Improved windmill rotor and sails

[Rufkut]

I propose an improved sail and rotor for Vintage Story's windmills. Currently, windmills have limited torque, necessitating multiple structures for increased power, leading to 4 rotor or skyscraper designs. To enhance both aesthetics and functionality, an improved windmill design is recommended, aligned with the game's technological progression.

 

The first improvement is cambered sails. Historically, sail designs used a curved shape called camber, similar to an airfoil, increasing lift and wind energy capture. Iron strips and nails strengthened the sails. In-game, improved sails can be crafted using more linen cloth, an "adjustable trim," iron strips, and nails. Visually, you'd see wider sails featuring pronounced camber and reinforced metal strips. For customization, colored sails would be a great addition. Players could dye sails, personalizing windmills and bases.

 

In the past, an adjustable trim mechanism allowed manual adjustment of sail angles using ropes and pulleys, optimizing based on wind conditions. In-game, the trim mechanism can be smithed using iron, then combined with ropes, nails, and a hammer to make an improved sail.

 

An improved rotor is necessary to withstand increased forces from enhanced torque. This is accommodates up to 10 sets of improved sails. Crafting requires a regular rotor, hammer, 8 iron plates, and 32 units of fat and resin. With 8 improved sails attached to the improved rotor, it should generate as much or slightly more power than four regular rotors with the maximum 5 sails each.

 

This would add another provide late-game tech progression, curb the end game resource surplus, and allow for efficient windmills without sacrificing aesthetics or resorting to unrealistical designs.

[Cosmic Hermit]

Hello, I'd like to add another consideration to this revised windmill mechanic. I'm going to skirt around the math as best I can.  I'll be using a previously established approximation for wind turbine power for the windmill here.  Something to consider is that the power generated by a windmill does scale with the cube of wind speed, but the length of your rotors are also a significant factor.  The power generated is proportional the swept area of the rotors, that's the area of a circle.  Which means the power produced by a windmill is proportional to the square of rotor length.  Don't worry about power versus torque for this particular issue, because power is just torque times angular velocity, which doesn't have a length component.  This means that one windmill with 6 meter long rotors should provide significantly more torque than 6 windmills with 1 meter rotors, or two windmills with 3 meter long rotors.  The raw ratio for 1,6 to 2,3 is 36:18, and for 1,6 to 6,1 its 36:6.  So if your model doesn't account for rotor length, numerous small blades seem much more reasonable than they should.

My recommendation is that the windmill torque is calculated by averaging the wind speed across the rotor span [just taking highest and lowest speed from height delta] and factoring in the length of rotors.  If you'd like a more detailed explanation [because I admittedly did a bad job] on the math of the concept, just let me know.

[PhotriusPyrelus]

A turret that turns with the wind wouldn't go amiss either...

[Thorfinn]

@Rufkut as I look at the sails whist standing next to the rotor, they are cambered, aren't they? Or is that my old eyes playing tricks on me?

@Cosmic Hermit interesting! That's probably why the angle of attack changes as it reaches the end of the blade in a modern wind turbine? It must change, or the wind speed is not sufficient to provide lift at the tips? Also, if it's a function of area, why not make the blades a bit wider? Obviously it is not optimal, but why? (If this is too OT, someone say so. I just find it fascinating.)

@PhotriusPyrelus isn't the wind direction always the same? I use cloud motion to orient myself and that appears to be constant worldwide, independent of seed, even. Or are you talking in a future release where both wind speed and wind direction vary?

[PhotriusPyrelus]

5 hours ago, Thorfinn said:

@PhotriusPyrelus isn't the wind direction always the same? I use cloud motion to orient myself and that appears to be constant worldwide, independent of seed, even. Or are you talking in a future release where both wind speed and wind direction vary?

...duh.  Been playing too much Valheim, I guess.

