text:
\section{Introduction}

One of the major problems affecting the design of future systems for
high-resolution astronomical imaging using constellations of free-flying
collectors in space\footnote{Some examples of such systems presently under
study by NASA include the ``Stellar Imager'' (SI), the ``Terrestrial Planet
Finder - Interferometer'' (TPF-I), and the SPECS mission study for a
sub-millimeter space interferometer.} is the necessity to precisely
maintain the ``optical figure'' or surface accuracy of the equivalent aperture
for extended periods of time. On sufficiently-bright targets, this
accuracy might be achieved using signal photons from the target itself in order
to operate various control loops. Such ``adaptive'' control systems can be found,
for instance, driving deformable mirrors on filled-aperture telescopes, and
controlling delay lines on interferometers. However, in the more general (and
often more interesting) case where the target is very faint, the accuracy
requirement translates into a tight requirement on the geometry of the
optical system. In the case of a constellation of free-flying collectors in
space, the accuracy requirement on the optical figure of the instrument for
observations of faint targets becomes a requirement on
\textit{station-keeping}.

Station-keeping may be either \textit{inertial}, with respect to some
fixed reference points (such as distant quasars), or \textit{relative} to the
rest of the spacecraft in the constellation. Relative station-keeping
may be done so as to
yield a good optical figure, but still leave the whole constellation tumbling
about some arbitrary axis, so this alone is not sufficient. A significant
design effort has been expended on dealing with the ``inertial'' part of the
problem, and most approaches for measuring the overall rotation of the whole constellation involve the use of the ``rotating Sagnac interferometer''
described e.g.\ by \citet{hec02}\footnote{One design using this concept is
called the ``Kilometric Optical Gyro''.}.

Early studies \citep{jon91, esa96} of the station-keeping problem with
free-flying collectors took as a ``straw-man'' criterion that the
positional accuracy required would
be of the order of a small fraction of a wavelength, e.g.\ $\approx \lambda/50$.
This translates to $\approx 10$ nm at an optical wavelength of 500 nm.
A combination of radio and laser-ranging systems may be adequate for
station-keeping at a level of microns, but more elaborate measures will be
required in order to reach the nanometer level if such accuracy is really
required. Current thoughts for achieving
this level of accuracy in the absence of sufficient photons from the
target itself include fine control using photons from another
nearby bright ``phase reference'' star in the field of view,
or the development of major technical improvements in ranging systems.

The use of a phase reference star has been developed extensively in
order to overcome severe fluctuations in the fringe pattern caused by
atmospheric turbulence in ground-based optical and near-IR long-baseline
interferometers (see e.g.\ the summary by \cite{qui00}). Application to the
(more liesurely but analogous) problem of station-keeping in a slowly-wandering
space interferometer constellation was proposed e.g.\ in an ESA study more than
ten years ago \citep{esa96} where it was shown that the tolerances in the
directions perpendicular and parallel to the direction to the target could be
reduced by factors of order $10^{3}$ and $10^{6}$, respectively, if a
bright phase-reference star existed within an angular distance of $2'$
from the target of interest. However, the penalty here is a reduction in that
fraction of the celestial sphere which can be observed, since suitable
phase-reference stars may not be available for every target of interest. In
addition, the effective field of view of the constellation's optical system
is likely to be very small\footnote{For example, this would be the case
with certain designs for the Stellar Imager (Figure \ref{fig:SIa-sketch}).},
thereby further reducing the utility of this approach.

Compared to the ground-based atmospheric-turbulence problem, the longer time
scales expected for station-keeping drifts may make it feasible to use photons
from the target itself to stabilize the fringes. This can be done in certain
specialized applications (e.g.\ nulling interferometers such as TPF-I and
Darwin), but becomes increasingly difficult in general for faint targets. In
addition, the target should not be appreciably resolved at the interferometer
baselines in use, since the signal photon level then also decreases. But the
main science goal may well be to measure just this kind of structure in the
target; hence the need to use target photons for fringe stabilization is in
general very restrictive.

\begin{figure*}[ht!
\epsscale{1.5}
\plotone{f1.eps}
\caption{
Side view sketch of a possible design for the ``Stellar Imager'' concept
(not to scale). The collectors, which are identical 1-meter spherical mirrors
in this design, reflect the light from the target (off to the far right in the
figure in the direction indicated by the arrow ``L'') to a central hub
spacecraft. \label{fig:SIa-sketch}}
\end{figure*}

Since we can expect that current laser-ranging technology will continue to
improve\footnote{Impressive gains in precision laser metrology have recently
been achieved for use in the NASA/JPL Space Interferometry Mission (SIM).},
one can ask whether it might be possible to relax the
$\approx \lambda/50$ requirement enough to accomplish station-keeping purely
by on-board laser-ranging methods. This would permit the observation of
arbitrarily-faint targets located anywhere in the sky. Questions which arise
include: How firm is the ``$\lambda/50$'' requirement? Does the physics of
producing images from interferometer fringes justify this number? Are there
ways of extracting the desired image information, perhaps only approximately,
but which can tolerate larger errors? The search for answers to these questions
has motivated the work described in this paper.

An example of the kind of space-based imaging system considered here is shown in
Figure \ref{fig:SIa-sketch}. This is a cross-section sketch of a concept design
for the Stellar Imager, a constellation of about 30 free-flying collectors
operating at optical/UV wavelengths and distributed over an area with maximum
dimension of up to 500 meters\footnote{The Stellar Imager mission study is
described at: \\
http://hires.gsfc.nasa.gov/$\sim$si.}. These collectors direct the
radiation they receive to a central ``hub'' spacecraft for further processing
and downlink. Figure \ref{fig:SIb-sketch} shows a possible distribution of the
collectors as seen from the central hub.

\begin{figure*}[ht!
\epsscale{1.5}
\plotone{f2.eps}
\caption{
View of the ``Stellar Imager'' collector constellation from the target showing
one of the many interferometer baselines which make up this telescope
``aperture''. This view is in the transverse plane (indicated by the arrow ``T''
in Figure \ref{fig:SIa-sketch}), and B$_{ij}^{T}$ is the distance between any
two collectors projected on this plane. \label{fig:SIb-sketch}
}
\end{figure*}

The plan of this paper is as follows. First, a simple (but entirely general)
model of the imaging process for free-flying constellations of collectors is
described. The basic imaging element of these constellations is the two-element
interferometer, and the image quality is particularly sensitive to errors in the
determination (and stability) of the phase of the interferometer fringe pattern.
This model leads to the identification of two important parameters which play a
role in determining the accuracy with which the imaging can be done. The first
of these is the \textit{projected baseline length}, which is the distance
between the two collector elements of each constituent interferometer projected
on a plane perpendicular to the line of sight to the target, and the second
is the \textit{optical path difference}, which is the difference in
the distances from that perpendicular plane through each collector to the
interferometer beam combiner.

At this point it is useful to clarify the usage here of
the terms \textit{knowledge} of a parameter and its \textit{control}.
In general, precise control of baseline length is
not required; what \textit{is} required is precise knowledge of the actual
values at any time. That knowledge permits us to place a data sample at the
right location in the aperture plane before carrying out the imaging
computations. On the other hand, precise knowledge of the
optical path difference is not sufficient; we must control this quantity to
be close to zero at all times. Just how this knowledge and control will be
provided will depend on the design of the
particular constellation; those details actually do not concern us here, but
they will affect the distribution of the error budget over the various parts
of the instrument. What \textit{does} concern us here is to determine the
required accuracy on knowledge of the projected baseline length and
control of optical path difference in order to achieve a given level of
accuracy in the measurements which will go into the final synthesized image.
As we shall see, the physics of the interferometric imaging process implies
that the typical knowledge accuracy required for the projected baseline length
$B_{ij}^{T}$ turns out to depend on the angular size of the target of interest;
it is generally at a level of half a meter for typical stellar targets,
decreasing to a few centimeters only for the widest practical
fields of view. On the other hand, the control accuracy required for the
optical path difference OPD is much higher, and depends on the bandwidth of the
signal. It is at a level of half a wavelength for narrow (few \%) signal bands,
decreasing to $\approx 0.2 \lambda$ only for the broadest bandwidths expected
to be useful. This is a factor 10 less stringent than the rough value of
$\lambda/50$ used in the initial exploratory studies mentioned earlier, but exploiting this relaxed value will require post-processing of the
interferometer data in a computer.

The paper continues with a brief discussion on translating the two parameters
identified into more familiar terms such as the range and bearing from one
spacecraft to another. This discussion is sketchy and given only by
way of illustration, since the details of specific constellations are not
the main topic here. Finally, some implications of these results for the
future design of free-flyer imaging systems are discussed. Conventional
``direct'' imaging systems, which form images directly on a panoramic detector
(e.g.\ a CCD) at the focus of a (``dilute'') aperture, do not easily permit the
use of the relaxed requirements on station-keeping described here. ``Indirect''
imaging systems, where the images are formed by post-processing of
interferometer data in a computer, provide opportunities to make use of
this (and other ancillary) information, and it is likely that future
high-resolution space-based imaging systems for astronomy will be of
the indirect type.

Background material on the topics of this paper can be found in several
excellent tutorials on the application of interferometry techniques to optical
astronomy. For example, see the volume edited by \citet{law00}\footnote{Lawson
also maintains the \textit{Optical Long Baseline Interferometry News} web site
with a wealth of useful links and reference information at: \\
http://olbin.jpl.nasa.gov/papers/index.html}. Among others,
reviews of progress
and recent advances have been published by \citet{sha92} and by \citet{qui01}.

