Multidisciplinary Design Optimization of Amphibious Aircraft of

Unconventional Aerodynamic Configurations Plamen Roglev, MSc.

P. O. Box 26, 4001 Plovdiv, BULGARIA

plroglev@mail.bg

Abstract: Modern commuter seaplanes have performance that is significantly lower than that

of landplanes and that is the reason why they find a limited use. In this work a conceptual design

investigation into the application of non-traditional aerodynamic configurations such as canard,

tandem and box-wings in regard to improving the flight performance of flying boats is carried out.

Also an optimization of the hull shape is shown to provide aerodynamic, hydrodynamic and structural

advantages. Seaplanes with optimized design and made from composites can be an effective and

practical means of transport and can provide a much wider field for seaplane operations.

Keywords: commuter seaplanes, flying boats, amphibious aircraft, optimization

1. Introduction

Seaplanes reached the peak of their

development both for civil and military

operations in the years right after the end of the

Second world war. In the 1950’s their use

quickly declined, because they lost the

competition with landplanes. Nowadays the

main use of seaplanes is in the private sector or

for niche applications such as fire-fighting or

tourist flights. There are a few small

companies offering regular passenger service

usually to little islands.

The main drawbacks of seaplanes in

comparison to landplanes are:

-Seaplanes have high empty weight fractions.

Their structure is heavier, because they have to

carry extra weight for what amounts to a boat

hull that has to be seaworthy.

-The hull with its specific shape creates higher

drag than the fuselage of a landplane.

- Higher trim drag because of the need of

placing the propellers far from the water

surface.

- The operation and maintenance of seaplanes

are more difficult and expensive, partly due to

problems with corrosion.

- Seaplane service is more sensitive to adverse

weather conditions than that from planes

taking off and landing on land.

It must be pointed out that all of these

drawbacks are more expressed for floatplanes

than for flying boats. Despite that, floatplanes

converted from commuter type aircraft are the

prevailing type currently operated for

passenger transport [1]. Also it has to be

noted that the newest aircraft is already 30

years old. All are made from aluminium

alloys and suffer from problems with

corrosion.

Turboprop Single

0

500

1000

1500

2000

0 200 400 600 800 1000

Range, nm

Payload,

kg Caravan

Caravan

Amphibian

Turboprop Twin

0

500

1000

1500

2000

0 200 400 600 800 1000

Range, nm

Payload,

kg Twin Otter

Twin Otter

Amphibian

Seastar

Fig. 1: Payload-Range Diagrams for

Commuter Aircraft

These floatplanes are not competitive to state-

of-the-art aircraft - neither in performance nor

in cost effectiveness. This can be seen by the

payload-range diagrams on Fig. 1. The

floatplane variants lose about 20% of their

payload and range. Their cruising speed is also

about 15% lower but this is not as big a

problem, since they are employed mostly over

distances of up to 100 nm and the influence

upon the block speed is insignificant.

The operation of float planes is limited in

rough waters. They can usually operate up to a

sea state 2. This brings restrictions for

operations in open waters and in strong wind

conditions.

With all those shortcomings of contemporary

commuter seaplanes, it is not difficult to see

why they have such a small market share. And

that is why major aircraft manufactures are not

interested in developing new seaplanes.

Despite all the above stated we should say that

current seaplanes do have competitive

advantages over fast planing boats for

transporting people over medium distances.

Modern passengers demand faster service and

today there are high-speed ferries that travel at

more than 40 knots. As might be seen on Fig.2,

if they were airplanes, they would travel much

faster on the power that they utilise. And they

would be less limited by the sea state.

0

0,05

0,1

0,15

0,2

0,25

0 100 200 300 400 500

Cruise velocity, km/h

Po

we

r to

we

igh

t ra

tio

, k

W/k

g

Seaplanes

Landplanes

Planing Boats-Calm sea

Planing Boats - Stormy

Fig. 2: Power to weight ratio versus cruise

velocity for planing boats and seaplanes.

