DeRosa, Michael - EWP - Rensselaer Polytechnic Institute

Optimizing Airfoil Sections for Remote Controlled
Pylon Racing
by
Michael DeRosa
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING
Major Subject: MECHANICAL ENGINEERING
Approved:
_________________________________________
Dr. Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
April 2012
(For Graduation May 2012)
© Copyright 2012
by
Michael R. DeRosa
All Rights Reserved
ii
TABLE OF CONTENTS
LIST OF TABLES .............................................................................................................. v
LIST OF FIGURES ............................................................................................................ vi
LIST OF SYMBOLS……………………………………………..……………….…….viii
ACKNOWLEDGMENT. .................................................................................................... x
ABSTRACT. ...................................................................................................................... xi
1. Introduction…………………………………………………………….……………...1
1.1 Background………………………...………………………………….……………...1
1.2 Problem Description……………………..…………………………….……………...3
1.3 Prior Work and Research on Pylon Race Simulations………………...……………...4
2. Methodology……………………………….………………………………………….6
2.1 Airfoil Selection Matrix…………………………………………………………….....6
2.2 Assumptions and Simplifications……….……….……………………...…………….8
2.3 Reynolds Number Calculation…………….…….……………...………….………...10
2.4 Airfoil Drag Coefficient Calculation Using XFOIL……….…………....…..……….12
2.5 Entire Plane Drag Coefficient Calculation…………….…..…………….….……..….15
2.6 Governing Differential Equations……………….………………….…….....……….16
3. Results……………………………………………………………….….……...…….21
3.1 Determination of Top Airfoil Candidates For Race Simulation……………………..21
3.2 Airfoil Race Simulation in Maple……………………………………………………23
3.3 Maximum Speed and Maximum Loss of Speed in Turns………………....……...….27
3.4 Maple Race Simulation Results…….……………………...……….………….....….27
3.5 Airfoil Polar Interpretations……….…………………….………….…………….….29
3.6 XFOIL Plot Comparison……….……………………….……….………….....….33
3.7 Validation of Results………….……………….…………………………….....…….35
3.8 Implications of Moment Coefficient………….…………………….……...……..….37
4. Discussion and Conclusion…….….…………………………………..………….….39
4.1 Summary of High Level Results……….………..…..………….……..………….….39
4.2 Recommendations for Further Results………….………..….….……..……………..39
5. References………………………………………………………...……..…..……….41
iii
6. Appendix……………….……………….………………………………..…….…….42
6.1 Email from Jett .40 Engine Manufacturer Concerning Actual Engine Power
Output…………………………………………………………………….….…….…….42
6.2 Email from Dr. Martin Hepperle on Calculating Thrust on Engine/Propeller
Combination…………………………………………………………………..….……....42
6.3 XFOIL Input Parameters……………..……………………………….…..………….43
6.4 Output of JavaProp Program on Engine/Propeller Combination……….…..………..43
6.5 Screenshots of Maple Calculation of Maximum Possible Velocity and Maximum
Speed Loss in Turns for NACA 66-012 Airfoil…………………………………..……...44
6.6 Maple Screenshots of Maple Calculation of Time and Velocity for Start Line to Take
Off and Around First Turn for NACA 66-012 Airfoil………………………….…..…....48
6.7 XFOIL Polar Accumulation Results (PACC command) for NACA 66-012 Airfoil for
α from -1 to 5 Degrees…………………………………………………………..…..…...51
iv
LIST OF TABLES
Table1 Airfoil Selection Matrix……………………………………………..….……........7
Table 2 Tabulations of drag coefficients for top 12 performing airfoils………..…….....16
Table 3 Maximum possible speed and speed loss in turns for each airfoil candidate.......23
Table 4 Simulated race for NACA 66-012 airfoil…………………..…………….……..26
Table 5 Overall airfoil race simulation results…………………..……..…………….......28
v
LIST OF FIGURES
Figure 1 A typical Quickie 500 pylon racing airplane………………….………………....2
Figure 2 Pylon race course…..………………………..…...…………….………………...3
Figure 3 NACA 66-012 Airfoil………………………………………….………………...4
Figure 4 Clark Y Airfoil…………………………………………………..…..………......4
Figure 5 The paneling of a NACA 66-012 airfoil………………………….………….....12
Figure 6 Coefficient of Lift Input into XFOIL………………………………..………....13
Figure 7 XFOIL output for NACA 66-012 airfoil at ……….……….....14
Figure 8 Pressure coefficient distribution for NACA 66-012 airfoil at ………………………………………………………………….………..……14
Figure 9 Estimation of drag contribution of components in Q-500 pylon racer…...….....16
Figure 10 Initial JavaProp inputs for engine/propeller…………………………….….....17
Figure 11 Estimation of an 8.8x8.75 in. propeller as JavaProp inputs……………..…....18
Figure 12 Thrust vs. Velocity Results as produced by JavaProp…………………..…….19
Figure 13 Maple output for top speed of NACA 66-012 airfoil at 60 seconds….............21
Figure 14 Maple plot for velocity vs. time for NACA 66-012 airfoil at …………………………………………………………………….……..…....21
Figure 15 Velocity of NACA 66-012 airfoil after 50 ft. radius turn at top speed….…....22
Figure 16 Velocity from start line to first turn for NACA 66-012 airfoil…………...…...24
Figure 17 Initial velocity for a particular portion of the race simulation…………..….....25
Figure 18 Velocity and time for first turn around pylon #1………………………..…….25
Figure 19 as a function of angle of attack for 12 airfoils…………………………......30
Figure 20 Drag polars for all 12 airfoils…………………………………...………….....31
Figure 21 Laminar bucket of NACA 66-012 airfoil with flaps……………...………......32
Figure 22 Lift curve for flapped NACA 66-012 airfoil…………………………...……..33
Figure 23 Plot for NACA 66-012 airfoil at ……………………….....34
Figure 24 Plot for MH-17 airfoil at ……………...…………………..34
Figure 25 NACA 66-012 Wind Tunnel Data from Theory of Wing Sections………...…35
Figure 26 Velocity vs. time result of race simulation by Dr. Hepperle…………...…......36
Figure 27 Velocity vs. time result of race simulation for NACA 66-012 airfoil…….…..37
vi
Figure 28 Airfoil pitching moment coefficient as a function of for the 12 airfoils…..38
vii
LIST OF SYMBOLS
dimensionless Reynolds number
free stream air density free stream air velocity airfoil chord length !"
#
free stream air absolute viscosity $
%
whole plane lift force (N)
&
wing area !' "
dimensionless whole plane lift coefficient
!
mass of airplane (kg)
(
gravitational constant *
centripetal acceleration around turns +
turn radius !"
,
dimensionless whole plane drag coefficient
-
dimensionless airfoil drag coefficient
,./
dimensionless wing induced drag coefficient
dimensionless Oswald span efficiency factor
*
dimensionless wing aspect ratio
-0
)
)
-1
change in velocity with respect to time ) 2
thrust from engine/propeller combination (N)
3
whole plane drag force (N)
345667899:
whole plane drag force at lift coefficient of 0.018776 (N)
,.45667899:
dimensionless whole plane drag coefficient of 0.018776
3456;:<'99
whole plane drag force at lift coefficient of 0.563277 (N)
,.456;:<'99
dimensionless whole plane drag coefficient of 0.563277
=
dimensionless power coefficient of engine/propeller combination
>
propeller diameter !"
viii
actual airplane velocity dimensionless pitching moment of airfoil
ix
ACKNOWLEDGMENT
I want to thank my grandfather for instilling a lifelong interest in model airplanes
when I was young, which ultimately put me on a path to pursuing an education and
employment in the aerospace engineering field. I also would like to thank my
grandmother for strongly encouraging me to pursue a Master’s in Engineering. Dr.
Ernesto Gutierrez- Miravete and Dr. Martin Hepperle provided invaluable assistance and
advice during the course of this project. Last, but not least, I want to thank my wonderful
girlfriend Liz for her encouragement during the times when this project seemed very
daunting.
x
ABSTRACT
In remote controlled pylon racing, the Quickie 500 class of airplanes has 500 square
inches of wing area, and with a Jett 0.40 cubic inch displacement methanol fueled engine,
has a top speed of about 150 miles per hour. They are flown 10 times around an oval
course marked by 3 pylons, for a total of 2 to 2.5 miles. These planes lose a significant
amount of speed in the 30 G’s turns. This project will explore several airfoils to find the
optimal airfoil that will minimize the loss of speed of turns while maximizing top speed
during straight and level flight. Airfoil selections include the popular NACA 66-012 and
airfoils designed by Martin Hepperle, Michael Selig, Clark, and Richard Eppler. XFOIL
airfoil analysis program will provide analytical drag coefficient data for each airfoil.
These airfoil drag coefficient will be used to calculate the finite wing drag for level and
turning flights. The blending of two airfoil sections to obtain the best of both will be
explored as well as flaps to increase lift during the turns. Finally, using Maple and Excel,
the airfoil sections will be run through a simulated race, and the one that completes the
race in the shortest amount of time is considered the optimal airfoil for Quickie 500 pylon
racing.
xi
1. Introduction
1.1 Background
Radio controlled pylon racing has been around since the 1960’s, and now there are 3
distinct classes: sport Quickie 500 (120 mph), AMA Quickie 500 (150 mph), and
Quarter 40 (180-200 mph). Academy of Model Aeronautics, known as AMA, is the
governing body of model aviation in the United States. The only difference between
sport and AMA Quickie 500 is that the former uses the 1.25 horsepower Thunder Tiger
Pro .40 engine, while the latter uses a 1.8 horsepower Jett .40 engine. Both are powered
by methanol fuel. The .40 signifies the size of the engines, at 0.40 cubic inch total
displacement. The Jett is able to gain a 0.55 horsepower advantage through the use of
advanced timing. This project focuses pylon racers in the AMA Quickie 500 class
powered by the Jett engine.
