Scaling by size

I am pointing out the difference between m and m2. As a kite scaling expert trained by KiteShip and many others, this is a topic where I can contribute.

For example, there is currently a scaling limit on how large and massive a kite can be handled on the ground without damaging the fabric, somewhere around 1000m2 even on grass. This implies we will have to develop kite assembly mid-air to scale further.

There are many such kite scaling factors to share.

The messages from Scaling by size don’t bring any positive value to the topic Scaling by size but distort and confuse the content. Some splitting would be welcome.

All unit-scaling factors apply to “scaling by size”. It seems reasonable to include tether-scaling here or form a tether-scaling topic.

A vertical scaling limit is the 2000ft airspace ceiling defined by FAA. The horizontal limit is far larger. Lets assume in metric unit an extended horizontal zone of ~500m vertical extent.

A sweeping wing’s pattern must be contained within, so due to normal turning limits, the sweeping wing should be not much larger than 200m WS, depending on specific kite design.

A larger kite could be flown and tapped that does not sweep a full figure-eight or loop, but does Dutch Roll in a tighter higher-solidity airspace. Imagine a powerful buffalo galloping, as seen for the front, tugging PTO lines by its gait. Imagine many such beasts side-by-side, optimally filling the space (by roughly 25-50%, for Dutch Roll sweep and bypass).

Current AWES prototypes like the M600 and AP3 occupy the defined airspace, but very sparsely. It was reckoned by Makani, and agreed by kPower, that a 10x Area soft wing is a rough equivalent by power (at least at smaller scales). Soft wings helpfully turn under power on a tighter radius and can be around 100x greater in Area in the defined airspace. This owes to the severe scaling limits that apply on “kiteplane” “energy drone” classes.

One of the most critical scaling factors is that probable wind velocity remains constant in the defined airspace while the minimum flight velocity of a kiteplane grows with higher mass and wingloading.

Using the scaling laws so loosely based like «mininum flight speed scales with mass» you face the problem that we have no clue to the impact of the scaling law. We all know the world is probably like this, but did we hit the wall at 5 kg mass, or are we hitting a wall at 50 tonnes?

The answer defines whether this is a worthwhile scaling law. As it stands, if you want to convince me (and maybe others), you need to back the scaling law by some reasoning.

Much on the same note, many early AWE texts state that tether drag is less of an issue with scale. With a few simple calculations I was able to figure out that tether length scales with wingspan. Thats quite different from «solved with scale».

To get these nuances right is super important. A lesser discussion is of little interest to me at least

Tallak,

In aerospace we use the case-base range of velocities and masses from scale-model to jumbo-jet for minimum flight velocity data. These data allow us confidence that “minimum flight speed scales with mass”.

It would be “clueless” not to apply this data heuristically. From WP-

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The figure above shows «speed» and not stall speed which would be a more relevant metric to make assumptions about lowest possible production windspeed.

The stall speed of the largest aircraft in the chart, a 747, is 75 m/s. The minimum/maximum weight is 272/408 tonnes. Wingspan is 60 m.

The relation between stall speed and AWE performance more or less relates lift to mass, so though a bit convoluted, it should be relevant.

An AWE optimized wing should only weigh a fraction of a 747. Lets assume 1/30 (based on some quick calculations). Thus the stall speed could be reduced to approx 14 m/s. Even with a large tether drag, this aircraft could be suitable for AWE. So my conclusion (based on a really weak foundation) is that AWE should scale to more than 60 m wingspan, which represents an altitude of approx 2.5 km above ground on average. Which does not sound all bad to me.

Nevertheless, the chart is a good one.

(I am considering single wing single tether AWE in this matter)

I see AWE scaling as a very clear subject.

Pierre,

You seem confused when I present standard aviation scaling laws in their plainest form.

For a cool example in modern aerospace scaling science, jumbo-jet engineers discovered they could scale greater than otherwise because unit-human parameters remained constant as airframe scale increased. That was not “clear” to anyone before.

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What you are saying is not clear to me now…

The topic is about scaling by size, not directly about area. And the fact that heavy planes have to take off at a higher speed is well known and obvious.

Because unit-human body mass is not scaling up under Galilean square-cube law, the jumbo-jet can grow bigger than if unit-humans were also becoming giants. Further, as internal volume grows at a cube, lots more constant units pack in.

Scaling limits in AWE are even more complex, and are not understood clearly by many ventures, as their down-select architectures reveal.

I dont necessarily see the correlation between cruise speed and stall speed. Cruise speed depends on glide number for aircraft. Stall soeed/takeoff speed depend on maximum lift…

Generally, most efficient cruise velocity is closer to stall velocity than to max velocity. Biological and engineered flight cases tend to optimize for efficient cruise.

We could also reason from max-velocity by scale to draw the same general conclusion, as well as recognize outliers like a Peter Lynn World Record Kite or an X-15. The calculated mean curve of the flight case-base scatter-plot holds.

This discussion sparked an interest in me to figure out what decides the minimum flying speed of a kite in crosswind flight. I have defined the problem somewhat simplistically by saying that you don’t want to stall when flying at the most vertical part of a loop. (I am still thinking about single kites on a tether.)

