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NOTICEWhen Government drawings, specifications, or other data are used for any purpose other than in connection with a definitely related Government prccurement operation, the United States Government thereby incurs no responsibility nor any obligation whatsoever; and the fact that the government may have formulated, furnished, or in any way supplied the said drawings, specifications, or other data, is not to be regarded by Implication or otherwise as in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use, or sell any patented invention that may in any way be related thereto. B ACopies of this report should not be returned unless return is required by security considerations, contractual obligations, or notice on a specific document. The overall objective of the program is to develop the tecbaolrgy to significantly reduce supersonic aircraft propulsion system noise witn minimua associated performance and weight penalties.To reach the objectives of this program a varied and comprehensive research program is bein;, carried out to

Fig. 2 Upwash interference at the plane of wing in rectangular tunnels with solid side walls of eight-to-width ratio 0.667. and (3). At the plane of the wing, x = y = z = 0, the expression may be simplified to = (sT k /2bh){Re(k) (15) yhere Be(k) = J7i»(*) = -+ + X + '} n-l L-i(2nk) = Modified Struve functionThe real and imaginary parts of the upwash interference relationship, Eq. (15), are plotted against reduced frequency for tunnels of height-to-width ratio X = 0.667 in Fig. 2. The results of the static case derived in Ref. 1 may be obtained by taking the limit k -> 0 in Eq. (15). Concluding RemarksResults are given here for incompressible flow and all frequencies; however, they may be used for low frequencies in subsonic compressible flow with a minor modification, as in Eq. (5). All results are obtained for a small-wing model on the centerline of the tunnel. The expression for a model with an off-centerline position may be derived in a similar manner. Within the assumptions of linearized theory, solutions of any wing configuration may be obtained by superposition since it may be regarded as made up of "small wings/ 7 that is, lifting elements of area. The over-all corrections to forces and moments in wind tunnels as for general wings may be calculated 7 by the utilization of the upwash interference.By examining the curves of the exact solutions given here, the validity of the approximation solution 2 in a power series of frequency up to the first order is within a rather narrow range of small values frequency, if the solution is extended to a slotted-wall tunnel.The present results for slotted-wall tunnels provide information that will assist in choosing a tunnel wall configuration. For example, the optimum slot parameter of a circular cross section is about P = 0.6 from Fig. 1. For rectangular tunnel of height-to-width rat'o of 0.667 (Fig. 2), the optimum slot parameter s in the range of 0.4

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