Scaling by size

Magnus Balloons are scale-limited by bending forces. The largest airships often broke in two, by simple wind shear, even without tethers pulling each end back. Even just bending is bad for a Magnus rotor.

There are some possibilities to lower bending forces. But the big problem is the huge power consumption. So Mothra and its variants to come have more potential. And the envisaged vertical trajectory for Magnus balloon is also very suitable for Mothra.

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How do you keep the pulley loops always in their tracks without a large secondary fairlead boom next to the Magnus rotor?

The strap used as belt should be wide enough and settled between two adhesive foams, and the tension on the tether below should maintain the strap. On the video there are no adhesive foams, so the belt slides a little.

Good Luck seeing the strap adhesive foam idea developed into practical form.

If only Magnus skin-friction itself scaled, like mega-fuzzy skin that grabs air better, like a giant tennis ball. The Magnus effect has historically only been strong enough to make sports balls curve slightly, to make games more interesting.

The strongest power-factors scale best, like highest power-to-weight.

The balloon on the video was about 1 m diameter and 1.8 m span. I experimented also a balloon of 2 m diameter and 8-10 m span with the same drill of 500 W turning the pulley. The tangential speed was about 2 times less. By the plausible equation (3) from

the power consumption should be 45 W, but the 500 W of the drill were fully used. Before I tried with my arms to turn a 2.6 m diameter and 10 m span balloon and it was difficult, for a similar low efficiency.
I believe balloons undergo air pressure which deforms it, adding drag.

Even the well shaped Omnidea’s 2.5 m diameter and 16 m span balloon consumes 400 or 500 W during rotation with a tangential speed of only 6.54 m/s, as showed by a curve (between 9’ and 10’ from the beginning of, while the cylinder on the paper consumes 3 or 4 times less, probably thanks to its more perfect cylindrical shape.

So I will not investigate more about Magnus balloons. The Sharp rotor looks to have more possibility but can be held only by the two ends. With its number curved surfaces it could resist better to bending. Tests of an inflatable rotor are needed. But it is for later.

Dave Culp found the single skin power kite to have the greatest theoretic scaling potential. For years now, I have been flying SS and standard parafoils of similar sizes and masses, and the SS kites are consistently ~2x more powerful by mass, and nicely hold their own by equivalent area.

All other AWE wings can be tested against COTS TRL9 SS kites of all sizes. Kiteship even has its original quiver of SS ship kites available for ever broader experimental AWE testing.

In classical aeronautics and aerospace, best power-to-weight has always been the most dominant design factor. It would be very unexpected if AWE is somehow not subject to shared essential wisdom.

The AWE debate will persist until rigorous testing confirms reality. May everyone have their best wings ready for fly-off.

Another double anchored kite but with tethers is on

Nice modern sea kite. See Old Forum for discussion. At KiteShip I asked Dave Culp to list all the known ways to stabilize a power kite, and “stake it out” was his top answer. That led to Arch studies at the World Kite Museum and WSKIF, where arches are specially celebrated. The Playsail is the archetypical Stone-Age spread-anchor kite. A latter example of scalable multi-anchor topological stability, Neptune with sea-kite-


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Scaling by size and Scaling in numbers rather than size, both ask a question: what is being scaling, an unity, or the kite-farm?

Assuming it is an unity. AWES could scale in a similar way as planes or current wind turbines, all elements scaling in 3D, or in a different way by the number (e.g. the number of the blades or the stacks of blades), the whole forming a well defined unity.

But in all way we don’t know what to do with a 1 km tether(s).

So it becomes a question for a kite-farm, comprising the question whether a kite-farm can be seen as an unity. Thus the question becomes similar.

As an element of response, let us rethink an AWES as a whole. It was possible to make planes or wind turbines then grow, but in the AWES field the tether length imposes to think the whole kite-farm from the beginning, at least for utility-scale.

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Scaling a single wing system by size implies it will either be
1 a massive soft wing with hard control demands or
2 a very heavy rigid wing requiring high-speed operation
both options requiring an extra long tether.

Scaling by number does not change the altitude at which you start flying your turbine.
Your initial tether length doesn’t change.
Tether drag per wing will go down as you scale by adding ring layers upwards.

