Morrow, John D

English

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NATIONAL ADVISORY COMMITTEE 
FOR AERONAUTICS 
TECHNICAL NOTE 3550 
MEASUREMENTS OF THE EFFECT OF TRAILING-EDGE 
THICKNESS ON THE ZERO -UFT DRAG OF 
TIDN LOW -ASPECT-RA TIO WINGS 
By John D. Morrow 
Langley Aeronautical Laboratory 
Langley Field, Va. 
Washington 
November 1955 
https://ntrs.nasa.gov/search.jsp?R=19930084314 2020-06-17T17:00:30+00:00Z
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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
TECHNICAL NOTE 3550 
MEASUREMENTS OF THE EFFECT OF TRAILING-EDGE 
THICKNESS ON THE ZERO -LIFT DRAG OF 
THIN LOW-ASPECT-RATIO WINGSl 
By John D. Morrow 
SUMMARY 
Results of an exploratory free-flight investigation at zero lift 
of several rocket - powered drag- research models having tapered 4-percent-
thick wings are presented for a Mach number range of 0.7 to 1.6. Wings 
having an aspect rat i o of 3 .11 and trailing-edge thicknesses e~ual to 0, 
1/ 3 maximum thickness, 2/3 maximum thickness, and the maximum thickness 
were tested. The sections were identical circular arcs back to the 
40-percent-chord station. The remainder of the section was formed by 
drawing a tangent from the trailing edges of various thicknesses to the 
extended circular arc. The data obtained indicated that an increase 
in the ratio of trailing- edge thickness to maximum thickness caused a 
corresponding increase in wing drag coefficient throughout the Mach 
number range investigated, which was due to the increased area over 
which the base suction acts . 
By use of the linear theory and base-pressure values measured on 
a 6- percent- thick blunt- trailing- edge wing, the calculated wing drag 
coefficients at Mach numbers from 1.3 to 1 .5 compared favorably with 
the test results . Thus, the base pressure coefficient of blunt-base 
airfoil sections appears to be constant with base thickness in the 
range of thicknesses from 6 to 1.3 percent chord for Mach numbers of 
1.3 to 1.5. 
INTRODUCTION 
Recent experiments indicate that airfoil sections having sharp 
leading and trailing edges heretofore considered good at supersonic 
speeds may be inferior to blunt-trailing-edge airfoils when compared 
on the basis of drag- stiffness ratio and when used as control surfaces. 
lSupersedes declassified NACA RM L50F26, 1950. 
2 NACA TN 3550 
References 1 and 2 point out the need for further research and the 
possibilities of the blunt-trailing-edge airfoil. The design of such 
wing sections depends largely on the magnitude of the pressures 
developed over the flat base of the trailing edge. 
In view of the scarcity of data on wings having blunt bases, a 
flight investigation of a rocket-powered model has been made at the 
Langley Pilotless Aircraft Research Station at Wallops Island, Va., to 
determine the effect of various-thickness wing bases on the drag of a 
thin tapered wing. An additional purpose was to obtain a comparison of 
the calculated wing drag coefficient, by use of the linear theory and 
measured base-pressure-coefficient values of reference 2, with the 
experimental wing drag coefficient. The results obtained with the four 
models used in this investigation are presented herein. 
The wing drag presented in this paper includes the mutual inter-
ference drag between wings, body, and stabilizing fins. Results are 
presented for a Mach number range of 0.7 to 1.6 corresponding to a 
Reynolds number range of 3.5 x 106 to 10.2 x 106 based on wing mean 
aerodynamic chord. 
