Far-field Prediction Research Articles

Near-field far-field predictions from single-intensity-planar-scan phase retrieval

Simulations are presented which demonstrate the feasibility of far-field predictions from a single near-field intensity planar scan using a phase-retrieval algorithm with spectral propagation.

Near-field measurements on plane-polar facility

Among the geometries used for acquiring the near-fields of microwave antennas, the plane-polar geometry is the most recent. This contribution describes far-field predictions obtained on a recently built plane-polar facility. The procedure for the transformation of the near-field to the far-field uses a fast algorithm for the calculation of the radiation integral and is presented in the form of a cross correlation which is carried out using the fast Fourier transform. Predictions of the far-field patterns of two antennas are shown. A numerical algorithm for the interpolation of the near-field from the plane-polar grid to the cartesian grid is derived and the interpolated data is used to predict the far-field patterns of the two antennas. A direct result of the interpolation to a cartesian grid is the adaptability of the near-field to processing for antenna metrology, enabling the surface diagnosis of antennas under test from measured plane-polar data. A technique for phase drift compensation is presented and verified. The phase drift compensation procedure is particularly suited for the plane-polar geometry.

Propeller noise prediction

Analytic propeller noise prediction involves a sequence of computations culminating in the application of acoustic equations. This paper describes the prediction sequence currently used by NASA in its ANOPP (Aircraft Noise Prediction) program. No attempt is made here to review the state of the art of noise prediction. Some elements of this sequence represent classic results while other represent the most recent publications. The elements of the sequence are called program modules. The first group of modules analyze the propeller geometry, the aerodynamics, including both potential and boundary layer flow, the propeller performance, and the surface loading distribution. This group of modules is based entirely on aerodynamic strip theory. The next group of modules deals with the actual noise prediction, based on data from the first group. Deterministic predictions of periodic thickness and loading noise are made using Farassat's time-domain methods. Broadband noise is predicted by the semi-emipirical Schlinker-Amiet method. Nearfield predictions of fuselage surface pressures include the effects of boundary layer refraction and (for a cylinder) scattering. Farfield predictions include atmospheric and ground effects. Comparisons are made to experimental data from subsonic and transonic propellers and NASA's future directions in propeller noise technology development are indicated.

Saturn Systems Holddown Acoustic Efficiency and Normalized Acoustic Power Spectrum

Saturn systems field acoustic data are used to derive mid- and farfield prediction parameters for rocket engine noise. The data were attained during Saturn vehicle launches at the Kennedy Space Flight Center. The data base is a sorted set of acoustic data measured during the period 1961 through 1971 for Saturn system launches SA-1 through AS-509. The model assumes hemispherical radiation from a simple source located at the intersection of the longitudinal axis of each booster and the engine exit plane. The model parameters are evaluated only during vehicle holddown. The acoustic normalized power spectrum and efficiency for each system are isolated as a composite from the data using linear numerical methods. The specific definitions of each allows separation. The resulting power spectra are nondimensionalized as a function of rocket engine parameters. The nondimensional Saturn system acoustic spectrum and efficiencies are compared as a function of Strouhal number with power spectra from other systems. [This analysis has been funded in part under contract under the cognizance of the George C. Marshall Space Flight Center.]

Farfield Prediction of Time Dependent Signals

It has been previously shown [Horace G. Ferris, “Computation of Farfield Radiation Patterns by Use of a General Integral Solution to the Time Dependent Scalar Wave Equation,” J. Acoust. Soc. Amer. 41, 394–400 (1967)] that the formulation of the farfield pressure in terms of an integral formula proceeded from the time-dependent scalar wave equation and thus had no single-frequency assumption. Thus, the farfield prediction theory should be valid for broad-band, as well as single-frequency signals. Measurements made by Hughes Aircraft Company and others have demonstrated the validity of the prediction theory, as applied to single-frequency steady-state signals. It has remained unverified, however, in the realm of time-dependent broadband signals. Measurements have been made in the Hughes Test Tank driving a narrow-bandwidth transducer with white noise. The pulse shape, as measured in the farfield has been accurately reproduced from measurements made over a small surface in the nearfield of the source. No attempts were made to predict the magnitude since such a small portion of the nearfield was covered. This suggests that the theory can be applied to the prediction of broad-band signals from measurements made in the nearfield.

Farfield Prediction from Nearfield Crosspower Measurements

A series expansion method for predicting the farfield from nearfield crosspower measurements is given. The method for the special case of coherent sound fields was presented previously [J. Acoust. Soc. Amer. 44, 35(A) (1968)]. The series method is based on an expansion in spherical wavefunctions truncated to include only the number of terms equal to the number of nearfield measuring points. A distinct advantage of the method is that the nearfield measuring points need not be restricted to the usual separable surfaces. An evaluation is presented through a set of numerical examples where the predicted farfield is compared with the exact farfield from a theoretical source of partially coherent sound. It is shown that good results can be obtained for partially coherent as well as coherent sound fields. [Work sponsored by the Office of Naval Research (Acoustics Programs Branch).]

Comparison of Methods of Farfield Prediction:

All farfield prediction methods utilizing nearfield measurements on a closed surface are describable as applications of a Green's integral formula. For truncated measuring surfaces, however, the corrections that must be made to the weighting functions derived from the Green's integral formula can severely limit their usefulness. For the case of spherical and cylindrical measuring surfaces, the corrections for truncated surfaces do not appear to be necessary; but for truncated planar surfaces they are dominant. The broadband “Green's transfer” functions used in farfield prediction for spherical surfaces have been described in a previous paper [J. Acoust. Soc. Am. 39, 1222(A) (1966)]. The Green's transfer functions for a cylindrical surface have been calculated and farfield predictions made on the digital computer. They are very similar to those for the spherical surface having the same weighting and phasing, although calculated from an altogether different mathematical expression. This expression will be compared to that used by Baker (Univ. of Texas Defense Res. Lab. Acoust. Rept. 196 (15 March 1962) for single-frequency measurements on a cylindrical surface.

Computer Simulation of Spherical Nearfield Measuring Array for Farfield-Pattern Predictions

A network of linear systems whose inputs are nearfield pressures measured on the surface of a sphere and whose summed output is the desired farfield pressure has been simulated on the digital computer. The transfer functions for these linear systems were calculated from the normal derivative of the Green's function of the scalar wave equation as suggested by Ferris [J. Acoust. Soc. Am. 38, 933(A) (1965)]. These “Green's transfer” functions have a particularly satisfying physical realization. They consist of time delays plus amplitude shading. They have a linear frequency dependence and no theoretical bandwidth limitation. Patterns of an infinitesimal dipole source have been calculated, using the Green's transfer functions to determine the accuracy of their farfield predictions. Errors in this pattern were determined as functions of frequency, probe spacing, and the angle between radius vectors to the nearfield and farfield points. The reciprocal nature of the measuring system was investigated by using it as a source and calculating its ability to produce a plane wave inside the measuring surface. [Work supported by U. S. Navy Bureau of Ships.]