Feasibility of stratopheric wind turbines?

[Sherwood Botsford]

1/2" kevlar rope has a breaking strength of 31,000 lbs and weighs 7.8 lbs/100 ft.

= 116 kg/km

So a a bit over metric ton gets you up to 10 km altitude. 2 metric tons at a 30 degree angle. Still gives you 25,000 pounds potential drag without breaking the rope.

Working strength is typically 1/3 of that especially unflexed.. And kevlar is weaker than HDPE.

Ok, why aren't we doing stratospheric wind turbines yet?

 

[trurle]

1/2" kevlar rope has a breaking strength of 31,000 lbs and weighs 7.8 lbs/100 ft.

= 116 kg/km

So a a bit over metric ton gets you up to 10 km altitude. 2 metric tons at a 30 degree angle. Still gives you 25,000 pounds potential drag without breaking the rope.

Working strength is typically 1/3 of that especially unflexed.. And kevlar is weaker than HDPE.

Ok, why aren't we doing stratospheric wind turbines yet?

Tethered wind turbines are been actively developed, although you underestimate needed margins. About factor of 8 strength multiplier is needed due gusts and vibrations.
https://en.wikipedia.org/wiki/Airborne_wind_turbine

 

[256bits]

So a a bit over metric ton gets you up to 10 km altitude. 2 metric tons at a 30 degree angle. Still gives you 25,000 pounds potential drag without breaking the rope.

Add in the weight of some copper cable also.
https://www.engineersedge.com/copper_wire.htm

 

[davenn]

Ok, why aren't we doing stratospheric wind turbines yet?

Add in the weight of some copper cable also.
https://www.engineersedge.com/copper_wire.htm

yeah that's what I was thinking as well when I read the OP, @Sherwood Botsford didn't even take into account how he was going
to get the generated power down to the ground and the huge amount of additional weight that was going to have

 

[russ_watters]

So a a bit over metric ton gets you up to 10 km altitude. 2 metric tons at a 30 degree angle. Still gives you 25,000 pounds potential drag without breaking the rope.

Is that a lot? How big would a stratospheric wind turbine need to be to produce 1 MW? How big is a 1MW ground-based turbine and how much drag is on it?

 

[russ_watters]

yeah that's what I was thinking as well when I read the OP, @Sherwood Botsford didn't even take into account how he was going
to get the generated power down to the ground and the huge amount of additional weight that was going to have

Er, or what the turbine/generator would look like and how he would keep that aloft.

 

[cjl]

Is that a lot? How big would a stratospheric wind turbine need to be to produce 1 MW? How big is a 1MW ground-based turbine and how much drag is on it?

Thrust load on a modern ~2.5-3MW wind turbine with a rotor diameter in the 120-130m range is on the order of half a megaNewton.

 

[russ_watters]

Thrust load on a modern ~2.5-3MW wind turbine with a rotor diameter in the 120-130m range is on the order of half a megaNewton.

I did actually google some specs and atmospheric conditions and do some calcs. I was waiting for the OP to respond with some attempt before posting what I found. The answers I got were satisfyingly...clean.

 

[256bits]

satisfyingly...clean.

made me think...
Ozone layer and stratosphere - along with the UV, depending upon how far up one expect their turbine to be placed, it should be a clean object.
On the other hand, what type of cable would not degrade under adverse condition.
see for example,
https://journals.sagepub.com/doi/abs/10.1177/0021998310381436

 

[cjl]

I did actually google some specs and atmospheric conditions and do some calcs. I was waiting for the OP to respond with some attempt before posting what I found. The answers I got were satisfyingly...clean.

Interesting. I assume you came up with a number that is pretty close to mine then?

(I didn't do any calculations - I do loads analysis and simulation on wind turbines for a living, so I'm just going off the actual numbers I know)

 

[russ_watters]

Interesting. I assume you came up with a number that is pretty close to mine then?

(I didn't do any calculations - I do loads analysis and simulation on wind turbines for a living, so I'm just going off the actual numbers I know)

Very cool!

Well, I suppose the OP isn't coming back, so...

The OP specified 25,000 lb (114,000 N), and I added 1 MW for easy math...but it was easier than I expected.

Turbines tend to be rated at 15 m/s.

At 59% efficient turbine with 25,000 lb of thrust does indeed give you 1 MW. I expect a lucky coincidence by the OP. Your 3 MW would be 342,000N by my calc, so I think we're close enough for the top of your head and back of my envelope.

The first link in my google was this:
https://en.wind-turbine-models.com/turbines/435-vergnet-gev-hp-1mw

62m diameter and if I'm reading the specs correctly, weighs 80 tons.

In the stratosphere, winds average around 45 m/s (9x the kinetic energy per unit mass) and the air is on the order of 1% as dense as at sea level.

With some minor rounding, a 1 MW turbine, weighing 80 tons, and having a diameter of 62m would produce a little less than 100 kW if lifted into the stratosphere. Just for the blimp, you'd need a spherical radius of 200m to keep it aloft.

And you'd need a turbine diameter if 200m to get 1 MW.