SYMBOLS 
CD drag coefficient based on exposed wing area of 2.072 square feet 
M Mach number 
c wing chord 
S exposed wing area, 2.072 sq ft 
R Reynolds number based on mean aerodynamic chord 
W weight of the test vehicle, powder expended, lb 
a measured acceleration, ft/sec2 
g acceleration of gravity, 32.194 ft/sec2 
e angle between model center line and horizontal, deg 
p density of air, slugs/cu ft 
V measured velocity, ft/sec 
NACA TN 3550 3 
T temperature of air, of abs 
t wing base thickness 
tmax maximum wing thi ckne s s 
MODELS 
The general arrangement of the drag-research vehicles used in 
this investigation is shown in figures 1 and 2. The models were 
wooden cylinders with pointed wooden ogival noses and were stabilized 
with four thin metal fins located near the base. The location of the 
4-percent-thick wings of aspect ratio 3.11 and taper ratio 0.423 is 
shown in figure 2. Four models with different wing sections were 
tested. The trailing-edge thickness of the.various sections was eQual 
to 0, 1/3 maximum thickness, 2/3 maximum thickness, and the maximum 
thickness. The wing sections of the models were identical circular arcs 
back to maximum thickness at the 0.4-chord station. From the trailing 
edge of the wing a line is drawn tangent to the extended circular arc 
to form the rear portion of the airfoils with various trailing-edge 
thicknesses. The center of gravity of the models was located so that 
the models vrere stable throughout the test flight. The models were 
propelled by 3.25-inch aircraft rocket motors contained within the 
fuselage and were boosted by 5-inch high velocity aircraft rockets. 
TESTS 
The models were flown at the Langley Pilotless Aircraft Research Sta-
tion at Wallops Island, Va. The test technique consists essentially of 
measuring the straight-line distance from the launching site to the 
model, ascertaining the flight path of the model, and obtaining an 
atmospheric survey at the time of firing. The data from these three 
sources are used in the following equations to determine the drag coeffi-
cient CD and Mach number M for a given model. 
== -2W(a + g sin e) 
gpSV2 
M == V 
4 NACA TN 3550 
The atmospheric quantities p and T are measured with respect to 
altitude by radiosonde and are tied into the flight history of the 
model by altitude-time measurements taken from the SCR 584 radar 
tracking unit. The angle e is determined from the trajectory 
described by the SCR 584 unit by assuming the model to be flying at 
zero lift. The velocity and acceleration time histories are reduced 
from measurements taken from the CW Doppler radar velocimeter unit. 
The Doppler unit furnishes a time history of the straight-line dis-
tance between the model and the launching site. Velocity is obtained 
from the first derivative of the distance-time variation and accelera-
tion is obtained from the second derivative corrected for flight-path 
curvature. The method by which these two differentiations are obtained 
has been analytically developed to its present state of precision, which 
generally results in a maximum possible velocity error of less than 
0·5 foot per second and possible acceleration error less than 3 feet 
per second per second. The probable inaccuracy in the values of wing 
drag coefficient is approximately ±0.002 except at the extreme ends 
of the Mach number range. The Mach number is believed to be accurate 
to within ±0.01. 
The average Reynolds number of the four models based on a mean 
aerodynamic chord of 0.962 foot varied from 3.5 X 106 at a Mach number 
of 0 . 7 to 10.2 X 106 at a Mach number of 1.6. A plot of Reynolds number 
against Mach number is shown in figure 3. 
RESULTS AND DISCUSSION 
The total-drag coefficient is plotted against Mach number in fig-
ure 4 for each of the models investigated. A curve for a wingless model 
(ref. 2) is also shown in figure 4 in order that the wing drag coeffi-
cient may be found. A comparison of the wing drag coefficients (fig. 5) 
shows that an increase in base thickness causes an increase in wing 
drag coefficient which is due to the increased area over which the base 
suction acts. 
Also shown in figure 5 are calculated wing drag coefficients for 
each of the four profiles, computed at three Mach numbers by use of 
base pressure coefficients measured on a 6- percent-thick blunt-base 
airfoil (ref. 2) . The calculated points agree reasonably well with the 
experimental results; this agreement indicates that, for a given Mach 
number, the base pressure coefficient appears to be constant in the 
range of base thicknesses from 6 to 1.3 percent chord for Mach numbers 
from 1.3 to 1.5 and in the Reynolds number range of the tests. This 
result is in agreement with reference 1 and other data from the Ames 1-
by 3-foot supersonic tunnel . 
