Drag Analysis of a Skyhopper

PART I
Drag Analysis Of 1 Ikyhopper
By J. V. Walsh, EAA 2351
INTRODUCTION
ahead of the static vent can make 115 TAS read as high
The membership of the EAA is made up of amateurs
with a sprinkling of trained aeronautical engineers. This
article is written by a non-professional for the use of nonprofessionals. For this reason, each step is detailed, so
that no doubt of the method used may exist.
The professional manufacturer can improve the performance of his design by increasing engine power, the
as 140 IAS. He also pointed out the fallacy of using
war surplus rate of climb instruments. In this particular
aircraft, we discovered that by shortening the pilot tube
12 in., the IAS increased 10 mph.
The remainder of the answer lies in what we shall
use of a constant-speed propeller, etc. The homebuilder
is limited in the performance of his aircraft by weight
and finances. Relatively few engines are priced within
the range of his pocketbook. He differs from the professional in that he works with a minimum of skills, a
minimum of means, and a minimum budget. The performance of his aircraft is, therefore, governed by the
thrust he can afford to purchase and the total drag of the
product of his labors.
Relatively little has appeared in SPORT AVIATION
in the past five years on drag analysis. This article is
presented in the hope that professional aeronautical engineers will criticize it in a constructive manner, and
offer refinements or better methods of analysis.
The net result hoped for is a system of drag analysis
that any homebuilder can apply to any project, in order
to obtain maximum performance from limited sources.
Since we are interested in efficient cruise, this
analysis was made at the engine manufacturer's recommended cruising rpm. If the performance figures seem
rather low, it is because they are honest. Many individ-
uals have been disappointed when the performance of
their aircraft fell short of published figures, even though
politely call "Oriental Hyperbolae." For example, in one
design formerly advertised in SPORT AVIATION, how do
you make a 170 Ib. pilot, a parachute, 28 gals, of gas, 6
qts. of oil, and 40 Ibs. of baggage come out to a total
of 300 Ib. payload? To cite another case, how do you
land a ship at 70 mph IAS, when pilots who have flown
it say it falls out of the air at 85-90 IAS? That such discrepancies should escape the notice of the amateur is
understandable. That those who quote such inconsistencies for their designs should fail to appreciate the disservice they are doing to EAA is difficult to understand.
In this analysis, you will note that in many cases
figures are worked out to three decimal points. Honesty
and accuracy are essential for a successful analysis. This
is particularly true of airspeed. True airspeed is essential; indicated airspeed will only compound error.
Principal Dimensions and Data
Total Wing Area
S
Wing Span
b
Aspect Ratio
A
Overall Length
L
Gross Weight
Cruise Speed
Power
Prop Efficiency
Altitude
W
V
BMP
Pe
100 sq.
25
6.25
18
ft.
ft.
ft.
ft.
1,230 Ibs.
161.37 (110 mph)
92.5%
86%
3,000 ft.
their workmanship was beyond reproach. In some cases,
Sources
this discrepancy has been due to the publishing of inaccurate data.
Part of the reason for this inaccuracy lies in faulty
Reference 1: Fluid Dynamic Drag—S. F. Hoerner, 1958
Edition
instrumentation. In his article, "How to Improve the Performance of Small Biplanes," EAA member Silas Well-
man pointed out how the addition of a small ring just
The installation of this Beech-Roby propeller has high
drag and should include a spinner. However, it is very
14
The Salvay "Skyhopper," CF-RDG, is the
difficult to mount the backing plates for a spinner. The
cowl openings are much too large, increasing cooling
subject of this article on drag analysis.
drag greatly.
JULY 1964
Reference 2: Aircraft Mechanics Pocket Manual, 5th Edition
Reference 3: Homebuilders Handbook—S. Urshan, 1955
Formula:
The formula for drag is Cd x S x q. "Cd" is the particular coefficient of drag; "S" is the particular drag area
in square feet; "q" is the dynamic pressure corrected for
altitude. Dynamic pressure at 3,000 ft. is only 92 percent
of sea level pressure, i.e., .92 x .00238 = .00219 — QUESTION: Should the dynamic pressure be corrected for tem-
perature also, and if so, how?
