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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.

case | A | b | v | r | q | f (e=1) | e | glide_ number |
config |

airplane type 1 | 4500 |
7,3 |
33 |
1 |
544,5 |
0,32 |
3 |
30,9 |
winggrid |

airplane type 1 | 4500 |
7,3 |
33 |
1 |
544,5 |
0,32 |
2 |
24,69 |
winggrid |

airplane type 1 | 4500 |
7,3 |
55 |
1 |
1512,5 |
2,5 |
0,8 |
14,99 |
normal |

test airplane used | 10000 |
12 |
35 |
1 |
612,5 |
0,63 |
2 |
24,50 |
winggrid |

airplane turbo_A | 40000 |
16 |
140 |
0,6 |
5880 |
7,5 |
1 |
13,90 |
normal |

airplane turbo_B | 15000 |
16 |
60 |
0,7 |
1260 |
5 |
1 |
11,25 |
normal |

airplane type 2 | 10000 |
7,9 |
64 |
1 |
2048 |
2 |
1 |
13,37 |
normal |

airplane type 2 | 10000 |
14,3 |
30 |
1 |
450 |
0,2 |
1 |
24,07 |
span doubled |

airplane type 2 | 10000 |
7,9 |
50 |
1 |
1250 |
0,7 |
2 |
20,41 |
winggrid |

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: 12 March, 2004**