 

[Baluncore]

It is a pity that the high altitude winds tend to be perpendicular to the gravity vector. It must rely on a tether. How do you get the energy down the tether, DC, AC or guided microwave? Copper is too heavy, is aluminium cable needed for a conductive tether?

I believe the best lift to drag ratio for a kite is probably a three bladed gyrokite. Is anything else being considered?

What is the speed of sound in the tether? How long will it take for the tension wave to travel along the tether? With a winch on the ground, if the kite starts to descend, it will need GPS and a radio link to notify the winch operator. How elastic will the tether need to be to prevent breakage before the far end starts to respond to winch activity or a change in kite drag.

 

[trurle]

It is a pity that the high altitude winds tend to be perpendicular to the gravity vector. It must rely on a tether. How do you get the energy down the tether, DC, AC or guided microwave? Copper is too heavy, is aluminium cable needed for a conductive tether?

I believe the best lift to drag ratio for a kite is probably a three bladed gyrokite. Is anything else being considered?

What is the speed of sound in the tether? How long will it take for the tension wave to travel along the tether? With a winch on the ground, if the kite starts to descend, it will need GPS and a radio link to notify the winch operator. How elastic will the tether need to be to prevent breakage before the far end starts to respond to winch activity or a change in kite drag.

Typical high strength mechanically loaded wires are A1370 aluminum interwoven with steel. Weaving with polymer (polyester or aramide) may be meaningful if you have more than 2 km altitude. That composite have the speed of sound about 5 km/s. For long tether, you usually should not rely on its own elasticity - need to insert shock absorbers along the line periodically.
UHMWPE usually is not good for loaded tether application due creep, although in last 2 years low-creep UHMWPE also starting to appear.

 

[cjl]

Very cool!

Well, I suppose the OP isn't coming back, so...

The OP specified 25,000 lb (114,000 N), and I added 1 MW for easy math...but it was easier than I expected.

Turbines tend to be rated at 15 m/s.

At 59% efficient turbine with 25,000 lb of thrust does indeed give you 1 MW. I expect a lucky coincidence by the OP. Your 3 MW would be 342,000N by my calc, so I think we're close enough for the top of your head and back of my envelope.

The first link in my google was this:
https://en.wind-turbine-models.com/turbines/435-vergnet-gev-hp-1mw

62m diameter and if I'm reading the specs correctly, weighs 80 tons.

In the stratosphere, winds average around 45 m/s (9x the kinetic energy per unit mass) and the air is on the order of 1% as dense as at sea level.

With some minor rounding, a 1 MW turbine, weighing 80 tons, and having a diameter of 62m would produce a little less than 100 kW if lifted into the stratosphere. Just for the blimp, you'd need a spherical radius of 200m to keep it aloft.

And you'd need a turbine diameter if 200m to get 1 MW.

That makes sense. Your thrust is a bit low, but your assumptions to get there make sense. Most modern turbines run at a power coefficient (mechanical power vs kinetic energy power of incoming airflow) of around 45-50% at rated or so, and they also have an electrical efficiency around 90%. They also tend to be rated at more like 13m/s than 15, so if you factor all of those in, I suspect you'll get up from your 340kN up to the 500kN or so I quoted.

Also, I hadn't run the numbers on a stratospheric wind turbine - that having been said, are you sure your numbers are correct? It is 9x the energy per unit mass and 1% density, so you end up with around 10% of the energy per unit volume, but it looks like you forgot to account for the fact that at 45m/s, you have 3x the volumetric flow rate through the rotor plane. As a result, your 1MW example turbine should make ~300kW in the stratosphere, unless I'm missing something...

 

[russ_watters]

That makes sense. Your thrust is a bit low, but your assumptions to get there make sense. Most modern turbines run at a power coefficient (mechanical power vs kinetic energy power of incoming airflow) of around 45-50% at rated or so, and they also have an electrical efficiency around 90%. They also tend to be rated at more like 13m/s than 15, so if you factor all of those in, I suspect you'll get up from your 340kN up to the 500kN or so I quoted.

Yeah, I realized my efficiency was way too high, but was being lazy about it.

Also, I hadn't run the numbers on a stratospheric wind turbine - that having been said, are you sure your numbers are correct? It is 9x the energy per unit mass and 1% density, so you end up with around 10% of the energy per unit volume, but it looks like you forgot to account for the fact that at 45m/s, you have 3x the volumetric flow rate through the rotor plane. As a result, your 1MW example turbine should make ~300kW in the stratosphere, unless I'm missing something...

Oops, you are indeed correct. I tripped myself up using the kinetic energy relation, missing that the mass(volumetric) flow is proportional to the speed; that's the other factor of 3.

Anyway, that fortunately doesn't change the conclusion much:

I think what people are expecting when they propose this idea is that higher and more consistent wind speeds in the stratosphere result in higher energy collection. Factoring in a capacity factor around 1/3 (from EIA data), a stratospheric turbine would produce about the same amount of electricity as a ground-based turbine. So it wouldn't be worth the extra trouble of lifting it and tethering it.