"q" equals one-half the dynamic pressure times the
velocity in feet squared. For the test specified, "q" equals
(110 x 1.467)2 times J/i(.00219) = (161.37)2 x .0011 =
28.64
SECTION ONE
Calculation of Thrust
In the first test, a metal prop 70 in. in diameter with
a 56 in. pitch was used. Applying the method described
Another source of
interference drag
is this little blister to cover the
landing gear leg.
in "Amateur Builder's Manual," (Vol. 2, page 30), the
effective pitch was determined to be 88 percent. RPM
used was 2350. The Lycoming Corp. power curve for the
0-235-C engine (No. 8210) indicates this to be 90 hp.
The total thrust at 110 mph, (TAS) using the formula
presented in Ref. 2, is—
90 x .88 x 375
110
A Beech-Roby variable pitch propeller was installed,
after a bit of engineering and a great deal of 17th century English to make it fit a Lycoming engine. At the
same altitude, 110 mph was obtained with 2400 rpm.
Using the same power graph, this worked out to 92.5
brake hp.
Since the speed was the same, thrust (and drag) were
the same. Therefore, the "Pe" of the Beech-Roby was—
90 x .88 x 375
92.5 x Pe x 375
—————————
equals
—————————
110
110
The Beech-Reby at 2400 rpm was .856 or 86 percent
efficient. While it did not improve the cruise, it did make
The "coke-bottle" tuselage effect on this "Skyhopper" is
caused by the '"Super Cub" cowl which is too wide and
has high drag.
an appreciable difference in take-off time and distance,
as well as rate of climb. The installation remained, and
all future calculations were made with it.
Incidentally, if anyone can tell me how to fit a spinner on a Beech-Roby—Lycoming installation, I will be
most grateful. This installation was once FAA approved,
but Univair, who made the modifications to the prop,
were unable to supply drawings on how it was done.
SECTION TWO
Induced Drag
We have seen that the thrust of the airplane (at altitude, power setting and speed specified) was
92.5 x .86 x 375
110
which equals 271.2 Ibs. In steady horizontal flight, the
total drag is equal to the thrust. Therefore, the total
drag under the conditions specified is 271.2 Ibs.
For any flight condition, lift coefficient equals W/S.
When computing W/S, don't forget to add the down-load
on the tail for the given flight condition, for the wing
must also Hit this load. In my case, W/S worked out to
12.5 Ibs. per sq. ft.
For the given flight condition, Cl equals
W/S
12.5
= .44
28.5
(Continued on next page)
This type of traffic - tread p a i n t
used for a wingwalk has a very
high interference
drag.
Such protuberances as tie-down rings, aileron control
fairings and inspection plates, while contributing to drag,
are located where the drag is lower.
SPORT AVIATION
15
DRAG ANALYSIS . . .
(Continued from page 15)
Because of tip shape, the effective aspect ratio is
reduced from the geometric 6.25 by an estimated minus
.13 to 6.12.
The wing planform has a taper of 2 to 1. This increases the induced drag by an estimated 2 percent. The
wing twist of 3 deg. increases it by another estimated 2
percent. The coefficient of induced drag bears the following relationship to the coefficient of lift and aspect ratio:
Cdi equals C12AA—this now becomes
Cdi equals 1.04 (CPAA)
Dihedral also has a bearing on induced drag, since
it lessens the span and therefore the aspect ratio. For the
3 deg. of dihedral in this ship, the results are so small
they can be ignored. However, if your project has a pronounced dihedral in relation to span, such as found in a
gull-wing, you might be well advised to investigate this
point.
Cd in-iuced = l.C4(C12AA)
= 1.04C.442/3.1416 x 6.12)
= .011
Induced drag equals Cdi x S x Q — equals .011 x
100 x 28.64. For the speed, weight and altitude specified,
the induced drag of the aircraft is 31.5 Ibs.
Conclusions:
The basic formula for induced drag coefficient is
C12/«rA. The larger we make "A," the greater the denominator of the fraction becomes, and the smaller the resultant drag coefficient.
This frontal view of the
"Skyhopper" easily
points up the high-drag items on the airplane.
Reynolds Number at sea level may be computed by
RN = V x c x 6380
with "V" as velocity in feet per second and "c" as the
chord in feet. However, since density of air and temperature decrease, with altitude, the RN for constant speed
also decreases with altitude. At 3,000 ft., RN would
be V x c x .92(6380), i.e., 92 percent of RN at sea level.