There is always a search for an edge to design these planes to fly as fast as possible,
while remaining within rules. The official rules posted on the Academy of Model
Aeronautics’ contest rules website [1] impose the restriction on Q-500 airplane wings:
•
Minimum projected wing area of 500 square inches
•
Wingspan range of 50-52 inches
•
Minimum wing thickness of 1.1875 inches
The purpose of these rules is to enforce equality among each racer. It also keeps the
speeds down which allows the planes to maintain structural integrity in turns. There are
also rules imposed on the fuselage size and tail thickness, but tails and fuselages have
been optimized for minimal sizes through years of experience. The tail is typically a Vtail configuration, and they have been optimized for size and stability. Any further
optimization on the tail and fuselage will yield an insignificant speed benefit through the
reduction of drag. Because the wing is the largest contributor of drag during racing, there
is room for improvement, particularly in the airfoil section. Figure 1 below shows a
typical Q-500 racer, a Viper 500, which is sold by Great Planes. Note the constant chord
wing and the V-tail.
1
Figure 1 A typical Quickie 500 pylon racing airplane [2]
Hence, the Q-500 rules provide sufficient constraint on design that lends the airplane
to be an ideal airfoil test bed. The wing area is fixed at 500 square inches, and the
minimum span is 50 inches, which leads to an aspect ratio of 5. With an aspect ratio of 5,
the chord is 10 inches. With a minimum airfoil thickness of 1.1875 inches, the airfoil
thickness to chord ratio, t/c is fixed at 11.875%. The chord and t/c are important inputs
for the selection of airfoils.
In pylon racing, four racers take off at the same time, fly around a course ten times,
and the first plane that crosses the finish line wins. Pilot skill being equal, the fastest
plane wins, obviously. Being that this is not a perfect world, and pilot skill does vary,
having a fast plane certainly does help. A typical racing course layout and dimensions
are shown below in Figure 2.
2
Figure 2 Pylon race course [3]
As seen in Figure 2, a typical course has 3 pylons, and the perimeter of the resultant
triangle is 951 feet, which translates to 2 miles when flown for 10 laps in a counter
clockwise direction. It is an inefficient flight path to fly a triangular course as shown, but
rather, an oval flight path is more typical. The overall distance covered is closer to 2.5
miles. All planes take off within 0.5 seconds of each other and immediately turn at the
far pylon. The way the course is designed, there are 2 turns per lap, for a total of 20 turns
between straight and level flight. Because there are significant penalties if planes turn
inside the pylons, this scenario will not be considered here.
1.2 Problem Description
While entering the 50 ft. radius turns at 150 mph, the airplane experiences 30G’s of
centripetal acceleration. This results in the wings having to adjust to a higher angle of
attack in order to create more lift to keep the plane in place while turning. An increase of
drag from a higher angle of attack will slow the plane down during turns. The most
3
popular airfoil for pylon racing, the laminar NACA 66-012, in Figure 3, typically loses
10-15 miles per hour in the turns, as exhibited in the radar gun tests. This airfoil is
desirable for low drag in straight and level flight, at the cost of high drag in the turns.
Figure 3 NACA 66-012 Airfoil, Coordinates from [4]
In contrast, a flat bottomed Clark Y airfoil, in Figure 4 below, has a higher lift to
drag ratio due to its higher camber. The high L/D ratio of the Clark Y reduces loss of
speed in the turns. However, its high form drag will not allow it to attain sufficient speed
in the straightway.
Figure 4 Clark Y Airfoil, Coordinates from [4]
There are several different newer airfoils created by Hepperle, Selig, and Eppler that
may have the benefits of both higher speeds in straight ways and lower speed loss in turns
[3]. Particularly, Hepperle and Eppler have designed airfoils specifically for pylon
racing, and they are good candidates. A formal evaluation of all possible pylon racing
airfoils has not been done to this date. A wing comprised of two different types of
airfoils may have the best of both worlds, as well as flaps deflected at small angles during
the turns. Those configurations need to be assessed as well. Although the anticipated
speed benefit of using the optimal airfoil over the NACA 66-012 for this application will
most likely be small, even a 2-3 mph speed benefit coming out of the turns would be
helpful, since it will allow the plane to jump ahead of the competition.
1.3 Prior Work and Research on Pylon Race Simulations
In his MH Aero Tools website [3], Dr. Hepperle performed race simulations for his
own airfoils, as well as existing airfoils of the time. He explored various aspects that
4
effect race times, such as retractable landing gear, tail plane layout, wing aspect ratio,
power of various racing engines, wing surface quality, and employing flaps in turns.
Various paths around a race course and the resultant race times were also explored by
him.
Dr. Hepperle has not performed any simulations on the popular NACA 66-012
airfoils, nor looked into the use of flaps to improve the turning performance of this
particular airfoil. Utilizing flaps for the NACA 66-012 in turns is one of the focuses of
this project. He also did not consider the effect a blended airfoil wing has on the
performance of a pylon racer. This project will attempt to fill in this knowledge gap in
the performance of blended airfoil wings, particularly to improve the race times of the
widely used NACA 66-012 airfoil.
5
2. Methodology
2.1 Airfoil Selection Matrix
Table 1 at the end of this section is the airfoil selection matrix. The first column is
the airfoil name, the second shows the actual shape as produced in XFOIL, and the third
column is the percent maximum thickness with respect to chord length. Even though the
AMA contest rules limit the minimum thickness to 11.875%, thinner airfoils, such as the
Clark Y, are included and tested for reference purposes. If the best performing airfoil is
indeed too thin, it will be disregarded, as it cannot be used in Quickie 500 pylon racers.
The airfoil coordinates for the NACA 66-012, Clark Y, Selig S-8052, and the Eppler
E-220 airfoils were found in the University of Illinois Aerospace Engineering department
(UUIC Airfoil Database) [4]. Coordinates for airfoils designed by Dr. Martin Hepperle,
designated by “MH-XX” are located in the pylon racing page on his MH Aero Tools
website [3]. The Viper 500 pylon racer, shown in Figure 1 above, uses the Selig S-8064,
which Dr. Michael Selig personally designed for this plane alone. The coordinates were
found in a different page in the University of Illinois Aerospace Engineering department
website [5]. Finally, the “MD-X” airfoils are entirely new airfoils created in XFOIL by
interpolating shapes between 2 existing airfoils.
6
Airfoil
Airfoil Shape
Airfoil
Thickness
NACA 66-012 (Baseline)
12.000%
Clark Y
11.706%
NACA 64-012
11.962%
NACA 64-212
11.964%
MH-27
11.990%
E-220
11.469%
S-8064
12.338%
S-8052
11.895%
MH-16
12.127%
MH-17
12.127%
MH-18
11.145%
MH-18B
11.734%
Combination of NACA66-012 and
Clark Y (0.5 Interpolation)- MD1
Combination of Clark Y and
NACA66-012 (0.5 Interpolation)MD2
11.650%
11.654%
Combination of NACA66-012 and
Clark Y (0.25 Interpolation)- MD3
11.772%
Combination of NACA66-012 and
Clark Y (0.75 Interpolation)- MD4
11.612%
Combination of NACA66-012
and MH-18B (0.5 Interpolation)MD5
Combination of NACA66-012
and MH-17 (0.5 Interpolation)MD6
11.815%
12.062%
Table1 Airfoil Selection Matrix
7
2.2 Assumptions and Simplifications
In Figure 2 in section 1.1, the dashed lines in blue in the pylon course layout are the
chosen race path to be used for the race simulation. Race course dimensions were
obtained from the Academy of Model Aeronautics contest rulebook for 426 level pylon
racing [1]. The twin pylons (pylons #2 and 3) are 100 ft. apart and pylon #1 is 475.5 ft.
from the midpoint of the twin pylons. The start line (black dashed line) is 100 ft. (30.48
m.) from the twin pylons so that the plane has to cover only 375.5 ft. (114.45 m.) to
initiate a turn around pylon #1 on the first lap. It assumes that the pylon racer flies just
outside the pylons in turns. The racing simulation takes into account the 475.5 ft. of
straight and level flight between sets of pylons and 50 ft. radii semicircular turning flight.
For simplification, the race course simulation within the project was as follows:
•
Start line to first turn in 114.45 meters (375.5 ft.)
•
19 instances of 50 ft. radius turn in 47.88 meters (157.0796 ft.) preceding a
144.93 meter level flight (475.5 ft.)
•
Final 50 ft. radius turn in 47.88 meters (157.0796 ft.) during lap #10.
•
Back to start/finish line from previous turn in 30.48 meters (100 ft.)
For further simplification, sea level air conditions were used, namely air density of
and absolute viscosity value of ?@A; B[6].
Since the racing airfoils were later found to have maximum speeds in the range of
/
/
146-157 CD , CD is an acceptable speed assumption for the Reynolds number and calculations for all airfoils tested. This speed was obtained from radar gun data of a
NACA66-012 pylon racer top velocity, which is set as our baseline airfoil. The Reynolds
number was calculated for that speed only to obtain all airfoil data in XFOIL. Whole
plane coefficient of lift calculations for both flight regimes were based on the speed of
/
CD for all airfoils.
In reality, the Reynolds number changes with velocity, which has an effect on the
drag coefficient of airfoils. If one looks at any wind tunnel data, one sees that drag
coefficients decrease with increasing velocity due to the delaying of the laminar to
8
turbulent transition. The Reynolds number increases with velocity, especially during the
initial acceleration from zero speed to the first turn, but velocity changes will be much
smaller after this point. To be able to compare each airfoil on an equal basis, a constant
Reynolds number was used at all portions of the race. Also for the same reason, the
straight and level flight regime and turning flight regime lift coefficients are the same for
all airfoils.
The wing is treated as the sole contributor of lift since lift from tail surfaces and
fuselage is insignificant when compared to the wing. Also, this allows each wing to be
compared on an equal basis.