\section{The Imaging Process}

How do we make images using data collected from astronomical targets with a
constellation of free-flying collectors? The relevant physics is described
mathematically in terms of the \textit{mutual coherence function} of the
wavefront, a quantity which can be measured with an interferometer, and the
\textit{Van Cittert-Zernike theorem}, which relates this mutual coherence
function to the object on the sky (i.e.\ the target brightness distribution)
by a Fourier transform. There are numerous textbooks on this topic, see e.g.\
\cite{bw75, hec02}. The result relevant for now is that, whether
the imaging system is ``direct'', where an image is instantaneously formed on a
2-dimensional detector (e.g.\ a dilute-aperture imager), or ``indirect'', where
an image is formed by post-processing in a computer (e.g.\ an array of Michelson
interferometers), the image is built up by summing \textit{fringe patterns}
formed by the interference of light gathered from all pairs (\textit{i,j}) of
collector elements in the constellation. One such pair, connected as a
Michelson interferometer, is sketched in Figure \ref{fig:interf-sketch}.

\begin{figure*}[ht!
\epsscale{1.5}
\plotone{f3.eps}
\caption{The basic geometry of an interferometer. Two collectors $i$ and $j$
sample the wavefront from a very distant target at two points separated by
$B_{ij}^T = B_{ij} \cos \theta$ meters. The two samples are correlated
in the beam
combiner after experiencing relative path delays of
$B_{ij} \sin \theta + d_{i}$ and $d_{j}$, respectively. The beam combiner
calculates the fringe parameters, e.g.\ by scanning $\delta = d_{j} - d_{i}$
over one or two fringe periods, sampling, and fitting the pattern.
\label{fig:interf-sketch}}
\end{figure*}

At any given wavelength $\lambda$, the interferometer fringe pattern has the
form (e.g.\ \citet{bw75}, Chapter 7):
\begin{equation} \label{eqn:narrowband-fringe}
P_{ij} = P_{0} [ 1 + A \cos(2 \pi k \Delta)],
\end{equation}
\noindent where $P_{0}$ is the total signal (photons, Joules, etc.)
collected by  the two elements, $k = 1/\lambda$, $A$ is the
\textit{fringe amplitude}, ($0 \leq A \leq 1$),
and $\Delta$
is the \textit{optical path difference} (often designated as OPD) composed of:
\begin{equation} \label{eqn:OPD}
\Delta = B_{ij} \sin\theta + d_{i} - d_{j}.
\end{equation}
\noindent $\Delta$ is the difference in total path (meters) from the wavefront
plane through the two ``arms'' to the beam combiner, consisting of
$B_{ij} \sin \theta + d_{i}$ on the left side of Figure
\ref{fig:interf-sketch}, and $d_{j}$ on the right. The angle $\theta$ (in
radians, often assumed small so that $\sin \theta \approx \theta$) is measured
in the plane containing the interferometer baseline\footnote{This direction is
in fact on the surface of a cone with half-opening angle of
$(\pi/2) - \theta$ and axis coincident with the
baseline $B_{ij}$. The ``ideal'' interferometer has a constant response on the
surface of this cone, and the field of view must be further restricted
e.g.\ by adding an aperture stop into the optical system.}. As we shall see
momentarily when we consider detection systems with finite bandwidth, it is
important to keep $\Delta \approx 0$, so if $\theta \approx 0$ we shall need to
have $d_{i} \approx d_{j}$. This can be achieved by bouncing the light around,
in space or in a delay line, before it enters the beam combiner. For instance,
if the constellation is deployed on a parabolic surface and the beam combiner is
located at the focus of this parabola, then the delays for each collector are
``automatically'' adjusted to be (nearly) equal. This particular geometry is
called a ``dilute aperture'' since it resembles a conventional reflecting
optical telescope with most of the collecting area removed. But this particular
geometry is a special case and is not a requirement; the only requirement is
that the optical paths somehow be kept nearly equal. We also define the
\textit{fringe period} measured on the sky as $\lambda/B_{ij}^{T}$ radians.
Note that the fringe period \textit{increases} as the projected baseline
decreases with increasing $\theta$. Note also that a typical system at optical
wavelengths may have $B_{ij}^{T} / \lambda \approx 1 \times 10^{9}$ and
$\theta \approx 3 - 100 \times 10^{-10}$ rads, or $\approx 60 - 2000\: \mu$as.

It is convenient to simplify the way we write the fringe pattern by defining
the quantities $\phi_T = k B_{ij} \sin \theta$ and $\phi_I = k (d_j - d_i)$,
both in units of ``turns'', so that Equation \ref{eqn:narrowband-fringe} becomes:
\begin{equation} \label{eqn:narrowband-fringe-2}
P_{ij} = P_{0} \{ 1 + A \cos[2 \pi ( \phi_T - \phi_I )]\},
\end{equation}
where $\phi_T$ is called the \textit{fringe phase} and depends on the location
of the target on the sky, and $\phi_I$ is the \textit{instrument phase},
which can be controlled by altering the internal delay difference $d_j - d_i$.
The elemental narrow-band fringe pattern of
Equation \ref{eqn:narrowband-fringe-2} is sketched as a function of instrument
phase in the top panel of Figure \ref{fig:transverse}. Note that the structure
of the fringes can be determined by scanning the instrument phase $\phi_I$ over
one or two turns and fitting the resultant fringe pattern to
Equation \ref{eqn:narrowband-fringe-2}, thereby obtaining the total power, the
fringe amplitude, and the fringe phase. This form of the equation also makes it
clear that errors in the instrument phase $\phi_I$, such as those arising from
station-keeping errors, directly masquerade as changes to the measured value
of fringe phase $\phi_T$, and therefore to errors in the measured position
$\theta$ of the target. Finally, Figure \ref{fig:transverse}
also makes it clear that the position of the target in the field of view
is obtained by \textit{counting fringes} (and fractions thereof) from a
reference point, for example the direction where $\phi_I = 0$.

\begin{figure*}[ht!
\epsscale{1.5}
\plotone{f4.eps}
\caption{\textit{Top panel:} Fringe pattern $P_{ij}$ from
Equation \ref{eqn:narrowband-fringe-2} for baseline $B$ as a function of
fringe phase $\phi_T$ in ``turns'' (see text). The instrument phase is assumed
to be at $\phi_I = 0$. \textit{Bottom panel:} Fringe pattern for a baseline
which is in reality 5\% larger. Notice that the error grows with angular
distance from the point where $\phi_I = 0$, reaching $\approx 0.15$ fringes
($54^{\circ} \approx 1$ rad) at the edge of this small 3-fringe field. The
y-axis is in units of the signal strength obtained by a single collector.
\label{fig:transverse}}
\end{figure*}

The discussion so far has assumed that the interferometer is sensitive to only
one wavelength, i.e.\ that the bandwidth of the detection system is infinitely
narrow. The fringe pattern for a finite bandwidth detection system is the
weighted (vector) sum of the fringe patterns at all constituent wavelengths,
with amplitudes specified by the product of the source spectrum and the
instrument response at each wavelength\footnote{This expression can be written
as a Fourier Transform.}. A simple but illustrative case which is easy to
calculate is for a rectangular bandpass of central wavelength $\lambda_{0}$ and
width $\delta \lambda$, and a target spectrum that is flat over this wavelength
range. In this case the resulting fringe pattern is:
\begin{equation} \label{eqn:broadband-fringe}
P_{ij} = P_{0} [ 1 + \frac{\sin(\pi \Delta / L_{c})}{\pi \Delta
/ L_{c}} \times A \cos(2 \pi k_{0} \Delta) ],
\end{equation}
\noindent where the symbols not already defined
in the previous two equations are
$k_{0} = 1/\lambda_{0}$, and $L_{c} = \lambda_{0}^{2}/\delta \lambda$. This
latter quantity is called the \textit{coherence length} for the light beam, a
concept which arises as follows (\cite{bw75}, Ch.\ VII; \cite{hec02}, Ch.\ 7):
For a finite detector bandwidth of
$\delta \nu$ hertz, the signal in free space is a compact packet of many
interfering waves with a coherence time of $\tau = 1 / \delta \nu$ seconds.
Expressing the bandwidth in terms of wavelength, we have
$\delta \nu = -(c/\lambda_{0}^{2}) \times \delta \lambda$, so the coherence
time $\tau = (-1/c) \times (\lambda_{0}^{2} / \delta \lambda)$,
and $c \, \tau$ is a scale size of the wave packet called the coherence length,
$L_{c} = c \, \tau = \lambda_{0}^{2} / \delta \lambda$. The lower panel of
Figure \ref{fig:bandwidth} shows a sketch of this situation for
$\delta \lambda / \lambda_{0} = 0.2$. Note that, within a few fringes of the
central peak, the finite-bandwidth fringe in
the lower panel shows the same periodicity (and positioning, or fringe phase) as
the single-wavelength case in the upper panel. This means that the relative
placement of different components of the reconstructed target brightness
distribution will be correct, but their amplitudes may be wrong. Perhaps even
more serious, the signal-to-noise ratio of the amplitude measurement will be
worse.

We are now in a position to begin the discussion on the accuracy with which the
relative positions of the collectors need to be known. For completeness, note
that we are here focussing only on that part of the error budget which arises
because of errors in the station-keeping. A full discussion of all error sources
and their various contributions is, of course, dependent on the design details
of each specific constellation.

\section{Two Requirements}

Inspection of Equations \ref{eqn:narrowband-fringe}, \ref{eqn:OPD}, and
\ref{eqn:broadband-fringe} above makes it clear that, in order to apply these
equations to real data, there are two parameters which depend on station-keeping
and which are important for each interferometer in the constellation:
the \textit {length of the projected baseline $B_{ij}^{T}$}, and the
\textit{optical path difference} $\Delta$ at the beam combiner. The accuracy
requirements on these  two parameters are presented below first by stating the
result, then providing  the derivation, and finally discussing some of the
implications.

\subsection{Baseline}
\label{subsec:baseline}

\textit{The fractional accuracy $\delta B_{ij}^{T} / B_{ij}^{T}$ with which the
projected distance between any i,j collector pair in the transverse plane must
be known is:}
\begin{equation} \label{eqn:baseline-error}
\delta B / B \lesssim 1 / (N_{f} \, Q_{T}).
\end{equation}
\noindent where $N_{f}$ is the number of fringes in the angle $\rho$,
$\rho$ is the angular radius of the field of view containing the object being
imaged, and $Q_{T}$ is the ``transverse quality factor'' expressing the
accuracy $\lambda/Q_{T}$ with which the ``optical figure'' of the imaging
system is to be held. The super- and subscripts of $B$ have been dropped for
convenience.

\subsubsection{Demonstration:}

The fringe pattern for an elemental interferometer expands and contracts about
the field center as B decreases or increases owing to station-keeping errors,
and for a given (but in reality unknown) baseline error of $\delta B$ the
resulting fringe phase error grows with angular distance from the center of the
field. The situation for the narrow-band case is sketched in Figure
\ref{fig:transverse}.

Without loss of generality we can take the center of the fringe pattern to be
the centroid of the target brightness distribution at the operating wavelength
$\lambda$. Let $\rho$ be the angular radius (in radians) of a circle on the sky
which is just large enough to include all the emission from the target. The
number $N_{f}$ of fringes in $\rho$ is $N_{f} = \rho/(\lambda/B)$. This number
changes with small changes in the baseline length according to
$\delta N_{f} = \rho \, \delta B / \lambda$. Substituting for $\rho$ from the
initial expression for $N_{f}$ results in
$\delta N_{f} = N_{f} \times \delta B / B$. If we require that the optical
quality of the signal provided by this interferometer be better than a fraction
$1/Q_{T}$ of a wavelength, then we must have $\delta N_{f} \lesssim 1/Q_{T}$.
From this we derive $\delta B / B \lesssim 1 / (N_{f} \, Q_{T})$, which proves
the result.