[Cosmic Hermit]

@Thorfinn Now that I have moment, I owe you some clarifications.  The equation I handwavely reference is technically an approximation of the maximum theoretical power a wind turbine could extract from the wind.  For this reason, the equation doesn't actually care about wind turbine geometry and just assumes an optimal blade shape. What it does care about is the swept area of the blade.  If you can imagine sticking a sharpy at the tip of a turbine blade and spinning the blade a full turn, the circle the blade draws in the sky is the swept area. here's the equation in question: Power (W) = 1/2 x ρ x A x v³  I decided that for a one off comment, actual efficiency calculations were a bit out of scope seeing as the current implementation doesn't really seem to account for the efficiency of the blades either [also I was sleepy], and just assumed 100% efficiency too.

As for the twist of the blades, there are a couple of reasons but the quickest one to explain is, imagine the wind from the perspective of the blade.  Hold the  blade still and the wind comes straight at you.  If you spin the blade a bit however, the wind kinda looks like its coming at you slanted.  The direction of the wind seems a little crooked because while the wind moves from front to back, you're running around in circles.  The other part of it is that while the whole blade rotates at the same speed, the distance actually moved as you get farther from the hub, gets longer and longer. You're running faster and faster just to keep up.  That speed means that as you get further and further from the hub, the wind looks not just faster, but more and more slanted. The blade twists to account for that.

[Thorfinn]

Cool, @Cosmic Hermit I take it rho is efficiency? Which is presumably empirically determined? Three blades is standard because more would involve both heavier bearings and "fouling" from vortex shedding? As opposed to, say, water windmills that need a higher torque, so fill more of the swept area with blades?

Do you happen to know why it's 3rd order? Wind resistance is a 2nd order function, and though it's been a while since I took diff, it seems to me that was derived relationship. It looks to me as if this equation is just the integral of wind resistance, but I'm not seeing right off-hand why that should be so. Or is it just as simple as summing up wind resistance over time?

[Cosmic Hermit]

@Thorfinn In the equation supplied [I really should've divided those thoughts into paragraphs for clarity] I still don't include anything for efficiency.  Before I get to this in earnest, let me introduce the players properly. Energy is measure in joules (J), watts are the amount of energy supplied per second (W, J/s), ρ is density, the mass per unit volume (kg/m^3), mass (m) in kg, area (A) is in m^2, and velocity (v) in m/s.  Just covering bases.

Now to the meat and potatoes; using wind resistance, drag, will cause us some problems.  Drag is a force, and while we can get from a force to energy provided we do some clever integrations, the problem with this particular force is that it's the resistance to movement of an object in a fluid.  If the fluid or the object stop moving and no force is exerted on either, drag is zero. Drag is sorta like friction in that way, if I plop something on the counter and don't touch it and nothing else tries to move it, there's no friction force, but the second I try to give it a push, even if the push fails to move it, friction has kicked into gear.

Why is that a problem?  The approximation mentioned earlier is for the maximum amount of power you can theoretically squeeze out of a perfect turbine.  In order to get that equation we basically ignored everything about the blade to get there.  Here's the horrible truth, we were never measuring the blade-wind interaction from the outset, we were figuring out the power of the wind itself! It was all a lie, oh the humanity! You see, the maximum theoretical power you can extract from the wind, is all of the power the wind makes available, or rearranged, its just the power of the wind.  To get a little more specific, we are figuring out the kinetic energy of the wind per second.

Do you remember the equation for kinetic energy from physics?  It's 1/2 x m x v²   This will help us figure out the kinetic energy of the wind as well. If you look at the original equation, (W) = 1/2 x ρ x A x v³, you'll notice some familiar faces. Let's cross out the terms that are the same between the two and see what's left: m for equation one and ρ x A x v for the second. This should clue you into something, some how, ρ x A x v serves a similar purpose to mass (m).  I said earlier that density is mass per unit volume right, so it stands to reason that if we multiply the density by a given volume, we'll get mass out.  So the purpose of A and v is to give us a volume.  Velocity has units of meters per second, so if we multiply the area by a distance per second, we get and a volume per second [this is called a volume flow rate]. Multiply that by our density and we get a mass per second [mass flow rate].  Reassembling the equation we now have 1/2 x m/2 x v²  Let's rearrange one last time it's: (1/2 x m x v²)/s. What we have here is the kinetic energy of the wind per second: energy per second. Behold, by the power of dimensional analysis you have discovered the power of the wind!

