1

SIZING MATRIX AND CARPET PLOTS

Serkan Özgen, Prof. Dr.

Middle East Technical University, Dept. Aerospace Eng., Turkey

1. Introduction

Aircraft design is an intellectual process that combines engineering knowledge, creativity and

art. For this reason, in major companies aircraft design work is undertaken by Integrated

Product Teams (IPTs) consisting of engineers, technicians, industrial design experts,

managers each with different backgrounds and even cultures. Therefore, aircraft design is not

done by one person aimed at a single goal but rather is an activity with multiple objectives.

A successful design is technically sound, feasible, affordable, safe, reliable and aesthetically

pleasing. When one looks at the History of Aviation and the airplanes that have become

benchmarks like the Douglas DC-3, Cessna 172, Supermarine Spitfire, McDonnell Douglas

F-4 and others, one notices that these were not the fastest airplanes of their class, nor they

were the ones carrying the heaviest payload, nor they were the cheapest or aesthetically the

most pleasant. These airplanes were a good combination of technical soundness, feasibility,

affordability, safety, reliability and aesthetics built around realistic requirements. Those were

optimum airplanes designed at the right time at the right place.

Therefore, the task of a designer is to create a flying machine that is technically sound, safe,

reliable, feasible and affordable. These objectives is to be kept in mind from the very

beginning, namely the conceptual design phase. However, the designer is immediately faced

with contradicting requirements to meet these objectives. For example a very safe airplane

will probably not be feasible or affordable. Likewise, an airplane with a high technological

level will be very expensive. This brings us to the concepts of trade and optimization. A good

design is an efficient compromise of performance, safety, reliability, cost and aesthetics.

This manuscript aims at outlining the basics of optimization of the performance and the

weight of a light sportive airplane. The simple methodology explained is most relevant for the

conceptual design phase where sizing and performance calculations constitute the major task.

A well-optimized airplane is less likely to encounter unsurmountable weight and cost

increases and performance deficiencies as the design progresses into preliminary and detail

design phases. The four main ingredients of the presented method are weight estimation,

aerodynamics, installed thrust and performance.

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2. Requirements

Each airplane is designed around a set of requirements. The key to the success of a design is a

set of realistic and consistent requirements. The requirements involve purpose and operation

of the aircraft, performance characteristics like speed, range, rate of climb, etc., and also

mission characteristics like payload, low observability, etc. The requirements may be set by

the customer, by safety and certification requirements or a combination of both. The sizing

process in the conceptual design phase is usually driven by performance requirements.

The requirements for the light sport aircraft for the VKI Short Course: UAVs & Small

Aircraft Design are given in Table 1. In addition to these “customer” requirements, the

designer may utilize additional requirements specified in the Certification Specifications. For

this airplane, the EASA Certification Specifications that may be applicable are: CS-23:

Certification Specifications for Normal, Utility, Aerobatic and Commuter Category

Aeroplanes [1]; CS-VLA: Certification Specifications for Very Light Aeroplanes [2]; CS-

LSA: Certification Specifications and Means of Compliance for Light Sport Aeroplanes [3].

Also FAR-23: Airworthiness Standards: Normal, Utility, Acrobatic, and Commuter Category

Airplanes [4] is applicable. Relevant CS and FAR performance requirements are given in

Table 2. In the current study, the light sport airplane will be designed and optimized according

to the “customer” requirements but the final optimized design will be checked against CS and

FAR requirements as well.

It should be noted that CS-23 and FAR-23 are applicable to Normal, Utility, Aerobatic and

Commuter Category airplanes. Normal, Utility and Aerobatic Category airplanes are those

with a certified maximum take-off weight of 5670 kg (12500 lb) or less, and those having a

seating configuration, excluding the pilot seats of nine or fewer. Commuter Category refers to

propeller-driven twin engine aeroplanes that have a seating configuration, excluding the pilot

seats of nineteen or fewer and a certified maximum take-off weight of 8618 kg (19000 lb) or

less. Certification Specifications for Normal, Utility and Aerobatic category is further divided

into two subcategories, namely airplanes heavier or lighter than 2722 kg (6000lb).

Certification requirements differ slightly between these three categories and only those

specifications corresponding to Normal, Utility and Aerobatic Category airplanes for a

certified maximum take-off gross weight of 2722 kg or less with a single reciprocating engine

are included in Table 2 because the Light Sport Aircraft designed according to the

requirements in Table 1 falls into this category due its weight, calculated below.