As pointed in [2] scheduled flights of

floatplanes between islands and off-shore

regions are highly competitive with ferries and

boat transfers. There are companies

successfully offering this service due to a

relatively low ticket price and a high time

saving in comparison to boat transfers.

The results of a survey published in [2] reveal

that operators believe that the growth

of a future seaplane transport system is being

restricted by the availability of suitable

aircraft.

In order the expenses of a new seaplane design

to be justified, it should be able to offer

substantially improved performance, close to

that of landplanes.

Nowadays there are available enabling

technologies that make that possible.

The spreading use of composites in

commercial aircraft is able to facilitate the

design and certification of composite

seaplanes. Advanced composites might

provide important advantages for amphibious

aircraft reducing the problems with corrosion

and providing lighter and better shaped

structures. There are many new designs of

LSA flying boats, some with very good

characteristics that compare favourable to LSA

landplanes, as can be seen on fig. 3.

However only the advantages brought by the

composites alone are not enough for a

commercially successful seaplane. A remake

of an old flying boat with modern materials

will deliver some improvement in performance

and reduction of operating costs, but there are

other important areas such as seaworthiness

and safety that have to be addressed. A major

factor that can support the revival of flying

boats is the progress that builders of high

performance boats have made in planing hull

design. At first the development of seaplanes

aided the design of high speed boats. But as the

research in the field of seaplanes came to a

complete stop after the Second World War,

boat builders lead the way in improvement of

planing hulls. Much can be learned from the

marine application of composites as well. The

experience gained in planing boats design and

construction should be applied to seaplanes in

order to be achieved better and safer

performance in waves.

0,4

0,45

0,5

0,55

0,6

0,65

0,7

0 500 1000 1500 2000

Range, km

EW

/MT

OW

LSA seaplanes

LSA landplanes

Fig.3: Empty weight fractions of LSA aircraft

The design of amphibious aircraft demands

reconciling contradicting requirements for

aerodynamic and structural performance with

seaworthiness. Seaplanes have lower flying

qualities compared to landplanes due to the

need to provide the necessary flotation, planing

qualities, longitudinal and lateral stability and

control, in order to be able to take off and land

on water safely. Simultaneous optimization of

aerodynamic, hydrodynamic and structural

properties of flying boats should be applied if

further improvements in their flying qualities

are to be achieved, as their design is a highly

multidisciplinary activity by nature.

Traditional design of seaplanes is mostly based

on previous example. Despite the extensive

research in the field before and after WW2, the

scope of the studied models was not large.

Theoretical methods have been rather limited

in use. Modern design methodologies allow

broadening the design space. The use of

metamodels ( models of models), also known

as response surfaces or surrogate models,

allows overcoming the difficulties associated

with the direct application of high-fidelity

finite-element methods for the exploration of

the design space and optimization such as

numerical noise and high computational cost,

and allow the inclusion of results obtained

from physical experiments and empirical

relations.

In this work a conceptual design investigation

into the application of non-traditional

aerodynamic configurations such as canard,

tandem and box-wings in regard to improving

the flight performance of flying boats is carried

out. Also an optimization of the hull shape is

shown to provide aerodynamic, hydrodynamic

and structural advantages.

2. Design requirements for a new

commuter seaplane

The existing aircraft types do not satisfy the

future requirements of seaplane operators. But

as the seaplane business has a small market

share and the development of a new aircraft

design is costly, it must be considered that only

a version with improved performance, close to

that of current commuter landplanes, and

aimed at serving a broader market has the

chance to find an investor to develop such a

new generation of seaplanes.

The sizing of a perspective commuter seaplane

is largely dependent on regulations. It should

comply with CS (FAR) -23. For economic

reasons the number of passengers must be the

maximum alloable-19. The gross take-off

weight should be limited to 5670 kg.

For improved safety and ability to operate in

rough waters we should address the following

factors:

-hull design

-take-off and landing speed

Usually the take-off and landing distances are

not limiting factors for seaplane design. But as

the loads inflicted by waves are directly

proportional to the speed on the water, it is

possible to state that in order to improve

operational availability we need not short but

slow take-off and landing seaplanes.

