2010
Dr. Figliola – ME 423

2

The purpose of this project is to design an airplane based loosely around previously existing planes in the single engine, retractable gear, high performance, four-seat class. The team is to meet certain mission parameters which are
1.
Take Off at Sea Level
2.
Climb from Sea Level to 10,000 ft within 5 minutes
3.
Cruise at 75% power for full range
4.
Descend to Sea Level
5.
Approach Maneuvers at 55% power for 10 minutes
6.
Ground Operations at 35% power for 20 minutes
7.
Land with cruise reserve fuel for extra 40 minutes of flight
In addition to the mission parameters, the plane should adhere to the following performance specifications. The plane should
1.
weight over 1900 lbs with a useful load of at least 1100 lbs (including fuel)
2.
have a range of over 900 nautical miles (cruising at 75% power)
3.
have a ROC of 1400 fpm @ sea level
4.
cruise at 160 knots at 75% power at 6000 ft
5.
have a stall speed under 60 knots clean and 53 knots dirty
6.
have a T/O roll under 1000 ft and clear 50 ft in 1500 ft
7.
have a landing roll under 900 feet and clear 50 ft in 1500 ft
8.
have a service ceiling of at least 18000 ft
Airframe b
S e
AR
W
C
DO
40 ft
210.5 sq ft
.8
7.6
.03
3100 # gross
1900 # empty
1200 # useful load
3

Fuel Capacity 60 gallons
NACA 2412 Airfoil α
OL
= -2 degrees
Engine: Continental IO-520 6 cylinder air cooled 285 bHP @2625 rpm fuel injected @ c=0.43 lbs/HP-hr
C = .45 #/hp-hr
Propeller: Hartzell 3-blade, 74-inch diameter, constant speed, η = .82
Performance:
Speed
Maximum
Cruise
181 kts @ sea level
171 kts @ sea level
Stall (clean) V s
Stall (flaps) V so
V y
(best R/C speed)
V x
(best AOC speed)
167 kts @ 5000’
161 kts @ 10000’
55 kts @ sea level
49 kts @ sea level
68 kts @ sea level
55 kts @ sea level
Best glide
Best sink
Climb (Sea level)
Service Ceiling
Absolute Ceiling
TTC to 10,000 ft
TTC to 15,000 ft
T/O Ground Roll
T/O (50’ Clear)
6.61min
531 feet
91 kts @ sea level
80 kts @ sea level
2039 fpm
26000 feet
28000 feet
12.02 min
1058 feet
Landing Ground Roll
Landing (50’ Clear)
447 feet
1003 feet
Endurance
5.7 hrs @ cruise (allowance for start, taxi, climb. No reserves)
Range
13.5 hrs maximum @ 80 kts
911 nm @ cruise (allowance for start, taxi, climb. No reserves)
1244 nm maximum @ 110 kts
Wing Loading 14.7 lb/ft 2
Mission
Best time to climb
Sea level to 12,000’
Fuel Required
Ground ops (20 min @ 35%)
Climb
Cruise (nm)
Maneuvers (10 min @ 55%)
Reserve
8.3 minutes
358 lbs. (60 gal)
14.3 lbs. (2.383 gal)
14.3 lbs. (2.383 gal)
285 lbs. (47.5 gal)
11.24 lbs. (1.873gal)
34.1 lbs. (5.683 gal)
4

40 ft
35 ft
5.26 ft
5

Thrust is one of the four aerodynamic forces acting on an aircraft in flight. It is the force that pushes an aircraft through the air and is represented by the equation
𝑇 = 𝐷 = 𝐶
𝐷 𝑞
∞
𝑆 when an aircraft is in unaccelerated, level flight. When combined with W = L, the equation for thrust required to produce steady, unaccelerated flight is
𝑇
𝑅
=
𝑊
𝐶
𝐿
𝐶
𝐷
=
𝑊
𝐿
𝐷
Since L/D is a function of U∞ and q∞, T
R
depends on the velocity and altitude of the aircraft.
Since the engine is rated in term of power, it is better for a designer to think in terms of power required.
𝑃 = 𝑇𝑈
∞
𝑃
𝑅
= 𝑇
𝑅
𝑈
∞
=
𝑊𝑈
∞
𝐿
𝐷
= (
2𝑊 3 𝜌𝑆𝐶
𝐶
3
𝐿
2
𝐷
)
1
⁄
2
The engine produces power which is used to turn the propeller, which produces thrust, which is different than a jet engine that directly produces thrust. For instance, if the plane was anchored to the ground and throttle was increased to full, the engine would be producing 100% power, yet the propeller would be producing no thrust, as shown by the equation above, since there is no speed.
Thrust L/D
600
500
400
300
200
100
0
0 50 100 150 200
Speed (fps)
250 300 350 400
20
18
16
14
12
10
8
6
4
2
0
Figure 1: Thrust vs Speed
6