This means RN becomes smaller as we ascend higher,
and Cdf becomes larger. Now you know why manufacturers engaged in the cut-throat game of selling airplanes
always quote performance figures at sea level, and one
of the main reasons why the performance of your aircraft decreases with altitude.
The aircraft in question has a mean geometric chord
of four feet. RN of the wing at sea level would be
4,118,290. But RN at sea level is of no value to us, unless we want to use the wing as a surf-board. RN at flight
level 3,000 ft. is what we need — and that is
V x c x .92(6380) = 3,788,826.
The Cd friction is, therefore,
Cdf = .036
- .036/12.48 = .0029
(3,788,826)'/6
The wing control gaps are another factor adding to parasite drag.
"A" is determined by b2/S. Therefore, to lessen induced drag, increase the span—never the wing area. Remember, though, you can only go so far with this. As
you increase span, you also increase weight, which will
raise your Cl and nullify your efforts. Take some paper
and work on it. Somewhere along the line, you will hit a
ratio of CP/irA that will give you the smallest Cdi
for your design.
SECTION THREE
Parasite Drag of the Wing
1. Basic Skin Friction
From Ref. 1, p. 2-5, the following formula is extracted
as adequate to approximate the friction-drag-coefficient
of a smooth and plane surface within the Reynolds Number range associated with aircraft, i.e., between RN 106
and RN 10?
Cd friction = K/(RN)'/6
where "K" is considered a constant of .036, and RN is the
Reynolds Number of the surface under consideration.
16
JULY 1964
Now, you can't have a smooth and plane surface,
such as a wing, without having two sides — top and bottom. Therefore, Cd section equals 2Cdf.
If our smooth and plane surface were such a thin
section, its thickness would be negligible, we could leave
the formula "like that and Cds/2Cdf would equal one.
But we have a section that is 15 percent thick at the
root and 12 percent thick at the tip—and average thickness of .15 plus .12 equals .135 — this will add to the
profile drag.
Our formula for the wing now becomes (Ref. 1,
p. 6-6)
Cds equals 1 plus 2(T/C) plus 100(T/C)<
2Cdf
If the wing surfaces were identically smooth on
both sides, friction drag would be the same on both sides,
and the above formula would be adequate to give us our
parasite drag. But such is never the case in actual construction. We always roughen the top and bottom surfaces by adding such things as skin joints, inspection
panels, rivets, etc. All these increase our friction drag,
and since we hardly ever add these things in equal
amounts to top and bottom surfaces, the increased fric-
tion-drag-coefficient is never the same for both top and
bottom.
Then, too. the dynamic pressure will only remain the
same for top and bottom if we use an elliptical section
at a constant zero angle of attack. Now, if we so desire,
we can do this — but it poses a slight difficulty — the
I
wing will never generate any lift and the airplane will
never get off the ground. To make the wing lift, we must
introduce angle of attack and/or camber. Actually, we do
both with an airfoil section — increasing the pressure on
the bottom side and decreasing the pressure on the top
side. This results in an increase of drag on the top side
and a decrease of drag on the bottom side. Now you can
see why if you must add barnacles, such as inspection
panels or struts, the best place for them is the bottom of
the wing — the side where the drag is lower.
Professor Hoerner says this increase due to angle of
attack and camber can be added to our equation by plus
or minus CI/5. Our equation for section drag now becomes
a) upper surface:
Cds = 1 + 2OVC + Cl/5) + 100(T/C + Cl/5)"
Cdf
b) lower surface:
The left wing has a tendency to drop sharply at the stall,
and it could be dangerous for an inexperienced pilot.
Suspect burbling from the pitot tube tends to aggravate
this condition by speeding up the tip stall.
not covered by the fuselage), our additional skin-frictioncoefficient equals .0171/87 = .0002.
Total skin friction Cd for the top surface equals
.0029 + .0002 = .0031.
For the bottom surface:
Cds = 1 + 2(T/C — Cl/5) — 100 T/C — Cl/5)4
Cdf
(Ref. 1, p. 6-11)
On this aircraft, with T/C = .135, and Cl/5 = .088
a) upper surface: Cds equals 1.693
Cdf
b) lower surface: Cds equals 1.093
Cdf
2. Surface Imperfections
Before we can compute the section drag of the wing
by the above formulae, we must compute all the surface
imperfections for both sides of the wing, in order to determine what additions we must make to our basic skin
friction-drag-coefficient of .0029.