NACA TN 3550 5 
Figure 6 shows the computed drag-coefficient components for a 
Mach number of 1.4 plotted against the ratio of wing base thickness to 
maximum thickness. The base drag component was calculated from the 
base-pressure-coefficient curve of a 6-percent-thick airfoil with a blunt-
base presented in reference 2. The wave-drag component was calculated 
by the linearized theory as presented in reference 3. The friction 
drag component was estimated to be 0.006 based on exposed plan-form 
area. Also shown in figure 6 are experimental points for the four 
different configurations. 
CONCLUDING REMARKS 
An exploratory flight investigation of rocket-powered drag-research 
models has been conductea at zero lift for a Mach number range from 0.7 
to 1.6 . The data obtained indicate that an increase in the ratio of 
wing base thickness to maximum thickness causes a corresponding increase 
in wing drag which is due to the increased area over which the base 
suction acts. By use of the linear theory and base pressure values 
measured on a 6-percent-thick wing, the calculated wing drag coeffi-
cient at Mach numbers from 1.3 to 1.5 compared favorably with the test 
results. Thus, the base pressure coefficients of blunt-base airfoil 
sections appear to be constant with base thickness in the range of 
thicknesses from 6 to 1.3 percent chord for Mach numbers of 1.3 to 1.5. 
The pointed trailing-edge airfoil had the lowest drag throughout the 
Mach number range investigated, and the section with base thickness 
equal to maximum thickness had the highest drag throughout the Mach 
number range. 
Langley Aeronautical Laboratory, 
National AdviSOry Committee for Aeronautics, 
Langley Field, Va., June 26, 1950 . 
6 NACA TN 3550 
REFERENCES 
1. Chapman, Dean R.: Reduction of Profile Drag at Supersonic Velocities 
by the Use of Airfoil Sections Having a Blunt Trailing Edge. NACA 
RM A9Hll, 1949. 
2 . Morrow, John D., and Katz, Ellis: Flight Investigation at Mach 
Numbers From 0. 6 to 1.7 To Determine Drag and Base Pressures on 
a Blunt-Trailing-Edge Airfoil and Drag of Diamond and Circular-
Ar c Airfoils at Zero Lift. NACA TN 3548, 1955. ,Supersedes NACA 
RM L50E19a.) 
3. Bonney, E. Arthur: Aerodynamic Characteristics of Rectangular Wings 
at Supersonic Speeds. Jour. Aero. Sci., vol. 14, no. 2, Feb. 1947, 
pp. 110-116 . 
NACA TN 3550 7 
Figure 1 .- Typical wing plan form for the configurations tested. 
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Notes: 
1 . The leading edges are identical circular 
arcs for all models back to the 
0 .4 chord station. 
2 . The portion of the wing from 0 .4 chord 
to the trailing edge is formed by 
drawing a line from the trailing ed~ 
tangent to the continued circular arc. 
3 . All secti ons are 4 percent thick . 
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Figure 2.- General arrangement of vehicle showing each airfoil section 
investigated. 
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Figure 3.- Reynolds number based on mean aerodynamic chord of 0.962 foot 
plotted against Mach number. 
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Figure 4.- Total-drag coefficient plotted against Mach number for four 
winged configurations and a wingless configuration. The total-drag 
coefficient is based on exposed wing area of 2.07 square feet. 
1.5 1.6 
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NACA TN 3550 
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tmax 0 
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Figure 5 .- Comparison of experimental and calculated wing-alone drag 
coeffic i ents for the four sections plotted against Mach number. The 
wi ng drag coefficients are based on exposed wing area of 2. 07 square 
feet. 
BaSH wdVB+fricfion 
.04f---i--t--t----t--
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Figure 6 .- Drag-coefficient components calculated at M = 1.4 plotted 
agai nst the ratio of wing base thickness to maximum thickness. 
NACA - Langley Field. Va. 
11 


Measurements of the Effect of Trailing-edge Thickness on the Zero-lift Drag of Thin Low-aspect-ratio Wings

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