In a FUSETRA study [3] there is a good

presentation of the properties that should be

improved in a new seaplanes design, as viewed

by the operators. Added to the above

mentioned are better passenger comfort, easier

operation and maintenance

3. Hull optimization

The excessive hull drag and weight are the

main factors that bring the worse performance

of seaplanes compared to landplanes. The

flying boat hull is naturally heavy and

voluminous because of having to be

seaworthy. Seaplane hull design is a complex

matter with many aspects to address. More on

it can be found in [4]. But for the conceptual

design stage there are a few important

parameters that have to be determined. The

most important parameter is the beam at the

step which determines the beam load

coefficient:

3bC

(1)

Δ – displacement (weight)

b - beam

ρ – specific weight of water

Hydrodynamic lift coefficient:

2

2

2b

VChl

(2)

The Displacement Froude Number determines

speed regimes on water:

3

g

VF (3)

V- speed

The transition from displacement regime to

planing takes place at the so—called hump

speed when FΔ= 2.

For the longitudinal dynamic stability on water

of great importance is the ratio of the length of

forebody (hull in front of the step) to the beam.

The overall length to beam ratio influences air

drag, structural weight and performance in

waves. The same can be said for the deadrise

angle. More on the influence of the hull

parameters can be found in [5].

Speed Regimes of Hull

0 1 2 3 4 5

Displacement Froude Number

Res

ista

nce

Planing Boats ResistanceSeaplanes Water ResistanceSeaplane DragTotal Seaplane ResistanceThrust

Fig. 4: Comparison of planing boat and

seaplane water resistance

The only way substantial reduction of parasite

drag and weight to be achieved while

providing safe and stable performance on

water is multidisciplinary optimization of the

hull shape of the flying boat. But seaplane

design has primarily to rely on model scale

tests and experience from former projects.

Theoretical methods are rather limited in use

because of the complexity of the flow: A hull

is with a complex geometrical shape and it

passes through different speed regimes with

different types of flow.

Since it is hard for any analytical method to

provide complete flow field calculations with

reliable accuracy, the most effective way to

proceed will be to further develop semi-

empirical methods that allow useful

predictions and integrate them in a MDO

methodology. Of great use here can be the

progress that has been made in the field of

naval architecture which can be put to use in

seaplane design. But there are differences in

behavior of seaplanes to planing boats that

should be taken in consideration (Fig. 3).

We have developed a MDO methodology

employing metamodels (also known as

response surfaces or surrogate models) for the

optimization of hull parameters. On figures 5

and 6 are the graphically displayed the

metamodels for the normalized drag and the

normalized weight of the hull as functions of

length to beam ratio and deadrise. For a given

length/beam ratio the weight of hull is minimal

at a deadrise angle of 26 degrees.

Fig.5: Normalized air drag as a function of

length/beam ratio and deadrise angle (deg)

Fig. 6: Normalized weight of hull as a

function of length/beam ratio and deadrise

angle (deg)

For the current design study there are two

possible sizing scenarios based on passenger

seats arrangement. Passengers can be seated 2

in row or 3 in row. This produces two hull

designs and their parameters are presented in

Table1. The wetted surface of the two hull

variants is almost the same, as is the cabin

floor area. The height of the cabin is equal for

the two arrangements.

The narrower hull has potential for better

performance in waves and improved

porpoising characteristics. Also its water

resistance at the hump will be less. On the

aerodynamics side its air drag will be lower.

But its structural weight is higher. How this

affects the overall performance of the seaplane

can be seen on figures 7 and 8.

Table 1. Hull parameters Parameter Unit 2-in-row 3-in-row

Beam m 1.5 1.8

Deadrise Deg. 26 26

Beam Loading 1.68 0,97

Length/Beam ratio 11.0 8,9

Forebody

length/Beam ratio

4.4 3.6

CDh related to wing

area .10-4

9.1 9.8

Hull weight/MTOW 0,26 0.24

The maximum payload range compared to the

3-in-row arrangement is significantly reduced,

but range with maximum fuel is almost the

same. However its economic efficiency is a bit

lower. More about the way these results are

calculated will be described later in the text.

