NAVWEPS OD-8OT-80  BASIC AERODYNAMICS  exists. This situation creates  an induced angle  of attack at the root which is less than the  average for the wing and a local section angle  of attack higher than the average  for the wing.  The result is shown by the graph of figure 1.32  which depicts a local lift coefficient  at the root  almost 20 percent greater than the wing lift  coefficient.  matched with a planformwhose chord is dis-  tributed in an elliptical fashion (the elliptical  wing), each square foot of area along the span  produces exactly the same lift pressure. The  elliptical wing planform then has each section  of the wing working at exactly the same local  lift coefhcient and the induced downflow at  the wing is uniform throughout the span. In  the aerodynamic sense, the elliptical. wing is  the most efficient planform because the uni-  formity of lift coefficient  and downwash incurs  rbt iea$t induced drag for a given aspect ratio.  The merit of any wing @anform is then meas-  ured by the closeness  with which the distribu-  tion of lift coefficient  and downwash approach  that of the elliptical planform.  The effect of the rectangular planform may  be appreciated by matching a near elliptical  lift  distribution  with  a planform with  a  constant chord.  The chords near  ‘ the  tip  develop less lift pressure than the root and  consequently have lower section lift coe&-  cients. The great nonuniformity of local lift  coefficient along the span implies that some  sections carry .more than their share of the  load while others carry less than their share  of the load. Hence, for a given aspect ratio,  the rectangular planform will be less efficient  -t--  -L.  -11:. -!-~I  LlLill UK C ‘ lqJLlCal wing.  For exampie, a  rectangular wing of AR=6  would have 16  percent higher induced angle of attack for the  wing and 5 percent higher induced drag than  an elliptical wing of the same aspect ratio.  The effect of the elliptical planform is illus-  trated in figure 1.32 by the plot of local lift  coefficient to wing lift coefficient, f!  G’  versus  scm:spnn L.“CY.ICG.  ,4;..t,or,  Tbac  e!liptical wing p*  duces a constant value of$=J.O  throughout  the span from root to tip.‘  Thus, the local  section angle of attack, LYE,  and local induced  angle of attack, CY,,  are constant throughout  the span. If the planform area distribution is  anything other than elliptical, it may be ex-  pected that the local section and induced angles  of attack will not be constant along the span.  At the other extreme of taper is the pointed  wing which has a taper ratio of zero. The  extremely small parcel of area at the pointed  tip is not capable of holding the main tip  vortex at the tip and a drastic change in down-  wash distribution results. The pointed wing  has greatest downwash at the root and this  downwash decreases  toward the tip.  In the  immediate vicinity  of the pointed tip,  an  upwash is encountered which indicates that  negative induced angles of attack exist in this  area. The resulting variation of local lift  coefficient shows low cr at the root and very  high c, at the tip.  This effect may be appre-  ciated by realizing that the wide chords at  the root produce low lift pressures  while the  very narrow chords toward the tip are sub-  ject to very high lift pressures.. The varia-  tion of 2 throughout the span of the wing of  L  taper ratio==0 is shown on the graph of figure  A planform previously considered is the  simple rectangular wing which has a taper  ratio of 1.0. A characteristic  of the rectangular  wing is a strong vortex at the tip with local  downwash behind the wing which is high at  the tip and low at the root.  This large non-  uniformity in downwash causes similar varia-  tion in the local induced angles of attack along  the span. At the tip, where high downwash  exists, the local induced angle of attack is  greater than the average for the wing.  Since  the wing angle of attack is composed of the  sum of at and aor a large local (x, reduces the  local a0 creating low local lift coefficients at  the tip.  ‘ Ihe reverse is true at the root of the  rectangular  wing where low local downwash  76 