I think there are some scaling laws that apply to a single kite that are kind of universal:

For a wingspan scaling factor x

  • Area scales x^2
  • Power scales x^2
  • Tether length scales x
  • Tether diameter scales x
  • Flying speed remains constant
  • The size of any path scales by x in size
  • Rotational speed is reduced by \frac{1}{x}
  • mass scales by x^y where 2 < y \le 3

One can always change the design during scaling to get around some of these, but these are some rules of thumb for scaling a single design

I’m going to disagree with some of the generalisation here…
For a wingspan scaling factor x

  • Area scales x^2
  • Power scales x^2
  • Tether length scales x
  • Tether diameter scales x (Need to double-check this (you and Storm Dunker are the tether experts) but … can tether diameter scale <x as speed will be higher, and the key is tether cross-sectional area for strength required. BTW Longer tethers have no chance of adding fairings, again an advantage in network forms. The L/D of whole net form should be considerably higher… )
  • Flying speed remains constant (Wing loading has to go up if mass scales by x^y where 2 < y \le 3 yet the wing area only scales x^2 So surely wing speed has to increase. as per unless we change to using very high lift stacked multi-foil wings)
  • The size of any path scales by x in size
  • Rotational speed is reduced by \frac{1}{x}
  • mass scales by x^y where 2 < y \le 3

EDIT - I’m wrong here about the tether diameter … see Tallaks next message for why

Rod is correct,

Tether Diameter scales less than x and Minimum Stall Speed increases with scale.

A giant power-kite confined under 2000ft FAA ceiling approaches “short-line” tether proportions with area-squared advantage in tether volume. As RolfL points out in Physics World, tether drag is a big issue with small AWES, but DaveC has long taught tether drag is not a big deal at ship-kite scale. Non-dimensional wind velocity also favors the bigger wing’s lesser tether drag factor.

Putting all secondary effekts aside, scaling wingspan will scale the tether force by x^2. Scaling tether diameter by x scales the tether cross-section-area, and thus the strength if the tether by x^2 as well.

If you keep the tether length constant, you are effectively changing the design as tether drag will be relatively smaller than kite drag. And kite will fly faster. But this would be breaking the scaling law above.

But: you could always scale wingspan without scaling tether. At one point, the kite will not fit anymore, as the wingspan and turning radius geometry will limit what can practically be done. Therefor I believe it’s more correct to consider «universal» scaling like I started out, and then say that scaling tether length by a lesser factor should be considered a design change. Also note that the «universal» scaling laws retain effective glide number of kite and tether, which is why it is possible to even state the scaling laws in the first place.

Reynolds number effects i did not put in there, nor wind gradient effects. I believe these should be considered secondary effects. Less important for a «rule of thumb» approach. Probably quite important though for a detailed design.

Wrt fairings, i would consider this a design advantage, that would most likely scale by the said rules once implemented in small scale and then scaled up

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Wing Area is not a “secondary effect” of Wing Span. With power kites like the NPW or C-kites, its the reverse, Wing Span is the secondary effect. Aspect Ratio must decline with scale for rigid wings, but soft arch kites can scale at super-high AR.

I dont think I ever said wing area is a secondary effect. Wing area is not an effect of scaling rather a physical property.

If you need to change AR I would consider that a design change in this «system».

If I were to guess what you were talking about, i would guess that the mass scaling could at some scale make mass transition from «too small to have a large impact» to «too large to operate effectively». By reducing AR one could reduce mass to scale somewhat further.

The rules apply to soft or rigid kites equally. I dont see the use of adding that to the rules of thumb for scaling.

One way to use the rules would be to make a soft and rigid kite at a reasonable scale, then scale them both to the same power, then finally consider the dimensions of both designs, scaled to the same power output


Then what are “secondary effects (to) scaling Wing Span”, if not Area by AR?

To understand me, understand the basic claim that highest-power-to-mass is the most predictive scaling advantage, and the soft power-kite has highest-power-to-mass of any AWES wing. Area, AR, tether numbers; all such are secondary factors.

You write-

“(Scaling Law) rules apply to soft or rigid kites equally.”

Not true. Rigid airframe structure suffers more in scaling under Galileo’s Square-Cube Law.

For Pierre, regarding whether one can simply extrapolate a 3D kite geometry to scale up, here is Galileo’s original graphic-


A secondary effect (in my meaning here) would be

  • better reynolds numbers at large scale
  • buildup of heat in thick tethers
  • wind gradient at altitude
  • (many more)

These are effects that would change with scale but don’t dominate the beforementiones scaling rules of thumb.

So A is neither a primary nor secondary effect of WS to you? Only conductive tethers can build up heat problematically, by scaling up. The largest pure polymer hawsers in the world stay about as cool as toy kitelines, by mechanical force super-conductance efficiency.

Note that dimensionless wind velocity within the same (FAA) airspace limit allows larger lower AR wings to have lower Re.

What is a “better” Re to you? Most aerospace engineers simply optimize to whatever Re the problem offers. The inherent Re regime of giant AWES kites is not “better” or worse, unless a kite must sweep fast just to stay up.