  Coronal mass ejections (CMEs) are routinely tracked with imagers in the
interplanetary space while magnetic clouds (MCs) properties are measured
locally by spacecraft. However, both imager and insitu data do not provide
direct estimation on the global flux rope properties. The main aim of this
study is to constrain the global shape of the flux rope axis from local
measurements, and to compare the results from in-situ data with imager
observations. We perform a statistical analysis of the set of MCs observed by
WIND spacecraft over 15 years in the vicinity of Earth. With the hypothesis of
having a sample of MCs with a uniform distribution of spacecraft crossing along
their axis, we show that a mean axis shape can be derived from the distribution
of the axis orientation. In complement, while heliospheric imagers do not
typically observe MCs but only their sheath region, we analyze one event where
the flux-rope axis can be estimated from the STEREO imagers. From the analysis
of a set of theoretical models, we show that the distribution of the local axis
orientation is strongly affected by the global axis shape. Next, we derive the
mean axis shape from the integration of the observed orientation distribution.
This shape is robust as it is mostly determined from the global shape of the
distribution. Moreover, we find no dependence on the flux-rope inclination on
the ecliptic. Finally, the derived shape is fully consistent with the one
derived from heliospheric imager observations of the June 2008 event. We have
derived a mean shape of MC axis which only depends on one free parameter, the
angular separation of the legs (as viewed from the Sun). This mean shape can be
used in various contexts such as the study of high energy particles or space
weather forecast.