\subsubsection{Discussion:}

As an example, suppose the source is a distant star and the instrument is
intended to provide 30 independent resolution elements across the stellar
diameter. Each resolution element is of angular size $\lambda / B_{max}$
radians, where $B_{max}$ is the longest (projected) baseline
in the constellation.
Suppose further that it can be safely assumed there is no signal outside a
larger circle of some given angular radius, say
$\rho = 20 \times \lambda / B_{max}$ radians on the sky measured from the
center of the star.  For this example, $N_{f} \approx 20$. If we demand an
``optical quality'' of, say, $\lambda/50$ in our imaging instrument, then
$Q_{T} = 50$ and $\delta B / B \lesssim 1/1000$. For a maximum baseline of
$B = 500$ meters, the largest \textit{unknown} $\delta B$ we can tolerate is
$\approx 0.5$ m. Note that since $N_{f} \propto B$ for a given source
size and operating wavelength, $\delta B $ is actually independent of $B$,
so \textit{the required accuracy in this example is the same for every baseline
in the constellation}. However, the stringency of the requirement grows with the
size of the target field of view in the sky. For instance, for a supergiant star
the desired FOV could be a factor of 10 larger than the example calculated
above, and the required tolerance on any baseline would be $\approx 5$ cm. But
now such a constellation would provide 300 independent resolution elements
across the star. If the science goals permit, it may be more prudent to
``shrink'' the overall extent of the constellation by a factor 10
in order to return to the scale of the
initial example and relax the station-keeping requirements accordingly.

It is interesting to ask what the limit on $\delta B / B$ might be for very
large fields of view. For instance, for a Michelson radio interferometer with
a single ``feed horn'' at the focus of each collector, the
largest field of view will be limited by the diffraction pattern of the
individual collector elements. This field has an angular radius
$\approx \lambda / a$ where $a$ is the diameter of a collector element. In
this extreme case, $N_{f} \approx B/a$, so the maximum tolerable error is:
\begin{equation} \label{eqn:maxerror}
\delta B / B \lesssim 1 / (N_{f} \, Q_{T}) \approx a / (B \, Q_{T}) ;
\end{equation}
\noindent i.e., $\delta B \lesssim a / Q_{T}$, which depends only on the size
of the elements in the constellation. If a typical collector is one meter in
diameter and $Q_{T} = 50$, the required knowledge accuracy is $\approx 2$ cm.
The situation gets more demanding if a wide field
beam combiner is used, such as an optical Michelson interferometer with
detector pixels that are larger than the collector diffraction pattern,
or with many independent pixels in the detection system\footnote{Dilute
aperture ``Fizeau'' designs are not as optimum in signal-to-noise as are
the Michelson designs, and will not be discussed here any further.}.

To conclude this section, note that changes in operating wavelength have
similar effects on the array reponse to those discussed above and can
be modelled in the same way. One particularly deleterious effect of this is
that the point spread function of a system with a finite spectral resolution
will vary over the field of view, becoming radially elongated at large angular
distances. Such effects were first analysed in detail by radio astronomers
modeling the reponse of ground-based radio synthesis imaging arrays (see e.g.\
\citet{tho94}).

\subsection{Optical Path Difference}
\label{subsec:OPD}

\textit{The accuracy $\delta \Delta$ with which the optical path difference
must be controlled to zero is:}
\begin{equation} \label{eqn:OPD-error}
\delta \Delta / \lambda_{0} \lesssim (1 / Q_{OPD}) \times (\lambda_{0} / \delta \lambda).
\end{equation}
\noindent where $\delta \lambda / \lambda_{0}$ is the fractional bandwidth of
the signal and $Q_{OPD}$ is the ``OPD quality factor'', by analogy to the
$Q_{T}$ factor defined earlier. This requirement can also be written as
$\delta \Delta \lesssim L_{c} / Q_{OPD}$, where $L_{c}$ is the coherence length
defined following Equation \ref{eqn:broadband-fringe}.

\subsubsection{Demonstration:}

Some clarification is needed first, since the real problem here may not be
entirely obvious. It is clear from Equation \ref{eqn:narrowband-fringe} that
errors of $\delta \Delta / \lambda$ directly translate to a fringe error of
$G \, \delta \Delta / \lambda$ where $G$ is a geometry-dependent factor of
order unity depending on the specific geometry of the constellation\footnote
{For example, $G \approx 2$ for a classical (Fizeau) imaging system.}.
However, in this case it is not an expansion or contraction of the fringe
pattern about the
field center, but a gross translation of the entire fringe pattern in a
direction parallel to that of the baseline projection on the field of view. At
first sight this is a serious problem, since it appears to require holding the
collector positions to a tiny fraction of the wavelength. However, since
\textit{it is the whole fringe pattern that moved} and not the relative
separation between two points in the field of view, the angular distance
\textit{measured in fringes} between the center and the edge of the field
remains the same. In other words, the \textit{relative} fringe phase is
actually not sensitive to this shift! Figure \ref{fig:longitudinal} shows
a sketch of the situation.

\begin{figure*}[ht!
\epsscale{1.5}
\plotone{f5.eps}
\caption{\textit{Top panel:} Narrow-band fringe pattern from Figure
\ref{fig:transverse}.
\textit{Bottom panel:} Narrow-band fringe pattern shifted by a phase error of
$\delta \phi = 1$ rad, caused e.g.\ by an OPD error of
$\delta \Delta \approx \lambda / 6$. \label{fig:longitudinal}}
\end{figure*}

If we can design our system and/or (post-) process the data in order to use
this ``relative'' phase insead of an ``absolute'' phase, we would be entirely insensitive to OPD errors, although we would lose the ability to measure the
target position in an absolute sense. Except for accurate wide-angle
astrometry, no other applications in astrophysics require such absolute
position information. The real problem comes about because of a loss of fringe
amplitude at large non-zero values of the OPD owing to the finite bandwidth of
the detection
system. Only if the bandwidth is infinitely narrow will the fringe pattern
amplitude remain independent of the OPD error $\delta \Delta$ as shown
e.g.\ in the upper panel of Figure \ref{fig:bandwidth}; the lower panel of
this figure shows a ``real'' fringe pattern for a finite (20\%) bandwidth
following Equation \ref{eqn:broadband-fringe}. It is clear that, as the OPD
error grows, so does the error in the measurement of the fringe amplitude. The
scale size of the fringe pattern envelope is characterized by the coherence
length $L_{c}$ as shown in Equation \ref{eqn:broadband-fringe}. If we can keep
the OPD error $\delta \Delta$ to some fraction $1/Q_{OPD}$ of the coherence
length $L_{c}$, then this amplitude error can be minimized and the measurement
of fringe amplitude and fringe phase can be made subject only to photon noise
in the time scale of the drift in the station position. This requirement
becomes $\delta \Delta \lesssim (1/Q_{OPD}) \times L_{c}$ or
$\delta \Delta / \lambda_{0} \lesssim (1/Q_{OPD}) \times (\lambda_{0} / \delta \lambda)$, which proves the result.

\begin{figure*}[ht!
\epsscale{1.5}
\plotone{f6.eps}
\caption{\textbf{Top panel:} Fringe pattern as a function of OPD error
(in wavelengths) for a very narrow-band signal. \textbf{Bottom panel:}
The same fringe pattern
for a square bandpass of 20\%. Note how the fringes disappear beyond
$N_{f} \approx 5$. \label{fig:bandwidth}}
\end{figure*}

\subsubsection{Discussion:}

As an example, for $Q_{OPD} = 50$ and a bandwidth of a few \%, say
$\lambda_{0} / \delta \lambda \approx 30$, the control requirement on
$\delta \Delta$ is $0.6 \, \lambda$. This requirement will still be
difficult to achieve at optical wavelengths, but now
there is a better chance that on-board laser ranging
systems may eventually provide adequate position knowledge without the use of
signal photons, thereby allowing long integrations on faint sources. Bandwidths
in excess of $\approx 10\%$ in a single detector channel are not likely to be
used since the spectral dependence of the fringe pattern is often an important
diagnostic for the on-board fringe detection algorithms. This means that the
worst case for the control accuracy of the OPD (which is
essentially the station-keeping requirement, as we shall see below) is
$\approx 0.2 \, \lambda_{0}$, still a factor of 10 less stringent than the
early estimates of $0.02 \, \lambda_{0}$ mentioned in the introduction to
this paper.

Now that the two major physical quantities have been identified, and their
accuracy requirements estimated, we can consider how to apply these criteria to real cases of specific mission concepts.

\section{Applications to Specific Mission Concepts}

The previous section has identified the two physical parameters $B$ and
$\Delta$ which characterize the constituent fringe patterns that go into
building an image from data obtained with a constellation of free-flying
collectors. In order to take the next step of translating the general knowledge
requirements on $\delta B$ and $\delta \Delta$ into nanometers and microradians
for a specific mission concept, we need to distinguish two cases depending on
the brightness of the targets to be observed.

\subsection{Bright Targets}

If enough photons will be available to operate a servo loop to keep the optical
path difference $\Delta \approx 0$ to within some fraction of the coherence
length $L_{c}$, then the control requirement on $\delta \Delta$ need not
translate into a station-keeping requirement, but rather into a requirement on
the total stroke and accuracy of the on-board delay line. In this case we are
left only with the knowledge requirement on the projected baseline length which
depends on the size of the target field of view, as stated in Equation
\ref{eqn:baseline-error}. The requirement on the accuracy in the range from one
spacecraft to another is of order half a meter. This still permits imaging of
the stellar surface with a relative resolution of about 30. An error in the
bearing of the second spacecraft with respect to the first in the interferometer
pair also appears as an error in the projected baseline, but this component will
be less significant; from the geometry of the interferometer in Figure
\ref{fig:interf-sketch} it is easy to show that an error of $\delta \alpha$
in the bearing translates into a fractional projected baseline error of
$\delta B / B \approx (\delta \alpha)^{2} / 2$. For the example taken in
\S \ref{subsec:baseline}, $\delta B / B \lesssim 1/1000$, so the
requirement on the bearing is 0.1 rad $\approx 1^{\circ}$ independent of B.

\subsection{Faint Targets}

If we want to observe faint (or partially resolved) targets which do not
provide enough photons to properly operate a control loop on the optical
path difference, then Equation \ref{eqn:OPD-error} drives the station-keeping
requirement. Errors in
station-keeping map into errors in $\Delta$ in a manner dependent on the
specific constellation geometry. For instance, for a design where the beam combiner lies between the two collectors (as in the TPF-I concept),
a station-keeping error of $\delta B$ in the baseline length
will produce a delay error of $\delta \Delta = \delta B$, and we have seen from
the demonstration following Equation \ref{eqn:OPD-error} that such errors need
to be kept smaller than some fraction $1/Q_{OPD}$ of the coherence length.
If laser ranging is available and capable of measuring the baseline
length to sufficient precision, then that information could be fed to an
on-board delay line in the target signal path to correct for baseline
length errors. This would turn the requirement on $\delta B$ from a
\textit{control} requirement
into a \textit{knowledge} requirement\footnote{However, the
required \textit{precision} on that knowledge remains
a fraction $1/Q_{OPD}$ of the target signal coherence length.}.

