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- Author or Editor: George H. Fichtl x

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## Abstract

The responses of rising or falling spherical wind sensors to atmospheric wind perturbations are analyzed using Fourier transform techniques. The linearized equations of motion of a sensor that is subject to drag and gravitational body forces are developed by perturbing a sensor about an equilibrium uniform motion with wind fluctuations which have vertical variations. The wind environment and sensor velocities are decomposed with stochastic Fourier-Stieltjes integrals, and the linearized equations of motion are used to derive the response functions and phase angles of the sensor motions. The results of the analysis are used to analyze the response properties of the Jimsphere balloon wind sensor.

The transfer functions and phase angles are functions of the wind perturbation frequency Ï‰(=Îº|*w*|, Îº and *wÌ„* being the wavenumber of the perturbation and the mean rise or fall rate of the sensor) and two parameters *T* and Î± which are functions of sensor mass, apparent mass of the sensor, the mass of air displaced by the sensor, the mean ascent or descent rate of the sensor as the case may be, and the acceleration of gravity. The quantity *T* is a time constant of the system and Î± is the ratio of the apparent mass to the mass of the system. Once these parameters are specified, the response properties of the sensor are completely specified in a linear context. In general, the system becomes more responsive as *T* and Î± approach zero and unity, respectively.

As Ï‰*T* â†’ 0, the transfer functions and phase angles approach unity and zero, respectively; so that at sufficiently low frequencies, the sensor essentially measures 100% of the wind perturbation Fourier amplitudes with no phase shifts. As Ï‰*T* â†’ âˆž, the transfer functions and phase angles approach Î±^{2} and zero, respectively; so that at sufficiently large frequencies, the sensor is capable of detecting 100_{a}% of the wind perturbation Fourier amplitudes, again with no phase shifts. If apparent mass effects were not present (Î± = 0), the sensor transfer functions would approach zero as Ï‰*T*â†’âˆž. Thus, the apparent mass effects make the sensor more responsive. At Ï‰*T* = Î±^{âˆ’Â½} for the horizontal fluctuations and Ï‰*T*=2Î±^{âˆ’Â½} for the vertical velocity fluctuations, the phase angles of the sensor Fourier amplitudes take on minimum values. In general, the transfer functions associated with the horizontal sensor motions are smaller than the transfer functions associated with the vertical sensor motions in the domain 0& lt; Ï‰*T* < âˆž; thus, the sensor is more responsive to vertical than to horizontal air motions.

## Abstract

The responses of rising or falling spherical wind sensors to atmospheric wind perturbations are analyzed using Fourier transform techniques. The linearized equations of motion of a sensor that is subject to drag and gravitational body forces are developed by perturbing a sensor about an equilibrium uniform motion with wind fluctuations which have vertical variations. The wind environment and sensor velocities are decomposed with stochastic Fourier-Stieltjes integrals, and the linearized equations of motion are used to derive the response functions and phase angles of the sensor motions. The results of the analysis are used to analyze the response properties of the Jimsphere balloon wind sensor.

The transfer functions and phase angles are functions of the wind perturbation frequency Ï‰(=Îº|*w*|, Îº and *wÌ„* being the wavenumber of the perturbation and the mean rise or fall rate of the sensor) and two parameters *T* and Î± which are functions of sensor mass, apparent mass of the sensor, the mass of air displaced by the sensor, the mean ascent or descent rate of the sensor as the case may be, and the acceleration of gravity. The quantity *T* is a time constant of the system and Î± is the ratio of the apparent mass to the mass of the system. Once these parameters are specified, the response properties of the sensor are completely specified in a linear context. In general, the system becomes more responsive as *T* and Î± approach zero and unity, respectively.

As Ï‰*T* â†’ 0, the transfer functions and phase angles approach unity and zero, respectively; so that at sufficiently low frequencies, the sensor essentially measures 100% of the wind perturbation Fourier amplitudes with no phase shifts. As Ï‰*T* â†’ âˆž, the transfer functions and phase angles approach Î±^{2} and zero, respectively; so that at sufficiently large frequencies, the sensor is capable of detecting 100_{a}% of the wind perturbation Fourier amplitudes, again with no phase shifts. If apparent mass effects were not present (Î± = 0), the sensor transfer functions would approach zero as Ï‰*T*â†’âˆž. Thus, the apparent mass effects make the sensor more responsive. At Ï‰*T* = Î±^{âˆ’Â½} for the horizontal fluctuations and Ï‰*T*=2Î±^{âˆ’Â½} for the vertical velocity fluctuations, the phase angles of the sensor Fourier amplitudes take on minimum values. In general, the transfer functions associated with the horizontal sensor motions are smaller than the transfer functions associated with the vertical sensor motions in the domain 0& lt; Ï‰*T* < âˆž; thus, the sensor is more responsive to vertical than to horizontal air motions.