Since the minimum wing (airfoil) thickness is specified by the AMA rules to be
11.875%, any airfoils that are too thin will typically be rejected, with few exceptions for
comparison purposes. Some airfoils are required to be fixed at a certain angle of attack,
either positive or negative, to produce lift during straight and level. This is permissible
since one can easily set a wing incidence (angle of attack) to trim it for high speed flight.
This is true for cambered airfoils which have negative angles of attack at zero lift. At
very small lift coefficients required for high speed flight, it is necessary for the airfoils to
be at a negative angle of attack. For symmetrical airfoils, such as a NACA 66-012
airfoil, zero angles of attack produces zero lift.
Flaps dramatically increase airfoil camber, and lift as a result. For this reason,
flapped airfoils require less angle of attack to produce the same amount of lift as their
unflapped counterparts. For the higher lift regime of turning flight, flaps are beneficial in
increasing lift for a particular airfoil with a small gain of angle of attack. As long as the
angle of attack for turning flight for a flapped airfoil is greater than the straight and level
unflapped angle of attack, the flapped configuration is acceptable. In some cases, so
much lift is created with high angle of flap deflection, that the required angle of attack is
actually less than the unflapped airfoil in high speed flight. Such flap angles are rejected
since it does not make sense for a wing to lower its angle of attack while transitioning
from low to high lift regimes.
For flapped airfoils, the drag coefficient during high speed flight is assumed to be
equal to their unflapped counterparts, due to the assumption of similar airfoil shape when
9
flaps are fully retracted. Realistically, there will be a slight increase in drag due to gaps
and breaks in the airfoil contours where the flap hinges are located.
In his own airfoil simulations, Dr. Hepperle assumed a 10% increase in airfoil drag
for 0.25 seconds to account for the ¼ roll into and out of turns. Overall, the increase of
race time due to this effect is only 0.2 seconds [3]. Since it affects airfoils approximately
equally, and since it has a very slight influence on lap times, the drag increase during
rolling into and out of turns will be ignored.
The above assumptions are required for the simplification of race simulations and to
keep all airfoils on equal basis for the ease of performance comparisons.
2.3 Reynolds Number Calculation
Radar gun data for a pylon racer with a NACA 66-012 (or slight variation of) show a
/
E
maximum speed of CD (
FGH). The 2011-2012 AMA contest rules specify a
minimum wing area of IJ' (!'), and wingspan range of 50-52 inches [1].
As stated before in the introduction section, for a 500 square inch wing, a 50 in. span was
selected to set the chord to 10 inches (0.254 m). With the maximum wing thickness
allowable set to 1.1875 inches by AMA rules, this allows a broader selection of airfoils as
set by a maximum thickness of 11.875%. Standard sea level absolute viscosity value of
?@A; $ and air density of [6] were selected for the Reynolds
number calculation. The Reynolds number is calculated from [6]:
K∞ 0∞ L
(2.1)
M∞
N(
!
B OP B @!
<
!
N(
?@A;
! $ OP
:
This value was used as the default Reynolds number in calculating the drag
coefficients and polars for each airfoil. Next, we must calculate the overall plane lift
/
E
coefficient for straight and level flight at CD (
FGH). The equation for lift is
[6]:
7
% ' ∞ ∞' &
Rearranging:
10
(2.2)
Q
(2.3)
K 0)R
) ∞ ∞
For steady, level flight, lift is equal to weight. The AMA rule book allows a
minimum weight of 3.75lbs (1.7009714 kg), this weight is used, since it reflects the ideal
weight of pylon racers. The final equation for the coefficient of lift during steady, level
flight at maximum speed is:
Q
)
(2.4)
K∞ 0∞) R
?
@N( B ?
!
OP '
N(
! '
B < B " B !'
OP
!
During turns, the wings (and the plane) undergo centripetal acceleration, which the
wing must counteract by creating more lift to oppose the centrifugal force in turns. It
does so by pitching itself to increase the angle of attack to create more lift in the direction
of the center of the turn. Equation 2.5 describes the centripetal acceleration which the
plane must counteract in 50 ft. (15.24 m) turns:
*
)
0S
(2.5)
D
! '
"
OP
*
@!
!
* ?@@
OP '
With gravitational acceleration being?
), this shows that centripetal
acceleration is 30 times gravitational acceleration, or 30G’s. This comes down to the fact
that the plane is effectively 30 times heavier in the turns, so the wing must increase the
lift force to compensate. The plane creates this lift in the horizontal direction when the
wing is banked nearly 90 degrees during turns. The overall coefficient of lift in turns is
given in equation 2.6:
<6B
Q
K 0)R
) ∞ ∞
B ?
@N( B ?
(2.6)
!
OP '
N(
! '
B < B " B !'
OP
!
11
Of course there is lift opposing gravity to keep the plane in the air. This is ignored,
since it will be small compared to lift that counteracts the centripetal force in turns. In
actuality, the wing is not banked a full 90 degrees, so some vertical component of lift is
used to keep the plane in the air during turns. Also, the fuselage is shaped to produce a
lifting surface in the vertical direction, and the tail can be trimmed to pitch the plane’s
nose upwards in turns. For simplification, the coefficients of lift and drag are assumed to
be constant throughout the turns, even though speeds do decrease during turns.
2.4 Airfoil Drag Coefficient Calculation Using XFOIL
The XFOIL airfoil analysis program, designed by Dr. Mark Drela of MIT [7], was
used to calculate the drag coefficient of each airfoil at both lift coefficients. The program
uses viscous flow equations to estimate the coefficients of lift and drag of an airfoil based
on its shape. Next, the airfoil coordinate files were loaded into XFOIL, and paneled
them with 280 panels. The XFOIL instructions [8] recommended keeping the angles
between panels to less than 10 degrees, and that requirement was consistently met with
280 panels. Figure 5 shows the paneling of a NACA 66-012 airfoil. The number of
panels and maximum angle between panels are shown in the upper left corner.
Figure 5 The paneling of a NACA 66-012 airfoil
Flaps are added to any airfoil in the geometry design menu by indicating the chord
station of the flap hinge, the vertical station of the flap hinge, and the flap deflection in
degrees. Creation of new airfoils that are interpolations of two existing airfoils is done in
12
the geometry design menu. This operation is performed by inputting the coordinate files
of two existing airfoils and the interpolation factor between 0 and 1. The higher the
interpolation factor, the closer the shape of the resulting airfoil is to the base airfoil,
which is the first airfoil input into XFOIL. Airfoils created using this operation is
designated with MD-x.
In the operation menu, the Reynolds number is set to
: , the viscous
equations option turned on (visc command), the constant Re number option (type 1) is
turned on, and the number of iterations to solve for a lift coefficient is set to 200 or 300.
Ncrit, the laminar to turbulent transition criteria number is left to the default value of 9,
which Martin Hepperle used in the calculation of his airfoils [3]. Figure 6 shows how the
straight and level coefficient of lift of 0.018776 is input into XFOIL.
Figure 6 Coefficient of Lift Input into XFOIL
Figures 7 and 8 are XFOIL outputs for NACA 66-012 airfoil at .
The laminar to turbulent transition location for each side is show at “transition at x/c” in
the form of the normalized chord location. The angle of attack value is given after “a”,
CL is the input coefficient of lift, and Cm and CD are the corresponding moment and
total drag coefficient at that particular lift coefficient. This drag coefficient value is used
for calculating drag at straight and level flight between turns. Drag coefficient is further
broken down into drag due to skin friction coefficient (CDf), and pressure drag (CDp).
CDf is 0.00388 and CDp is 0.00142, the sum of which is 0.00529.
13
The plot in Figure 8 also reiterates the coefficient values and the angle of attack.
Most importantly, it shows the pressure coefficient distribution over both surfaces, which
is a function of air velocity over the wing. The dashed line is the invisicid (theoretical)
plot, and the solid lines are the plot from the viscous calculations.
Figure 7 XFOIL output for NACA 66-012 airfoil at Figure 8 Pressure coefficient distribution for NACA 66-012 airfoil at 14
For each airfoil, corresponding drag coefficients are calculated and tabulated for
(straight and level flight between turns) and (turning
flight).
2.5 Entire Plane Drag Coefficient Calculation
In order to calculate the whole plane drag at the two flight regimes, we must
calculate the whole wing , then proceed to calculate the whole plane, . Since turning
flight is dominated by induced drag, this drag must be included with the airfoil profile
drag. Equations 2.7 and 2.8 calculate the whole wing , using equations from Anderson
[6].Hepperle [3] assumed the Oswald span efficiency factor, e, to be 0.9, which he felt
gave good results for induced drag calculations. With a 500 square inch rectangular wing
with chord of 10 inches, the wing aspect ratio (AR) is easily calculated to be 5.
, - T ,./
, - T (2.7)
4U)
(2.8)
VWX
The NACA 66-012 airfoil has - at and - ?at , and the whole wing drag is calculated as follows:
,.45667899:
'
T Y B ? B ,.45667899: ,.456;:<'99 ? T '
Y B ? B ,.456;:<'99 Note that the turning flight , is more than six times than the straight and level, ,
even though the airfoil profile - differs by only 2x. This indicates that induced drag
dominates the turning flight mode. Next, we must find the whole plane drag coefficients
for both regimes of flight. In his comparison of pylon racing airfoils, Hepperle [3]
estimated the wing drag to be 27% in level flight and 76% in turning flight as shown in
Figure 9 below. To calculate both whole plane, ′O, the wing , is multiplied by the
inverse of each respective percentage. For NACA 66-012 airfoil, the whole plane drag
coefficients are , ?@at and , @?at . These drag coefficient values are inputs into the Maple routine that simulates
15
a race in Sections 3.1 and 3.2. Note that with the inclusion of drag from the fuselage, tail
and landing gear, the turning flight , is 2.2 times the level flight, .