Power Cl^(3/2)/Cd
200
180
160
140
120
100
80
60
40
20
0
40
16
14
12
10
8
6
4
2
60 80 100 120
Speed (knots)
140 160 180 200
0
Figure 2: Power vs Speed
Total drag on an airplane can be divided into two parts: induced drag (the wing drag) and parasitic drag (the drag of everything else). Parasitic drag is the sum of pressure and friction drag, which is due to the airplane’s configuration and is independent of lift. At high speeds, parasitic drag dominates, while at low speeds, induced drag dominates.
Parasitic drag increases exponentially with speed. If the speed doubles, the parasitic drag becomes four times as great, and the power required to overcome it becomes eight times as great.
Induced drag changes with speed for very different reasons. It is mainly a function of angle of attack. Near the stall speed, the wing is inclined at a high angle creating high drag.
Once the plane achieves cruise altitude, the angle of attack is reduced to nearly zero and induced drag becomes minimal.
7

350,00
300,00
250,00
200,00
150,00
100,00
50,00
Induced Drag
Parasitic Drag
Total Drag
0,00
0 50 100
Velocity (U∞) [knots]
150 200
Figure 3: Sum of Drag Forces
Since thrust equal drag, the thrust required is the sum of the parasitic and induced drag on the aircraft.
8

Since the density at altitude is less than the density at sea level, the density ratio is less than one for any altitude above sea level. This means that the parasite power required decreases as the altitude increases, but the effective induced power required increases as the altitude increases. The right side of the power required curve is determined primarily by the parasite power required while the left side is based on the effective induced power required.
350,00
300,00
250,00
200,00
150,00
100,00
Pa Sea Level
Pr Sea Level
Pa 6000'
Pr 6000'
Pa 10000'
Pr 10000'
Pa 28000'
Pr 28000'
50,00
0,00
0 50 100
Velocity (U
∞
) [knots]
150 200
Figure 4:Power at Altitude
In the above chart, the power available and power required curves intersect in two places. Since in steady level flight the power required must equal the power available, the intersection of the curves gives the velocities at which the airplane will fly at that power setting at that altitude. For any other velocity, the airplane will either descend or climb. For example, if a plane is stabilized in cruise at a particular velocity, and without changing the power setting, the velocity is then decreased by pulling back on the yoke, and the airplane starts to climb. It will continue to climb until the power available equals the power required at some new higher altitude but at a lower velocity.
9

The right hand intersection of the curves gives the maximum velocity in level flight at that altitude. The left hand intersection gives the minimum velocity at which the aircraft can maintain steady level flight. At high altitudes, the minimum velocity for steady level flight is greater than the power on stall velocity.
As the altitude increases, the velocity envelope, which is the minimum to maximum velocity in steady level flight, narrows. This makes speed control particularly important at high altitudes. At the highest point, the absolute altitude, the aircraft can maintain steady level flight at only one velocity.
That velocity is the velocity for minimum power required.
If at any point the power required to maintain steady level flight exceeds the power available, the aircraft must descend. At high velocities, which are to the right of the intersections in the above chart, the velocity in the descent exceeds the maximum steady level flight velocity for that altitude. At low velocities, which are to the left of the intersections, the velocity in the descent is less than the minimum steady level flight velocity.
𝑃
𝑅𝑎𝑙𝑡
= 𝑃
𝑅𝑜
( 𝜌 𝜌
0
)
.5
As we can see in the equation above, the minimum power required for steady level flight increases with altitude. Also, the velocity for minimum power required increases with altitude, as seen below.
𝑈 𝑎𝑙𝑡
= 𝑈 𝑜
( 𝜌 𝜌 𝑜
)
.5
10