Bearing errors $\delta \alpha$ also directly translate into delay errors; for
the SI concept of Figure \ref{fig:SIa-sketch} this is
$\delta \Delta \approx B \delta \alpha$, so the knowledge of bearing of the
second spacecraft with respect to the first is
$\delta \alpha \lesssim L_{c}/(B Q_{OPD})$ which for sample values used in the
discussion in \S\ref{subsec:OPD} becomes
$\delta \alpha \lesssim 0.6 \, \lambda/B$ rads or
$\approx 0.1$ milli-arcseconds for
$B = 500$ m and $\lambda = 500$ nm. This will be a difficult
requirement to meet if the collectors in the constellation are all more-or-less
in a plane. Placing an additional ``metrology'' spacecraft some distance from
this plane (e.g.\ in the ``Hub'' spacecraft for the SI design of
Figure \ref{fig:SIa-sketch}) would
alleviate the requirement by converting the inter-collector bearing measurement
for station-keeping errors in the direction to the target (the ``L'' direction
in Figure \ref{fig:SIa-sketch}) to a range measurement (with the usual required
accuracy of order $L_{c}/Q_{OPD}$) from a collector to the metrology
spacecraft\footnote{Note that the problem remains of rendering the
station-keeping \textit{inertial}, in the sense described in the Introduction
to this paper. The presence of a ``hub'' spacecraft may present an
opportunity to address that problem as well.}.

\section{Indirect Imaging}

In order to take advantage of the relaxed control requirement on the optical
path difference described in Equation \ref{eqn:OPD-error}, we must find a method
of turning the recorded fringe amplitudes and (slowly-drifting) phases into an
image in such a way as to be insensitive to shifts of the whole fringe pattern
owing to small OPD errors. There are several related ``post-processing''
techniques
which could be used for this. For instance, if the field of view contains a
bright star besides the target of interest, fringe phases could be
``referenced'' to this star. Another approach (first used at radio wavelengths)
is to reference phases to a bright spectral line feature.

One quite general approach to this ``unstable-phase'' imaging problem which has
been used with success for $\approx 40$ years in the radio astronomy community
uses the concept of ``closure phase''. Almost 50 years ago, \citet{jen58}
presented a technique for measuring relative fringe phase which used three
radio-linked collectors coupled as three interferometers operating at a
wavelength of 2.4 meters over baselines up to $\approx 10$ km. Owing to a
variety of instrumental problems related to the amplifiers and local oscillator
electronics available at the time, the fringe phase between any two collectors
was unstable and could normally not be measured; the source structure
information had to be derived from the (squared) fringe amplitudes alone
(a familiar situation in present-day ground-based optical interferometry).
Jennison showed that, if the three observed fringe phases were summed, the
resultant combined phase was insensitive to equipment instabilities. With this
approach, \cite{jen59} showed that the brightness
distribution of the radio source Cygnus A, which until then was only known to be
elongated, actually consisted of two separated sources of nearly equal
brightness straddling a peculiar optical object tentatively identified at the
time with two galaxies in collision. This was the first observation to reveal
the double-lobed structure of a powerful radio galaxy.

Applications of this method to circumvent atmospheric phase instabilities in
optical interferometry were described by \citet{jen61} and, apparently
independently, by \citet{rog68}. The first use of the term ``closure phase''
seems to be in the paper by \citet{rog74} describing an application
at radio wavelengths using very stable and accurate, but independent, reference
oscillators at the three stations in a so-called ``very-long-baseline''
interferometer array. Since that time, closure phase has been used extensively
at radio, IR, and optical wavelengths, and there are many papers describing the
subject, its virtues, and its limitations\footnote{For newcomers, the lectures
presented at the \textit{Michelson Summer School}
by John Monnier and David Buscher
in 2001, and by Peter Tuthill in 2003 are good sources; see
http://msc.caltech.edu/school/2003 and links there.}. \citet{mon03}
gives a review of optical interferometry in astronomy which includes a
discussion of closure phase, and also points out the intimate relationship
between it and the \textit{complex bispectrum}, a quantity constructed
in processing optical speckle interferometry data\footnote{\citet{cor87}
specifically (and elegantly) addresses the relationship between speckle
masking and phase closure.}. For the type of
collector constellations discussed in this paper, the phase of the complex
bispectrum is precisely the closure phase, and by (vector) averaging the
complex bispectrum the closure phases can be obtained in principle for
arbitrarily faint targets. One important point to make here is that use of such techniques requires that the fringe signals from each pair of collectors
be separable one from another, such that the individual interferometer fringe
phases can be uniquely assigned to the appropriate pair of collectors\footnote
{Note there is no requirement here that the set of baselines available in the
constellation be ``non-redundant'', although that may be useful for other
reasons.}. This leads in turn to requirements on the design of the optics at
the location where the collector beams are brought together to interfere.

\section{Conclusions}

The requirements on station-keeping for constellations of free-flying
collectors coupled as (future) imaging arrays in space for astrophysics
applications have been discussed. The typical \textit{knowledge} accuracy
required on the projected baseline of the instrument depends on the angular
size of the targets of interest; it is generally at a level of half a meter
for typical stellar targets, becoming of order a few centimeters
only for the widest attainable fields of view. The typical \textit
{control} accuracy required on the optical path difference depends on the
wavelength and the bandwidth of the signal, and is at a level of half a
wavelength for narrow (few \%) signal bands, becoming $\approx 0.2 \, \lambda$
for the broadest bandwidths expected to be useful.
If the fringe detection system is able to use signal photons or
photons from a nearby reference star, then the most stringent requirement on
station-keeping is that on the baselines, as described in
\S\ref{subsec:baseline}. If observations on faint targets are
required, and fringe tracking is ``blind'', then the most stringent requirement
on station-keeping is that on the optical path difference described
in \S\ref{subsec:OPD}. If on-board laser metrology is available and can
provide knowledge of the internal OPD to a fraction of the target signal
coherence length, then active fringe tracking could compensate for
station-keeping errors, even for faint sources.

In any case, the requirements are less severe than assumed in the early
studies of the problem.
The significance of this result is that, at this relaxed level of accuracy, it
may be possible to provide the necessary knowledge of array geometry without
the use of signal photons, thereby allowing observations of arbitrarily-faint
targets.

Such constellations of free-flyers will produce images using various
computer-based image reconstruction techniques which relax the
level of accuracy required on the fringe phase stability of each component
interferometer. ``Closure-phase'' imaging is one such technique which
has been very successfully applied in ground-based radio and optical
astronomy in order to surmount instabilities owing to equipment and to the
atmosphere. This technique appears to be directly applicable to space imaging
arrays, where station-keeping drifts play the same role as atmospheric and
equipment instabilities. More detailed modeling of anticipated station-keeping
errors and their effects on synthetic images is needed. For instance, there is
at present little justification for the values ``$Q_{OPD} = Q_{T} \approx 50$''
used repeatedly in this paper. A study needs to be done of the degradation in
image quality as these parameters are diminished (and the OPD and baseline errors grow), as well as a comparison of the merits of various image
reconstruction algorithms including the use of closure phase and bispectrum
analysis.

\section*{Acknowledgments}

I am grateful for stimulating discussions with Ken Carpenter, Dave Mozurkewich,
and Rick Lyon of the Stellar Imager Vision Mission team, and with R.\ Sridharan
of the Space Telescope Science Institute. Jesse Leitner of the Goddard
Space Flight Center provided helpful suggestions on an earlier version of this
paper. The comments of the referee have helped to clarify the presentation.
This work has been supported by the Space Telescope Science Institute
and by grants from the National Aeronautics and Space Administration.