Figure 9 Estimation of drag contribution of components in Q-500 pylon racer [3]
Table 2 is a tabulation of drag coefficient results for the top 12 airfoils. The whole
plane drag coefficients in the last two columns are used as inputs for the race simulation
created in Maple.
Airfoil
MH-17 @ 5 Degrees 15% Span Flaps
MH-17
MH-18B
S8064
NACA 66-012 @ 10 Degrees 15% Span
Flaps
Combination of NACA66-012 and MH-18B
(0.5 Interpolation)- MD5
Combination of NACA66-012 and MH-17
(0.5 Interpolation)- MD6
Combination of NACA66-012 and Clark Y
(0.5 Interpolation)- MD1
E-220
NACA 66-012 (Baseline)
MH-18
Clark Y
CD @ CL = CD @ CL =
0.018776 0.563277
0.00437
0.00507
0.00437
0.00657
0.00470
0.00594
0.00497
0.00636
Whole Wing Whole Wing Whole Plane
CD @ CL =
CD @ CL =
CD @ CL =
0.018776
0.563277
0.018776
0.004395
0.027513
0.016278
0.004395
0.029013
0.016278
0.004725
0.028383
0.017500
0.004995
0.028803
0.018500
Whole Plane
CD @ CL =
0.563277
0.036201
0.038175
0.037346
0.037899
0.00528
0.00602
0.005305
0.028463
0.019648
0.037451
0.00490
0.00964
0.004925
0.032083
0.018241
0.042215
0.00487
0.00994
0.004895
0.032383
0.018129
0.042609
0.00543
0.00568
0.00528
0.00637
0.00810
0.00558
0.00579
0.01089
0.00538
0.00538
0.005455
0.005705
0.005305
0.006395
0.008125
0.028023
0.028232
0.033333
0.027823
0.027823
0.020203
0.021129
0.019648
0.023685
0.030092
0.036872
0.037147
0.043859
0.036609
0.036609
Table 2 Tabulations of drag coefficients for top 12 performing airfoils
2.6 Governing Differential Equations
In order to calculate the maximum speed and speed loss in turns for each airfoil in
Maple, a differential equation describing the physics of flight must be created first.
Starting from F=ma, the following differential equation is derived:
-0
! -1 2 Z 3
(2.9)
In its derivative form, the equation states that velocity is a function of forces acting
on the airplane. Velocity is constant when all forces (T-D) on the plane are zero, or when
the drag force equals the thrust from the engine/propeller combination. In equations 2.10
16
and 2.11, the equation for drag was obtained from Anderson [6] to calculate drag for both
regimes of flight for the all airfoils. Note that , is the whole plane drag coefficient.
7
345667899: ' ∞ ∞' &,.45667899:
7
3456;:<'99 ' ∞ ∞' &,.456;:<'99
(2.10)
(2.11)
The other variable that must be accounted for is thrust from the engine/propeller
combination, which also varies as a function of velocity. Dub Jett, the sole producer of
AMA Quickie 500 engines, stated that the expected power of the Jett 0.40 cubic inch
displacement engine is 1.6-1.8 horse power [Appendix 6.1]. With a handheld optical
tachometer, it can spin an 8.8 in. diameter prop with an 8.75 in. pitch up to 18,000
revolutions per minute on the ground.
After an email exchange with Dr. Hepperle [Appendix 6.2], he determined the most
effective manner to obtain thrust as a function of velocity was to use his JavaProp
program on his MH Tools website. Initial engine/propeller inputs for JavaProp include
ground RPM of 18,000, 8.8 in. diameter propeller with a 1 inch diameter spinner, 1.8
horsepower, and near zero speed, as seen in Figure 10. Note that all original units have
been converted to their respective metric counterparts.
Figure 10 Initial JavaProp inputs for engine/propeller
17
The initial engine power value of 1.7 hp produced results that were too slow
compared to real life data, while 1.8 hp produced results that correlate with real life data
very well. The next step is to estimate the propeller airfoil and angle of attack that
produces results that matches real life data for a pylon racer equipped with a NACA 66012 airfoil. Figure 11 below is the estimation of propeller airfoils of an 8.8 in. diameter
and 8.75 in. pitch racing propeller.
Figure 11 Estimation of an 8.8x8.75 in. propeller as JavaProp inputs
After calculating the engine/propeller efficiency, power, thrust, and velocity,
JavaProp outputs data as shown in the Appendix. Dr. Hepperle advised to check the
coefficient of power,= against a known velocity to ensure the result matches. Zero
speed (or close to zero) was used. Equation 2.12 is the = formula provided by Dr.
Hepperle.
=
= KB[ B-\
= .?
]
N(
+^ <
" B !;
< B OP
!
= ?
18
(2.12)
This power coefficient value matches very well with the JavaProp output power
coefficient of 0.073635 at zero speed. The reason for the difference is that one cannot
input zero velocity as input in the first page for JavaProp, so the lowest allowable value
of was used. This validates the JavaProp results. JavaProp gave the thrust result
for each velocity, as seen in the plot in Figure 12.
Thrust vs. Velocity for 1.8 HP Engine and 8.8 x
8.75 in. Propeller
30
Thrust (N)
25
20
15
10
5
0
0
20
40
60
80
100
120
Velocity (m/sec)
-5
Figure 12 Thrust vs. Velocity Results as produced by JavaProp
The sixth order trend line seen in the plot above gives thrust as a function of
velocity, shown in equation 2.13 below.
2 Z@
A77 B : T @
?A_ B ; T A: B ` Z
@A` B < T @
A' B ' Z ? B T
@@ (2.13)
Now, the complete governing differential equation can be constructed by
substituting 2.10, 2.11, and 2.13 into 2.9 to develop the governing equations for both
flight regimes. Equation 2.14 is the straight and level flight with and
equation 2.15 is the governing equation for turning flight with .
-0
! -1 2 Z 34566789::
19
(2.14)
2 Z@
A77 B : T @
?A_ B ; T A:
B ` Z @A` B < T @
A' B ' Z ? B T @@
345667899: ' &
∞ ∞ ,.45667899:
345667899: '
!
-0
-1
2 Z 3456;:<'99
(2.15)
2 Z@
A77 B : T @
?A_ B ; T A:
B ` Z @A` B < T @
A' B ' Z ? B T @@
3456;:<'99 ' &
∞ ∞ ,.456;:<'99
3456;:<'99 ?? '
-L
The velocity of the plane, in
-1
(2.16)
, is the derivative of position !", as shown in
Equation 2.16. For Equations 2.14 and 2.15, the initial condition of any starting velocity
is determined by the velocity at the end of the preceding stage of the race. For example,
the initial velocity is the speed at the end of the straightway before the plane turns, and is
the initial condition of the governing equation that describes velocity behavior at that
turn. At the start line, initial velocity is zero. The initial position condition is always
zero for each stage of the race, since we are concerned with only the distance covered by
that stage of the race. More details on this method will be covered in Sections 3.1 and
3.2.
20
3. Results
3.1 Determination of Top Airfoil Candidates for Race Simulation
All of the above equations and drag coefficients are input into Maple for each airfoil
to determine the top speed of the plane and the maximum loss of speed in turns from top
speed. The top speed is determined by entering the whole plane drag coefficient for
with zero initial speed and applying equation 2.15 in Maple and
querying the output at 60 seconds (first blue output line). Figure 13 is the Maple output
for the NACA 66-012 airfoil at 60 seconds, and Figure 14 is the velocity vs. time plot
produced by Maple.
Figure 13 Maple output for top speed of NACA 66-012 airfoil at 60 seconds
Figure 14 Plot of velocity vs. time for NACA 66-012 airfoil at 21
At 60 seconds, a plane equipped with a NACA 66-012 airfoil will reach a top speed
of
, or@?
/
CD
, which agrees with the radar gun data of
/
CD
. From the
plot, you will see that velocity stabilizes at 15-20 seconds and is constant at 60 seconds.
To determine the maximum speed loss in turns, Equation 6.15 was solved in Maple
with the initial velocity set to the top speed for this particular airfoil. In the case of the
NACA 66-012 airfoil, the initial speed is
, and will decrease during the turn. The
distance covered in a 50 ft. (15.24m) radius turn, from zero initial distance, is 157.0796
ft. (47.88 m).
Figure 15 Velocity of NACA 66-012 airfoil after 50 ft. radius turn at top speed
The velocity after a 50 ft. radius turn is shown in Figure 15 (third blue output line),
and does not show the exact metric equivalent, 47.88 meters, ordered by time. The
closest distance is used, since it is only off by 0.01 meters, or 0.39 inches, which is
sufficiently accurate. From this distance, one can read the corresponding
velocity,?
, and time to complete the turn, 0.762 sec. Since the actual distance is
not available, the closest distance and corresponding time and velocity are used. Time is
within 0.001 seconds and velocity is accurate within
/
, or CD , which is
sufficiently accurate for this purpose. The speed loss is simply the difference of the
velocity going into the turn (maximum speed) and the velocity after a 50 ft. radius turn,
/
which is ?? , or@ CD . All maximum velocities and speeds are tabulated for all
32 airfoil candidates in Table 3 below.
