Theoretical calculation of the effect of the fuselage on the spanwise lift distribution on a wing Page: 3 of 29
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NACA RM L51J19
Consequently, development of a theoretical method for predicting these
effects is very desirable at this time.
In estimating the effect of the fuselage on the spanwise lift distri-
bution on a wing, it is necessary in general to consider the following:
(1) The fuselage causes a change in the longitudinal velocity in the
vicinity of the wing. This effect is hereinafter referred to as the
(2) If. the fuselage is at an angle of attack relative to the free
stream, it changes the flow about the wing in planes normal to the free
stream. This effect is hereinafter referred to as the "cross flow effect."
(3) The fuselage has a blocking effect; since there can be no flow
normal to its surface.
The inflow effect, which is a result of the finite length of the
fuselage, changes the longitudinal velocity in the vicinity of the wing
and, hence, the lift on the wing. This change is not large for a slender
fuselage but may be important when the fuselage is relatively thick, so
that a substantial change is caused in the local longitudinal velocity.
For the same reason this effect may be important for a wing-nacelle
The cross-flow caused by the fuselage changes the component of free-
stream velocity normal to the fuselage axis and also affects the downwash
flow produced by the wing. The blocking effect of the fuselage is always
present even if the fuselage is an infinite cylinder alined with the free
stream, in which case the other two effects are not-present.
In the following analysis the blocking and cross-flow effects will
be treated by an application of a conformal-mapping procedure to the sim-
plified lifting-surface theory, and the inflow effect will be treated as
a separate correction. The conformal-mapping procedure for calculating
the blocking and cross-flow effects is derived in a somewhat intuitive
fashion from Multhopp' s method (reference 1) and is not theoretically
justified because it applies a conformal transformation to a flow which
is not strictly two-dimensional. However, the method presented herein
(referred to as the new method) is shown to be in good agreement with
experimental results and to give the same result as more exact theory for
two limiting cases - namely, for wing-fuselage configurations having a
wing of infinite aspect ratio and for those having a wing of vanishingly
small aspect ratio.
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Zlotnick, Martin & Diederich, Franklin W. Theoretical calculation of the effect of the fuselage on the spanwise lift distribution on a wing, report, March 3, 1952; (digital.library.unt.edu/ark:/67531/metadc58939/m1/3/: accessed January 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.