As first explanation see our primer.
Nonlinear vortex interaction results in near rectangular span load if lift per span unit of main wing are comparable, see [1]. Rectangular spanload is not possible with linear vortex interaction wings since due to the Munks stagger theorem (which applies to all present day classical wings including winglets) the effects of streamwise staggered winglets are not reproduced. (This is the reason, why the performance potential of multiple staggered winglet configurations is grossly underestimated not including the grid effect of such configurations, an important effect shown by the means of the deflected massflow model in paper AIAA-2004-2120).
As
shown by the extension
to LINAIR PRO with Betz grid theory, the grid effect on lift and deflected
airmass is not reproduced for any calculation which assumes application of the
Munk stagger theorem such as the linearized Prandtl-Munk model with vortex sheet
leaving in stream direction having no drag and vortex rollup neglected.
See
also the comparison chart of the elliptic spanload
versus the rectangular spanload.
For a wing grid configuration specific key conditions experimentally verified [2]
are that stagger angle must be big enough for a given angle of attack to assure
individual lift contribution based on individual deflected airmass of the wing grid blades (confirmed by lift load
calculations assuming individual vortex model of wing grid blades and tested span
efficiency)
Resulting
in increased airmass deflected by wing grid for creating set lift value.
e = (1 + L2/L * (N – 1)) * 4 / p [3]
with:
Span-efficieny
e = airmass actual wing / airmass elliptic spanload wing at identical span
L2/L
relative span wing grid to halfspan L of wing considered
N number of blades of wing grid
Summary:
The wing grid is a new aircraft wing design, which departs completely from
classical wings. Its feature is a rectangular spanload with span efficiency >
2, which means a wing design incorporating winggrid deflects for the same span
typically more than double the airmass compared to near elliptical wings. See also the ICAS96,
ICAS98 and CEAS00
paper (all in pdf format) for further explanations.
New:
Completed
analysis integrating turbomachinery theory explain the the cutoff phenomenon
of the winggrid.
[1]
If the winggrid does not attain essentially the same lift per span unit as the
main wing, we will not reach rectangular spanload. This appears to be a quite
critical condition. In a recent fullscale check at a prospective clients
aircraft, in the unchecked status, the winggrid had negative lift and the total
wing had near elliptic spanload. A seemingly minuscule correction of
2 degrees on 3 of total 5 winggrid blades switched the whole setup
successfully to rectangular spanload at a Cl-value of 1.4 and below.
[2] Experimental
verifications of rectangular spanload winggrid:
-
windtunnel tests 93/94
- fullscale Mollis 97 winggrid blade loads
- fullscale idaflieg 99 smoke trails analysis supported by Biot-Savart
calculations
[3] Updated
expression 30.10.00, this expression slightly
differs from the ones formulated earlier, however without invalidating designs
already done
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