The results that came out were quite interesting. If the combined glide number of the kite and tether is around 5.2, the stall speed of the kite flying as an aeroplane should match the minimum windspeed for using it for AWE. The minimum windspeed will increase with better glide numbers, and vice versa.

Though this also means that it’s not easy to directly compare a 747 to a AWE kite, because you need to account for tether drag. But if you have a higher glide number for your 747 and then add tether until the glide number is 5.2, the two numbers should align. That being said, my equations show that minimal windspeed may be reduced to as much as 40% below stall speed, if the glide numbers are very high. OR you could say that a glide numer of 15 relative to 5.2 allows an extra 40% mass to be used while still maintaining minimum flying speed.

Furthermore, I ended up with the following equation:

w_{min}^2 \propto \frac{m}{C_L S}

This basically means that, very approximated and with many details left out, to maintain minimum windspeed for an AWE rig, when scaling, this ratio (mass to lift) must remain constant.

I believe for this kind of AWE rig, this metric is important and useful to describe minimum usable windspeed

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The tether length should be included in the dimensions of the AWE device in the same way that mast is included in the dimensions of a ground-based wind turbine.

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Below there is an interesting example of scaling by size (from Barnard's predictions ) :


For what I remember Mothra1 is an arch of 300 m². As this kite contains several elements it can be seen also as Scaling in numbers rather than size , even as a kind of Kite Networks.

I don’t know the conditions of this test. With a wind speed of 10 m/s, the force could be quite huge, several tons when the kite accelerates by rising.

With some first changes (adding a winch and a generator) and some research (depower for recovery phase) it could work as a yoyo system.

Pierre I think you’re confusing a “kite network” with simply being too lazy to join, sew, or otherwise properly attach the tarps together to better create a solid, high-aspect-ratio wing surface of reasonable efficiency, rather than a punctuated, leaky wing full of “tip losses” every few feet.

The 50 tarps were rigged like a classic ship sail plan, and similarly effective. Not a single “sail” blew out in high wind. Modular wing sections vitally enable mega-scaling. The Megafly parafoil also comes in sections. Choked bypass flow helps with flutter-mode stability and gust resilience. The splayed wings of large birds, the multi-sail golden age of sailing, share those principles.

Dave Culp started the Blue Tarp Kite Village Power challenge. Let anyone do better, more power to them. Mothra was no lazy effort, but more work-kite sooner and cheaper than anyone else at that time, a prophetic flying machine.

The new Toyota Mothership concept closely matches Mothra aerotecture. The Mothership is emerging from US Tornado Alley, not just Japan, via OSU and Toyota’s Midwest network. Proposed final scale is beyond what any AWE player, except kPower, has diligently studied.

From the video I dont see how this kite structure could produce much power. Nor does it seems that the cloth is flying cleanly. While I applaud the effort, there is still a long way to go before arriving at something commercially useful.

I would see this akin to looking at Makani’s first 1-2 meter wingspan experiments and conpating them to the current 600 kW model. Say what you will, but there is a lot of effort that went into developing that. The Mothra it seems needs a similar development effort before one could assess if this is worthwhile.

I am going to go against what I read about some of the comments about the video.
The Mothra video shows all in few seconds: high power during rising, then depower.

The sand was used to hold the kite at the ground before launching, but in the same time it shows the force (several tons), so the potential of power by multiplying the force with the reel-out speed. As the power of a wind turbine is the torque X the angular speed, the power of a pulling kite is the force X the reel-out speed.

Then on the video we see the kite stung from his nose: it is a potential efficient depower way to study.

I remember some discussions on the old forum, with Mothra lifting turbines. But turbines are not needed. They will be cumbersome and dangerous when the set scaled and will be subject to uncontrollable aeroelastic divergence.

For this the yoyo mode is specially appropriate as during the vertical trajectory (see Magenn) it flies crosswind, certainly on a short trajectory, implying a short power phase since the kite can fly at 26.6 m/s (let us assume a wind speed of 10 m/s, and a L/D ratio of 4, and a reel-out speed of 3.3 m/s). Then the depower recovery phase by the nose could be fast and without too much expense of energy as the video suggests.

A ground installation allowing facing all winds has been documented, but I have some idea for a simpler and more robust installation as it must undergo tons of traction, thousands tons for a 85 MW 1 km span arch. After all if (as @tallakt indicates) “Makani’s first 1-2 meter wingspan experiments and conpating them to the current 600 kW model”, the first 50 m span arch could be a model for a 1 km span arch.

And a complete arch AWES matches the power/space use ratio I often invoke, and that far better than a crosswind kite like Makani.

A quick calculation (always with 10 m/s wind speed) for a 1 km span and 120 000 m² (1km X 0.12 km) arch and 1 km tethers leads to a force of 5100 tons (51 000 000 N) then 170 MW then 85 MW by taking account of the time and the expense of energy for the recovery phase, while Makani could use only one device of 5 MW, perhaps 10 MW in spite of the higher wing efficiency.

So Mothra deserves more analysis, more R&D, and a 300 m² permanent rig on a AWES test site, perhaps Establishing a Highly Windy AWES test site.