[hexane360]

You were downvoted because your calculations were for regular sails, and sailboats, instead of for Magnus effect.

Wikipedia says:

    F = L*rho*v*2*pi*r^2*omega

where L is the length of the cylinder, rho is the fluid density, v is the fluid velocity, r is the cylinder radius, and omega is the cylinder angular velocity.

What angular velocity are you assuming in your calculations?

[qume]

My back of the napkin assumed all energy from the wind over the entire cross sectional area.

Magnus effect or not, i'm just dealing in orders of magnitude and for the average wind speeds on shipping routes, I just don't understand how this works even if 100% of the wind energy is extracted from the cross sectional area of the sail.

[nikdaheratik]

After looking at the math a bit (including the one helpfully provided above), I think you're missing alot by ignoring the effect of the rotational velocity when thinking about this effect. The spinning rotation has a multiplier effect on the air movement similar to a how a much larger/fuller sail could redirect the air flow to produce more forward motion in a traditional sail.

[Edited] The effect is similar to how a rotational wing aircraft also produces lift that is not strictly proportional to the area of the wing (although for different reasons).

[jameshart]

Without seeing your back-of-napkin numbers it’s hard to know where you might be going with this, but the idea that sail efficiency has something to do with the amount of energy in the wind in a particular cross section seems in need of justification. You’re probably better off considering air/sail interactions as a momentum transfer - the goal of the sail is not to extract all of the energy from a packet of air (presumably leaving blocks of frozen nitrogen in the sail’s wake), but rather to extract as much forward momentum as possible out of the interaction, leaving the air with more rearward momentum than it started with.

[nikdaheratik]

[Snipped after looking at how it works again]

[danielvf]

No, I don’t think that’s what it’s doing. It’s actually powered - using electricity to make it spin. As a result of the spin, it creates vortexes that push 90 degrees to the wind.

[nikdaheratik]

Yeah I think I was still confused about how it works, but I've just decided to snip out my comment instead.