Investigations on the Downwash Behind a Tapered Wing With Fuselage and Propeller Page: 13 of 52

N.A.C.A. Technical Memorandum No. 876

is current coordinate
1, circulation at point t
'o, circulation at wing center
I, mean circulation
w, vertical interference velocity
u, horizontal interference velocity
V, wind velocity
The wing is assumed as lifting line.
The lift distribution of the given tapered wing was
interpolated from the collected data of Fuchs and Hopf (ref.
erence 11) (fig. 17). The drop in lift distribution at the
wing tip was approximated with
- 1525 (1 - Cq)
within the limits = 0.96 to 1.0, and the share of this
range on the downwasR computed by simple approximation
(square terms disregarded). For the range of E = 0 to
0.20 the lift distribution was approximated with
1 a
= 1 - 0.875 Eq and tho integral within Eq = 0 to 0.96
was graphically defined. In view of the chosen high-dis-
tance factor t = 1;0 the denominator term was put as
before (reference 1) equal to i.
The theoretical curve for nonrolled-up vortex sheet is
shown in figure 6, with the computed curve shifted by the
amount h = -0.2. The result is approximately the same as
that obtained with the dual tube recorder at a = 6.80,
while the nondisplaced curve* computed for the trailing
*There is no cause for a displacement as the marginal vor-
tices lie - as stated - at wing height, But shifting the
downwash curve computed for the trailing vortex also by h
-0.2, affords, of course, a better agreement with the meas-
ured values, as the peaks of the curves then are at the same


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Muttray, H. Investigations on the Downwash Behind a Tapered Wing With Fuselage and Propeller, report, September 1938; ( accessed May 25, 2019), University of North Texas Libraries, Digital Library,; crediting UNT Libraries Government Documents Department.

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