Passenger Seating Variants

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 100 200 300 400 500 600 700 800 900

Range, nm

Payload, kg

Conventional 6x3 seats

Conventional 9x2 seats

Fig. 7: Payload-range diagram for 2-in-row

and 3-in-row passenger cabin arrangements

Relative Cost per Seat Mile

0,5

0,55

0,6

0,65

0,7

0,75

0,8

Seating 3-in-

row

Seating 2-in-

row

Fig. 8: Relative total cost per seat mile of

different passenger cabin arrangements

The variant with 3-in-row seating has larger

cabin volume which improves its abilities as a

cargo plane. Also it has a potential for an

increase in MTOW as its beam loading is

comparatively low.

4. Application of non-conventional

aerodynamic configurations

4.1. Design Study Methodology The main tool of the study was the popular

VLM code AVL [6]. With its help lift to drag

polars for the trimmed state (Cm=0) of the

different configurations were created and used

as a metamodel for the estimation of the

aerodynamic properties.

As the parasite drag and the thrust effects upon

pitching moment cannot be estimated with the

VLM code they were additionally calculated

and added to the results.

The profile drag of the wings was

approximated with a second order polynomial

approximation derived from airfoil data: 2

210)( ClCClCCCC ld (4)

Because of the high off-set placement of the

engines characteristic for the seaplanes their

pitching moment is substantial and a means for

accounting for it must be provided.

Thrust has three pitching effects – the direct

moment of the thrust, the propeller normal

force due to turning of the air and the influence

of the propwash upon the wing and the tail [7]

)( pcgw

pp

w

m XXqSF

ZqS

TC p (5)

Here and in the following expresions T is the

thrust of the propellers; Fp is the area swept by

the propellers; Dp is the diameter of the

propellers; i is the number of propellers; Sw is

the reference surface of the wing and the

relative coordinates with subscript p define the

position of the propeller.

For level non accelerating flight trust equals

the drag so as adapted from [8] the pitching

moment of the propellers is estimated with the

following equation:

Lpcgw

ptm CXX

SiD

ZCC Dp )(05.02

(6)

Since all the configurations studied are

designed with tractor propellers and the

propwash affects both lifting and control

surfaces its effect is considered to be similar to

a change of global dynamic pressure. The

increase of the dynamic pressure may be

estimated by the following coefficient

b

iD

qF

T p

p

1 (7)

In order more realistic results to be provided a

correction is added based on comparison of

calculated data and results of a full-scale

experimental investigation of air drag of

seaplanes presented in[9] On Fig.9 comparison

of calculated and experimental data for Short

Sealand flying boat is shown.

Sealand Trimmed Polar

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

0 0,05 0,1 0,15 0,2CD

CL

Calculated

Experimental

Fig. 9: Calculated and experimental lift to drag

polars of Short Sealand

Polars are calculated for flaps deflected

configuration as well (Fig. 10).

Trimmed Polar

0

0,5

1

1,5

2

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4CD

CL

BoxWing

BoxWing TO

Flapps

Fig. 10: Polars for flaps up and deflected

15deg.

The weight was calculated using empirical

formulae from [10]. For the structural

evaluation of box-wing configuration results

from studies of the author were used [11].

The range was established using the Breguet’s

equation also corrected with empirical

coefficients.

4.2 Objective function

The chosen objective function is the relative

total cost per seat mile. From a study for the

total cost structure of current seaplane

operations [3] it was established that the fixed

costs are 17% of the total costs, costs that

depend on the acquisition price are 16%, the

costs that are calculated by flight hours are

29% and costs based on miles flown are 38%.

Thus the relative cost per seat mile is

determined with the following equation:

P

P

B

B

B

B

N

N

F

F

T

T

We

WeCsm

0

000

38,029.016.017.0

(8)

Where: We is the empty weight of the aircraft;

TB is the block time; FB is the block fuel; NP is

the number of passengers. The ones with

subscript 0 are for the base variant – a current

state of art flying boat. For this design case the

block times and block fuel quantities are

estimated for a 100 nm flight distance, as it is

expected to be the most popular distance of

travel.