To find the maximum airspeed for a prop aircraft at any altitude, a comparison of the P
A
vs P
R
is required, and is governed by the equation
𝑉 𝑚𝑎𝑥
@ 𝑃
𝐴
= 𝑃
𝑅
Cruise speed is defined at 75% of rated power available at a given altitude. If maximum power available falls below 75% of the rated power at high altitudes, the maximum power available is used.
250,00
200,00
150,00
100,00
50,00
Power Required
100% Power Available
75% Power Available
0,00
0 50 100
Velocity (U∞) [knots]
150 200
Figure 5: Power at Sea Level
The maximum attainable speed at sea level is 181 kts in level, unaccelerated flight. Cruise speed at sea level at 75% power is 171 knots.
Cruise speed at 10000 feet is 161 knots.
11

The rate of climb an airplane can achieve is a crucial element in design in that it determines how long a runway must be for takeoff and whether or not the airplane will make it over any obstacles at the end of the runway. Because cruise performance is enhanced at higher altitudes, a quick climb increases overall efficiency of the flight. In its simplest form, the equation becomes
𝑅𝐶 = 𝑒𝑥𝑐𝑒𝑠𝑠 𝑝𝑜𝑤𝑒𝑟 𝑤𝑒𝑖𝑔ℎ𝑡
=
𝑃
𝐴
− 𝑃
𝑅
𝑊
As shown in the above equation, an aircraft can climb only if it can produce excess thrust. The excess is the pounds of thrust force being produced beyond that needed to overcome drag.
In climb, a component of weight acts rearward along the flight path, and the steeper the climb angle, the greater the amount. The forward acting thrust must equal the rearward-acting forces of drag plus the weight component. Therefore, the greater the excess thrust, the steeper the possible climb.
Weight has a very direct impact on the rate of climb. If weight is added, the plane must fly at a higher angle of attack to maintain a given altitude and speed. This increases induced drag of the wings and parasitic drag of the airplane and, because of this, additional thrust is needed to overcome it. This translates to less excess thrust being available for climbing.
Figure 6: Weight has a rearward component
12

2500,00
2000,00
1500,00
1000,00
500,00
0,00
0 50 100 150 200 250 300
-500,00
Velocity (fps)
Figure 7: Rate of Climb at Altitude
This plane design produced a max rate of climb of 2039 fpm at sea level.
As shown above, an increase in altitude decreases the rate of climb. This is due to the increase in power required and decrease in power available discussed in section 5.i.a.
To maximize excess thrust, an airplane will climb at a speed where drag is minimum. This is the best angle of climb speed V
X
. Because more thrust is produced at lower airspeeds, the V
X
speed for a propeller aircraft is close to the stall speed. This angle is given by
𝐶𝑙𝑖𝑚𝑏 𝑎𝑛𝑔𝑙𝑒 = sin
−1
𝑇ℎ𝑟𝑢𝑠𝑡 − 𝐷𝑟𝑎𝑔
𝑊𝑒𝑖𝑔ℎ𝑡
An interesting note is that many people wrongly think that excess lift makes an airplane climb.
Excess lift does not produce the climb, but it instead creates a non-linear vertical flight path. In essence, excess lift deflects the flight path upward and excess thrust sustains the flight path once deflected.
Since thrust and power are not the same thing, the airspeed where maximum excess thrust is available (V
X
) is not the same as the airspeed where maximum excess thrust horsepower is available
(V
Y
). As an airplane climbs, the thrust and power available and required curves shift. Therefore, the
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
22000
24000
25000
25500
13