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Table 1. Design requirements for the VKI Short Course: UAVs & Small Aircraft Design.

Definition Light Sport Aircraft

General

Number of engines

Occupants (80 kg each)

1

2

Performances

Optimized for

Speed range (km/h)

Altitude (m)

Range (km)

Rate of climb (m/s)

Take-off run (m)

Stall speed (km/h)

Cruise

≈ 280

2400

1000

> 5

< 300

< 100

Useful weight

Luggage/crew member (kg) ≈ 10

Miscellaneous

Comfortable

Green

Safe

Cheap

Table 2. EASA and FAA design requirements and specifications

for Normal, Utility, and Aerobatic Category airplanes

(Wo ≤ 2722 kg/6000 lb, single reciprocating engine category only).

Definition FAA

FAR-23

EASA

CS-23

EASA

CS-VLA

EASA

CS-LSA

Applicability

Maximum take-off weight

Number of engines

Type of engine

Number of crew

Max. number of seats

2722 kg

one

reciprocating

2

9

2722 kg

one

reciprocating

2

9

750 kg

one

spark or

compression

ignition

2

0

600 kg

one

non-turbine

or electric

2

0

Performances

Stall speed, VSO1

Rotation speed, VR

Climb speed (@15m/50ft height), VCL

Climb rate or gradient @ VCL

Approach speed, VA

Climb gradient @ VA

61 kt

≥ VS12

≥ 1.2VS1

≥ 8.3 %

≥ 1.3VSO

≥ 3.3 %

113 km/h

≥ VS1

≥ 1.2VS1

≥ 8.3 %

≥ 1.3VSO

≥ 3.3 %

83 km/h

≥ 1.3VS1

≥ 2 m/s

≥1.3VS1

1:30

83 km/h

1 VSO: stall speed in the landing configuration. 2 VS1: stall speed obtained in a specified configuration. In this case, take-off configuration.

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3. The Baseline Design

An airplane is designed, which will be referred to as the Baseline Design hereafter, using

well-known methods outlined by Raymer [5], Roskam [6] and Anderson [7]. The Baseline

Design is accomplished following the steps:

i. Competitor study,

ii. First weight estimation,

iii. Airfoil and wing planform selection,

iv. Power-to-weight ratio (P/W) and wing loading (W/S) selection,

v. Refined sizing and a better weight estimation,

vi. Geometry sizing and configuration,

vii. Configuration sizing,

viii. Aerodynamics,

ix. Empty weight estimation using statistical component weight estimation method,

x. Installed and uninstalled thrust,

xi. Performance and flight mechanics.

Sizing and trade studies is the twelfth step and is the subject of this study. The configuration

of the Baseline Design is as follows:

Low-wing monoplane with conventional tail configuration,

Tricycle fixed landing gear,

Single naturally aspirated reciprocating tractor engine with a three blade constant

speed propeller,

Number of crew: 2 with side by side seating.

Figure 1 shows the three view drawing of the Baseline Design prepared using OpenVSP [8],

with its important design characteristics. Table 3 compares its performance characteristics

with the requirements given in Table 1. Data in Figure 1 show that the designed airplane falls

into the CS/FAR-23 Classification because of its weight but not the VLA or LSA

Classification. Also, the positive limit load factor selected for the design puts this airplane in

the Aerobatic Category. From Table 3, it can be seen that the airplane satisfies all the

“customer” requirements by a comfortable margin. The questions that remain are: Is this the

best airplane satisfying the requirements? Can a lighter, i.e. greener and less costly airplane to

acquire and operate be designed that can still meet the requirements?

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Characteristics Value

Length (m) 7.54

Wing area (m2) 11.2

Wing span (m) 10.0

Aspect ratio 9.0

Maximum take-off

gross weight (kg) 944.7

Wing loading, W/S

(kg/m2) 84.3

Wing airfoil NLF(1)-0115 [9]

Engine Lycoming IO-360-L

Propeller 3 blade/76” diam.

Engine power

(hp/kW) 160/119.3

Power-to-weight

ratio (kW/kg) 0.126

g-limits +6, -3

Figure 1. Three view drawing of the Baseline Design with important characteristics.

Table 3. Performance characteristics of the Baseline Design.