22
Maximum Possible
Speed (m/sec)
66.72
58.23
66.49
66.43
67.23
65.30
67.88
66.83
67.20
70.30
70.30
70.30
63.05
68.93
Speed After 50 ft.
radius turn (m/sec)
59.73
56.58
60.04
61.28
60.96
60.70
62.07
61.39
61.78
63.52
63.97
64.06
59.48
62.87
Maximum
Possible Speed
Loss in Turns
(m/sec)
6.99
1.65
6.45
5.15
6.27
4.60
5.81
5.44
5.42
6.78
6.33
6.24
3.57
6.06
66.72
59.85
6.87
149.25
15.37
NACA 66-012 @ 5 Degrees 10% Span Flaps
NACA 66-012 @ 7.5 Degrees 10% Span
Flaps
NACA 66-012 @ 10 Degrees 10% Span
Flaps
NACA 66-012 @ 2.5 Degrees 15% Span
Flaps
66.72
59.97
6.75
149.25
15.10
66.72
60.04
6.68
149.25
14.94
66.72
60.11
6.61
149.25
14.79
66.72
59.83
6.89
149.25
15.41
NACA 66-012 @ 5 Degrees 15% Span Flaps
NACA 66-012 @ 7.5 Degrees 15% Span
Flaps
NACA 66-012 @ 10 Degrees 15% Span
Flaps
NACA 66-012 @ 2.5 Degrees 20% Span
Flaps
66.72
59.95
6.77
149.25
15.14
66.72
60.02
6.70
149.25
14.99
66.72
61.46
5.26
149.25
11.77
66.72
59.78
6.94
149.25
15.52
NACA 66-012 @ 5 Degrees 20% Span Flaps
NACA 66-012 @ 7.5 Degrees 20% Span
Flaps
NACA 66-012 @ 10 Degrees 20% Span
Flaps
Combination of NACA66-012 and Clark Y
(0.5 Interpolation)- MD1
Combination of Clark Y and NACA66-012
(0.5 Interpolation)- MD2
Combination of NACA66-012 and Clark Y
(0.25 Interpolation)- MD3
Combination of NACA66-012 and Clark Y
(0.75 Interpolation)- MD4
Combination of NACA66-012 and MH-18B
(0.5 Interpolation)- MD5
Combination of NACA66-012 and MH-17
(0.5 Interpolation)- MD6
66.72
59.90
6.82
149.25
15.26
66.72
59.98
6.74
149.25
15.08
66.72
61.56
5.16
149.25
11.54
66.18
61.31
4.87
148.04
10.89
65.47
60.88
4.59
146.45
10.27
67.88
61.43
6.45
151.84
14.43
60.30
57.87
2.43
134.89
5.44
68.15
61.02
7.13
152.45
15.95
68.26
60.98
7.28
152.69
16.28
Airfoil
NACA 66-012 (Baseline)
Clark Y
NACA 64-012
NACA 64-212
MH-27
E-220
S8064
S8052
MH-16
MH-17
MH-17 @ 2.5 Degrees 15% Span Flaps
MH-17 @ 5 Degrees 15% Span Flaps
MH-18
MH-18B
NACA 66-012 @ 2.5 Degrees 10% Span
Flaps
Maximum
Possible Speed
(mi/hr)
149.25
130.26
148.73
148.60
150.39
146.07
151.84
149.49
150.32
157.26
157.26
157.26
141.04
154.19
Maximum Possible
Speed Loss in Turns
(mi/hr)
15.64
3.69
14.43
11.52
14.03
10.29
13.00
12.17
12.12
15.17
14.16
13.96
7.99
13.56
Table 3 Maximum possible speed and speed loss in turns for each airfoil candidate
3.2 Airfoil Race Simulation in Maple
Based on the highest attained velocities and minimal loss of velocity in turns, the top
12 airfoil candidates were selected for race simulations in Maple. The NACA66-012
airfoil was selected as the baseline airfoil for comparison purposes, as well as the Clark
Y.
23
Each portion of the race is measured in meters, for ease of use. To reiterate the race
simulation from section 2.1, the race simulation is as follows:
• Start line to first turn in 114.45 meters (375.5 ft.)
• 19 instances of 50 ft. radius turn in 47.88 meters (157.0796 ft.) preceding a
144.93 meter level flight (475.5 ft.)
• Final 50 ft. radius turn in 47.88 meters (157.0796 ft.) during lap #10.
• Back to start/finish line from previous turn in 30.48 meters (100 ft.)
The total length covered in the race simulation outlined above is 3.856 km (12,651.6
ft. or 2.3691 miles). The perimeter of the triangle marked by the pylons over 10 laps is
exactly 2 miles; hence it is referred to as the 2 mile course. Since this is an impossible
flight path, the above race simulation is a much more realistic representation of a race.
The straight and level flight in between turns is governed by equation 2.14, and
turning flight is governed by equation 2.15., so there are two distinct equations and
solutions in a Maple worksheet. In Maple, each stage of the race simulation is calculated
for velocity and time for each corresponding length in a similar manner as calculating
velocity and time after a 50 ft. radius turn in Section 2.6. For example, in Figure 16
below, with zero initial velocity, it takes 4.273 seconds to reach the first pylon from the
start line, as seen in the box. The distance covered is 114.45 meters, but time and
velocity was read from the closest distance, 114.4295 meters (fourth blue output line).
Figure 16 Velocity from start line to first turn for NACA 66-012 airfoil
Velocity at the end of this portion of the race is set as the initial velocity into the
governing equation that describes turning flight around pylon #1, as seen in Figure 17
below. The second black input line shows where the velocity at the end of the preceding
24
portion of the race is entered as an initial condition (ic3). The third blue output line is the
Maple output which validates the initial velocity, where time is zero, at the beginning of
this portion of the race.
Figure 17 Initial velocity for a particular portion of the race simulation
Since this portion of the race is a turn around pylon 1, equation 2.15 is used to
describe this flight regime, which covers a distance of 47.88 meters. Figure 18 below
shows the velocity and time at the end of the first turn. 47.885 meters (fifth blue output
line) is the closest to the actual distance of 47.88 meters; therefore velocity and time is
read from this distance. The velocity a thousandth of a second before and after the
velocity highlighted in the box is well within
.
Figure 18 Velocity and time for first turn around pylon #1
This process continues until the velocities stabilize at about lap #4. Stabilization
occurs when the velocity at the beginning of a straight and level flight regime is equal to
the previous straight and level flight regime since the loss of speed in turns is now
constant. This can be seen in lap 3 in Table 4 below for a simulated race for a NACA66012 airfoil. Distance in meters is used to find the closest velocity at the end of this
portion of the race and the time it takes the plane to cover this distance. Velocity is then
converted into miles per hour.
25
Speed at the end of each piece of the race is recorded in Table 4 below, and the
change of speed in turns is the difference of speed going into and out of turns. From the
table, you can easily see that a plane equipped with a NACA 66-012 airfoil reaches a
/
/
maximum speed of @@ CD at the end of straight and level flight and loses? CD in
/
turns. The maximum speed in a race is lower than the maximum speed of@? CD for a
plane with this airfoil because the race course is not sufficiently long enough to allow the
plane to reach a steady state velocity. The maximum speed loss in turns during a race is
lower than the maximum possible@
/
CD
because maximum possible speed has not
been attained.
Piece #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
Lap #
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
9
10
10
10
10
10
Location
Start Line to Pylon 1
Around Pylon 1
Pylon 1 to Pylon 2
Around Pylons 2 and 3
Pylon 3 to 1
Around Pylon 1
Pylon 1 to Pylon 2
Around Pylons 2 and 3
Pylon 3 to 1
Around Pylon 1
Pylon 1 to Pylon 2
Around Pylons 2 and 3
Pylon 3 to 1
Around Pylon 1
Pylon 1 to Pylon 2
Around Pylons 2 and 3
Pylon 3 to 1
Around Pylon 1
Pylon 1 to Pylon 2
Around Pylons 2 and 3
Pylon 3 to 1
Around Pylon 1
Pylon 1 to Pylon 2
Around Pylons 2 and 3
Pylon 3 to 1
Around Pylon 1
Pylon 1 to Pylon 2
Around Pylons 2 and 3
Pylon 3 to 1
Around Pylon 1
Pylon 1 to Pylon 2
Around Pylons 2 and 3
Pylon 3 to 1
Around Pylon 1
Pylon 1 to Pylon 2
Around Pylons 2 and 3
Pylon 3 to 1
Around Pylon 1
Pylon 1 to Pylon 2
Around Pylons 2 and 3
Pylon 3 to Finish Line
Distance (m)
114.45
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
144.93
47.88
30.48
Speed (m/sec)
49.39
49.91
61.74
56.83
63.69
57.96
64.03
58.15
64.08
58.18
64.09
58.19
64.09
58.19
64.09
58.19
64.09
58.19
64.09
58.19
64.09
58.19
64.09
58.19
64.09
58.19
64.09
58.19
64.09
58.19
64.09
58.19
64.09
58.19
64.09
58.19
64.09
58.19
64.09
58.19
60.09
Time (sec.)
4.273
0.964
2.549
0.811
2.380
0.791
2.355
0.788
2.351
0.787
2.350
0.787
2.350
0.787
2.350
0.787
2.350
0.787
2.350
0.787
2.350
0.787
2.350
0.787
2.350
0.787
2.350
0.787
2.350
0.787
2.350
0.787
2.350
0.787
2.350
0.787
2.350
0.787
2.350
0.787
0.515
Distance(ft.)
375.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
475.5000
157.0796
100.0000
Speed (mi/hr)
110.48
111.65
138.11
127.13
142.47
129.65
143.23
130.08
143.34
130.14
143.37
130.17
143.37
130.17
143.37
130.17
143.37
130.17
143.37
130.17
143.37
130.17
143.37
130.17
143.37
130.17
143.37
130.17
143.37
130.17
143.37
130.17
143.37
130.17
143.37
130.17
143.37
130.17
143.37
130.17
134.42
Table 4 Simulated race for NACA 66-012 airfoil
26
Speed Loss in
Turns (mi/hr)
10.98
12.82
13.15
13.20
13.20
13.20
13.20
13.20
13.20
13.20
13.20
13.20
13.20
13.20
13.20
13.20
13.20
13.20
13.20
The time for each piece of the race is summed to be the total race time. This
process is repeated for the top 12 airfoil candidates to obtain the total race time for each
for the overall airfoil performance comparison.