## Abstract

In order to properly design aerospace systems (conventional airplanes, V/STOL vehicles, space vehicles, etc.) the engineer must consider the vertical structure of the horizontal wind during the launch and landing phases of flight. One way do this is with vertical two-point wind differences (wind shear). In turbulent flows like those found near the ground, wind shear is composed a steady-state part associated with the mean wind profile and a fluctuating part produced by atmospheric turbulence. Mean wind profile theory can be used to specify the steady-state wind shear; however, the fluctuating part is a stochastic process which can only be specified statistically. This paper discusses some recent measurements of third and fourth moments of vertical differences (shears) of longitudinal velocity fluctuations obtained in unstable air at the NASA 150 m meteorological lower site at Cape Kennedy, Fla. Each set of measurements consisted of longitudinal velocity fluctuation time histories obtained at the 18, 30, 60, 90, 120 and 150 m levels, so that 15 wind-shear time histories were obtained from each set of measurements.

It appears that standardized third and forth moments *S* and *K* of wind shear are universal functions of Î”*z*/*zÌ„* and *zÌ„*/*L*
_{0}, where Î”*zÌ„* is the vertical distance between the two points over which the wind difference is calculated, *zÌ„* the height of the mid-point of Î”*z* above natural grade, and *L*
_{0} the surface Monin-Obukhov stability length. As Î”*z*/zÌ„ â†’ 2, *K* â†’ 3, *S* â†’ 0, and *S* > 0, *K* > 3 for Î”*z*/*zÌ„* < 2. Thus, it appears that the joint distribution function of the longitudinal wind fluctuations at two levels is not bivariate Gaussian and that it can only be approximated with a Gaussian distribution for sufficiently large value of Î”*z*/*zÌ„*. The kurtosis *K* appears to be independent of *zÌ„*/*L*
_{0}. However, the skewness *S* seems to experience a rather abrupt transition at *zÌ„*/*L*
_{0}âˆ¼O(âˆ’1). The implications of these and other results relative to the design and operation of aerospace vehicles are discussed.

## Abstract

In order to properly design aerospace systems (conventional airplanes, V/STOL vehicles, space vehicles, etc.) the engineer must consider the vertical structure of the horizontal wind during the launch and landing phases of flight. One way do this is with vertical two-point wind differences (wind shear). In turbulent flows like those found near the ground, wind shear is composed a steady-state part associated with the mean wind profile and a fluctuating part produced by atmospheric turbulence. Mean wind profile theory can be used to specify the steady-state wind shear; however, the fluctuating part is a stochastic process which can only be specified statistically. This paper discusses some recent measurements of third and fourth moments of vertical differences (shears) of longitudinal velocity fluctuations obtained in unstable air at the NASA 150 m meteorological lower site at Cape Kennedy, Fla. Each set of measurements consisted of longitudinal velocity fluctuation time histories obtained at the 18, 30, 60, 90, 120 and 150 m levels, so that 15 wind-shear time histories were obtained from each set of measurements.

It appears that standardized third and forth moments *S* and *K* of wind shear are universal functions of Î”*z*/*zÌ„* and *zÌ„*/*L*
_{0}, where Î”*zÌ„* is the vertical distance between the two points over which the wind difference is calculated, *zÌ„* the height of the mid-point of Î”*z* above natural grade, and *L*
_{0} the surface Monin-Obukhov stability length. As Î”*z*/zÌ„ â†’ 2, *K* â†’ 3, *S* â†’ 0, and *S* > 0, *K* > 3 for Î”*z*/*zÌ„* < 2. Thus, it appears that the joint distribution function of the longitudinal wind fluctuations at two levels is not bivariate Gaussian and that it can only be approximated with a Gaussian distribution for sufficiently large value of Î”*z*/*zÌ„*. The kurtosis *K* appears to be independent of *zÌ„*/*L*
_{0}. However, the skewness *S* seems to experience a rather abrupt transition at *zÌ„*/*L*
_{0}âˆ¼O(âˆ’1). The implications of these and other results relative to the design and operation of aerospace vehicles are discussed.

## Abstract

Recent observations of turbulence obtained at the NASA 150-m meteorological tower located at Kennedy Space Center, Fla., are presented. The wind data were obtained at the 18-, 30-, 60-, 90-, 120- and 150-m levels, while temperature data were obtained at the 3-, 18-, 60-, 120- and 150-m levels. Most of the tests were made during the daylight hours, and the duration time of each test ranged between 30â€“60 min.

