Wow, Rita now Cat. 5 (165 mph)

[DeanDavis]

I just heard that hurricane Rita is now a category 5 with sustained winds of 165 mph. If anyone can appreciate a wind of 165 mph it is someone who has lived through a hurricane or the wind-riding group. So lets put that number in perspective. The power in the wind goes up with the cube of the wind speed so lets say we are out at the beach well powered on our 14 m^2 kite and the winds are a nice 16.5 mph. Now lets say Rita comes to town and we want to ride (which would be stupid, but for argument sake, go with it). We now have 10 times the wind speed or 10^3 (1000) times the power. So instead of pumping up the 14 m^2 we need a 0.014 m^2 or a 22 in^2 kite. A kite the size of a jumbo photo (4”x6”) would be overpowering! For the windsurfers my guess is that a 7.5 m^2 might be nice sail size in the 16.5 mph winds. So when Rita hits town we want 1000 times less sail or 0.0075 m^2 or 12 in^2. A Post-it note (9 in^2) might be a little underpowered but close.

For wind turbines we design (for the very worst case at the highest wind resources) for 72 m/s or about 161 mph. Above about 55 mph we usually give up and shut the machine down. Above 160 mph we just hold the rotor tight and pray. I hope those guys in Texas realize what is headed their way.

[Marty Lowe]

Great post Dean,

Very informative.

-Marty

[Craig Goudie]

Ditto,

Also very fun. How do I get a job like yours, Dean? (I am an engineer)

-Craig

Great post Dean,

Very informative.

-Marty

[rizzle]

nice ive been waitin to use my 22 in^2 kite.....I have a few buddies that work on off shore oil rigs down there, they have been evacuated and I'm glad they are all safe.......

Ry...

[Rick McClain]

Ok. So who's up for heading to South Padre Island this weekend for a little sailing?

[Marty Lowe]

Jon M, Jim and I are heading down the end of Oct.

Hope the hotels are still there,,,

Looks like the brunt of the storm
is passing to the North and missing Padre.

-Marty

[JimSouthwick]

Fascinating post!

Is the power of the airstream (which, as you point out, varies as the cube of the wind speed) really what determines how big a sail/kite we can control? I had always thought that what matters is the FORCE on the sail/kite which, as I understand it, is purportional to dynamic pressure, which varies as the square of the windspeed. [/u]

[DeanDavis]

DCJIM,

Reality falls somewhere less than the cubic. Here is the way I see it. The power (in the wind) is going with the cubic (^3) of the wind speed so “in theory” to extract the same power from a 16.5 mph wind and a 165 mph wind would only require that we use a 10^3 (or 1000) times smaller sail. But the piece I left out (for simplicity reasons) is that what we really care about is the “extracted” power (that’s where the fun is). We don’t extract all (100%) of the kinetic energy in the wind, if we did we would have to stop the wind and if we stopped the wind the wind behind it would tend to slow down or go around us, so we let some wind pass*. So if we wanted to use the 1/1000th size sail we would need that sail to be operating at the same efficiency as the full size sail. That might be tough to do. We would be operating at a different Reynolds number and I think it would require that we be riding really fast (I think 10 times faster than normal). Not only would riding this fast (150-200 mph) be uncomfortable for us mere mortals but it would also require much more power (due to all the things I was ignoring like hydrodynamics drag). So the bottom line is I think it would be impossible to get the same efficiency out of a Post it Note size sail assuming all of the real world limitations.

But getting back to your comment more specifically the sail force is a function of the square of the wind speed (as you said). But the wind speed is not the freestream wind speed it is the vector sum (resultant wind speed) of the freestream wind speed and the board speed. It is the board speed (and the fact that the board speed and required power are related) that complicate things and which make it impossible for one to extract the same efficiency with such a small sail assuming you were not moving very fast. Said another way if you can’t keep the board speed at some optimum (which I think might be close to the freestream wind speed and very fast in the Rita example) then you would have to make up lost efficiency with more sail area. When thinking about it I think if you didn’t allow the board speed to increase (at all) then you probably would want a sail size that is closer to the squared ratio so that you got a similar aerodynamic force. Clear as mud?