3.3 Maximum Speed and Maximum Loss of Speed in Turns
Table 3 from section 3.1 shows the maximum possible speed and maximum loss of
sped in turns for each airfoil. The NACA 66-012 airfoil is selected as the baseline airfoil,
as it is the most common airfoil used for racing today. Since it is the lowest speed airfoil,
the Clark Y was chosen as the high lift airfoil for the race simulation in Maple for
comparison purposes. As for the other 10 airfoils, the first priority was given to the
highest top speed, and the second priority was given to the minimal loss of speed. Only
12 out of 32 airfoils were selected for the race simulation in Maple, as simulating a race
is a time consuming process that takes 20-30 minutes per airfoil. Because the goal of this
project is to determine the airfoils with the lowest race times, airfoils that produce high
race times were not incorporated. For example, the MD-4 airfoil produced a top speed of
only
/
CD
. It is for this reason that it is not a competitive airfoil. Conversely, even
/
though the MH-18 airfoil has a top speed of only@ CD , it is a viable candidate due to
/
its low maximum speed loss in turns of CD , second only to the Clark Y airfoil.
As with any selection process in the field of Engineering, one must find the best
compromise between two or more selection metrics. A balance between top speed and
minimal loss of speed in turns during the airfoil selection process must be found. Upon
completion of a various race simulations, it can be determined that airfoil top speed is a
greater driver of race times than maximum loss of speed in turns.
3.4 Maple Race Simulation Results
Table 5 below shows the outcome of the Maple airfoil simulation results, ordered by
the lowest to highest race times for the 12 airfoil candidates selected. The MH-17 with
15% span flaps during turns is the clear winner in this simulation. Even the MH-17
airfoil without flaps is less than 0.4 seconds slower than its flapped counterpart, the
complexity of the flap installation alone is not worth the 0.4 second.
27
Airfoil
Cd @ CL =
0.018776
Cd @ CL =
0.563277
Max Race
Speed
(mi/hr)
Max Speed
Loss in Turns
(mi/hr)
Race Time
(sec)
MH-17 With 5 Degrees 15% Span Flaps
0.00437
0.00507
151.13
11.65
62.146
MH-17
0.00437
0.00648
150.66
12.64
62.509
MH-18B
0.00470
0.00594
148.55
11.39
63.567
S-8064
0.00497
0.00636
146.65
10.98
63.814
NACA 66-012 With 10 Degrees 15% Span
Flaps
0.00528
0.00602
144.75
9.95
64.396
MD5- Combination of NACA66-012 and
MH-18B (0.5 Interpolation)
0.00490
0.00964
146.12
13.38
64.484
MD6- Combination of NACA66-012 and
MH-17 (0.5 Interpolation)
0.00487
0.00994
146.21
13.65
64.485
MD1- Combination of NACA66-012 and
Clark Y (0.5 Interpolation)
0.00543
0.00558
143.95
9.28
64.607
E-220
0.00568
0.00579
142.34
8.84
65.203
NACA 66-012
0.00528
0.01089
143.37
13.20
65.619
MH-18
0.00637
0.00538
138.38
6.93
67.668
Clark Y
0.00810
0.00538
126.49
3.27
70.189
Table 5 Overall airfoil race simulation results
28
It is surprising to note that the NACA 66-012 baseline airfoil performance is near the
bottom, albeit slower by only 3.473 seconds than the MH-17 with 5 degrees 15% span
flaps. Another commonly used airfoil in pylon racing, the S-8064, outperformed the
NACA 66-012 airfoil by 1.8 seconds. The performance of the NACA 66-012 airfoil can
be improved by 1.2 seconds by including 15% span flaps at 10 degrees during turns. This
added benefit of flaps may not be worth the complexity of flap installation for some
airplane builders. Another way to improve the NACA 66-012 airfoil is by blending it
with a higher lift airfoil (MH-18B, Clark Y) to create a new airfoil. One can also
improve the 66-012 airfoil by incorporating a wing with 3 various airfoil sections
consisting of a smooth transition between them.
Raymer [9] suggested using washout for constant airfoil wings to lower the angle of
attack of outboard wings. Washout is the twist of the wing where the outboard sections
are set to lower angles of attack than the inboard section. Washout results in two things:
it prevents the wing tips from stalling first, which will cause a violent stall and to make a
more elliptical lift distribution. Such lift distribution allows lift to naturally decrease
towards the wing tips. With a more elliptical lift distribution, the effect of induced drag
is lower. Rather than reducing the angle of attack towards the wing tips, one can design
a blended airfoil wing with a higher lift airfoil, such as a MH-18B in the inner 1/3,
transition to a MD-5, and finally to NACA 66-012 in the following manner:
• Inboard 1/3: MH-18B
• Mid 1/3: MD-5 airfoil, which is a blend of NACA 66-012 and MH-18B
• Outboard 1/3: NACA 66-012
The beauty of calculating the section , of a wing blended in the above manner is
that the average, of each airfoil will be very close to the drag coefficient of the airfoil
that is the 50% blend of the inner and outer airfoils. In other words, the, of the blended
airfoil, MD-5, can represent a wing comprised of those 3 airfoils or of just the MD-5
airfoil only.
3.5 Airfoil Polar Interpretations
XFOIL has the capability to create polars for a given range of angles of attack and
lift coefficients through the polar accumulation command (pacc) in the operations menu.
29
The XFOIL output polar text file was read into an Excel spreadsheet and plotted. An
example of the XFOIL polar output file for the NACA 66-012 airfoil is found in section
6.7 in the Appendix.
Clark Y
MH-18
MH-18B
S-8064
E-220
MD-1
MD-5
MH-17
MD-6
CL = 0.018776
CL = 0.563277
Lift Coefficient
NACA 66-012
-4
-3
-2
1.40
1.30
1.20
1.10
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
-1
-0.10 0
-0.20
-0.30
1
2
3
4
5
6
7
8
9
10
Angle of Attack (Degrees)
Figure 19 as a function of angle of attack for 12 airfoils
Figure 19 above shows the coefficient of lift as a function of α for the top 11
performing airfoils and the Clark Y. It can be seen that the Clark Y airfoil produces
higher a at all α than all airfoils. Even the Clark Y must be kept at a negative α during
the high speeda , marked by purple dashed lines. Since it is at a higher absolute α at
lowa , its - will be higher.
The NACA 66-012 is a relatively low-lift airfoil, and requires higher α than a
majority of airfoils in turning flight regime, marked by a blue dashed line. This is why its
, is higher in this flight regime than the other airfoils. Conversely, the Clark Y airfoil
requires low α during turning flights, which leads to lower , in that flight regime.
Since XFOIL is incapable of solving for coefficients at and near stall α, a sudden
drop in the curve at higher α will not be seen. You can see that the Clark Y, MH-17,
30
MH-18, and MH-18B lift slope flatten out at 9-10 degrees α as stall is being approached.
These high lift airfoils are excellent candidates for the inboard airfoil section of a blended
airfoil wing, since they will stall first. Since the NACA 66-012 is known to have
somewhat more abrupt stall behavior, it will be ideal for the outboard section of a
blended airfoil wing. The NACA 66-012 curve does not start to flatten out at 9-10
degrees α, since it is not yet close to stalling.
Figure 20 shows the drag polar for those 12 airfoils run through the race simulation.
It shows - as a function ofa . for high speed flight is marked by blue dashed lines
on the left, and in turns is marked by orange dashed lines on the right.
NACA 66-012
Clark Y
MH-17
MH-18
MH-18B
S-8064
E-220
MD-1
MD-5
MD-6
CL = 0.018776
CL = 0.563277
Drag Coefficient
0.024
0.023
0.022
0.021
0.020
0.019
0.018
0.017
0.016
0.015
0.014
0.013
0.012
0.011
0.010
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
Lift Coefficient
Figure 20 Drag polars for all 12 airfoils
From the drag polar on the left, one can easily see why the Clark Y airfoil is the
slowest in high speed flight regime, but yet has the minimal loss of speed in turns. Its
- is the highest at high speed, and is lowest during turning flight. On the other hand, the
NACA 66-012 loses the most speed in turns because of high - at the for turning
31
flight. From the plot, it can be observed that the MH-17 airfoil has the lowest - at
low , and yet has significantly lower - in the turns than the NACA 66-012 airfoil.
The NACA 66-012 airfoil has high - at higher a because of the airfoil’s inherent
laminar bucket. This laminar bucket is a a range where - does not increase due to
strong laminar flow attachment. The plot in Figure 21 below illustrates the laminar
bucket.
0 Degrees Flaps
2.5 Degrees Flaps
5 Degrees Flaps
7.5 Degrees Flaps
10 Degrees Flaps
-2.5 Degrees Flaps
CL = 0.563277
Drag Coefficient
0.03500
0.03000
0.02500
0.02000
0.01500
0.01000
0.00500
-0.2
0.00000
-0.1
0.0
Lift Coefficient
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Figure 21 Laminar bucket of NACA 66-012 airfoil with flaps
The unflapped NACA 66-012 airfoil emerges out of the bucket at
approximately , so it is out of the laminar bucket and into higher , regime at
the turning flight regime , marked by the black dashed line. Increasing
flap angle shifts the laminar bucket to the right until the 10 degree flap is just inside the
laminar bucket at , which is why flaps minimize speed loss in turns. For
reference, the orange curve represents -2.5 degree flaps, which shifts the laminar bucket
to the left.
32
0 Degrees Flaps
2.5 Degrees Flaps
5 Degrees Flaps
7.5 Degrees Flaps
10 Degrees Flaps
-2.5 Degrees Flaps
CL = 0.563277
1.0
Lift Coefficient
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
-7
-6
-5
-4
-3
-2
0.0
-1
0
-0.1
-0.2
1
2
3
4
5
6
7
8
9
10
11
Angle of Attack (Degrees)
Figure 22 Lift curve for flapped NACA 66-012 airfoil
As seen in Figure 22 above, the reason flaps lower - at from
lowering α required to attain this lift coefficient. The unflapped NACA 66-012 airfoil
(dark blue) requires just over 5 degrees α to maintain turning flight, while the 10 degrees
flaps require less than 1 degree. This lowers the amount of exposed surface area of the
airfoil relative to the free steam flow, and thus lowers - during turns.