A survey of the surface roughness length associated with the tower site is presented. Estimates of the roughness length were calculated with wind profile laws consistent with the Monin-Obukhov similarity hypothesis. In the case of those wind directions *Î¸* in the ranges 0Â° â‰¦ *Î¸* < 150Â°, 180Â° â‰¦ *Î¸* < 240Â°, and 300Â° â‰¦ *Î¸* < 360Â°, the roughness length is 0.23 m, while for those wind directions in the ranges 150Â° â‰¦ *Î¸* < 180Â° and 240Â° â‰¦ *Î¸* < 300Â°, the roughness length has the values 0.51 m and 0.65 m, respectively. Longitudinal turbulence spectra calculated from recent observations are also presented. It is shown that the nondimensional frequency *nz/u*, associated with the peak of the logarithmic spectrum is proportional to *z*
^{â…˜}, where *u* is the wind speed at height *s* and *n* the frequency. Based upon an analysis of the logarithmic spectrum in the inertial subrange, it is implied that the local mechanical production of turbulent energy is balanced by the local viscous dissipation at the 18-m level.

## Abstract

Recent observations of turbulence obtained at the NASA 150-m meteorological tower located at Kennedy Space Center, Fla., are presented. The wind data were obtained at the 18-, 30-, 60-, 90-, 120- and 150-m levels, while temperature data were obtained at the 3-, 18-, 60-, 120- and 150-m levels. Most of the tests were made during the daylight hours, and the duration time of each test ranged between 30â€“60 min.

A survey of the surface roughness length associated with the tower site is presented. Estimates of the roughness length were calculated with wind profile laws consistent with the Monin-Obukhov similarity hypothesis. In the case of those wind directions *Î¸* in the ranges 0Â° â‰¦ *Î¸* < 150Â°, 180Â° â‰¦ *Î¸* < 240Â°, and 300Â° â‰¦ *Î¸* < 360Â°, the roughness length is 0.23 m, while for those wind directions in the ranges 150Â° â‰¦ *Î¸* < 180Â° and 240Â° â‰¦ *Î¸* < 300Â°, the roughness length has the values 0.51 m and 0.65 m, respectively. Longitudinal turbulence spectra calculated from recent observations are also presented. It is shown that the nondimensional frequency *nz/u*, associated with the peak of the logarithmic spectrum is proportional to *z*
^{â…˜}, where *u* is the wind speed at height *s* and *n* the frequency. Based upon an analysis of the logarithmic spectrum in the inertial subrange, it is implied that the local mechanical production of turbulent energy is balanced by the local viscous dissipation at the 18-m level.

## Abstract

An engineering spectral model of turbulence is developed with horizontal wind observations obtained at the NASA 150-m meteorological tower at Cape Kennedy, Fla. Spectra, measured at six levels, are collapsed at each level with [*nS*(*n*)/*u*
_{*0}
^{2},*f*]-coordinates, where *S*(*n*) is the longitudinal or lateral spectral energy density at frequency *n*(*Hz*), *u*
_{*0} the surface friction velocity, and *f* = *nz*/*Å«*, *Å«* being the mean wind speed at height *z*. A vertical collapse of the dimensionless spectra is produced by assuming they are shape-invariant in the vertical.

An analysis of the longitudinal spectrum in the inertial subrange, at the 18-m level, implies that the local mechanical and buoyant production rates of turbulent kinetic energy are balanced by the local dissipation and energy flux divergence, respectively.

## Abstract

An engineering spectral model of turbulence is developed with horizontal wind observations obtained at the NASA 150-m meteorological tower at Cape Kennedy, Fla. Spectra, measured at six levels, are collapsed at each level with [*nS*(*n*)/*u*
_{*0}
^{2},*f*]-coordinates, where *S*(*n*) is the longitudinal or lateral spectral energy density at frequency *n*(*Hz*), *u*
_{*0} the surface friction velocity, and *f* = *nz*/*Å«*, *Å«* being the mean wind speed at height *z*. A vertical collapse of the dimensionless spectra is produced by assuming they are shape-invariant in the vertical.

An analysis of the longitudinal spectrum in the inertial subrange, at the 18-m level, implies that the local mechanical and buoyant production rates of turbulent kinetic energy are balanced by the local dissipation and energy flux divergence, respectively.

