<DOC>
<DOCNO>
433
</DOCNO>
<TITLE>
application of two dimensional vortex theory to the
prediction of flow fields behind wings of wing-body
combinations at subsonic and supersonic speeds .
</TITLE>
<AUTHOR>
rogers,a.w.
</AUTHOR>
<BIBLIO>
naca tn.3227, 1954.
</BIBLIO>
<TEXT>
  a theoretical investigation has been made of a general method for
predicting the flow field behind the wings of plane and cruciform wing
and body combinations at transonic or supersonic speeds and slender configurations
at subsonic speeds .  the wing trailing-vortex wake is
represented initially by line vortices distributed to approximate the
spanwise distribution of circulation along the trailing edge of the
exposed wing panels .  the afterbody is represented by corresponding
image vortices within the body .  two-dimensional line-vortex theory is
then used to compute the induced velocities at each vortex and the
resulting displacement of each vortex is determined by means of a numerical
stepwise integration procedure .  the method was applied to the
calculation of the position of the vortex wake and the estimation of
downwash at chosen tail locations behind triangular-wing and
cylindrical-body combinations at supersonic speeds .  the effects of
such geometric parameters as aspect ratio, angle of attack and
incidence, ratio of body radius to wing semi-span, and angle of bank on
the vortex wake behind wings of wing-body combinations were studied .
the relative importance of wing vortices, the corresponding image
vortices within the body, and body crossflow indetermining the the total
downwash was assessed at a possible tail location .
  it was found that the line-vortex method of this report permitted
the calculation of vortex paths behind wings of wing-body combinations
with reasonable facility and accuracy .  a calculated sample wake shape
agreed qualitatively with one observed experimentally, and sample
results of the line-vortex method compared well with an available exact
crossflow-plane solution .  an empirical formula was derived to estimate
the number  of vortices required per wing panel for a satisfactory
computation of downwash at tail locations .  it was found that the shape
of the vortex wake and the ultimate number of rolled-up vortices behind
a wing depend on the circulation distribution along the wing trailing
edge .  for the low-aspect-ratio plane wing and body combinations
considered, it appeared that downwash at horizontal tail locations is
largely determined except near the tail-body juncture by the wing
vortices alone for small ratios of body radius to wing semispan, and by
the body upwash alone for large values of that ratio .
</TEXT>
</DOC>
