Division The start-of-roll directivity function Δ SOR

United Kingdom

The noise of jet aircraft — especially those equipped with lower by-pass ratio engines — exhibits a lobed radiation pattern in the rearward arc, which is characteristic of jet exhaust noise. This pattern is the more pronounced the higher the jet velocity and the lower the aircraft speed. This is of special significance for observer locations behind the start of roll, where both conditions are fulfilled. This effect is taken into account by a directivity function Δ _SOR .

The function Δ _SOR has been derived from several noise measurement campaigns using microphones adequately positioned behind and on the side of the SOR of departing jet aircraft.

Figure 2.7.r shows the relevant geometry. The azimuth angle ψ between the aircraft longitudinal axis and the vector to the observer is defined by

ψ = \arccos (\frac{q}{d_{SOR}})

(2.7.47)

The relative distance q is negative (see Figure 2.7.j) so that ψ ranges from 0° in the direction of the aircraft forward heading to 180° in the reverse direction.

The function Δ _SOR represents the variation of the overall noise emanating from the takeoff ground roll measured behind the start of roll, relatively to the overall noise from takeoff ground roll measured on the side of the SOR, at the same distance:

L_TGR(d_SOR,ψ) = L_TGR(d_SOR,90°) + Δ_SOR(d_SOR,ψ)

(2.7.48)

where L_TGR (d_SOR ,90°) is the overall takeoff ground roll noise level generated by all takeoff ground roll segments at the point distance d_SOR to the side of the SOR. At distances d_SOR less than a normalising distance d_SOR,0 , the SOR directivity function is given by

$Δ_{0}^{SOR} = 51,47 - 1,553 \times ψ + 0,015147 \times ψ^{2} - 0,000047173 \times ψ^{3}$	if 90° ≤ ψ < 148,4°	(2.7.49)
$Δ_{0}^{SOR} = 339,18 - 2,5802 \times ψ - 0,0045545 \times ψ^{2} + 0,000044193 \times ψ^{3}$	if 148,4° ≤ ψ ≤ 180°	(2.7.50)

If the distance d_SOR exceeds the normalising distance d_SOR,0 , the directivity correction is multiplied by a correction factor to account for the fact that the directivity becomes less pronounced for greater distances from the aircraft; i.e.

$Δ_{SOR} = Δ_{0}^{SOR}$	if d_SOR ≤ d_SOR,0	(2.7.51)
$Δ_{SOR} = Δ_{0}^{SOR} \times \frac{d_{SOR,0}}{d_{SOR}}$	if d_SOR > d_SOR,0	(2.7.52)

The normalising distance d_SOR,0 equals 762 m (2 500 ft).

Notes on Division 2.7.19

Footnotes

f1: NPD specifications require that the data be based on measurements of steady straight flight, not necessarily level; to create the necessary flight conditions, the test aircraft flight path can be inclined to the horizontal. However, as will be seen, inclined paths lead to computational difficulties and, when using the data for modelling, it is convenient to visualise the source paths as being both straight and level.