Performance characteristic Baseline Design Requirement Satisfied?

Range, R (km) 1050 > 1000

Rate of climb, R/C (m/s) 7.8 > 5

Take-off run, sg,to (m) 268 < 300

Stall speed, VSO (km/h) 94.3 < 100

4. Sizing and Trade

Sizing and trade studies constitute an important part of conceptual design. After this step is

completed, the designer knows that the calculated design parameters represent a good

combination of performance and weight. Since the weight of the airplane has a direct

influence on cost, in a way, the cost is also optimized. For sizing and trade studies, two

methods are outlined in the present study, namely the sizing matrix plot and carpet plot

analyses. These methods are basically identical, they essentially represent the same data in

different formats.

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4.1. Sizing Matrix Plot

The sizing matrix plot quickly allows the designer to find an optimised combination of

selected design parameters. The outline of the method is as follows:

i. The parameters to be varied or optimized are selected. These are chosen among wing

loading (W/S), thrust-to-weight (T/W) or power-to-weight (P/W) ratio, taper ratio (),

aspect ratio (A), etc. However, as the number of parameters increase, the number of

combinations increase by at least 3n, n being the number of parameters chosen, and the

process becomes more cumbersome. The smallest number of parameters to be chosen

is 2, which means that the minimum number of combinations to be worked with is 9.

Usually, wing loading (W/S) and thrust-to-weight (T/W) or power-to-weight (P/W)

ratios are chosen for the sizing and trade studies since these have the greatest effect on

performance and weight. Actually, in this study, S (trapezoidal wing planform area)

and P (power) are chosen as the trade parameters because the weight estimation

method utilized requires these parameters as inputs.

ii. The Baseline Design is perturbed by ±20% for W/S and ±20% for T/W or P/W. One

can increase the number of “perturbed” designs both for W/S and P/W but this will

result in 5n or 7n designs to work with. In this study, the trapezoidal wing reference

area is perturbed by ±20% and power is varied such that more powerful and less

powerful engines belong to the same engine family as the Baseline Design, which may

not always correspond to ±20% variation. While choosing candidate engines, choosing

engines that have similar sizes to the Baseline Design simplifies the analysis

significantly because the nacelle and the fuselage size will be unaffected from the

engine choice. The trapezoidal wing planform areas and the engines that are studied

are as follows (those of the Baseline Design are underlined):

Wing planform areas: 9.0 m2, 11.2 m2, 13.4 m2.

Engines: Lycoming O-235-F (125 hp), Lycoming IO-360-L (160 hp),

Lycoming IO-360-F (180 hp).

While perturbing the wing planform area, the horizontal and vertical tail sizes (SHT and

SVT) are varied proportionately in order to keep the tail volume ratios (VHT and VVT)

the same as the Baseline Design. This also relieves the designer from the burden of

varying the fuselage length in order keep the tail volume ratio constant.

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Fuselage size is kept constant for all perturbed designs since the cockpit size and tail

moment will remain constant, independent of the wing size and the powerplant.

Fuel volume is initially kept constant for the sake of simplifying the analysis. If the

available fuel is enough to satisfy the mission requirements (especially the range), the

designer may keep the original fuel volume. If the range requirement is not satisfied,

one needs to increase the fuel volume, which will have an effect on the total weight.

iii. The preliminary sizing matrix is constructed. Table 4 shows the preliminary sizing

matrix constructed for the current design.

Table 4. Preliminary sizing matrix.

S=13.4 m2 S=11.2 m2 S=9.0 m2

P=180 hp Config.1 Config. 2 Config. 3

P=160 hp Config. 4 Config. 5 Config. 6

P=125 hp Config. 7 Config. 8 Config. 9

iv. The performance requirements that will be used for optimization are selected. For a

sound analysis, at least three requirements shall be selected. The chosen requirements

shall be balanced between the ones where wing loading (W/S) has a dominant effect

like the stall speed (VSO) and the landing distance (sg,l), and those where power-to-

weight ratio (P/W) has a dominant effect like the rate of climb (R/C), maximum speed

(Vmax), and take-off distance (sg,to). In this study, the performance requirements chosen

are the range (R), rate of climb (R/C), take-off run (sg,to), and the stall speed (VSO),

which are the “customer” requirements.

