Thrust greater than drag

Nothing Gonzo has said contradicts the fact that windmill boats can sail upwind. He is trying to explain the physics to you, as am I. I'm still not clear what you mean by levers with regards to a windmill boat. The only levers in the system are the blades of the wind turbine and the propeller. Those blades are in fact foils, so in this case the levers are foils. To explain:

The wind turbine blades, as levers, apply a moment (force x distance) to the turbine shaft, creating a torque (rotational force). That torque is transmitted to the propeller shaft and if we consider the propeller blades as levers, the torque applies a moment to the propeller blades. Because the torque is the same in both cases, the moments will be the same. Now, the density of water is higher than that of air, so the force on the propeller blades will be higher. Therefore we make the propeller smaller than the wind turbine so that the moments balance while maintaining an efficient rotational speed for both the propeller and the turbine. The moments (or torques) will always balance, regardless of the size of either, because the rotational speeds will self adjust to balance out the forces. Gearing up or down the propeller changes the rotational speed and hence the force on the blade, balancing out the greater or lesser torque of the geared shaft.

None of the above has anything to do with whether the boat makes any forward progress or not, it only describes the mechanism of transmitting the power of the turbine to the propeller. The progress of the boat depends on the difference in pitch angle between the turbine and propeller blades, which is a separate issue regarding the aerodynamic and hydrodynamic forces on the turbine and propeller.

 

Here's a vector diagram showing my thoughts on how a turbine powered boat might sail directly into the wind:

 

The 1:1 gear ratio you show will not work. There needs to be mechanical advantage between the Wind Turbine blade and the water propeller. The turbine blade should move further than the propeller blade and that is where the leverage comes from. Gonzo please tell me if you believe a wind turbine boat can go directly into the wind?

 

Here's an interesting video I found:

 

In your nicely produced vector drawing, some things are not exactly clear. Which way is the boat going? You have not taken into account the different diameters of the turbine and the propeller. It is unlikely they would both be the same. So one blade on the turbine would be travelling through the air a much greater distance than one blade on the propeller through the water. So there is a gear ratio between them, but it is not 1:1. The turbine drag is rediculously high. On an aerofoil (as you should know) lift to drag ratios can be as high as 30:1 and some sailplanes have more even approaching 60:1

 

Yes, I have watched most of Peter Worsley's videos. Have you also seen this one with a 1:1 drive?

 

1) I have shown the direction of the wind and said that the diagram is for a boat sailing directly into the wind. Actually, it doesn't matter which way the boat is going, the principle is still the same, you just rotate the propeller part of the diagram. But I think it makes it easier to understand diagrammatically if the boat is going directly into the wind.

2) The diameters of each not important to the general principle. They are determined with respect to the different fluid densities and viscous properties, which is a given. The diameters, aspect ratio's, number of blades etc. only affect the efficiency of the system. It's a complex relationship, but the aim would be to have both the propeller and the turbine operating at the point of best L/D, which usually means at max. CL, or close to stall.

3) I think you are referring to the lever thing again with the blade lengths, which as stated previously is, to be blunt, nonsense. The gear ratio I'm talking about is the gear ratio of the shaft speeds. Again, this only affects the efficiency of the system, matching the propeller speed with the other variables, and is part of my point 2 above.

4) The drag shown on the diagram is the drag of the turbine as a discreet device, not the drag of the turbine blades themselves. The turbine blades are operating in their own apparent wind, not in the true wind. The power you can extract from a turbine is determined by how much you can slow the airflow before and after the turbine. The maximum power occurs when the air velocity after the turbine is reduced to zero, at which point you have infinite drag. Unfortunately you can't do that with a turbine. There is a point somewhere between no velocity reduction and maximum velocity reduction where the turbine works most efficiently at extracting energy from the airflow. So in fact what you want from the turbine as a device is to get as much drag as possible, and that's the point you should be aiming for with the design. The issue is similar but opposite for the propeller, in which case ideally you would get an infinite velocity increase in the water velocity behind the propeller, also not possible.

 

You did. Propellers and windmill blades are foils.

I don't believe there is any system at the scale of a ship that works. That is what I've seen. Further, it is obvious to people with scientific and engineering background that it can't be scaled to that size.

 

This video is a good example of a 2nd class lever. Just because there is 1:1 gearing does not mean there is no leverage. The shaft is the fulcrum or pivot and then there is a load position and an effort position.
The load position is the propeller blade and the effort position is the turbine blade.
https://static.sciencelearn.org.nz/...vot_diagram_of_a_Class_2_lever.jpg?1674168090
Because the turbine blade is a much greater diameter than the water propeller disk. The turbine blades cover more distance in one revolution than the propeller disk. For example: if the windblades were 15 diameter and the water propeller was 5 diameter then the propeller blades would cover a distance (approx) 3rd of the distance of the wind blades but their force would be 3 times greater, that's called leverage - you increase your force by reducing your distance using a fulcrum. This is why the Peter Worsley model works.

 

That model has the hulls in a box so there is no wind force applied to the hulls. Further, there are no waves, which affect the resistance of the hull and the overall efficiency of the system. This is a typical rigged test in artificial conditions.

 

There are plenty of videos not in a box using natural wind conditions. What do you think of the Jim Bates boat Tango?

 

Seriously?

No, it isn't. Firstly, you stated earlier that the gearing was a factor in the turbine boat working. From the video, clearly it is not. Next, levers work by having equal and opposite moments on either side (or on one side) of the fulcrum. The moments are balanced. The balance beam on a set of scales is not called a balance beam for nothing.

Moment = force x perpendicular distance. The important factor here is force. The force on both the turbine blade and the propeller blade is:

CL x 0.5 x density x V^2 x blade area

We can assume that CL is roughly the same for both the turbine and the propeller. The velocity V is within the same order of magnitude for both. But the density of air is about 0.0013 times that of water. Due to the large difference in density you need a much larger turbine blade, both diameter and area than propeller blade. Like in a lever, the rotational forces (the torque) on both the turbine and the propeller must balance. You don't magically get something for nothing. The boat is not being levered along. The boat moves forward due to the pitch difference between the turbine and the propeller blades. Please refer to my diagram.

 

Here's a video of a similar 1:1 model of his working in open water -

These are crude models, but they still work.

 

Can't really comment to someone who does not understand how simple levers work. like the wheelbarrow, scissors nutcracker etc.

 

It shows a model held by a string.