3.6 XFOIL b Plot Comparison
At the turning flight regime , the MH-17 airfoil has lower - than
the NACA 66-012. The plots in Figures 23 and 24 below offer an explanation for this
difference in- .
33
Figure 23 Plot for NACA 66-012 airfoil at Figure 24 Plot for MH-17 airfoil at 34
Since the coefficient of pressure is related to the local velocity of air over the airfoil,
the more severe spike near the leading edge of the NACA 66-012 airfoil on the left
indicates high local velocity. This translates to higher drag coefficient at 3.7 Validation of Results
Figure 25 NACA 66-012 Wind Tunnel Data from Theory of Wing Sections [10]
Wind tunnel data for NACA 66-012 is found in pages 662-663 in [10], copied as
Figure 25 above. At Re = 3,000,000, - c @ at . At this Reynolds
number and , XFOIL predicted, , an 8.7% difference. XFOIL predicted
- @ at , which is 7.0% lower than the published - ?
at the same . The difference could be due to some viscous effects not accounted for in
XFOIL or even in the wind tunnel data itself. The data was produced in the 1940’s, when
wind tunnel technology and measurement was not as advanced as modern methods. This
discrepancy between both sets of data is expected to be similar for all airfoils, which still
allow relative comparisons to be made using XFOIL results. There is relatively good
35
agreement between XFOIL and published wind tunnel data, thus validating XFOIL
results.
The lowest race time achieved with a NACA 66-012 airfoil (or a slight variation of)
is 63 seconds with a course layout similar to the one used in the airfoil simulations. The
Maple simulation predicted this airfoil to complete the race in 65.6 seconds, a good
agreement at 4.16% difference. In the race simulation, the plane initiates turns when
pylons are reached, but in reality, the turns are initiated before the pylons are reached.
This reduces the flight distance covered, and accounts for the 2.6 second difference. All
in all, the race simulation ensures the race course is similar between all airfoils for equal
comparison.
As posted in his pylon racing page of his MH Aero Tools website [3], Dr. Hepperle
also completed a similar race simulation, with results shown in Figure 26 below.
Figure 26 Velocity vs. time result of race simulation by Dr. Hepperle [3]
36
Figure 27 Velocity vs. time result of race simulation for NACA 66-012 airfoil
Velocity vs. time results between Figures 26 and 27 show similar trends, which
validates the race simulation. As mentioned before, the velocities stabilize after the 4th
lap, so the amplitude of the sine graphs are the same after the 4th lap.
3.8 Implications of Moment Coefficient
The airfoil pitching moment coefficient as a function of for each of the 12 airfoils
is plotted in Figure 28 below. The vertical dashed line represents the high speed flight
regime and the vertical dashed line on the right is the turning flight
regime . From the plot, you will see that the NACA 66-012 airfoil pitch
moment coefficient remains nearly zero at all , which indicates that lift from small tail
is sufficient in counteracting this moment. On the other end of the spectrum, the Clark Y
produces significant pitching moment at all , which would require a larger tail to
counteract this moment. A larger tail will add to the drag penalty of the whole plane.
The MH-17 airfoil does have more pitching moment than the NACA 66-012, and might
require a larger tail than a plane equipped with a NACA 66-012 airfoil. The difference in
moment coefficient isn’t as great as the Clark Y, but in reality even the smaller horizontal
37
tails are large enough, because they are usually designed for safe operation during takeoff
and landing conditions [3].
NACA 66-012
Clark Y
MH-17
MH-18
MH-18B
S-8064
E-220
MD-1
MD-5
MD-6
CL = 0.018776
CL = 0.563277
0.050
0.030
0.020
0.010
0.000
-0.05
-0.010 0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
-0.020
-0.030
-0.040
-0.050
-0.060
-0.070
-0.080
-0.090
-0.100
Lift Coefficient
Figure 28 Airfoil pitching moment coefficients as a function of for the 12 airfoils
Overall, moment coefficient should be considered as a factor when selecting an
airfoil for pylon racers. It would be pointless to select a low drag airfoil that requires a
larger tail, which can offset the drag benefit of the airfoil alone.
38
Moment Coefficient
0.040
4. Discussion and Conclusion
4.1 Summary of High Level Results
My race simulation shows that Martin Hepperle’s MH-17 airfoil with 15% span 5
degree flaps has the lowest race time of 62.146 seconds, 3.511 seconds faster than the
baseline NACA 66-012 airfoil. The NACA 66-012 airfoil performance can be improved
by 1.261 seconds by the use of 15% span 10 degree flaps during the turns. This airfoil
can also be improved by blending it with another airfoil, such as the MH-18B to create a
new airfoil, the MD-5. A wing comprised of this airfoil offers a 1.173 second benefit
over the NACA 66-012. Also, the performance of this new airfoil can also be
representative of a wing composed of the NACA 66-012, MH-18B, and the intermediate
MD-5 airfoil. Blending a wing with the NACA 66-012 and a higher performance airfoil
should improve the race time of the NACA 66-012.
Consistency is stressed, down to the race course layout, drag calculations, and the
engine performance to be able to offer relative comparisons between airfoils in the form
of race times. In this project, I did not include the effect the pilot has on the pylon racers
equipped with the different airfoils. An experienced pilot who can fly a tight and
consistent race far outweighs the benefit one airfoil has over another. A pilot who flies
the plane all over the race course will quickly erase a 2-3 second advantage of a plane
equipped with a MH-17 airfoil. Even a top pilot racing a plane equipped with a Clark Y
airfoil can handily beat a novice pilot flying a plane with an airfoil such as the MH-17 by
minimizing the distance flown during a race. It all comes down to flying the race course
in a smooth, consistent manner.
4.2 Recommendations for Further Research
If anyone has the interest or desire to continue my research, he or she can start off by
incorporating the effect of the airfoils’ moment coefficient by determining the tail size
required, and applying the drag penalty or benefit to the overall plane drag. Even the
increase of airfoil drag as a plane rolls into and out of turns can be included. Also, the
race simulation could be further automated by only inputting both ′O and automatically
calculating the overall race time. If such a person has sufficient time on his or her hands
and wishes to be much more detailed, he/she could even link the XFOIL program with a
race simulation to allow the calculation of more accurate ′Oand , ′Oas velocity (and
39
Reynolds number) changes during a race. Still, I would expect the result to be very close
to my race simulations using my assumptions.
One also can perform a design of experiment (DOE) for determining the most
effective airfoil cross section with the least drag coefficient for both flight regimes.
Airfoil parameters, such as maximum thickness, camber, leading edge radii, curvature,
location of maximum thickness, etc. can be set for a range of values. There could
potentially be thousands of airfoil sections as determined by the number of airfoil
parameters, and XFOIL is a great tool to assess each airfoil’s - for both high speed and
turning flight regimes. The optimal airfoil is that with the lowest - for both modes of
flight while meeting the thickness requirement of 11.875%.
40
5. References
[1] 2011-2012 Academy of Model Aeronautics Competition Regulations, Rules
Governing Model Aviation Competition in the United States.
http://www.modelaircraft.org/files/2011-2012RCPylonRacing2JAEdit.pdf.
[2] Tower Hobbies, Viper 500 Kit. http://www3.towerhobbies.com/cgibin/wti0001p?&I=LXEUN4&P=7
[3] Hepperle, Martin. MH- Aero Tools Website. http://www.mh-aerotools.de/airfoils/
[4] University of Illinois at Urbana-Champaign Department of Aerospace Engineering
Airfoil Data Site, Maintained by Dr. Michael Selig. http://www.ae.illinois.edu/mselig/ads/coord_database.html
[5] Selig S-8064 Airfoil Coordinate File. University of Illinois at Urbana-Champaign
Department of Aerospace Engineering Airfoil Data Site, Maintained by Dr. Michael
Selig. http://www.ae.uiuc.edu/m-selig/ads/coord_updates/s8064.dat
[6] Anderson, John D. Jr. 2000. An Introduction to Flight, Fourth Edition. Boston:
McGraw-Hill.
[7] Drela, Mark. XFOIL Subsonic Airfoil Development System. Last updated April 7,
2008. http://web.mit.edu/drela/Public/web/xfoil/
[8] Drela, Mark. XFOIL 6.9 User Primer, xfoil_doc.txt. Last updated 11/30/2001.
http://web.mit.edu/drela/Public/web/xfoil/
[9] Raymer, Daniel P. 1989. Aircraft Design: A Conceptual Approach. Washington,
DC: American Institute of Aeronautics and Astronautics, Inc.
[10] Abbot, Ira H. and Von Doenhoff, Albert E. 1959. Theory of Wing Sections. New
York: Dover Publishing, Inc.
41
6. Appendix
6.1 Email from Jett .40 Engine Manufacturer Concerning Actual Engine Power
Output
“There are much data that conflicts with what I say. The manufacturers over the years
have exaggerated more and more, particularly since there is not industry standard to keep
them in check. Nevertheless, I think you can safely use a number between 1.6 and 1.8
HP.”
6.2 Email from Dr. Martin Hepperle on Calculating Thrust on Engine/Propeller
Combination
“Michael,
The actual thrust of a Propeller depends on engine characteristics and forward
speed. Generally it has its maximum at static conditions or low speed and then drops
towards zero when the propeller "overtakes" the engine and starts to act as a windmill.
You could calculate it if you have the engines performance curve P=f(n) and the
propeller performance curves CP=f(v/(n*D)) and CT=f(v/(n*D)) . I did this and for the
simulation program I had approximated the resulting curves by the formula shown on the
web page.
In later simulations I reverted to the direct simulation of the engine /propeller match as
computers are fast enough to do this during the simulation.
