New Method of Determining the Polar Curve of an Airplane in Flight Page: 4 of 39
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NACA TM No. 1076
On.. the other hand, .from the velocity triangle there is
tan 0 = V' = _ (2)
U 2nrns Tr r
where A is the advance ratio of the propeller and 7= r/R
is the nondimensional radius of the blade section,
From formulas (1) and (2) there is obtained
Cx r r
It is soon, from the above formula, that for a given radius
r for zero thrust for the same values of A the efficiencyy
of the blade section is the same, independent of the shape
of the profile or of the thickness and pitch, Moreover it
follows from formula (3) that the efficiency of the various
blade elements of the snam propeller varies inversely pro-
portional to F and is equal to 2.5 XA/ at r = 0.4.
Remembering that the value of X for present day propellers,
with account taken of the increase in velocity of the air--
plano, ; .:y vary within the limits of 1 to Tr it may be as--
sumod that the efficiency at the blade tip varies from 1/n
to 1 and at r = 0.4 from 2v5/ to 2,F Thus, for a thrust
equal to zero, the efficiency of the blade sections in the
most divergent cases may vary within the small limits frota
1/n to 2.5, Considoring the wind tunnel tests of various
profiles it uay be seen that for such snall values of the
efficiency for profiles with equal values of cy/cx the
angles of attack are approximately equal if they are rock-.
oned from the aerodynamic chord of the section, By the
latter the chord parallel to the direction of the velocity
is meant for which the lift of the section is equal to zero,
The effective blade sections are those lying at the radii
from r = 0.3 - 0,4 to F = 1.0,. At smaller radii the
blade either is entirely ineffective or only slightly ef-
As has already been said, for a given value of A the
efficiency of the various elements for soro thrust varies
inversely proportional to F,. The moan value of the effi-
ciency will be possessed by the blade .section at radius
r = 0,65 - 0.7, Fron a preliminary check on the basis of
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Yegorov, B. N. New Method of Determining the Polar Curve of an Airplane in Flight, report, March 1, 1945; (digital.library.unt.edu/ark:/67531/metadc64555/m1/4/: accessed September 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.