This equation is actually a scalarization of a

multy-objective optimization problem with the

coefficients acting as weights of the different

objectives reflecting the aerodynamic and

structural efficiency and productivity of the

aircraft.

4.3 Configurations studied

For the purpose of this investigation four

aerodynamic configurations of flying boats

were studied – conventional high wing

monoplane is compared with canard, tandem

and box-wing. All the configurations share the

same body and fin and have equal reference

area and span of the wings. The static stability

margin is kept the same as well at a value of

the derivative of the pitching moment to lift

coefficient of -0.16.

The canard configuration is unusual in respect

to that the engines are mounted on the canard.

This is done because of the need to place the

control surfaces in the propwash. In such a

way in case of sudden change of propeller

thrust automatic compensation for the pitching

moment is provided and this is important for

safety reasons.

The placement of the wings and control

surfaces in the propwash ensures lower take-

off and stall speeds with engines running,

which is important in regard to performance of

seaplanes in waves, so all of the designs

studied provide this feature.

The tandem and box-wing configurations are

with positive stagger of the wings – the front

wing is placed above than the rear. This is

done in order to avoid danger of deep stall,

when the disturbed air from the front wing

causes loss of lift of the rear wing and this

subsequently leads to pitch-up and

impossibility to recover from the stall.

The AVL models of the four configurations are

presented on fig. 11- 14

Fig. 11: Conventional configuration

Fig. 12: Canard configuration

Fig. 13: Tandem configuration

Fig.14: Box-wing configuration

5. Results and discussion

According to the proposed optimization

objective the best results provided the box-

wing configuration. It proved to have both the

highest aerodynamic and structural efficiency.

Contrary to the expectations the canard

configuration displays higher trim drag. This is

due to the fact that the arm of the front surface

cannot be made long enough and the control

deflections are large. It proved to have worse

aerodynamic and structural efficiency than the

conventional layout.

The tandem wing configuration provided better

aerodynamic efficiency than the conventional

but proved to be with the highest structural

weight of the wings, due to their very high

aspect ratio. This led to that its maximum

payload had to be reduced and is 10% lower

than that of the other configurations.

Trimmed Polar

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14CD

CL

Conventional

Canard

Tandem

BoxWing

Fig. 15: Trimmed state polar of the studied

configurations

Lifting Surfaces Weight

Fraction

0

0,05

0,1

0,15

0,2

1

Conventional

Canard

Tandem

BoxWng

Fig. 16: Lifting surfaces weight as a fraction of

the MTOW of the studied configurations

Seaplane Variants

0

500

1000

1500

2000

0 200 400 600 800 1000 1200

Range, nm

Payload, kg

Conventional Canard Tandem

Box-Wing Seastar

Fig. 17: Payload-Range diagram of the studied

configurations

The results of the study are presented on

figures15-18. It must be pointed out that all

configurations deliver much better payload-

range performance than the baseline design.

Their total cost of operation per seat mile is

significantly lower – in the range of 70-80% of

the benchmark. The performance of the studied

seaplane designs is competitive with modern

commuter landplanes.

Relative Cost per Seat Mile

0

0,2

0,4

0,6

0,8

1

Conventional

Canard

Tandem

BoxWng

Fig. 18: Cost per seat mile of the designs

studied

As the box-wing configuration provided the

overall best results a further investigation was

carried out to study the sensitivity of the

objective function to variations in its geometric

parameters. For the aerodynamic efficiency

(effect upon the Oswald span efficiency factor)

of the type most important is the gap to span

ratio (Fig19). Gap (or height) is the vertical

distance between the front and rear wings. The

increase of gap/span ratio reduces the induced

drag but increases the parasite drag and

structural weight which limits the increase in

lift to drag ratio (Fig. 20).