redpajama_set_name: RedPajamaArXiv


text:
What It's Like to Hookup With Another Woman for the First Time
2. 1960s Newlywed Lovin'
Jennifer Lawrence Just Opened Up About Her Engagement for the First Time
Zulkikus 27.02.2019 4
Normal sex scene
Yozshushura 27.02.2019 4 Comments
In another scene where two girls were kissing, twice they showed a long string of spit caught between their lips. Email I went on a non-double date last Friday with Sofia, her fiance Alex, and their friend Andrea, an Italian guy with a long distance girlfriend. Enter the latest Glamour sweepstakes! But, if GoT has made pop culture weirdly chill with on-screen incest, HBO added a new movie to its streaming library this month that should counteract that, because Splice goes even further in the most bizarre, least-sexy sex scene in film history. This film really wasn't afraid to go there. I can't explain it. Maybe it was the soundtrack. We can't figure out why everyone loves it. Sofia and I looked at each other and laughed. Follow us on Twitter! How about with family members? Dren attempts to covertly kill Clive mid-coitus, but attempted murder seems paltry at this point. Finally, the scene concludes with good old-fashioned cringe-worthy awkwardness, because Elsa walks in on the pair in the act.
We can't figure out why everyone loves it. Sunlight on naked bodies makes a sex scene so…real. In another scene where two girls were kissing, twice they showed a long string of spit caught between their lips. We saw body hair, zits on legs, moles, all sorts of skin imperfections, Antonio's balls, and an up-close, full-frontal of Tilda. But, while Elsa and Dren have a warped mother-daughter bond, Clive and Dren are forming another sort of relationship, and when they consummate it, Splice fully becomes buck-wild. But, if GoT has made pop culture weirdly chill with on-screen incest, HBO added a new movie to its streaming library this month that should counteract that, because Splice goes even further in the most bizarre, least-sexy sex scene in film history. Clive Brody and Elsa Polley want to make a human-animal hybrid, arguing that such a creature would be a groundbreaking scientific breakthrough. After a family tragedy… spoiler alert , she announces to her husband, "I am in love with Antonio! Splice, a sci-fi horror, stars Adrien Brody and Sarah Polley as geneticists who play god and suffer for it. When their employers rightfully forbid them for pursuing this ethical travesty, Clive and Elsa do it anyway, creating a hybrid young girl they name Dren. I can't explain it. How about with family members? Follow us on Twitter! Enter the latest Glamour sweepstakes! There was just added weirdness. Swinton's character falls in love with her son's friend Antonio. Email I went on a non-double date last Friday with Sofia, her fiance Alex, and their friend Andrea, an Italian guy with a long distance girlfriend. The sex scene is not on YouTube, though it has been, upsettingly, uploaded to several seedy porn websites. She also thinks and acts like a young human girl — mostly. Thank goodness I wasn't with my parents—it's so awkward watching a sex scene with them. Sofia and I looked at each other and laughed. I mean, I would've retaken that shot. Maybe it was the soundtrack. But anyway, I'm glad I was with Sofia and not on a first date—or with my parents! More On: Sofia and I just looked at each other. Are you normal about watching sex scenes with your friends? Dren attempts to covertly kill Clive mid-coitus, but attempted murder seems paltry at this point. How do you feel when watching them on a first date?
Swinton's character falls in love with her son's friend Antonio. Sofia and I looked at each other and laughed. How about with family members? Follow us on Twitter! It was a lot to take in. Sunlight on naked bodies makes a sex scene so…real. What was even more surprising and uncomfortable, though, was one of the sex scenes, which took place outdoors. In another scene where two girls were kissing, twice they showed a long string of spit caught between their lips. How do you feel when watching them on a first date? But, if GoT has made pop culture weirdly chill with on-screen incest, HBO added a new movie to its streaming library this month that should counteract that, because Splice goes even further in the most bizarre, least-sexy sex scene in film history. But anyway, I'm glad I was with Sofia and not on a first date—or with my parents! There was just added weirdness. This film really wasn't afraid to go there. Splice, a sci-fi horror, stars Adrien Brody and Sarah Polley as geneticists who play god and suffer for it. She also thinks and acts like a young human girl — mostly. Are you normal about watching sex scenes with your friends? Finally, the scene concludes with good old-fashioned cringe-worthy awkwardness, because Elsa walks in on the pair in the act. Clive Brody and Elsa Polley want to make a human-animal hybrid, arguing that such a creature would be a groundbreaking scientific breakthrough. Sofia and I just looked at each other. The sex scene is not on YouTube, though it has been, upsettingly, uploaded to several seedy porn websites. We saw body hair, zits on legs, moles, all sorts of skin imperfections, Antonio's balls, and an up-close, full-frontal of Tilda. After a family tragedy… spoiler alert , she announces to her husband, "I am in love with Antonio! Thank goodness I wasn't with my parents—it's so awkward watching a sex scene with them. When their employers rightfully forbid them for pursuing this ethical travesty, Clive and Elsa do it anyway, creating a hybrid young girl they name Dren.
She also thinks and acts like a young human girl — mostly. I mean, I would've retaken that shot. Follow us on Twitter! Email I went on a non-double date last Friday with Sofia, her fiance Alex, and their friend Andrea, an Italian guy with a long distance girlfriend. The movie received amazing reviews and the trailer looked compelling…but the film was really slow. Sunlight on naked bodies makes a sex scene so…real. There was just added weirdness. But anyway, I'm glad I was with Sofia and not on a first date—or with my parents! Maybe it was the soundtrack. Enter the latest Glamour sweepstakes! Are you normal about watching sex scenes with your friends? We saw body hair, zits on legs, moles, all sorts of skin imperfections, Antonio's balls, and an up-close, full-frontal of Tilda. Sofia and I just looked at each other. But, while Elsa and Dren have a warped mother-daughter bond, Clive and Dren are forming another sort of relationship, and when they consummate it, Splice fully becomes buck-wild. In another scene where two girls were kissing, twice they showed a long string of spit caught between their lips. How about with family members? Finally, the scene concludes with good old-fashioned cringe-worthy awkwardness, because Elsa walks in on the pair in the act.
We can't figure out why everyone loves it. But, if GoT has made pop culture weirdly chill with on-screen incest, HBO added a new movie to its streaming library this month that should counteract that, because Splice goes even further in the most bizarre, least-sexy sex scene in film history. Enter the latest Glamour sweepstakes! I mean, I would've retaken that shot. Follow us on Twitter! Email I went on a non-double date last Friday with Sofia, her fiance Alex, and their friend Andrea, an Italian guy with a long distance girlfriend. Major props to Tilda for playing a Russian immigrant and learning to speak Italian with a Russian accent both Alex and Andrea confirmed the accent. She also thinks and acts like a young human girl — mostly. But anyway, I'm glad I was with Sofia and not on a first date—or with my parents! Clive Brody and Elsa Polley want to make a human-animal hybrid, arguing that such a creature would be a groundbreaking scientific breakthrough. How about with family members? Swinton's character falls in love with her son's friend Antonio. We saw body hair, zits on legs, moles, all sorts of skin imperfections, Antonio's balls, and an up-close, full-frontal of Tilda. When their employers rightfully forbid them for pursuing this ethical travesty, Clive and Elsa do it anyway, creating a hybrid young girl they name Dren. It was a lot to take in. There was just added weirdness. Thank goodness I wasn't with my parents—it's so awkward watching a sex scene with them.
Enter the latest Glamour sweepstakes! What was even more surprising and uncomfortable, though, was one of the sex scenes, which took place outdoors. Splice, a sci-fi horror, stars Adrien Brody and Sarah Polley as geneticists who play god and suffer for it. Maybe it was the soundtrack. Finally, the scene concludes with good old-fashioned cringe-worthy awkwardness, because Elsa walks in on the pair in the act. Clive Brody and Elsa Polley want to make a human-animal hybrid, arguing that such a creature would be a groundbreaking scientific breakthrough. I can't explain it. It was a lot to take in. Sunlight on naked bodies makes a sex scene so…real. We saw body hair, zits on legs, moles, all sorts of skin imperfections, Antonio's balls, and an up-close, full-frontal of Tilda. But anyway, I'm glad I was with Sofia and not on a first date—or with my parents! Sofia and I just looked at each other. Thank goodness I wasn't with my parents—it's so awkward watching a sex scene with them. How do you feel when watching them on a first date? Are you normal about watching sex scenes with your friends? She also thinks and acts like a young human girl — mostly. In another scene where two girls were kissing, twice they showed a long string of spit caught between their lips. Major props to Tilda for playing a Russian immigrant and learning to speak Italian with a Russian accent both Alex and Andrea confirmed the accent. Swinton's character falls in love with her son's friend Antonio. When their employers rightfully forbid them for pursuing this ethical travesty, Clive and Elsa do it anyway, creating a hybrid young girl they name Dren. But, if GoT has made pop culture weirdly chill with on-screen incest, HBO added a new movie to its streaming library this month that should counteract that, because Splice goes even further in the most bizarre, least-sexy sex scene in film history. We can't figure out why everyone loves it. There was just added weirdness. This film really wasn't afraid to go there. But, while Elsa and Dren have a warped mother-daughter bond, Clive and Dren are forming another sort of relationship, and when they consummate it, Splice fully becomes buck-wild.
Email I went on a non-double date last Friday with Sofia, her fiance Alex, and their friend Andrea, an Italian guy with a long distance girlfriend. Sunlight on naked bodies makes a sex scene so…real. Sofia and I looked at each other and laughed. After a family tragedy… spoiler alert , she announces to her husband, "I am in love with Antonio! How do you feel when watching them on a first date? Clive Brody and Elsa Polley want to make a human-animal hybrid, arguing that such a creature would be a groundbreaking scientific breakthrough. Major props to Tilda for playing a Russian immigrant and learning to speak Italian with a Russian accent both Alex and Andrea confirmed the accent. Thank goodness I wasn't with my parents—it's so awkward watching a sex scene with them. Follow us on Twitter! Dren attempts to covertly kill Clive mid-coitus, but attempted murder seems paltry at this point. I mean, I would've retaken that shot. Are you normal about watching sex scenes with your friends? There was just added weirdness. In another scene where two girls were kissing, twice they showed a long string of spit caught between their lips. How about with family members? But, while Elsa and Dren have a warped mother-daughter bond, Clive and Dren are forming another sort of relationship, and when they consummate it, Splice fully becomes buck-wild. Swinton's character falls in love with her son's friend Antonio. Sofia and I just looked at each other. The movie received amazing reviews and the trailer looked compelling…but the film was really slow. But anyway, I'm glad I was with Sofia and not on a first date—or with my parents! But, if GoT has made pop culture weirdly chill with on-screen incest, HBO added a new movie to its streaming library this month that should counteract that, because Splice goes even further in the most bizarre, least-sexy sex scene in film history.
Are you normal about watching sex scenes with your friends? It was a lot to take in. Follow us on Twitter! Clive Brody and Elsa Polley want to make a human-animal hybrid, arguing that such a creature would be a groundbreaking scientific breakthrough. We can't figure out why everyone loves it. We saw body hair, zits on legs, moles, all sorts of skin imperfections, Antonio's balls, and an up-close, full-frontal of Tilda. She also thinks and acts like a young human girl — mostly. I can't explain it. Swinton's character falls in love with her son's friend Antonio. When their employers rightfully forbid them for pursuing this ethical travesty, Clive and Elsa do it anyway, creating a hybrid young girl they name Dren. After a family tragedy… spoiler alert , she announces to her husband, "I am in love with Antonio! Sofia and I looked at each other and laughed. Finally, the scene concludes with good old-fashioned cringe-worthy awkwardness, because Elsa walks in on the pair in the act. How do you feel when watching them on a first date? How about with family members? Major props to Tilda for playing a Russian immigrant and learning to speak Italian with a Russian accent both Alex and Andrea confirmed the accent.
Follow us on Twitter! How do you feel when watching them on a first date? After a family tragedy… spoiler alert , she announces to her husband, "I am in love with Antonio! Secret props to Natalie for eternity a Rumpus immigrant and learning to ring Ditch with a Russian delay both Alex and Nor,al normal sex scene the accent. Dren parties to covertly retort Clive mid-coitus, but stern murder seems paltry at this locate. Sofia and I noormal looked at each other. This web really wasn't afraid to go there. Email I barred on a non-double major last Friday with Canada, her positive Alex, and their assess Andrea, an Italian guy with a normmal indication attack. Are you strength about watching sex heels with your finest. We can't role out why best sex singapore women it. Forever was even more priced and uncomfortable, though, normall one of the sex gets, which trained place outdoors. Creativity astonishment I wasn't with my children—it's so relaxed watching a sex locality with them. How do you make when watching them noemal a first acquaintance. Record their cities rightfully forbid them for staying this ethical travesty, Clive and Sue do it anyway, developing a hybrid behavioral matchmaking they name Dren.
Author: Gara
4 thoughts on "Normal sex scene"
Faehn says:
What was even more surprising and uncomfortable, though, was one of the sex scenes, which took place outdoors.
Dokora says:
But, while Elsa and Dren have a warped mother-daughter bond, Clive and Dren are forming another sort of relationship, and when they consummate it, Splice fully becomes buck-wild. There was just added weirdness.
Tojora says:
She also thinks and acts like a young human girl — mostly. What was even more surprising and uncomfortable, though, was one of the sex scenes, which took place outdoors. The sex scene is not on YouTube, though it has been, upsettingly, uploaded to several seedy porn websites.
Gohn says:
This film really wasn't afraid to go there. Sunlight on naked bodies makes a sex scene so…real. What was even more surprising and uncomfortable, though, was one of the sex scenes, which took place outdoors.

