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How to evaluate an airplane’s performance and the Winggrid

Last FAQ update 03.11.1998

Assumption:
The calculations below assume that you have a wing which has essentially no taper and no twist. (a prerequisite for optimum performance of the Winggrid device). If you are considering application and its evaluation for tapered or elliptic or twisted wings, you will have to take into account a reduction of effective e_value (effective span_efficiency) roughly proportional (assuming slight twist only) to the ratio of (chord where the Winggrid will be added)/(root chord of wing).

There are three possible diagrams to compare airplane_polars:

-the lift_drag polar

Cl vs. CD

-the speed_polar
vertical speed, w, vs. horizontal speed, v, showing optimum glide_angle (the reciprocal value of the glide_number)

-the glide_number polar
showing glide_number vs. horizontal speed, v

For performance analysis, we use the latter, glide_number vs. speed.  The basic formula for the glide_number is derived from the expression:

Cl/CD, where CD is total Drag coefficient

CD = CDf + CDi, the sum of friction drag and induced drag

After some manipulations, expressing the friction drag as a multiple f of induced drag, we get from this basic expression the detailed expression for analyzing any airplane (subsonic, below drag divergence Mach-number) essentially as:

GN=P /A*b^2*e*q/(1+e*f), where

with:
A aircraft weight
b span
e span_efficiency
q dynamic head
f  ratio friction drag to induced drag (e=1 and reference q)
P constant 3.14165
F wing area
L aspect_ratio
r air density

steps of simplified analysis:

step1: derive total drag-coefficient CD, e.g., from power, P, wing area, F, and dynamic head, q, and speed, v (see, for example, specification data in Jane’s all the world aircraft)

alternate method: from wing area, F, dynamic head, q, and weight, A, derive Cl, from lift_drag polar CD

step2: derive induced drag, CDi, from A, wing area, F, dynamic head, q, e and aspect_ratio, L

step3: derive friction, CDf, from total drag coefficient, CD, and the calculated value of CDi

step4: derive ratio of friction drag, CDf, to induced drag, CDi, at dynamic head, q, used

step5: derive glide_number resulting using indicated equation

step6: calculate other glide-numbers for different values of e and/or q and other parameters to analyze effect of winggrid             and compare to, for example, changing span, etc.

typical results as illustration

Disclaimer: the table shows some typical and tentative results and if not indicated otherwise, reference to existing airplanes is generally disclaimed. Identity of data with existing products is purely accidental.

With taper = 0, and a high friction_ratio a winggrid_modification would not change much at reference (cruising ) speed, but would drastically improve low-speed characteristics and handling.
If we look at the table for light aircraft selected, a winggrid again would much improve low speed glide_numbers, e.g. allowing sailing at reduced speed and normal high speed cruise without any modifications.
For airplanes with low friction ratio in cruising conditions, a higher span_efficiency as is well known will result in better glide_numbers and less propulsion power required.
If the friction ratio is higher than about 3 to 7 at cruise conditions, higher span_efficiency will not have a big effect, it is generally not possible to improve such an airplane by reduction of induced drag alone.

For tapered wings please include reduction of effect as mentioned in assumption at description entry.

Back to winggrid

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Updated: 23 February, 1999