## Abstract

A first-order theory of the fluctuating lift and drag coefficients associated with the aerodynamically induced motions of rising and falling spherical wind sensors is developed. The equations of motion of a sensor are perturbed about an equilibrium state in which the buoyancy force balances the mean vertical drag force. It is shown that, to within first order in perturbation quantities, the aerodynamic lift force is confined to the horizontal, and the fluctuating drag force associated with fluctuations in the drag coefficient acts along the vertical. The perturbation equations are transformed with Fourier-Stieltjes integrals and the resulting equations lead to relationships between the power spectra of the aerodynamically induced velocity components and the spectra of the fluctuating lift and drag coefficients.

Experimental evidence shows that the aerodynamically induced motions of the Jimsphere balloon occur predominantly in the horizontal plane. This implies that the root-mean-square (rms) horizontal lift coefficient is much larger than the rms vertical drag coefficient. The aerodynamically induced motion of the Jimsphere is found to be sinusoidal in nature. The dimenionless frequency (Strouhal number) and nondimensional variance of the induced zonal and meridional velocity components are given as functions of the Reynolds number. The experimental range of the Reynolds number is 1.4 Ã— 10^{5} to 6.6 Ã— 10^{5} The ratio between the rms lift coefficient and the mean, or zero-order, drag coefficient is found to be approximately 0.36.

The theory shows that the Fourier components of the first-order fluctuating horizontal lift coefficient vector lead those of the induced horizontal velocity vector, and that the fluctuating part of the drag coefficient lags the induced vertical velocity for rising balloons and leads the induced vertical velocity in the case of falling balloons. The phase angles of the induced lift and drag associated with the characteristic frequency of oscillation of the Jimsphere are given as functions of the Reynolds number.

The rms lift coefficient of smooth 2 m ROSE balloons operating at supercritical Reynolds numbers is found to be approximately twice the value obtained from wind tunnel data. This result suggests that caution should be exercised when wind tunnel data of constrained bodies are applied to free balloons.

## Abstract

A first-order theory of the fluctuating lift and drag coefficients associated with the aerodynamically induced motions of rising and falling spherical wind sensors is developed. The equations of motion of a sensor are perturbed about an equilibrium state in which the buoyancy force balances the mean vertical drag force. It is shown that, to within first order in perturbation quantities, the aerodynamic lift force is confined to the horizontal, and the fluctuating drag force associated with fluctuations in the drag coefficient acts along the vertical. The perturbation equations are transformed with Fourier-Stieltjes integrals and the resulting equations lead to relationships between the power spectra of the aerodynamically induced velocity components and the spectra of the fluctuating lift and drag coefficients.

Experimental evidence shows that the aerodynamically induced motions of the Jimsphere balloon occur predominantly in the horizontal plane. This implies that the root-mean-square (rms) horizontal lift coefficient is much larger than the rms vertical drag coefficient. The aerodynamically induced motion of the Jimsphere is found to be sinusoidal in nature. The dimenionless frequency (Strouhal number) and nondimensional variance of the induced zonal and meridional velocity components are given as functions of the Reynolds number. The experimental range of the Reynolds number is 1.4 Ã— 10^{5} to 6.6 Ã— 10^{5} The ratio between the rms lift coefficient and the mean, or zero-order, drag coefficient is found to be approximately 0.36.

The theory shows that the Fourier components of the first-order fluctuating horizontal lift coefficient vector lead those of the induced horizontal velocity vector, and that the fluctuating part of the drag coefficient lags the induced vertical velocity for rising balloons and leads the induced vertical velocity in the case of falling balloons. The phase angles of the induced lift and drag associated with the characteristic frequency of oscillation of the Jimsphere are given as functions of the Reynolds number.

The rms lift coefficient of smooth 2 m ROSE balloons operating at supercritical Reynolds numbers is found to be approximately twice the value obtained from wind tunnel data. This result suggests that caution should be exercised when wind tunnel data of constrained bodies are applied to free balloons.

## Abstract

Television photos of smoke plumes an analyzed to estimate meridional wind shear on the space shuttle Challenger associated with the accident of Mission 51-L. Gust velocities were obtained by detailed examination of the debris trails. The shuttle exhaust trail was used to establish altitudes of significant features in the photographs. Wind data obtained from the photographs compare favorably with data obtained from a rawinsonde released 9 min after the launch of the shuttle.

## Abstract

Television photos of smoke plumes an analyzed to estimate meridional wind shear on the space shuttle Challenger associated with the accident of Mission 51-L. Gust velocities were obtained by detailed examination of the debris trails. The shuttle exhaust trail was used to establish altitudes of significant features in the photographs. Wind data obtained from the photographs compare favorably with data obtained from a rawinsonde released 9 min after the launch of the shuttle.