I'm always glad to be proven wrong as that allows me to learn more. Seems like you share that approach.

[sailor2]

Originally Posted by Rick Willoughby

You seem horribly bent in discrediting Bauer's work. I just accept it for what it is - a simplistic approach.

I do my own prop and turbine analysis that I know gives reliable results. I consider his numbers highly optimistic.
Rick W

No I don't want to discredit his work, I just don't want it to be used for something it can't be used due to the error it had, resulting over-estimating how easy the ddwfttw on the water would be according to his analyses for even heavy cruising boats. Clearly a false result.

He did a fine job of being the first to try scientific analyses on prop & turbine propulsion and deserves all the credit for that. That doesn't change the fact it had one vital error in the first formulas used and everything else was based on that formula. I mean the ignoring induced velocities part. The other simplifications even brought together are much smaller inaccuracies compared to the ignoring induced velocities part.

If you want to call this discrediting be my guest, but that's not how I see this issue. I consider far more important to present accurate analyses that recognizes it's own inaccuracies. That's a mandatory requirement on scientific papers as far as I'm conserned. Someone failing to do that in doctors theses would have bad result of not becaming a doc at all for sure. It was my understanding those papers were intended for scientific audience and that they were used for that too. I don't know what the reaction from AIAA was after the presentation. Is my point of view clear now ?

[sailor2]

Originally Posted by Rick Willoughby

Don't be sorry or afraid to disagree with me. It sounds like a put down - intended or otherwise. I don't think you are sorry or afraid at all. Just say what you mean. If I am wrong it won't be the first time. I can remember I was once wrong but it rarely happens.
Rick W

Not being afraid at all, just trying to be polite as required on the rules of this forum. Not being a native english speaker might lead to over do that to avoid being accused of personal attacs leading to be thrown out of here by forum policy. That won't have any effect what I say, just how I say it. Have been lurking for years, but joined just yesterday after weaks of trying. So a newbie here, but certainly not a newbie on the substance.

[Rick Willoughby]

Originally Posted by sailor2

No I don't want to discredit his work, I just don't want it to be used for something it can't be used due to the error it had, resulting over-estimating how easy the ddwfttw on the water would be according to his analyses for even heavy cruising boats. Clearly a false result.

He did a fine job of being the first to try scientific analyses on prop & turbine propulsion and deserves all the credit for that. That doesn't change the fact it had one vital error in the first formulas used and everything else was based on that formula. I mean the ignoring induced velocities part. The other simplifications even brought together are much smaller inaccuracies compared to the ignoring induced velocities part.

If you want to call this discrediting be my guest, but that's not how I see this issue. I consider far more important to present accurate analyses that recognizes it's own inaccuracies. That's a mandatory requirement on scientific papers as far as I'm conserned. Someone failing to do that in doctors theses would have bad result of not becaming a doc at all for sure. It was my understanding those papers were intended for scientific audience and that they were used for that too. I don't know what the reaction from AIAA was after the presentation. Is my point of view clear now ?

Bauer has simply made assumptions that he discusses. I did not bother too much with his analysis because I knew his assumptions would cause underestimations. I believe he aimed to prove a point that a turbine/prop boat can go directly to windward and DDWFTTW.

If his experience was with powered props he would not appreciate the high velocity ratio required to generate the thrust needed to propel such a large boat in very low far field wind speed. For the low power water props I design and build I neglect near field conditions because the velocity ratio is so low.

Rick W

[sailor2]

Originally Posted by Rick Willoughby

If his experience was with powered props he would not appreciate the high velocity ratio required to generate the thrust needed to propel such a large boat in very low far field wind speed. For the low power water props I design and build I neglect near field conditions because the velocity ratio is so low.

Do I understand correctly that the velocity ratio you are talking about is defined as induced speed / free stream speed ?
If so what about swirl losses ? If you size prop diameter up to low down that ratio, you also lower the revs for a given power meaning you increase torque.
That means you increase swirl losses, there is optimum diameter in real world due to that even ignoring Re-number effects. Not sure if you are anywhere near that diam, but if you are ...

[Rick Willoughby]

I have done some design work on a manned boat to achieve DDWFTTW.

It is easy to look at numbers and not appreciate what they mean. Something showing the proportions provides greater meaning.

I was intending to show a bike chain drive between the turbine and prop but that would be too unwieldy. I expect a carbon shaft up the prop mast would be the best.

This is not something I would ever contemplate building and I doubt anyone else will. It might be possible to reduce the prop size but it means it will need higher wind to operate.

The exercise of looking at a large model boat might yield something more practical but it will still need quite a large prop.

I have included a performance curve to give an idea what this could achieve. In the current configuration power transfer becomes a serious consideration over 10m/s. I did not go above 15m/s wind because the power is over 10kW. This would require much heavier components than I have allowed for in the displacement.

Rick W

[sailor2]

Originally Posted by Rick Willoughby

I have done some design work on a manned boat to achieve DDWFTTW. Rick W

Wow, surprising shape on that curve except the lower end.

How does assumed rpm of turbine change with boat speed ?
How does assumed torque from turbine change with boat speed ?
If not by square law, turbine efficiency changes. If by square law prop efficiency changes. I just can't see how both could be kept reasonably high for so wide operating range dispate of pitch & gear changes.

How does assumed propeller efficiency change with boat speed ?
How does assumed turbine efficiency change with boat speed ?

Or did you simply assume different prop & turbine combination for each boatspeed optimized for the conditions and was pitching moment assumed to be balanced by shifting weight in form of airprop & tower aft to compensate ?
Considering how little boatspeed/windspeed ratio changes seems to indicate just that.

[Rick Willoughby]

I have modeled all elements of this with reasonable accuracy - all within 2%. So I have a VPP where I set the windspeed, and automatically increase the boat speed from 80% of windspeed till I get overall thrust and power balance.

I assume the boat can be trimmed so it sits on the waterline with the outriggers just skimming. I have not determined how the pilot weight would need to be moved around to achieve this. I expect it may need a trampoline between the outriggers

The turbine has quite low slip through out the speed range so its rpm is almost liner with speed. At 13.4kts it does 193rpm.

The model only works with a narrow range of mechanical gear ratio. The optimum at all windspeed is 5.1:1. I cannot get the model to start if the ratio is below 4.9 and higher than 5.6. This could be just an issue with setting the starting conditions but I have played quite a lot to increase the range. I have not yet determined what limits it. The 5.1:1 mechanical ratio gives an effective ratio of 0.6 allowing for the geometric pitch of both turbine and prop.

The power input to the prop at a few wind speeds is:
3m/s, 97W
6m/s, 849W
10m/s, 4273W

The overall efficiency of power transfer from water to air improves considerably as the prop improves its operating regime. At windspeed of 5m/s it is 37% and increases to 63% at 10m/s. Both relate to the steady state boat speed for the given windspeed.

The wave drag on this hull is about 10% of total drag throughout the speed range. I use Michlet data for this that I know is good up to about 5m/s on this particular hull. Error may increase as speed increases but it will not be huge as it is dominated by viscous drag.

Rick W