speed where maximum excess power occurs decreases and maximum excess thrust speed increases with altitude. Once V
X
and V
Y
are equal, the airplane has reached its absolute ceiling. This absolute ceiling is the limit where all thrust available is necessary to sustain level flight. If it were to fly any slower, it would stall. The service ceiling is a more useful figure, as this is the altitude where an airplane can still climb at 100 fpm. This is the practical limit to unaccelerated flight.
The place design gives a service ceiling of 26000 ft and an absolute ceiling of 28000 ft.
Stall is an unfavorable condition that occurs when an airfoil exceeds its critical angle of attack. It occurs as the C
Lmax
. Stall is created when the airflow around a wing is separated and the low pressure area on top of the wing disappears.
Stall speed is governed by the equation
𝑈 𝑠𝑡𝑎𝑙𝑙
2𝑊
= ( 𝜌𝑆𝐶
𝐿𝑚𝑎𝑥
)
This speed will differ between clean V
S
(no flaps, no gear), and dirty V
SO
, because C
Lmax
changes depending on flaps.
For the designed plane, V
S
= 55 kts and V
SO
= 49 kts
Takeoff of an airplane is divided into three stages; ground acceleration distance to reach rotation speed, distance traveled during rotation of the aircraft, and distance to climb to a specific altitude. In order to takeoff, the airplane must increase its velocity past the stall velocity; the point where the airplane can produce enough lift to balance the aircraft weight. The velocity commonly used to determine when a plane can rotate to gain lift is the takeoff velocity, U to
, twenty percent greater than the stall velocity.
The distance between the start point and when the plane begins to rotate is the ground roll, x g
, which is 531 feet. Pilots normally allow the plane to rotate for 1 to 3 seconds before leaving the ground.
Using one second for this design, the rotation distance, x r
, is 109 feet. The total takeoff distance is defined as the ground roll distance and the rotation distance. Therefore, the takeoff distance for this
14

plane is 640 feet. After the plane rotates for one second, the pilot allows the plane to leave the ground and begin to ascend. The last portion of takeoff is the immediate climb past an obstacle, in this case, one that is 50 feet tall. The distance to clear an obstruction, x c
, is combined with the takeoff distance to obtain a takeoff to 50 feet distance, x to50
of 1058 feet.
Both the takeoff roll distance and the takeoff to 50 feet distances are well below the requirements of the design and will give the pilot some flexibility in runway lengths.
Similar to takeoff, landing distance is broken into several sections; approach to clear a 50 ft obstacle, flare to position tires on runway, free roll to allow tires to become stable and stopping ground roll. For large commercial aircraft, the approach angle is close to 3 ° ; however, light aircraft such as this can use higher angles to clear obstacles and still land safely. This analysis used an approach angle of 6 ° .
The approach distance consists of the distance between when the plane is flying at 50 feet in altitude to when it is at the flare height. The approach distance for the conceptual plane is 396 feet.
During flare, the pilot increases the drag on the plane by raising the nose, thus decreases the speed of the plane. When the plane reaches 10% higher than its stall speed, the pilot places the plane’s landing gear on the runway. This flare distance for the plane is 160 feet. During the next 1 to 3 seconds, the plane is in free roll along the runway. This time is dependent upon the reaction time of the pilot and the smoothness of the touchdown. The free roll distance is 100 feet for this plane. After the free roll, the pilot applies the brakes and pulls the plane to a stop. The ground roll distance is 348 feet. The total distance traveled in the free roll and ground roll portions is known as the landing distance, x
L
. The total of all four components of landing are known as the landing distance to clear an obstacle, x
L50
. For the conceptual plane designed, x
L
and x
L50
are 448 feet and 1003 feet, respectively. Both of which are well under the specified values of 900 feet and 1500 feet, respectively.
Glide performance is a crucial element of design as it tells the pilot exactly how far they can travel if they lose all thrust. It is defined when T
A
=0. For small values of θ, the glide angle becomes 𝜃 =
1
𝐿
𝐷
𝑎𝑛𝑑 𝐺𝑙𝑖𝑑𝑒 𝑅𝑎𝑡𝑖𝑜 = cot 𝜃
In order to get maximum range during a glide, the glide angle needs to be a minimum so that the glide ratio, the horizontal distance traveled per altitude lost, is maximized. Therefore, the minimum glide angle occurs when (L/D) is at its max. This is because drag needs to be minimized as each pound of drag represents deficit thrust.
15