The wings of this aircraft contain a number of imperfections in the form of inspection panels, streamline
blisters, fasteners, etc. — all of which are necessary for
service and maintenance.
In addition, we have traffic tread on each wing
walk. A search of all available sources failed to produce
a drag-coefficient for such paint. Because of its composition and surface roughness, its drag must be very high
and therefore it should not be ignored. Perhaps some
reader can supply the coefficient.
In computing "drag area" in square feet, the following methods were used:
a) inspection panels — spanwise and chordwise edges
were multiplied by the thickness of the metal.
b) sheet metal blisters — frontal area of width times
height.
c) screws and bolts — surface area of all sizes was
totaled and an average "Cd" struck for entry in the table.
d) all drag-coefficients were taken from Ref. 1, pp.
5-7ff.
Spanwise edges
Chordwise edges
Two metal blisters
Tie-down rings
110 assorted screws
12 inspection rings
Spanwise surface gaps
Chordwise surface gaps
Two metal blisters
14 No. 4 p.k. screws
"Drag Area'
Ft.2
.042
.094
.11
.003
Cd
.05
.04
.1
.04
Cd"S"
.002
.004
.011
.0001
Cd
.016
.018
.07
Cd"S"
.175
.01
.07
.0028
.0002
.0049
.0110
.023
.024
.04
.334
.0009
.0080
Total
.0278
Referred to the exposed bottom area of 87 sq. ft., additional skin-friction-coefficient is .0278/87 -— .00032, and
the total skin friction Cdf for this side equals .0029 +
.00032 = .00322.
3. Section Drag Coefficient
Returning to our previous determinations, viz.,
Cds upper surface = 1.693 x total Cdf top
Cds lower surface = 1.093 x total Cdf bottom
the total section drag Cds of the wing becomes
Cds = (1.693 x .0031) plus (1.093 x .00322)
= .0087678
= .009
On an exposed wing area of 87 sq. ft.:
Cd x S = .009 x 87 =, .783
4. Additional Sources of Drag
The following sources of drag are common to both
sides of the wing:
Item
Aileron spanwise gaps
Aileron chordwise gaps
Navigation lights
Pitot static tube
For the Top Surface:
Item
"Drag Area'
Ft.2
Item
.872
"Drag Area"
Ft.2
1.9
.04
.02
Cd
Cd"S"
.03
.5
.057
.020
.1
.002
.010
Total
.089
The total Parasite Drag CdS equals .783 plus .089 =
At "q" = 28.64, total parasite drag is:
Cd x S x q = .872 x 28.64 = 24.974 = 25 Ibs.
Conclusions:
1) The total drag of the wing for speed, weight and
altitude specified is the sum of the induced and parasite
Total
.0171
drag, i.e., 31.5 + 25 = 56.5 Ibs. This works out to 20.8
Referring this to the exposed top surface of 87 sq. ft.
percent of the total drag of the airplane.
(in drag analysis, consider only that portion of the wing
(Continued on bottom of next page,
SPORT
AVIATION
17
Flight-Flutter Testing
By John W. Thorp, EAA 1212
909 E. Magnolia, Burbank, Calif.
HE FLIGHT-FLUTTER test is intended to demonT
strate that the subject airplane is free from flutter
behaviors within the specified operating limits of the
airplane. This demonstration necessarily requires that the
airplane be flown at high speed, which in itself introduces
certain hazards. These hazards may be minimized when
the structural part of the flight test program (see SPORT
AVIATION, November, 1961) is conducted prior to the
flight-flutter test.
In order to demonstrate freedom from flutter, it is
the usual practice to dive the airplane to a speed V,,
which is 10 percent greater than the maximum indicated
air speed at which the airplane need ever be flown. This
"never exceed" speed, V X K , is the speed which is marked
with a red line on the face of the airspeed indicator.
At V n , an effort is made to excite flutter by shaking
the controls. It is obvious that if flutter does develop under these conditions, the consequence will likely be the
loss of the airplane.
As in structural flight testing, the secret of longevity
in flight-flutter testing is to creep up on critical speeds
cautiously, and to be equipped with a parachute that can
be used if someone has guessed wrong.