v. The empty (Wempty) and take-off gross weights (Wo) of each configuration is

calculated. The empty weights are calculated using the Statistical Weights Method

explained in [5]. This method consists of 14 empirical relations for estimating the

weights of the wing, horizontal tail, vertical tail, fuselage, main landing gear, nose

landing gear, installed engine, fuel system, flight controls, hydraulics, electrical

system, avionics, air conditioning/anti-icing system and furnishings as a function of

design gross weight, ultimate load factor, sizes and the geometric shapes of the major

components, cruise speed of the airplane, dry engine weight, etc. It is highly

recommended to use this method for sizing and trade, although it is a bit more

cumbersome than other less comprehensive weight estimation methods since it results

in a more detailed and accurate weight breakdown.

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vi. The Aerodynamics module is updated for each configuration. The Aerodynamics

module is a spreadsheet involving calculations of the maximum lift coefficient (CLmax),

parasite drag coefficient (CDO), induced drag factor (K), and the drag polar as a

function of speed and altitude. In these calculations, the effect of high lift devices and

the landing gear are taken into account.

vii. The uninstalled thrust or power data obtained from the engine manufacturer or by

using a scaling approach is analysed in order to obtain the installed thrust values. Here,

the losses due to altitude, power extraction, blockage, compressibility, scrubbing drag,

cooling and miscellaneous drag are calculated and the installed thrust is calculated as a

function of speed and altitude. Here, the methods outlined in [5] are used.

viii. Performance calculations are performed for the requirements selected in step iv.

Stall speed (VSO):

Here, the lift equation is employed with the wing planform size (S) selected for the

configuration in step i, and the maximum lift coefficient (CLmax) calculated in step vi.

Here, the airplane is in landing configuration, where the flaps are fully extended.

SCV2

1LW maxL

2 . (1)

Rate of climb (R/C=dh/dt):

For the calculation of the rate of climb, the specific excess power equation is used,

which can also be used in order to calculate other performance characteristics like the

maximum speed, acceleration, service ceiling and the maximum sustained load factor

that can be achieved at a given altitude and speed [5].

dt

dV

g

V

dt

dh

S

W

q

Kn

S/W

Cq

W

TVP 2DO

s

. (2)

For rate of climb calculations, the load factor n=1 and take-off conditions are used. For

take-off, flaps are partially extended and their effects on the parasite drag coefficient

and induced drag are accounted for.

Take-off run (sg,to):

Take-off distance is calculated using the expression given in equation (3) [5]:

T

2TOAT

Ato,g

K

VKKln

gK2

1s , (3)

9

,W/TKT (4)

2LDOLA KCCC)S/W(2

K

. (5)

In the above equations, μ=0.03 is the coefficient of rolling friction between the runway

and tyres. The parasite drag coefficient, CDO includes the additional drag of the

partially extended flaps and the induced drag factor, K is corrected for the ground

effect. During take-off, the airplane is fairly horizontal so CL≈0.1 is assumed.

Range (R):

Range is calculated from the Bréguet Range Equation [7]:

f

i

power

p

W

Wln

D

L

CR . (6)

In this equation, ηp is the propeller efficiency, calculated as a function of the advance

ratio, J=V∞/nD, n: propeller revolutions per second and D: propeller diameter. The

propeller efficiency is corrected for blockage, compressibility and scrubbing drag

effects. The specific fuel consumption is denoted by Cpower and is dependent on the

engine chosen. For the candidate engines in this study, the specific fuel consumptions

are obtained for the cruise condition from manufacturer’s data and have slightly

different values for the three different engines:

Lycoming O-235-F, Cpower=0.4638 lb/h/hp=0.773*10-6 N/W/s,

Lycoming IO-360-L, Cpower=0.4500 lb/h/hp=0.750*10-6 N/W/s,

Lycoming IO-360-F, Cpower=0.4446 lb/h/hp=0.741x10-6 N/W/s.

L/D is dependent on the weight and the speed of the airplane. In order to maximize

range, a propeller-driven airplane must fly at L/D)max. For the Baseline Design and the

remaining configurations this occurs at a speed around 72 m/s (259 km/h) at the cruise

altitude of 2400m. However, it is seen in the calculations that, cruise flight at a speed

of 280 km/h does not significantly alter the range performance of the airplane.

When the performance calculations are performed, the final sizing matrix can be

constructed as can be seen in Table 5. The requirements that are not satisfied are

shown underlined.