Anyway, if you have the propeller and engine characteristics (e.g. calculated with
JavaProp), you can follow these steps:
1) select one point on the given performance curve: rpm -> Power
2) calculate CP for this power and the propeller of interest: CP = P/(rho*n^3*D^5)
3) from the propellers CP=f(v/(n*D)) find the advance ratio v/(n*D)
4) find the matching flight speed from v/(n*D) (n and D are already known)
5) from CP=f(v/(n*D)) find CT and from this T = CT*rho*n^2*D^4.
You now have one point where engine and propeller match. Repeat for other
points on the engine performance curve. This yields curves of thrust, n, p versus flight
speed which you can then approximate (for simplicity) or use by interpolation.
Good luck,
Martin”
42
6.3 XFOIL Input Parameters
File name: xfoil.def
6.4 Output of JavaProp Program on Engine/Propeller Combination
Velocity and Thrust outputs highlighted
v/(nD)
[-]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.42
1.44
1.46
1.48
1.5
1.52
1.54
1.56
1.58
1.6
1.62
1.64
v/(?R)
[-]
0
0.032
0.064
0.095
0.127
0.159
0.191
0.223
0.255
0.286
0.318
0.35
0.382
0.414
0.446
0.452
0.458
0.465
0.471
0.477
0.484
0.49
0.497
0.503
0.509
0.516
0.522
Ct
[-]
0.086714
0.081407
0.084094
0.08456
0.085989
0.086405
0.084973
0.082217
0.078487
0.071823
0.062046
0.052101
0.041969
0.031689
0.021251
0.01914
0.017022
0.014898
0.012767
0.010616
0.008484
0.006354
0.004182
0.002024
-0.00016
-0.0024
-0.00462
Cp
[-]
0.073635
0.07247
0.073814
0.075175
0.074455
0.074884
0.076969
0.078576
0.079756
0.078374
0.072929
0.065874
0.057105
0.046601
0.034287
0.031595
0.028828
0.025984
0.023064
0.020045
0.016987
0.013865
0.010612
0.007308
0.003894
0.000319
-0.00328
Cs
[-]
0.000053
0.169032
0.336823
0.503392
0.672482
0.839637
1.002046
1.164235
1.32659
1.497642
1.688185
1.895177
2.127387
2.400288
2.748536
2.833775
2.926848
3.029794
3.145403
3.278619
3.43416
3.623546
3.872291
4.225666
4.853323
8.107395
5.147183
Tc
[-]
9.999999
9.999999
5.353579
2.392553
1.368562
0.88011
0.601064
0.427276
0.312291
0.225797
0.158
0.109648
0.074217
0.047749
0.02761
0.024171
0.020904
0.017798
0.014843
0.012015
0.00935
0.006822
0.004376
0.002064
-0.00016
-0.00233
-0.00437
Pc
[-]
9.999999
9.999999
9.999999
7.090067
2.962487
1.525533
0.90741
0.583356
0.396676
0.273769
0.185712
0.126031
0.084153
0.054014
0.031819
0.028099
0.024585
0.021261
0.018117
0.015124
0.012318
0.009667
0.007118
0.004718
0.002421
0.000191
-0.0019
43
?
[%]
0
11.23
22.79
33.75
46.2
57.69
66.24
73.24
78.73
82.48
85.08
87
88.19
88.4
86.77
86.02
85.03
83.71
81.93
79.44
75.91
70.57
61.48
43.75
0
0
0.19
?*
[%]
0.01
34.95
56.19
69.61
77.9
83.41
87.32
90.16
92.27
94.04
95.56
96.74
97.68
98.43
99.05
99.16
99.26
99.37
99.47
99.56
99.66
99.75
99.84
99.92
99.99
99.99
49.59
stalled
[%]
20.00 !
99.00 !
76.00 !
30
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
v
[m/s]
0
6.71
13.41
20.12
26.82
33.53
40.23
46.94
53.64
60.35
67.06
73.76
80.47
87.17
93.88
95.22
96.56
97.9
99.24
100.58
101.93
103.27
104.61
105.95
107.29
108.63
109.97
rpm
[1/min]
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
18000
Power
[kW]
1.354
1.333
1.358
1.383
1.369
1.377
1.416
1.445
1.467
1.442
1.341
1.212
1.05
0.857
0.631
0.581
0.53
0.478
0.424
0.369
0.312
0.255
0.195
0.134
0.072
0.006
-0.06
Thrust
[N]
23.8
22.3
23.1
23.2
23.6
23.7
23.3
22.6
21.5
19.7
17
14.3
11.5
8.7
5.8
5.2
4.7
4.1
3.5
2.9
2.3
1.7
1.1
0.6
0
-0.7
-1.3
Torque
[Nm]
0.7
0.7
0.7
0.7
0.7
0.7
0.8
0.8
0.8
0.8
0.7
0.6
0.6
0.5
0.3
0.3
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.1
0
0
0
6.5 Screenshots of Maple Calculation of Maximum Possible Velocity and Maximum
Speed Loss in Turns for NACA 66-012 Airfoil
44
45
46
47
6.6 Maple Screenshots of Maple Calculation of Time and Velocity for Start Line to
Take Off and Around First Turn for NACA 66-012 Airfoil
48
49
50
6.7 XFOIL Polar Accumulation Results (PACC command) for NACA 66-012 Airfoil
for α from -1 to 5 Degrees
alpha
------1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5.0
CL
--------0.1151
-0.1037
-0.0922
-0.0807
-0.0692
-0.0577
-0.0462
-0.0346
-0.0231
-0.0116
0.0000
0.0115
0.0230
0.0345
0.0460
0.0576
0.0691
0.0806
0.0921
0.1150
0.1264
0.1378
0.1492
0.1605
0.1719
0.1832
0.1945
0.2058
0.2169
0.2280
0.2392
0.2503
0.2614
0.2725
0.2833
0.2931
0.2988
0.3057
0.3126
0.3194
0.3269
0.3345
0.3419
0.3501
0.3592
0.3691
0.3795
0.3900
0.4004
0.4106
0.4212
0.4316
0.4415
0.4520
0.4625
0.4728
0.4832
0.4930
0.5026
0.5129
CD
--------0.00523
0.00525
0.00525
0.00526
0.00526
0.00526
0.00527
0.00528
0.00529
0.00529
0.00529
0.00529
0.00529
0.00528
0.00527
0.00526
0.00526
0.00526
0.00525
0.00523
0.00523
0.00521
0.00519
0.00518
0.00517
0.00517
0.00515
0.00514
0.00514
0.00514
0.00515
0.00515
0.00516
0.00518
0.00522
0.00533
0.00581
0.00624
0.00668
0.00713
0.00750
0.00786
0.00824
0.00855
0.00877
0.00892
0.00902
0.00912
0.00922
0.00933
0.00940
0.00949
0.00963
0.00971
0.00979
0.00988
0.00998
0.01012
0.01028
0.01036
51
CDp
--------0.00136
0.00137
0.00138
0.00139
0.00139
0.00140
0.00141
0.00142
0.00142
0.00142
0.00142
0.00142
0.00142
0.00142
0.00141
0.00140
0.00139
0.00139
0.00138
0.00136
0.00136
0.00135
0.00134
0.00133
0.00132
0.00132
0.00130
0.00129
0.00128
0.00126
0.00125
0.00125
0.00126
0.00127
0.00128
0.00128
0.00140
0.00155
0.00170
0.00185
0.00199
0.00213
0.00227
0.00241
0.00252
0.00261
0.00270
0.00279
0.00287
0.00298
0.00306
0.00315
0.00329
0.00338
0.00347
0.00356
0.00366
0.00380
0.00398
0.00408
CM
-------0.0012
0.0011
0.0010
0.0009
0.0008
0.0007
0.0005
0.0004
0.0003
0.0001
0.0000
-0.0001
-0.0002
-0.0004
-0.0005
-0.0006
-0.0007
-0.0009
-0.0010
-0.0012
-0.0013
-0.0014
-0.0015
-0.0015
-0.0016
-0.0017
-0.0017
-0.0018
-0.0018
-0.0018
-0.0019
-0.0019
-0.0019
-0.0020
-0.0019
-0.0017
-0.0009
-0.0003
0.0002
0.0007
0.0011
0.0016
0.0020
0.0024
0.0026
0.0027
0.0028
0.0028
0.0029
0.0030
0.0030
0.0031
0.0032
0.0032
0.0033
0.0033
0.0034
0.0035
0.0037
0.0038
Top_Xtr
-------0.7741
0.7736
0.7728
0.7720
0.7713
0.7705
0.7698
0.7691
0.7684
0.7676
0.7667
0.7657
0.7644
0.7627
0.7610
0.7594
0.7579
0.7563
0.7543
0.7500
0.7479
0.7443
0.7412
0.7376
0.7343
0.7308
0.7256
0.7195
0.7122
0.7027
0.6945
0.6863
0.6780
0.6683
0.6525
0.6161
0.5244
0.4519
0.3773
0.3023
0.2398
0.1795
0.1201
0.0750
0.0489
0.0381
0.0339
0.0309
0.0286
0.0267
0.0256
0.0243
0.0229
0.0222
0.0216
0.0209
0.0203
0.0195
0.0190
0.0187
Bot_Xtr
-------0.7500
0.7521
0.7542
0.7563
0.7579
0.7594
0.7610
0.7627
0.7644
0.7657
0.7667
0.7676
0.7684
0.7691
0.7698
0.7705
0.7712
0.7720
0.7728
0.7741
0.7747
0.7754
0.7760
0.7767
0.7774
0.7782
0.7789
0.7797
0.7805
0.7814
0.7821
0.7828
0.7835
0.7842
0.7850
0.7859
0.7869
0.7879
0.7889
0.7900
0.7909
0.7917
0.7925
0.7935
0.7944
0.7954
0.7965
0.7975
0.7986
0.7995
0.8003
0.8013
0.8023
0.8033
0.8044
0.8055
0.8067
0.8077
0.8086
0.8096