There is no point in picking a V X F for basis of the
V,, test which is far above any speed that the airplane
may logically use. In correllary, the speed should not be
so low as to seriously limit the usefulness of the airplane. For most airplanes, a V N F of 15 to 20 percent
above the maximum speed that the airplane will attain
in level flight is adequate. Airplanes which are not aerodynamically clean and which are used for aerobatics may
require a higher ratio of V NI , to maximum level flight
speed. It doesn't seem likely that the ratio would ever
need to be more than 1.33, however.
Flutter susceptibility is a function of true air speed.
The red line is indicated air speed. Just because an airplane doesn't flutter at 110 percent of V N K at sea level
is no assurance that it will not flutter at altitude at this
indicated air speed. Also, there is less aerodynamic damping at altitude. These facts, plus consideration of "bail
out" in the event of a flutter disintegration, point up the
desirability of running the flight-flutter test at the highest feasible altitude.
In conducting the flight-flutter test, it is desirable to
only test one set of control surfaces at a time. Since the
elevator, ailerons and rudder will each be tested up to
VD, a number of dives will be required.
To minimize the risk of flutter, it is well to attempt
to execute flutter first at low air speeds. A good speed
for the first attempt at producing flutter is probably in
level flight at normal cruise power. When steady conditions exist and the airplane is trimmed hands-off, "slap"
DRAG ANALYSIS . . .
(Continued from poge 17)
2) Cd of the actual construction wing is D/Sq = .022.
Checking with Report 824, we find this is almost twice
the section drag-coefficient listed for the airfoil section
at RN 6 million and standard roughness. The homebuilder who proportions his design around the listed
section drag-coefficient and fails to consider other sources
of drag is going to experience reduced performance.
18
JULY
1964
the stick a sharp blow in the aft direction. This so that
if the elevator is going to flutter, the speed is in the
process of being reduced, greatly reducing the danger of
a divergent flutter condition. If the stick oscillations
have been heavily damped, the test may be repeated at
a 2 to 5 mph higher indicated air speed. This is repeated
again and again until a speed of 10 percent over the red
line (VN1.;) has been attained without any evidence of flutter. It is desirable to make at least three attempts at
excitation for each condition before proceeding.
The ailerons may be tested next. Again, it is well to
start at cruising speed. With the airplane trimmed, pull
back slightly on the stick then "bat" the ailerons a sharp
blow with the open hand. A large surface displacement
is not required and can be structurally dangerous at higher speeds. Displacement of surface should be at least 3
deg., however. If the ailerons are well damped, a higher
speed may be selected a few miles per hour faster than
the last. In every case, back pressure is exerted on the
stick before exciting the ailerons. A transitory air speed,
particularly diminishing, minimizes the possibility of a
divergent flutter condition developing. However, if an
incipient flutter condition is encountered, a few undamped oscillations of the surface will be evidence that
the "dragon's tail" has been "tickled" enough until corrective measures have been taken.
After 110 percent of V N E has been attained and the
ailerons have demonstrated no tendency to flutter, a similar series of tests are conducted attempting to excite
the rudder. In every case after a steady trim speed is
attained, the stick is pulled back slightly before kicking
the rudder, so that the air speed will be decreasing as
the rudder is excited.
All surfaces must be free from flutter up to VD.
To demonstrate freedom from flutter at V n with a transient speed, it will be necessary to start the final check
on each surface at a speed slightly above Vn.
All elastic structures have critical flutter speeds.
Flutter can destroy a structure in a matter of seconds.
Unless measures are taken to prevent flutter, all airplanes
will experience flutter in one or more components at some
speed, possibly very high.
If the operating speeds are low enough, the flutter
prevention measures may be pretty elementary. As speeds
increase, a greater degree of sophistication will be required to insure against flutter. In any case, the builder
of an airplane has the obligation to demonstrate that his
airplane will not flutter within the airspeed limits established for the particular airplane.
Since flutter is apt to be destructive, be cautious in
all phases of the flight-flutter testing — you are taking
your life in your hands. Good luck!
A
3) The parasite drag almost doubles the published
drag-coefficient. Therefore, for performance—
a) Keep those control gaps and control areas to the
minimum required for adequate control and safety. Keep
the number and size of access panels to a minimum.
b) Flush mount all inspection covers and access
panels with countersunk screws. It's a lot more work,
but it should really pay off.
(To be continued)
A