From Table 5, we immediately see that the range requirement is satisfied by all 9

configurations. This means that there is no need to vary the fuel weight between

configurations but the range data cannot be used for sizing trade.

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We also see that there is 100 kg difference between the heaviest (configuration 1) and

the lightest configurations (configuration 9). Configurations 3 and 6 do not satisfy the

stall speed requirement, while the take-off distance requirement is violated by

configurations 7, 8 and 9. Configuration 7, which has the large wing but the small

engine violates the rate of climb requirement also. Configurations 1, 2, 4 and 5 satisfy

all the requirements.

Table 5. Final sizing matrix.

S=13.4 m2 S=11.2 m2 S=9.0 m2

P=180 hp

1

Wo=994.2 kg

VSO=88.5 km/h

R/C=7.9 m/s

sg,to=228 m

R=1006 km

2

Wo=965.4 kg

VSO=95.5 km/h

R/C=8.3 m/s

sg,to=259 m

R=1034 km

3

Wo=937.2 kg

VSO=102 km/h

R/C=9.3 m/s

sg,to=269 m

R=1080 km

P=160 hp

4

Wo=973.2 kg

VSO=87.6 km/h

R/C=7.4 m/s

sg,to=235 m

R=1028 km

5

Wo=944.7 kg

VSO=94.3 km/h

R/C=7.8 m/s

sg,to=268 m

R=1050 km

6

Wo=916.7 kg

VSO=101 km/h

R/C=8.2 m/s

sg,to=292 m

R=1088 km

P=125 hp

7

Wo=950.8 kg

VSO=86.6 km/h

R/C=4.9 m/s

sg,to=319 m

R=1041 km

8

Wo=922.6 kg

VSO=93.4 km/h

R/C=5.2 m/s

sg,to=365 m

R=1061 km

9

Wo=894.9 kg

VSO=99.8 km/h

R/C=5.6 m/s

sg,to=398 m

R=1100 km

ix. The next step is to crossplot the data in Table 5 as illustrated in Figure 2. First, for

each power value, the take-off gross weights are plotted as shown in the first column

of Figure 2. In the plots, hollow circles denote data from Table 5. From the take-off

gross weight graphs of Figure 2, wing areas corresponding to regularly-spaced gross

weights are determined, shown with full circles in the plots. Then the data is

transferred to a wing area (S)-engine power (P) graph as shown in Figure 3. This graph

is already useful as it is because it yields the take-off gross weight for any combination

of wing planform area (S) and engine power (P).

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Take-off weight, Wo Stall speed, VSO Rate of climb, R/C Take-off distance, sg,to

P=180 hp

P=180 hp

S=13.4 m2

S=13.4 m2

P=160 hp

P=160 hp

S=11.2 m2

S=11.2 m2

P=125 hp

P=125 hp

S=9 m2

S=9 m2

Figure 2. Sizing matrix crossplots.

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Figure 3. Preliminary sizing matrix plot.

Then, stall speeds, climb rate and the take-off runs are crossplotted in the most convenient

manner as shown in the second, third and fourth columns of Figure 2. In Figure 2, the hollow

circles represent the actual data from Table 5, while full circles correspond to the wing area

(S)-power (P) combinations that exactly meet a given requirement. The combinations that

exactly meet the requirements are transferred to the sizing matrix plot of Figure 3 and joined

by smooth curves, resulting in Figure 4. Again, the hollow circles represent the actual data

from Table 5. These curves constitute the constraint lines and the small arrows indicate the

direction of the feasible region. The Baseline Design is also included in the figure, shown

with a large circle having a dashed outline.

The Optimum Design is the one satisfying all the requirements, having the lowest take-off

gross weight. The Optimum Design will therefore will be at the intersection of two constraint

curves. Hence, the Optimum Design lies at the intersection of the stall and take-off distance

constraint curves, shown with a big black circle at the lower left of the Baseline Design.

4.2. Carpet Plot

As mentioned previously, the carpet plot is an alternative format for presenting the data in

Figure 2. The take-off gross weight plots in the first column of Figure 2 are superimposed as

illustrated in Figure 5. When the data points corresponding to the same wing areas are

connected with straight lines, the resulting shape looks vaguely like a carpet! In the same

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figure, the data points in Figure 2 that exactly meet the stall speed, take-off run and rate of

climb requirements are plotted and joined by smooth curves, constituting the constraint lines.