*As an aside, for wind turbines we use momentum theory to calculate the maximum theoretical power, which is the Betz limit and is 59%. If we attempt to extract more power (maybe by adding more blades) then we slow the wind too much and get a lower efficiency.

**As another aside, in the wind turbine we get to increase the resultant wind speed (by increasing the rotor speed, via variable speed) as the wind speed increases without significant penalty (higher rpm doesn’t cause significantly higher losses). By doing this we can stay at a peak efficiency.

[JimSouthwick]

DeanDavis,

Thanks!!

[Marty Lowe]

Doood,

After reading that,
My head is spinning 165 mph.

-Marty

P.S. Airfare went down to Padre today. $203
You better go with us.....

[Emmanuel Pons]

DCJIM,

Reality falls somewhere less than the cubic. Here is the way I see it. The power (in the wind) is going with the cubic (^3) of the wind speed so “in theory” to extract the same power from a 16.5 mph wind and a 165 mph wind would only require that we use a 10^3 (or 1000) times smaller sail. ....

humm still doesn't make sense to me. I'll have to think about that tonight but what a windsurfer react when sailing is a force and this force should only grow as a sqare of the wind speed..... I think Or may be I am just really confused..

[DeanDavis]

Emmanuel,

Yes if you stuck your sail in the ground then the force would change as the square of the wind speed but you don't do that you use that force to propel you across the water. As you do that you increase the resultant wind speed across your sail. Lets assume that the winds are 20 mph and you are riding 20 mph (my guess is that is possible). The resultant wind speed over the sail is now 28 mph and your force is now a function of 28^2 and not 20^2. You are extracting power from the wind more efficiently.

P.S. I have probably confused everyone, including myself.

[Craig Goudie]

Well, I'm not confused, yet, that is how apparent wind works, if there were no drag (friction),
this would be a positive feedback syetem, and you'd continue to
accelerate until you reach a very high speed. And the forcing function is a squared function.

-Craig

Emmanuel,

Yes if you stuck your sail in the ground then the force would change as the square of the wind speed but you don't do that you use that force to propel you across the water. As you do that you increase the resultant wind speed across your sail. Lets assume that the winds are 20 mph and you are riding 20 mph (my guess is that is possible). The resultant wind speed over the sail is now 28 mph and your force is now a function of 28^2 and not 20^2. You are extracting power from the wind more efficiently.

P.S. I have probably confused everyone, including myself.

[DeanDavis]

Craig,

That is exactly right. If there were no drag (hydrodynamic or aerodynamic) then you would continue to accelerate forever, ignoring things like compressibility effects (breaking the speed of sound). If you had the aerodynamic drag on the sail but very little or no hydrodynamic drag (visualize an ice skate buggy with ice skates on ice) then you would continue to accelerate until your sail (think wind surfer sail for now) was almost perpendicular to the wind (for simplicity reasons you are traveling perpendicular to the wind direction). At that point the lift force is getting pretty large (high apparent wind) but most of the force is trying to topple you downwind (lift force is (by definition) perpendicular to the apparent wind vector). A tiny lift vector would still be in the forward direction. The drag force is getting pretty large as well (again high apparent wind) but that force is almost exactly opposite your direction of travel (acting like a brake). At this point you would find an equilibrium speed (like Craig said “very fast”) but ironically you would not be generating much power. In this configuration you would actually be approaching a zero efficiency point.

For a wind turbine we call this the no-load tip speed (ratio). This is the speed a turbine rotor will get to if the generator is disconnected in a given wind. For a fixed pitch turbine it can easily be at a tip speed ratio of 18 which means the tip of the blade will be traveling at a speed 18 times the wind speed. Assuming this happened in a 30 mph wind the tip will be traveling at 540 mph and starting to get into that transition point of compressibility where the drag would start to spike. I don’t think the neighbors will be happy, I think it would be making a lot of noise (we try very hard to not let a turbine operate at the no-load tip speed).

[jason morton]

Dean-
I don't want to be around you if you're passing wind. Especially downwind. Thanks for the physics lecture.