Input
  • Example 1 of Section 6.1
  • Example 2 of Section 6.2
  • Rectangular wing example
  • Positive wing-body angle, $\delta$, example
  • DEBUG examples
  • - Debug example
  • Set as m
  • Set as ft
Summary

ESDU 95009 presents a theoretical method, based on slender-body theory, for estimating the change in lift and aerodynamic centre position resulting from moving a wing from a centrally-mounted position to one above or below the centre line of a forebody-cylinder combination. It applies to a plane wing with sweptback leading edge, local span increasing (and then possibly constant) streamwise, and an unswept trailing edge. The body has a constant diameter circular section over the wing root chord and the wing may be set at an angle to the body centre-line.

Equations and graphs are given in the Data Item for the ratios of the lift (excluding that on the body alone) due to angle of attack and due to wing setting angle for the combination with wing off-centre to those for the combination with net wing removed and remounted centrally.

The program follows the method of ESDU 95009, with the graphical data held in digital form.

Within the program, the lift of the combination with a centrally-mounted wing is either estimated using the method of ESDU 91007 or else the slender-body value is used.

The slender-body value for the aerodynamic centre shift due to moving the wing from centrally-mounted to off-centre is added to the aerodynamic centre position for a centrally-mounted wing (obtained by use of the method of ESDU 92024).

The Data Item should be consulted for full descriptions of the parameters, the method and its derivation, and the accuracy and applicability.

General
Geometry data
Case data
Additional data required from ESDU 91007

Based upon the values entered above, a test is performed to determine whether it is sufficient to take a slender-body theory value for , or whether a better value can be obtained from the method of ESDU 91007. As described in that Data Item, this involves testing if

$\beta A (1 + \lambda) \big [ \frac{1}{\beta \textrm{cot} \Lambda_0} + 1 \big ]$ > 4

In this case

$\beta A (1 + \lambda) \big [ \frac{1}{\beta \textrm{cot} \Lambda_0} + 1 \big ]$ = {{occ.oodleCore.utils.valPrintPrecision(tba.rt.test91007, 4)}}

Values for and are thus required.

Results : Warning - the input has changed! Rerun the calculation contain errors or warnings
Save results as

Note: The user should consult ESDU 95009 for full specification and discussion of the wing-body configurations and flow conditions covered by the data used in the derivation of the method, and additional advice on the applicability.

Table 6.1
Calculation step Quantity Chordwise Station
0 1 2 3 4
1 $(x - x_0) / (x_1 - x_0)$ {{occ.oodleCore.utils.valPrintFormatted(x, 'f', 3)}}
2 $\psi^\prime = r / s^\prime (x)$ {{occ.oodleCore.utils.valPrintFormatted(x, 'f', 3)}}
3 $K_{WB}(x) = (1 + \psi^\prime)^2$ {{occ.oodleCore.utils.valPrintFormatted(x, 'f', 3)}}
4 $K_{WB}(x) (1 / \psi^\prime - 1)^2$ {{occ.oodleCore.utils.valPrintFormatted(x, 'f', 3)}}
5 $F_{WBO}(x)$ from Figure 2 {{occ.oodleCore.utils.valPrintFormatted(x, 'f', 3)}}
6 $F_{WBO}(x) K_{WB}(x) (1 / \psi^\prime - 1)^2$ {{occ.oodleCore.utils.valPrintFormatted(x, 'f', 3)}}
Rectangular wing case
Values from slender-body theory
For a non-zero wing-body setting angle, $\delta$, calculation of total lift on the wing-body combination, from Equation (3.8):
Thus, from Equation (3.8)
$(C_L)_{CO}$ = $\alpha$ + $\delta$
= {{occ.oodleCore.utils.valPrintFormatted(tba.os.dcldalphaco.value, 'p', 4)}} $\alpha$ + {{occ.oodleCore.utils.valPrintFormatted(tba.os.delta_positive.fwbolower.value, 'p', 4)}} $\times$ {{occ.oodleCore.utils.valPrintFormatted(tba.os.delta_positive.kwblower.value, 'p', 4)}} $\times$ {{occ.oodleCore.utils.valPrintFormatted(tba.ep.i.dcldalphaw.value, 'p', 4)}} $\times$ $\delta$
= {{occ.oodleCore.utils.valPrintFormatted(tba.os.dcldalphaco.value, 'p', 4)}} $\alpha$ + {{occ.oodleCore.utils.valPrintFormatted( tba.os.delta_positive.fwbolower.value * tba.os.delta_positive.kwblower.value * tba.ep.i.dcldalphaw.value, 'p', 4) }} $\delta$
where $\alpha$ and $\delta$ are in radians.
Thus, from Equation (3.8)
$(C_L)_{CO}$ = $\alpha$
= {{occ.oodleCore.utils.valPrintFormatted(tba.os.dcldalphaco.value, 'p', 4)}} $\alpha$
where $\alpha$ is in radians.
DEBUG
tba:
{{tba | json}}

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