An interesting this about glide speed is that it is always found at the same angle of attack regardless of current weight. It will be the same if the engines fail during takeoff, cruise, or near landing.
This is because the glide angle is a function of C
L
and C
D
. Since these don’t depend on weight, neither does glide angle, but weight does affect the airspeed at which this angle of attack is flown. The higher the weight, the faster the airspeed, but the decent angle will remain the same.
In some cases, the range of the plane after engine failure is not as important as the amount of time the plane will remain in the air. The best sink rate minimizes the vertical component of the plane’s velocity. This best sink rate occurs at velocity that is approximately 76 percent of the best glide speed.
For the conceptual design, the best sink rate is 7.77 feet per second at a sink speed of 80.1 knots. This rate and speed will keep the plane in the air the longest time in the case of an emergency.
An aircrafts range is the maximum distance it can fly given a specific amount of fuel, while the endurance is the maximum amount of time the plane can stay in the air given the same amount of fuel.
The endurance of an aircraft is determined by the fuel available and the fuel consumption rate.
The fuel consumption rate is governed by 𝑑𝑊 𝑑𝑡
= 𝑐𝑃
𝑅 where W is the weight in fuel. This is in terms of pounds per hour.
16
14
12
10
8
6
4
2
0
20
Endurance at 10000'
70
Velocity (knots)
Power Required at 10000'
120
140,00
120,00
100,00
80,00
60,00
40,00
20,00
170
0,00
Figure 8: Endurance and Power Required
16

1000
800
600
400
200
0
0
In order to maximize endurance, fuel flow must be minimized. Since the fuel flow is proportional to the power required, the fuel flow is minimized at the point where the power required is a minimum.
This is the speed at the bottom of the power required curve.
In this design, endurance is maximized at 80 knots, with a value of 13.5 hours at 10,000 feet. At a cruise speed of 161 knots, endurance becomes 5.7 hours.
To maximize the range, we want to get the maximum distance for each pound of fuel burned.
Since fuel flow is directly related to power, if we divide the power by velocity and the fuel flow by velocity, we obtain 𝑙𝑏 𝑜𝑓 𝑓𝑢𝑒𝑙 𝑛𝑚
∝
𝑃𝑜𝑤𝑒𝑟
𝑈
In order to minimize the left side, we can minimize the ratio of power over velocity.
Range at 10000' Power Required at 10000'
1400 140,00
1200 120,00
20 40 60 80 100
Velocity (knots)
120 140 160 180
0,00
Figure 9: Range and Power Required
20,00
100,00
80,00
60,00
40,00
17

Looking at the power required chart, a line from the origin to any point on the curve has the slope of power over velocity. The slope will be at a minimum when the line is tangent to the power required curve. This also corresponds to the minimum point on the thrust required curve. This value corresponds to the maximum range at altitude.
911 nm.
Therefore, the maximum range of the airplane is 1244 nm at 110 knots, while the cruise range is
In order to begin designing the plane, initial parameters must be set to observe the performance. These values can then be adjusted to meet the design specifications required by the
Federal Aviation Administration (FAA) or the customer. Some of these values, such as the propeller efficiency and engine size cannot change during the design process. The table below shows the initial design values of the plane.
Design Iteration 1
Gross Weight [lb]
Span [ft]
Wing Area [ft 2 ]
Aspect Ratio
Parasitic Drag Coefficient (C
Do
)
Maximum Coefficient of Lift (C
Lmax
)
3100
33
156
7
0.03
1.4
Using these values, the clean stall speed at sea level and cruise speed at 6000 feet were 65 knots and 141 knots, respectively. The clean stall speed must be below 60 knots as specified by the FAA. The cruise speed required by the customer must be at least 160 knots at this altitude.
In order to improve these values, several options may be taken independently or taken; these options include, decrease weight, increase span, increase aspect ratio, increase the maximum coefficient of lift, and/or decrease parasitic drag. In this design, the span was increased to 40 feet; the aspect ratio was increased to 7.6; the parasitic drag was decreased to 0.015; and the maximum coefficient of lift was increased to 1.45. These values yield results that are well within the design specifications and are shown in the design performance table in the introduction.
18

Aerodynamics. Model Aircraft. October 25, 2009. http://adamone.rchomepage.com/index.html
Aircraft Performance. Free Online Private Pilot Ground School. 2006. http://www.free-online-private-pilot-ground-school.com/aircraft_performance.html
Dave Esser. Aircraft Climb Performance. Embry-Riddle Aeronautical University. March 2002. http://www.erau.edu/er/newsmedia/articles/wp6.html
Figliola, Richard. Aircraft Static Performance Notes. Clemson University, copyright 2009.
Thrust. U.S. Centennial of Flight Commission. http://www.centennialofflight.gov/essay/Theories_of_Flight/Thrust/TH5.htm
19