The optimum design is the lowest point in the carpet plot, i.e. the lightest airplane that meets

all the requirements, which is shown with a full circle in Figure 5, at the intersection of two

constraint lines. The Baseline Design is also shown in the figure with a large dashed circle.

Figure 4. Final sizing matrix plot.

Figure 5. Carpet plot.

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4.3. Optimum Design

As mentioned above, the Optimum Design is the one satisfying all the requirements, with the

lowest take-off gross weight. Therefore, judging from Figure 4 and 5, the Optimum Design

corresponds to S=9.26 m2 and P=154.5 hp and Wo=915 kg, about 29.7 kg lighter than the

baseline design. However, the engine found that delivers 155 hp is heavier and to be on the

safe side (exceeding the requirements with a comfortable margin) the Optimum Design is

chosen as S=9.7 m2, P=160 hp and Wo=926.4 kg shown in Figures 4 and 5 with a dotted

circle. The Optimum Design is illustrated in Figure 6, together with important characteristics.

The group weight statement of the Optimum Design is presented in Table 6.

Characteristics Value

Length (m) 7.54

Wing area (m2) 9.7

Wing span (m) 9.34

Aspect ratio 9.0

Maximum take-off

gross weight (kg) 926.4

Wing loading, W/S

(kg/m2) 95.5

Wing airfoil NLF(1)-0115 [9]

Engine Lycoming IO-360-L

Propeller 3 blade/76” diam.

Engine power

(hp/kW) 160/119.3

Power-to-weight

ratio (kW/kg) 0.129

g-limits +6, -3

Figure 6. Three view drawing of the Optimum Design with important characteristics.

In the cruise conditions, the drag polar of the airplane is estimated as:

.C0452.0023.0C 2LD (7)

The performance data are presented in Tables 7 and 8. In Table 7, the performance

characteristics are compared with the customer requirements, while in Table 8 comparison

with respect to CS/FAR requirements is presented. Table 9 depicts the manoeuvrability

characteristics of the Optimum Design.

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Table 6. Group statement format of the Optimum Design.

Group Weight (kg)

Structures

Wing

Horizontal tail

Vertical tail

Fuselage

Main landing gear

Nose landing gear

101.1

7.4

4.7

111.3

57.5

18.7

Propulsion

Engine

Fuel system/tanks

176.4

17.4

Equipment

Flight controls

Hydraulics

Avionics

Electrical

Air conditioning & anti-ice

Furnishings

19.4

2.0

30.0

61.0

18.7

24.3

Total empty weight 649.9

Useful load

Crew

Fuel

Payload

160

96.5

20

Take-off gross weight 926.4

Table 7. Performance characteristics of the Optimum Design compared

with customer requirements.

Performance characteristic Optimum Design Requirement Satisfied?

Range, R (km) 1069 > 1000

Rate of climb, R/C (m/s) 6.6 > 5

Take-off run, sg (m) 278.5 < 300

Stall speed, VSO (km/h) 98.0 < 100

Table 8. Performance characteristics of the Optimum Design compared

with CS/FAR requirements.

Performance characteristic Optimum Design Requirement Satisfied?

Stall speed, VSO (km/h) 98.0 < 113 (CS/FAR)

Climb gradient @ VCL, γ 13 % > 8.3% (CS/FAR)

Climb gradient @ VA, γ 9.2% > 3.3% (CS/FAR)

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Table 9. Manoeuvrability characteristics of the Optimum Design.

Parameter Value

Instantaneous turn rate

Instantaneous turn radius

43.6°/s @ Vcorner = 271 km/h, n=6

98 m @ Vcorner = 271 km/h, n=6

Sustained turn rate

Sustained turn radius

25°/s @ V=245 km/h, n=3.2

155.5 m @ V = 245 km/h, n=3.2

In Table 9, the most forward and backward positions of the centre of gravity with respect to

the mean aerodynamic chord are given together with the corresponding static margin values.

The neutral point is calculated using the method outlined by Etkin and Reid [10]. As can be

seen, the airplane is stiff in longitudinal flight, which can be easily remedied with relocating

certain systems in the airplane during preliminary and detail design phases or moving the

wing a few inches forward.

Table 10. CG positions and longitudinal stability of the Optimum Design.

