| Topic for open discussion: Mass
Scaling Exponents
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| Feb. 19, 2021, post by Dave Santos Mass Scaling Exponent (MSE)
Markus brought in MSE in a recent paper.
This one I think- WESD - Ground-generation airborne wind energy design space exploration (copernicus.org)
Rod is right about Kite Network (KN) scaling. KiteMill can't scale. MSE too high. Networks not on NO radar. Tether mass hardly matters for giant kites or KN flying 500m high. |
| November 23, 2020, note from Markus Sommerfeld I am not an expert on soft kite design and their structural integrity. There might be an upper load limit that I am not aware of where the fabric or supporting structure fails. The approximation of a mass scaling exponent of a bit more than 2 could be a decent first assumption (need more mass to withstand the increased forces). The limit will probably be the bending moment and shear forces along the supporting structure or the tensile strength of the fabric. Other researchers at AWESCO who focus on soft kites might be a better source of information. Nov. 23, 2020, response note by Dave Santos Markus, The upper load limits of polymer fiber are in the manufacturers' data-sheets. Nothing comes close to pure polymer on a power-to-mass basis. The lightest paragliders of about 2kg handle dynamic-stall and turbulence transients of about 50kW, without damage. Kitesurfers jumping big provide a similar videogrammetric estimate of polymer power-to-mass. Parachute opening shocks provide comparable estimation as well. There is no compressive-limit bending-moment in pure tensile power kite structure. AWESCO never had power kite experts as such. These are found in the professional power kite design community. I worked and apprenticed under Dave Culp (KiteShip) the Ship Kite pioneer. North Sails makes SkySails' wings. These are our direct affiliates. Kitetplanes with high Mass Scaling Exponents and no crashworthiness are a design dead-end. This has been known for decades by power kite and classic kite experts. We knew and predicted Makani would hardly fly a few hours between total crashes, and use more power than generated. Academic research like yours is slowly but surely validating empirical power kite domain expertise. |
| Nov. 22, 2020, post by Dave Santos Re: Mass Scaling Exponents Starting from [Sommerfeld et al., 2020], an SS kite's Mass Scaling Exponent will tend close to κ = 2, as the fabric panels can maintain constant thickness, but κ >2 by progressively power-law thickened load-paths trunks with k = 3. Given
the power-law assumption, Mass Scaling Factors start low and grow with
scaling, until they become a barrier to functional viability. With
kites, this a rising minimum velocity zero-point energy "cut-in" into
high improbable wind velocities.
There
are many other higher-order complexities, positive and negative, that
tend to cancel out, like tether surface area growing less fast than its
structural volume, or how fast a given size kite kite can accelerate in
a limited-size kite window, where a larger kite might never reach its
terminal velocity. Fortunately, most probable wind velocity is the same
for a static smaller and larger kite at the same place in the wind
gradient. This is at least a neutral scaling factor. Double skinned
parafoils are filled with air at neutral buoyancy, which is neutral
weight scaling exponent, but a negative-acting inertial mass scaling
exponent.
kPower
identified an SS scaling factor in ground-handling Mothra1 (~300m2,
~100kg of cheap rope and tarps) in packed state, that dragging friction
on the bundle was considerable, but could be mitigated, yet larger
kites would be vulnerable to larger forces on thin fabric. NASA Power
Wing (NPW) research had friction issues packing larger wings for
spacecraft deceleration. Roller Reefing of large yacht sails has
progressed to sail storage in long rolled format, which mitigates
friction peaks. The outer sail margin left exposed after rolling can
also be thickened to present a more friction-resistant surface.
As noted elsewhere, Scaling
of Networked Kites is vertically limited by current FAA ceiling of
2000ft, and ultimately by the Tropopause, ~10km high, but horizontally
unlimited by "staking-out" across an anchor field with no further
mass-aloft penalty. Network unit-kites need not be the largest
possible, but small enough to be better operationally. 1000m2 and 100kg
are a good assumptions, well below the validated scale maximum for a
power kite (ie. MegaFly), and easy to calculate from as a reference
model number. We empirically expect such wings to fly in 10m/sec or
less wind velocity and rate up to 10MW in good wind, with heavier
versions even higher rated.
A
key kPower calculation is that a soft power kite beats a rigid power
wing of equivalent mass in power potential. Lower Specific Power by
Area is overcome by far greater Area. There are many ways to formulate
this. Makani rightly estimated a power kite is roughly equivalent in
power to a good rigid wing of 1/10 the area, but its easy to prove that
rigid wing mass by area is >10x of comparable soft kite mass. A
heuristic AWES law is that maximum power-to-mass is pure engineering
polymer (ie. UHMWPE) optimally configured and continuously operated at
its tensile working load. A rigid wing is mass-burdened by composite
resin, compressive structure, and ancillary components. The Mass
Scaling Exponent of an SS power kite is thus close to κ = 2, while a rigid power wing is close to κ = 3.
------------------------
Misc-
The Area Scaling Exponent is 2 (r2- radius squared radiation law). The
vertical Wind Gradient is a complexity, with common onshore LLJ
structure. A smaller kite in the LLJ sweet-spot will do better by area
than a larger kite that overlaps outside the sweet-spot. Small kites
also experience higher non-dimensional wind, and also higher
non-dimensional fabric mass when made of the same fabric weight that is
optimal for a larger size.
------------ reference -------------
This
paper re-confirms the grim scaling prospects long predicted for GoogleX
Makani M600, ultimately making less power than consumed to operate.
Other prominent AWES "Reference Models" face the same scaling barrier,
which begs the question, when will scaling limits be recognized as a
no-go engineering space (?).
Ground-generation airborne wind energy design space exploration Markus Sommerfeld 1 , Martin Dörenkämper 2 , Jochem De Schutter 3 , and Curran Crawford 1 1 Institute for Integrated Energy Systems, University of Victoria, British Columbia, Canada 2 Fraunhofer Institute for Wind Energy Systems, Oldenburg, Germany 3 Systems Control and Optimization Laboratory IMTEK, Freiburg, Germany Quote- "Aircraft
mass m and inertia J are scaled relative to the Ampyx AP2 reference
model (Malz et al., 2019; Ampyx) according to 120 simplified geometric
scaling laws relative to wing span b (see equation 1). The mass scaling
exponent κ ranges from 2.7 to 3.3. An exponent of 3 represents pure
geometric scaling, while κ = 2.7 implies positive scaling effects and
weight savings with size, while κ = 3.3 assumes negative scaling." Omissions to Previous Post [just above] partly related to Mass Scaling Exponents-
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