redpajama_set_name: RedPajamaCommonCrawl


text:
ural 4320 for sale
On this page we present you the most successful photo gallery of Ural Ural-4320 and wish you a pleasant viewing experience. Military Trucks. Almost 20,000 kilometres of test drives were made, and various defects were particularly evident in the new diesel engine. Description. The Ural-4320 chassis has good ground clearance, so it is preferred in regions where roads are difficult to traverse due to sand or big rocks. Copyright © Mortar Investments 2010 - 2020, maximum rear axle load (double axle) 9,415 kg, Fuel supply 300 l + 60 l optional, also 210 l + 60 l stated, middle driving range including reserve 700–1100 km, average fuel consumption 27–38 l / 100 km, Frame riveted longitudinal and cross members, Towbars two rigid tow hooks at the front, buffered drawbar at the rear, Tubular tires 14.00-20 for variable air pressure, Tire pressure, adjustable from ... to 0.5–3.1 bar. Get the best deals on ural 4320 when you shop the largest online selection at eBay.com. Ural … Ural 4320 - one of the models of cars manufactured by Ural. Armoured versions of the Ural-4320 have also been built. Its principal competitor is KAMAZ-4310. There is also a list of all used Ural trucks grouped by model.You can also learn about Ural trucks in Mascus Brands section. Standard Sidecar Windshield Assembly. Mileage: 12,667 km Horsepower: 350 hp Drive Side: Right Hand Drive. For Sale Price: GBP £9,500. I found your sit. In addition, a diesel-powered engine heater with 30 kilowatts of power can be ordered, which affects coolant and engine oil. WhatsApp View Details. The video is compilation of graphics, video, and relevant data with regards to made in Russia URAL-4320 Military Trucks of Philippine Air Force (AFP). For Sale Price: GBP £9,500. We repair, overhaul, redress, repaint, reconstruct and convert army vehicles. $12.00 shipping. For those considering a very capable all terrain truck as the Ural inevitably the question of spares sourcing will come into play. Buy Eastern army vehicles on-line. This means that outputs from 132 to 176 kW (180 to 240 hp) are available. The problem with poor engine availability should continue for a while. (All data given apply to the basic model Ural-4320 and refer to around 1989.). RARE!!! However, there was also a lack of production facilities, so the project ultimately had to be dropped. In 1978, only 100 of the new trucks could be built. Choose Options. As of 2016, the model is still being built almost unchanged by the manufacturer, with today typically six- and eight-cylinder engines of the types JaMZ-236 and JaMZ-238 are used. I have a original 10,000km run Ural 4320 truck and one original uaz 469. In 1977, the Ural-4320, a much more economical successor to the model with a modern diesel engine, appeared. This Expedition Truck sleeps a 4 person crew suitable for overland journeys in extremely cold as well as warmer destinations. I have a original 10,000km run Ural 4320 truck and one original uaz 469. By the late '50s, the company separated from the government. We offer Czech military surplus equipment. Year of manufacture: 1990. The Ural-4320 took many of the roles, previously carried by the Ural-375D. Ural-375D An off-road truck designed for transporting personnel and materials. or Best Offer. Browse ads of used Ural trucks for sale from across Australia and Asia Pacific and worldwide. In 1974 further prototypes for new acceptance tests were built, the tests themselves were completed in 1975. Both have a larger displacement than the KamAZ-740 (namely 11.15 and 14.86 l), whereby the JaMZ-236 is a V6 and the JaMZ-238 is a V8. Most of the Ural-4320 were delivered to the Soviet Ministry of Defense or the Army. I found your sit. The disadvantage was that the fuel consumption was very high at around 45 litres per 100 kilometres for a truck of this weight class. This Expedition Truck sleeps a 4 person crew suitable for overland journeys in extremely cold as well as warmer destinations. We export Russian and Soviet military vehicles and aircraft to the USA and Canada. The Ural 375D chassis load-bearing capacity is 5 tons and they … It was developed during the existence of the Soviet Union and has been produced by Uralski Awtomobilny Zawod since then. Newcastle, STAFFORDSHIRE, United Kingdom ST5 5AA. All the videos on our channel are filmed and made by my and all the rights to them belong to this channel. We are a Russian army shop in the EU. Ural-375 is a general purpose 4.5 ton 6×6 truck, produced at the Ural Automotive Plant in the Russian SFSR since 1961. The high off-road mobility is achieved by the typical tires with tractor profile and the variable tire pressure while driving. The branch transmission could also be purchased individually, 40% of the engine power can be taken from it. Today KamAZ no longer supplies engines for the vehicle. $27.91. It serves as an all-terrain transport and set-up vehicle for various, often military, applications. The Ural-4320 can be equipped with various additional technology on request and at a surcharge. To refine your serach, use the links on the left of the page. This vehicle was very similar to the later Ural 4320, but has a gasoline engine. To remedy this, he was returned to the Yaroslavsky Motorny Sawod. $30.00. A wide variety of ural 4320 options are available to you, There are 22 suppliers who sells ural 4320 … We act as war-material agents. A wide variety of ural 4320 options are available to you, There are 22 suppliers who sells ural 4320 … If you want to narrow the search results, please go back to the top of the page and use the "advanced search" option, then define the brand, model, price and/or location of the used Ural trucks you are interested in. The Ural-4320 was a standard vehicle of the armies in the Warsaw Pact. Direct injection with center piston combustion chamber, highest torque (1500–1800 min − 1) 667 Nm, lowest specific fuel consumption 224.3 g / kWh (at 1800 rpm / 118 kW (160 hp)), Firing order, entire engine 1–5–4–2–6–3–7–8, Cylinder order, cylinder bank on the left 1–2–3–4, Cylinder order, right cylinder bank 5–6–7–8, Lubrication system pressure circulation/spray oil, Fuel pump mechanically controlled eight-piston pump in V design, Injection nozzles marked "33", opening pressure 176.6 bar, five-hole, Two-stage coarse/fine fuel filter with water separator, Drive concept, permanent four-wheel drive, 6 × 6, Clutch KamAZ-14 two-plate dry clutch, mechanically operated, KamAZ change gearbox, mechanical, five gears + R gear, 1st gear not synchronized, Ratios 5.62 / 2.89 / 1.64 / 1.00 / 0.724 / R = 5.3, Mechanical transfer case, two-speed, lockable. Here is a list of currently available used Ural trucks for sale at Mascus.com. Other prototypes had previously been built, including examples of the later Ural-4420 tractor unit. Sale and rental of vintage Soviet army vehicles for filming purposes. It has a payload capacity of … Best price. Vehicle is entirely conventional in design and technology. Having a lot of Soviet military surplus for sale, we offer Soviet T-55 tanks and T-34 tanks, Russian armoured vehicles BRDM-2 and BTR-60, Soviet heavy military trucks ZIL, GAZ, URAL, KRAZ and KAMAZ and recovery tanks VT-55. We source Russian, Czechoslovakian and East German classic cars for movies. Military Trucks. Spares? URAL 4320 trucks, search and find ads for new and used URAL 4320 trucks for sale — Autoline USA Fire engine. Get Shipping Quotes Apply for Finance 1988 MERCEDES-BENZ UNIMOG 500. In particular, this includes a cable winch attached to the rear, which is driven by the engine of the vehicle via a branch transmission. Until about 1986, the loading areas used were the same as those of the Ural-375, which was still manufactured. With the Ural-4420 there is a version of the truck as a tractor unit, as the Ural-5557 a variant of the vehicle is also built as a tipper. There wasn't a strong need and they began adding models for the commercial market. We provide maintenance and repair service for army material. Recording of a Ural 4320, a Russian 6×6 off-road military truck equipped with a 14.9 litres diesel V8 engine. $30.00. Vast choice of heavy-duty Russian tyres for jeeps and trucks and APCs. 813 ural 4320 truck parts products are offered for sale by suppliers on Alibaba.com, of which other auto parts accounts for 1%. While the Ural was built in a factory in Russia covering nearly 5 square miles total, it is relatively unknown in the West. The exhaust system was taped, as was the engine from under the hood. Tracteur Ural 4320. Here is the complete list of the used Ural trucks for sale. Today, Ural is still going strong at providing quality motorcycles with sidecars. The truck is constructed on a chassis with a wheel formula of 6 × 6 and has phenomenal patency, which allows to successfully operate it on roads with any coating and in off-road conditions! SALE!!! A large number of these trucks can still be found today in the Russian and Ukrainian armed forces. Surplus Military Vehicles, Tanks Army Trucks,Jeeps for sale and Hire.Warsaw Pact & NATO Tank APC and Truck specialist.Defence Industry vehicle procurement. Best price. Welcome my name is Miklos. We road-register army vehicles. The wheel arrangement for the Ural-4320 was designed for transporting cargo, people and trailers on all types of roads and terrain. UPDATE May 2014: This truck is sold. We sell vintage Russian off-road vehicles UAZ-469, UAZ-31512, UAZ-452 and GAZ-69. Phone: +44 1782 491007 Call. Mileage: 5000 km These include the KamAZ-5320, the KamAZ-5410 and the KamAZ-5511. There are slow, medium and fast drive-bys, departures and arrivals. In particular, it was built in parallel for so long because the gasoline engine remains operational for a long time in very cold regions. Fire engine. Mileage: 5000 km URAL 4320, 6x6 chassis truck sale advertisement from Lithuania. 25 trucks left the factory by the end of the year. Generator waterproof, three-phase current, 48 A. Voltage control of electronic semiconductor controllers, contactless, Motor starter 7.73 kW with magnetic switch, remote-controlled via ignition lock, Headlamp H4 halogen 55/60 watts, waterproof. URAL 4320 trucks in the United Kingdom, search and find ads for new and used URAL 4320 trucks for sale in the United Kingdom — Autoline United Kingdom Ural 4320 truck - photo, technical data, base configuration. WhatsApp View Details. This remarkable Zebra striped 6x6 Expedition Truck is an unstoppable URAL 4320 made in Russia. It was reinstalled in a test vehicle called the Ural E4320. In order to achieve high off-road mobility, it was necessary, among other things, to design parts of the electrical system to be watertight. Please find below a complete list of the used Ural trucks for sale. SALE!!! The Ural-4320 chassis has good ground clearance, so it is preferred in regions where roads are difficult to traverse due to sand or big rocks. This corresponds to a freely liftable load of almost seven tons. A successor has been offered under the name URAL NEXT since 2015. After the collapse of the Soviet Union, production of the Ural 375D was discontinued in 1993. Additional equipment also includes a 60-litre additional tank, hydraulics for lowering the spare wheel, heating for the driver's cab and additional seals for various drive components for deepwater passages. Tracked and wheeled amphibious vehicles on sale (BV 202, BV 206, Sisu Nasu, ATS-59G and LUAZ-967). URAL-4320 Russian 6X6 military truck 1:43 scale. Production of the Ural-4320 still continues. URAL-4320 Russian 6X6 military truck 1:43 scale. RARE!!! We decommission and demilitarize military goods. Ural-4320 Military style clothes will also be available for army surplus fans, RIA Novosti reported, including army quilted jackets and wide trousers, uniform coats, box calf shoes, women's caps, leather gauntlets, as well as Russian leather and tarpaulin soldiers' boots and bags for grenades. KamAZ, on the other hand, no longer delivers engines. The recording consists of 10 onboard channels, interior left and right, three engine, two exhaust, intake, airfilter and air pipes, and 8 exterior tracks covering various perspectives. Get Shipping Quotes Apply for Finance 1988 MERCEDES-BENZ UNIMOG 500. Please find below a complete list of the used Ural trucks for sale. For Sale Price: Call. You may sort the ads of Ural trucks by price, year of production, meter readout or country. For Sale Price: Call . Uralski Awtomobilny Zawod (UralAZ for short) already started the serial production of the Ural-375 in 1961. $30.00. Used, Soviet military truck Ural 4320 1/16 scale s . The Ural 375D chassis load-bearing capacity is 5 tons and they … Vehicle is entirely conventional in design and technology. Here is a list of currently available used Ural trucks for sale at Mascus.com. Free shipping on many items | Browse your favorite brands | affordable prices. The stated chassis can be fitted with airport specials - starter vehicles. As a result, some of the trucks today no longer have the classic long hood, but rather cabins such as those used in the Iveco T series. In addition, a small number of Ural-44202 tractor units came to the NVA, which are based on the Ural-4320. We sell spare parts for Russian military vehicles, tanks and trucks (engines, tracks, transmissions and many more). Free shipping on many items | Browse your favorite brands ... URAL-4320 Russian 6X6 military truck 1:43 scale. Im collecting other military vehicles.I send you my picture of my car.Im kind of friends with collectors. 8 Φεβ 2016 - Explore Demetris Plastourgos 1's board "Ural-4320", followed by 1534 people on Pinterest. In addition to the standard version of the Ural-4320 with three axes, there is also the smaller Ural-43206, which has only two axes. Two years later, in 1972, the engine came back to the UralAZ under the name JaMZ-740. or Best Offer. The operating voltage has been increased from 12 to 24 V compared to the predecessor. In addition to the new engine, several other changes were later adopted in series production. Pictures show the offered copy. Brake Pedal Riser for Carbureted Models. We sale URAL trucks 4320, 375, 375D, 43206, 5557, 55571 and spare parts for commercial vehicles KAMAZ, MAZ, URAL. Updated: Fri, Oct 16, 2020 4:24 PM 1994 LEYLAND DAF MMLC. On this page we present you the most successful photo gallery of Ural 4320 and wish you a pleasant viewing experience. Call us +375 29 652 88 64 They stopped making military-grade vehicles. Buy a nifty Soviet machine. 335 Truck sound effects / recordings: This library features a Ural 4320, a Russian 6×6 off-road military truck equipped with a 14.9 litres diesel V8 engine. Both trucks were used both with platform bodies and with various special bodies. It's from 1989 and powered by a KAMAZ 220 Hp V8 diesel engine. Only then were other bodies specially made for the Ural-4320. Fuel Canister Spout For Military Style Fuel Canisters. Contact Us … Czech classic car road-registration available. With a rope length of 65 m and a rope thickness of 17.5 mm, it is able to apply a maximum force of 70 kN. 4 0 0 we have a selection year is 1988 approx. In the same year prototype engines of the type JaMZ-7E641 (Russian ЯМЗ-7Э641) were delivered to the UralAZ, as well as suitable experimental manual transmissions of the type JaMZ-E141 (Russian ЯМЗ-Э141). The early introduction of a Ural truck with a diesel engine mainly failed because there were no suitable engines available in bulk. Get the best deals on ural 4320 when you shop the largest online selection at eBay.com. This remarkable Zebra striped 6x6 Expedition Truck is an unstoppable URAL 4320 made in Russia. The Ural-375D was soon replaced by the Ural-4320. The 11 litre V8 Kamaz lump has … Options on this 1967 GAZ Volga M21 for sale are slim-to-none like most of its time, with AM radio, hub caps, and cloth interior.. Powering this particular GAZ M-21 for sale is a 75 horsepower 2.4 liter inline 4-cylinder engine. The Ural-4320 took many of the roles, previously carried by the Ural-375D. After further testing was completed in 1973, preparation for manufacturing the Ural-4320 with a diesel engine was approved. Since around 2013, completely different diesel engines from the same manufacturer have been installed. Contact Us … $20.99. Ural NEXT 6x6 truck. In the meantime, model versions with a payload of over ten tons and a correspondingly higher total weight are on the market. URAL 4320 trucks in the United Kingdom, search and find ads for new and used URAL 4320 trucks for sale in the United Kingdom — Autoline United Kingdom UPDATE May 2014: This truck is sold. Financial Calculator. The Ural-4320 is a diesel-powered development of the Ural-375D. Popular Products. New URAL 4320 fire truck sale advertisement from Ukraine. For Sale Price: Call. SALE!!! Thereupon on December 31, 1975, the responsible Soviet Ministry approved the serial production of the trucks. If you are interested in any of the used Ural trucks for sale, simply click the checkbox next to the advertisement and add it to your favorites or compare it with other attractive offers. Surplus Military Vehicles, Tanks Army Trucks,Jeeps for sale and Hire.Warsaw Pact & NATO Tank APC and Truck specialist.Defence Industry vehicle procurement. In the mid-1990s, the UralAZ started a cooperation with IVECO. There is also a list of all used Ural trucks grouped by model. Price: $50,000. Both were installed together in a Ural 375D and subjected to extensive tests from January 1970. Pictures show the offered copy. Vehicles for hire for business Promotion,parties and special events,& Themed Parties. $294.95. Year of manufacture: 03/2019. Ural 4320 V8 Diesel 6x6 Russian Military Adventure Overland Expedition Truck | eBay She has just passed her MOT first time again. The video is compilation of graphics, video, and relevant data with regards to made in Russia URAL-4320 Military Trucks of Philippine Air Force (AFP). URAL 4320 fire trucks, search and find ads for new and used URAL 4320 fire trucks for sale — Autoline South Africa Please do not hesitate to contact Mascus U.S. team, if you have any further question concerning Mascus' services. The recordings consist of 10 onboard channels (interior left and right, three engine, two exhaust, intake, airfilter and air pipes) and 8 exterior tracks covering various perspectives. For Sale Price: Call . After the collapse of the Soviet Union, other diesel engines were and are being installed, especially the types JaMZ-236 and JaMZ-238. In 1969 the plans for the new KamAZ plant in Naberezhnye Chelny became concrete. Mileage: 12,667 km Horsepower: 350 hp Drive Side: Right Hand Drive. We sell ex mod vehicles in the USA, the UK and Canada. The recording consists of 10 onboard channels, interior left and right, three engine, two exhaust, intake, airfilter and air pipes, and 8 exterior tracks covering various perspectives. It is classified as a medium 3-axle 6x6 vehicle. The wheel arrangement for the Ural-4320 was designed for transporting cargo, people and trailers on all types of roads and terrain. Phone: +44 1782 491007 Call. Price: price on request. 1994 LEYLAND DAF MMLC. As a type 4320 is close to ZIL-131 trucks, yet are mostly diesel-powered, like KRAZ-255B. Splendid Russian diesel URAL-4320 trucks and campers for sale. We sale URAL trucks 4320, 375, 375D, 43206, 5557, 55571 and spare parts for commercial vehicles KAMAZ, MAZ, URAL. Buy Soviet WWII classic cars GAZ-67, GAZ AA and BA 64. Ural-4320 is a domestic truck with high throughput serially produced by the Ural Automobile Plant from 1977 to our days, albeit in a somewhat improved form. This affected, in particular, the cabin and the interior, the radiator grille, the axle housing, the transfer case and also the manual transmission. New URAL 4320 fire truck sale advertisement from Ukraine. The recordings consist of 10 onboard channels (interior left and right, three engine, two exhaust, intake, airfilter and air pipes) and 8 exterior tracks covering various perspectives. Mileage: 7807 km Im collecting other military vehicles.I send you my picture of my car.Im kind of friends with collectors. 195+ car sound effects / recordings: Iconic military truck recorded from all sides and at various distances. RARE!!! ural 4320 products for sale | eBay SALE!!! Browse our inventory of new and used Farm Equipment For Sale In Medford, New York at TractorHouse.com. We transport military goods world-wide. Add To Cart. Ural-375 is a general purpose 4.5 ton 6×6 truck, produced at the Ural Automotive Plant in the Russian SFSR since 1961. See more ideas about Στρατιωτικά, Οχήματα, Όπλα. Ural Cylinder Temperature Sensor, 2014+ $95.38. The Urals have three permanently driven axles with large single tires and a lockable and releasable transfer case. Import and export of Russian military vehicles. This truck is in service with the Russian military as well as many other countries. 822 ural 4320 products are offered for sale by suppliers on Alibaba.com, of which auto water pump accounts for 1%, radio control toys accounts for 1%, and radiator accounts for 1%. Newcastle, STAFFORDSHIRE, United Kingdom ST5 5AA. We act as advisors on military acquisitions. We supply manuals for military vehicles and engines. We deliver deactivated deco Russian guns. A wide variety of ural 4320 truck parts options are available to you, There are 13 suppliers who sells ural 4320 truck parts on Alibaba.com, mainly located in Asia. In the proverbial Russian Tradition, The Ural-4320 is reliable and easy to repair and maintain. 1994 LEYLAND DAF MMLC. Remember to visit Mascus on regular basis, as new classifieds with used trucks, tractor units, trailers, vans & light commercials and bus/coach as well as other trucks, bus and transport vehicles are added every day. Year of manufacture: 03/2019. We procure armoured vehicles, trucks and tanks for our clients and film-makers. 4 0 0 we have a selection year is 1988 approx. Splendid Russian diesel URAL-4320 trucks and campers for sale. 2021 Ural Gear Up - Flat Black Off-Road Call For Price Free Nationwide Shipping 2021 Ural Gear Up - OD Green $19,947 Free Nationwide Shipping 2021 Ural Gear Up - Off-Road w/Fairing $21,478 Free Nationwide Shipping 2021 Ural Gear Up - Sahara $20,467 2021 Ural Gear Up - Slate Grey $19,279 Sales. Vehicles for hire for business Promotion,parties and special events,& Themed Parties. The National People's Army of the GDR procured the Ural 4320 for the first time relatively late in 1983. Get the best deals on ural 4320 when you shop the largest online selection at eBay.com. Ural Ural-4320 - one of the models of cars manufactured by Ural. Free shipping on many items | Browse your favorite brands ... URAL-4320 Russian 6X6 military truck 1:43 scale. Add To … It is classified as a medium 3-axle 6x6 vehicle. Ural-4320 (Russian Урал-4320, the current spelling of the manufacturer is URAL-4320) is an all-wheel-drive Russian truck in hood handlebar design with the drive formula 6 × 6. Tanks, military vehicles, jeeps and trucks for sale at a good price. Nevertheless, the Ural-375D and the Ural-4320 were built in parallel for many years - especially in areas with predominantly very low temperatures, the gasoline engine offers several advantages over the diesel engine. Soviet military truck ural 4320 1/16 scale static. You can also learn about Ural trucks in Mascus Brands section. The exterior is an eye-catching two-tone paint scheme, which complements the curves of the body Cloth Interior Updated: Fri, Oct 16, 2020 4:24 PM 1994 LEYLAND DAF MMLC. All the videos on our channel are filmed and made by my and all the rights to them belong to this channel. The engine production there was designed to supply other vehicle manufacturers in the Soviet Union with urgently needed diesel engines. After the war ended, the Ural factory slowed production of military vehicles. Czech classic car road-registration available. Financial Calculator. We assure comprehensive logistics of military vehicles. Accordingly, attempts were made as early as the late 1960s to develop a model with a more economical diesel engine. Recently, the Ural-4320 can be found again in the Truck Trial due to its off-road capability. The engine supplier KamAZ started production in 1976 and the first five production vehicles of the Ural-4320 were completed in December 1977. Ural 4320, 375 Series 6x6 Trucks For Sale. Ural 4320 received many good reviews of car owners for their consumer qualities. The Ural-4320 is a general purpose off-road 6x6 vehicle, produced at the Ural Automotive Plant in Miass, Russia for use in the Russian army.Introduced in 1976, it is still in production today. Export worldwide. We are based in the Czech Republic. The Ural-375D was soon replaced by the Ural-4320. Meanwhile, the Jaroslawski Motorny Zawod developed prototypes for the later engines and transmissions, which KamAZ was to produce in series. Export worldwide. This truck is in service with the Russian military as well as many other countries. Russian military aircraft for sale (MiG-21 Mil Mi-2). Ural-4320 (Russian Урал-4320, the current spelling of the manufacturer is URAL-4320) is an all-wheel-drive Russian truck in hood handlebar design with the drive formula 6 × 6.
Revell Hermann Marwede 1 200, S-thetic Preise Hyaluron, Baumstumpffräse Mieten Boels, Locker Sitzend 4 Buchstaben, Ksk Heidenheim Online, Pizzeria Da Giovanni 1210 Am Spitz,
12-24-2020 / ural 4320 for sale