Think about it like this, we are measuring the energy of a circle cut out of wind [the swept area of the blades] as it blows by. Its like a giant tube of air in the sky that we measure the energy of as it moves for just one second.

The reason why the drag equation, the kinetic energy equation, and this equation all look the same, is that they are all different applications of the same original equations.  I'm not sure how far to go down this road, but they can all be derived from the equation for conservation of energy  of a control volume.  As for the order of the equations, that comes down to the interplay between force, energy, and power. Energy is the space integral of force.  Power is the time derivative of Energy.  So a watt is actually (N x m)/s.

I hope the level of my explanation was not insulting, my intent was that other readers who happened to be interested might also be able to parse this. To any who made it all the way down here, I meant no disrespect by the way I explained this, I just wanted to be clearish... and have a little fun, this stuff is my bread and butta  ; )

[Thorfinn]

Oh, ok. I figured rho meant something other than density, because most of these types of equations in engineering are for STP and you have to adjust from there. I was actually amazed the equation was that simple. There's generally an empirically-determined eta or alpha or mu or f or something embedded in the formulas/correlations to account for efficiency or properties of specific materials.  But this is generalized to the point it works for any fluid, from microtorr helium to molten neutronium.

As such it's not very useful in this case, is it? It's just an upper limit that is in no danger of being breached, kind of like the quart of gas in my chainsaw is not going to be getting anywhere close to E=mc^2.

[EDIT]

The main reason this piqued my interest is that I'm doing some engineering on an off-grid wind power application, and according to the documentation the manufacturer was supplying, power output did not increase with the cube of the wind velocity or any exponential equation at all, except for a very narrow band near v=0. Indeed, it looks more like the limit of an infinite series, converging on a constant. Maybe a log function. I was hoping that maybe there might be some way to take advantage of the cubed term instead, but that is clearly not the limiting factor in real-world wind power applications.

[/EDIT[ 

Edited June 15, 2023 by Thorfinn

[Cosmic Hermit]

Just noticed this many months later. Yes the equations I mentioned only give you the literal energy content of the mass of moving air.  In reality the turbine airfoils are optimized to operate with a maximum efficiency within a certain range of incident wind speeds.  It's all the same issues as an aircraft wing, just turned sideways.  Though you have a decent amount of pitch control on a turbine, the shape of the blades themselves can't be altered, so after a certain amount of wind velocity, turbulence and stalling [starting near the hub], aggressively limit the amount of energy you can extract.  That converges on some maximum value, which theoretically might lead to a negative trend on the other side of that plateau if wind speed increased even more, but that's near the super sonic regime, and stuff tend s to break long before that.

Using the energy equation as is, provides a more reasonable model for the game, without the complexity of creating an efficiency coefficient that's a function of wind speed, blade length, airfoil geometry, etc. Perhaps you could multiply it by a static or linearly varying coefficient, but landing on a number for these approximations would take some doing.  Definitely not suitable for real life applications, unless you want a ball park idea for the generation capacity of some region, which is still iffy.  This solution is more for this application, where precision and computational time are battling to the death in a cage match.

For reality, you'll want to visit the 3d lift and drag equations, and embrace some pretty crummy integrations for the length of the blade. Then you can perform an optimization for wind speed and you'll have a more reasonable approximation.

[Kriss]

This post needs to be brought up again, as imo - the current mechanical power system in the game is kind of broken. I can understand that its not as simple as just increasing some numbers, but something sure has to change. From what I've seen from Vintage Story, they try to make the game as realistic as they possibly can (while of course still enjoying the gameplay).

What I've done is create a windmill structure that seem realistic for a full set of sails and run axles all the way down to run the following equipment:

• Helve Hammer
• Quern
• Pulverizer

I've been playing around with different setups for running all them at the same time, and efficiently but haven't been able to get anywhere. Either I'm being a dumbass, or something needs to be changed.

EDIT: Posted a quick clip of what my setup looks like.

• The axles coming down from the top is the primary windmill
• The axles coming from the cobblestone walls is the secondary windmill and doesn't work as much, this is what i want to prevent, and just stick with one windmill.

 

 

Edited January 5 by Kriss