CG position Chordwise CG position Static margin

Most forward 0.38 16.0 %

Most backward 0.42 12.5 %

Finally, in Table 11, the characteristics of the Optimum Design are compared with those of

competitor aircraft. Seven competitors are chosen, which are: Grob 115E, Grob 120A,

Slingsby T-67, Aermacchi Sf.260D, Cirrus SR.20, Cirrus SR.22, and Diamond DA.20. As can

be seen, the Optimum Design compares well with the competitors. Although it has the

smallest engine except the Diamond DA.20 (which is a VLA Class airplane), it promises

superior performance than the competitors for most of the performance characteristics. It is

also the lightest airplane except for Diamond DA.20. The superior performance is possible

due to laminar flow airfoil, use of smooth moulded composites for the entire airplane that

offers a potential for significant amount of laminar flow (~25% over the fuselage, ~50% over

the wing and tails) and finally optimized weight and performance as explained above. Had a

lighter aeroengine existed delivering 155 hp, it would have been possible to reduce the weight

of the airplane further.

The unit civil purchase price of this airplane is estimated to be $382 000 (€274 000) in 2014

prices estimated using the DAPCA IV Cost Model assuming that 250 airplanes will be

manufactured in 5 years after commencement of production [5].

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Characteristic Optimum

Design

Grob

G115E

Grob

G120A

Slingsby

T-67

Aermacchi

Sf.260D

Cirrus

SR.20

Cirrus

SR.22

Diamond

DA.20

Performance

Maximum speed (km/h) 360 250 319 281 441 287 339 277

Range (km) 1069 1130 1537 753 2050 1454 1943 1013

Rate of climb (m/s) 6.6 5.3 6.5 7 9.1 4.2 6.5 5.1

Take-off run (m) 278.5 461 707 274 451 295 390

Stall speed (km/h) 98 96 102 100 109 104 111 78

Geometric

Length (m) 7.54 7.54 8.60 7.55 7.00 7.92 7.92 7.16

Wing area (m2) 9.7 12.2 13.3 12.6 10.1 13.7 13.7 11.6

Wing span (m) 9.34 10.00 10.19 10.69 8.22 11.68 11.68 10.87

Aspect ratio 9.0 8.2 7.8 9.1 6.7 10.0 10.0 10.2

Weights

Maximum take-off weight (kg) 926 990 1490 1157 1300 1386 1633 800

Wing loading (kg/m2) 95.5 81.1 112.1 91.8 128.7 101.1 119.1 68.9

Empty weight (kg) 650 685 960 794 675 965 1009 529

Empty weight fraction 0.70 0.69 0.64 0.69 0.52 0.70 0.62 0.66

Power

Engine power (kW) 119 139 190 194 195 149 230 93

Power to weight ratio 0.129 0.140 0.127 0.168 0.150 0.108 0.141 0.116

Table 11. Comparison of the Optimum Design with competitor aircraft (data for competitor aircraft obtained from Internet sources).

18

5. Conclusions

Sizing trade and optimization of a light sport aircraft is outlined. The trade study is performed

for obtaining the optimum wing area-engine power combination. Two methods are described,

namely the sizing matrix plot and carpet plot approaches, both methods having visual

emphasis, which is their main strength. These methods are applicable using widely used

general purpose computational and graphical tools, without the need for costly, dedicated

software. These aspects render the methods suitable for student projects, academic purposes

and also for design of real airplanes in the conceptual design phase. The methods can be

developed further to include a higher number of parameters but then their simplicity and

visual aspects will quickly fade away and programming the methods as a software will

become necessary. The methods are applicable to conventional configurations and should be

used with care when the designed airplane configuration is unconventional like UAVs, tailless

aircraft or aircraft powered by unconventional powerplants like electrical.

While dwelling in the fascinating world of aircraft design, technical knowledge, experience,

and creativity are all vital. On the other hand, it is also beyond doubt that “the airplane” is

aesthetically the most pleasant invention of mankind. We, aircraft designers are privileged to

be following the footsteps of great designers like Marcel Dassault, quote:

„For an aircraft to fly well, it must be beautiful“

19

References

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3. European Aviation Safety Agency, Certification Specifications and Acceptable Means of

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4. Federal Aviation Administration, Airworthiness Standards: Normal, Utility, Acrobatic and

Commuter Category Airplanes, Amendment 55, 2002.

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