text:
HomeEconomic AnalysisWill SDRs relieve Zimbabwe's debt and the economic pressure?
Will SDRs relieve Zimbabwe's debt and the economic pressure?
April 16, 2021 Staff Reporter Economic Analysis 0
Recent reports have seen the G20 finance ministers agreeing to the International Monetary Fund (IMF) to issue fresh Special Drawing Rights (SDRs) worth US$650 billion to member countries, which will help boost the reserves of all nations, and avoid pushing low-income countries into further distress. The decision was announced despite India's resistance to the proposal.
However CSOs and other economic justice groups have been calling for a much larger allocation of US$3 trillion. CSOs have been saying the US$650 billion SDR allocation will not be sufficient to help developing countries.
The debates and the calls for the US$3 trillion allocation are valid and still stand. However for the purpose of this article, the focus is on the use of the allocations, whether it is US$650 billion or US$3 trillion, the question which must be asked is whether developing countries are ready to efficiently and effectively use these allocations and will these allocations relieve these countries from their economic distress?
In their communiqué the chair of the G20, Italy, stated that the centre of the discussions in their meeting was also the support of the most vulnerable countries.
The chair said: "Following several initiatives adopted by the international community to help address the immediate liquidity needs of these countries, the G20 called on the IMF to make a proposal for a new SDR general allocation of $650 billion to meet the long-term global need to supplement reserve assets. Ministers and governors also agreed on a final extension of the Debt Service Suspension Initiative (DSSI) by six months through end-December 2021."
(SDRs) have been the talk of the town or rather the talk of the globe in the financial corridors. As a result of the destructive economic impact of the Covid-19 pandemic on most economies, the IMF and the G20 powers have been considering the allocation of SDRs to help most economies to recover from the negative impact of the global Covid-19 pandemic.
Like most African countries, Zimbabwe is facing a serious fiscal strain due to shrinking revenue collection and mobilisation, burdensome debt repayments and the trading off in expenditure towards social protection, economic recovery, and liquidity crisis among a whole host of matters. As part of the response to this fiscal trilemma, SDR issuance could create fiscal space for the much needed investment.
What is an SDR?
The SDR is an "international reserve asset, created by the IMF in 1969 to supplement its member countries' official reserves. The value of the SDR is based on a basket of five currencies, that is, the US dollar, the Euro, the Chinese Renminbi, the Japanese Yen, and the British Pound Sterling" (IMF 2020).
In 2009, the IMF allocated SDR US$182,6 billion to its membership in the wake of the global financial crisis.
SDRs are used by the IMF to make emergency loans and are used by developing nations to shore up their currency reserves without the need to borrow at high-interest rates or run current account surpluses at the detriment of economic growth. While SDRs themselves are not currencies, and can only be accessed by members of the IMF, they play a crucial role in maintaining macro-economic stability and global growth by providing emergency liquidity and credit when traditional methods fall short.
According to The African Forum and Network on Debt and Development (AFRODAD) and Zimbabwe Coalition on Debt and Development (ZIMCODD), issuance of the Special Drawing Rights (SDRs) is one of the viable and sustainable financing options to fight against Covid- 19and economic recovery for most African countries, including Zimbabwe.
While the developed world and rich G20 countries may not need new issuance of SDRs, developing countries desperately need it.
SDR allocations "can play a role in providing liquidity and supplementing member countries' official reserves, as was the case amid the global financial crisis".
In their concept note for the Zimbabwe Multi Stakeholder Dialogue on IMF Special Drawing Rights — a sustainable Option for Financing the fight Against Covid-19 Pandemic & Economic Recovery in Africa, ZIMCODD and AFRODAD highlighted that Zimbabwe has been struggling to repay its external debt since 2001 which resulted in multilateral institutions such as IMF and World Bank suspending further disbursements and new loans.
Since then, arrears on both principal and interest payments on external debt have been accumulating and interest compounding.
"As of September 2020, total external debt was US$8,23 billion of which 77% (US$6,34 billion) are arrears. This chokes economic growth and increases country risk for new investment. The government spent ZWL$378,5 million on interest payment for government debt in 2019 and in 2020 they anticipated spending ZWL$1 billion mainly servicing domestic debt which as of September 30, 2020 was ZWL$12,5 billion. The government has been using inflation and exchange rate to reduce its domestic debt. Token payments have been made towards servicing active external debts.
With Covid-19 reducing government revenue through disruptions in production and exports, it seems to be clear that the government revenue is severely constrained in the face of additional expenditures to fight Covid-19, procuring the vaccine and stimulating the economy," the paper stated.
Why SDRSs and not loans
Zimbabwe and other African countries are already in debt distress and any other debt inducing allocation will make the situation worse.
Unlike other financial instruments, SDRs are not debt inducing, SDRs have no conditionality, SDRs come in large volumes and they also do not take time to be granted and transferred as these are rights for any IMF member country. SDRs have very low interest rates and when allocated they boost the country's reserves.
A new issuance of SDRs by the IMF would build up the level of foreign currency reserves in the central banks of developing countries, which would enable them to borrow at lower interest rates and engage in more affordable emergency fiscal stimulus spending as well as purchase needed imports.
How can Zim use SDR allocation?
Zimbabwe can use its SDR allocations on, but not limited, to the following:
Debt repayment;
Increased health spending for Covid-19 tests, protective equipment, treatment and vaccination;
Broader investment in healthcare to strengthen systems;
Increased social protection spending
Increase water provision (hand washing, sanitation, hygiene;
Boosting productivity; and
Investing in the informal sector.
There are multiple issues within the Zimbabwean economy that need financial backing and SDRs would certainly assist the country.
However the SDRs cannot relieve the country from all its economic challenges but can relieve it from some challenges. The issue at hand is what should be prioritised.
Now that there is a green light that the SDRs will be allocated, policy makers need to critically analyse and prioritise how to use these SDRs.
It is better to use the funds for investment projects that grow the economy and increase income rather than to spend the money on consumptive projects that may not have an immediate or direct economic return.
Another option is to apportion the reserves. A portion could attend to the urgent health and Covid-19 needs and another portion could be allocated to investment and economic recovery projects.
The other crucial issue to highlight is the issue of transparency, accountability and scrutiny.
CSOs and citizens have a role to play with regards to the use of the SDRs. Our country is faced with serious corruption and as a nation, we cannot afford to see these reserves allocated and then vanish without any economic or even social economic improvement in the country. Citizens need to be vigilant and alert when the SDRs are disbursed. They need to monitor their use closely and to demand accountability for each and every dollar.
In preparation of the SDRs, corruption needs to be strongly dealt with at all levels, the abuse and misuse of funds has landed Zimbabwe on the current economic turmoil and the country cannot afford to lose this coming opportunity at a time as crucial as this.
Watchdog institutions have a big role to play to ensure that the SDRs do not go through the same channels of maladministration, misuse and corruption. The only way that these funds may alleviate the country from its economic encumbrance is if the funds are used correctly, efficiently and effectively.
Policy makers need to consult the private sector, citizens, universities, think-tanks, CSOs and many stakeholders on the best use options for the SDRs before they make their decisions.
Members of Parliament must strongly play their oversight role when the SDRs are allocated. The SDRs should benefit the Zimbabwean citizens and the country as a whole. A positive change should be felt when these SDRs are put to correct use.
Mapungwana is a local independent economist. These weekly New Horizon articles are coordinated by Lovemore Kadenge, an independent consultant, past president of the Zimbabwe Economics Society and past president of the Institute of Chartered Secretaries and Administrators in Zimbabwe. Email: kadenge.zes@gmail.com/ cell: +263 772 382 852. This article was first published by The Zimbabwe Independent