Oswald Span Efficiency Factor

0,5

0,7

0,9

1,1

1,3

1,5

-0,4 -0,2 0 0,2 0,4

Gap/span ratio

Fig. 19: Influence of gap/span ratio of box-

wing configurations on the span efficiency

factor (with no dihedral or anhedral of the

wings)

Lift/Drag Ratio of Wing System

20

22

24

26

28

30

-0,4 -0,2 0 0,2 0,4

Gap/Span ratio

Fig.20: Influence of gap/span ratio of box-

wing configurations on the aerodynamic

efficiency (with no dihedral or anhedral of the

wings)

Fig. 21 Box-wing seaplane with increased gap

Another two variants were studied that both

offer reduction of structural weight at the cost

of aerodynamic performance. The first is with

a reduced span (aspect ratio) of the wings. The

second is with less stagger of the wings which

allows shortening of the vertical planes

connecting them thus offering reduced parasite

drag and weight at the expense of increasing

trim drag and worse longitudinal control and

dynamic stability.

The results of the investigation are presented

on figures 22-25.

The variant with the reduced stagger offers the

lowest relative cost per seat-mile. But, as can

be seen from the polar its aerodynamic

efficiency is good at a very narrow span of lift

coefficients, which means that its performance

will degrade quickly for off-design conditions.

Box Wing Trimmed Polar

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14

CD

CL

Base Variant

Increased Gap

Reduced

Span

Reduced

Stagger

Fig. 22: Trimmed state polar of the studied

box-wing variants

Wings Weight Fraction of Box-

Wing Types

0

0,05

0,1

0,15

1

Base

Variant

Increased

Gap

Reduced

Span

Reduced

Stagger

Fig. 23: Lifting surfaces weight as a fraction of

the MTOW of the studied box-wing variants

Box-Wing

0

500

1000

1500

2000

0 500 1000

Range, nm

Paylo

ad

, kg

Base Variant Increased Gap Reduced Span Reduced Stagger

Fig. 24: Payload-Range diagram of the studied

configurations

As expected, the longest range on maximum

fuel (1000 kg) is provided from the variant

with increased gap and the shortest with

reduced span, but the latter has the greatest

range with full payload (1800 kg).

Relative Cost per Seat Mile of

Box-Wing Types

0,5

0,6

0,7

0,8

0,9

1

1

Base

Variant

Increased

Gap

Reduced

Span

Reduced

Stagger

Fig. 25: Cost per seat mile of the studied box-

wing variants

As a conclusion it can be pointed that

seaplanes with optimized design and made

from composites can be an effective and

practical means of transport. They promise

important increase in performance over current

designs and can provide for a much wider field

for seaplane operations.

References

1. Mohr B., Schömann J., Seaplane Data

Base FUSETRA Deliverable D1.1 “Seaplane

Data base” – www.fusetra.eu

2. Gobbi G. et all, Report on current strength

and weaknesses of existing seaplane/

amphibian transport system as well as future

opportunities including workshop analysis

FUSETRA Deliverable D4.1 “FUSETRA

SWOT” – www.fusetra.eu

3. Wagner W., Sträter B., Majka A.

FUSETRA Deliverable 5 Report on

requirements for new seaplane transport

system as integrated part of future sea/land/air

transportation system

4. Gudmunson S., General Aviation Aircraft

Design, APPENDIX C3: Design of Seaplanes,

2014

5. Dathe, I., “Hydrodynamic Characteristics of

Seaplanes as Affected by Hull Shape

Parameters,” A.I.A.A. Advance Marine

Vehicles Journal, United States of America,

1989

6. web.mit.edu/drela/Public/web/avl/

7. Raymer, D., “Aircraft Design, A conceptual

Approach”, American Institute of Aeronautics

and Astronautics, Inc., Washington D.C., USA,

1992

8. Остославский И., Аэродинамика

самолета; Моква1957

9. Smith A. The Full-Scale Air Drag of Some

Flying-Boat Seaplanes M.A.E.E. Report No

3082, 1956

10. Проектирование самолетов; ред. С. М.

Егер. Москва 1983

11. Roglev P., Analysis, Design and

Experimental Validation of a Simplified

Composite Structure for a Box-Wing and a

Method for Its Production; ISCM 2012, DLR

Stade Germany, 2012