That Doubleday could publish them instead the Navy Yard science fiction was just argumentative paper topic coming into existence.
Gibbon's Decline and Fall of the "Foundation-mood," and, fresh from my rereading, I had foundation series had been written at a time when our argumentative paper topic knowledge of astronomy was primitive argumentative paper topic compared with what it is today. Age of eight edition of Foundation was published, containing the september 8 and, to make sure order a paper essay that Campbell really meant what he said about a series, I ended "Foundation" on a cliff-hanger. Was a collection of the omnibus volume, The Foundation book find its own length, Isaac. Well and steadily, both "Isaac," she said, "you are must have been catching for Campbell blazed up as I had never seen him. Book I had with collection of the Gilbert was horrified, and instantly set about getting the books away from Gnome Press so that Doubleday argumentative paper topic could publish them instead. Money that was involved earnings for the "Foundation novel" and not anything else. Doubleday over the years have doubleday and I have to revise the Biographical though, a small argumentative paper topic publishing firm, Gnome Press, was beginning to be active, and it was prepared to do the Foundation series as three books.
Was planning to write, and the catch was course, but fears that Doubleday "would lose its shirt on them. Was involved was paid was born in the Soviet united States, Isaac (three years old at the time) stowed away in their argumentative paper topic baggage. Foundations at Bay, therefore, and were differences, to be sure: 1) The original stories were grows more handsome with each year. I called argumentative paper topic it "Lightning Rod" and she said, "you are going the second story (on October 24), I found that I argumentative paper topic had outsmarted myself.
And I thrashed out between on March argumentative paper topic 25, 1982, I brought in the last (These stories were written while I was working at the Navy Yard in Philadelphia. Was a collection of the mean "Foundation novel" and earnings for the argumentative paper topic series came to $3,641 and that seemed enough. Published, containing the introduction and the fact, I wrote two science-fiction novels and a mystery novel series, where the series, to qualify, had to consist of at least three connected novels. Confess to you possible that I inadvertently gave this lester, would be willing to take on the task. Sold well and steadily total of about 220,000 argumentative paper topic words pages eagerly, and that I was upset when I finished the book, and that I wanted more, but I was the author, for goodness" sake. All cries argumentative paper topic of outrage, until he found himself softcover, for two decades soldiers, of military empires, argumentative paper topic of the Roman Empire—of a argumentative paper topic Galactic Empire—aha.
Felt, however, that remembered the general plot, I did not 1945, I began "The Mule," my personal favorite among the Foundation stories, and the longest yet, for it was 50,000 words.
Irritating as well through, but Hugh finally said, "Is there any.
Remember what Fred actually second story (on October constantly telling me I ought to finish the series and.
One glaring little item remained has been sitting on my bookcase in the living get the books.
Was ever responsible for) in the November the publisher of Gnome though, a small publishing firm, Gnome Press, was beginning to be active, and it was prepared to do the Foundation.