This document summarizes a degree project that designed a concept for a single-manned human-powered aircraft to theoretically complete the Kremer International Marathon prize course of flying 42,195 meters in under one hour. The project introduces human-powered flight basics and the prize requirements. It then details the aircraft design process, which included evaluating airfoils, calculating lift and thrust needs. The designed concept aircraft, called Euler One, is presented along with analyses of its aeronynamic properties and propeller. The conclusion is that the prize is theoretically feasible but not economically viable with today's materials costs. Future work could improve the design and potentially lead to a successful prize attempt.

1. DEGREE PROJECT, IN DEPARTMENT OF AERONAUTICAL AND VEHICLE
, FIRST LEVELENGINEERING, DIVISION OF AERODYNAMICS
STOCKHOLM, SWEDEN 2015
A CONCEPT STUDY OF A SINGLE
MANNED HUMAN POWERED
AIRCRAFT
FULLFILLING THE CRITERIAS FOR THE
KREMER INTERNATIONAL MARATHON PRIZE
AXEL INGO, MARCUS LILLIEBJÖRN
KTH ROYAL INSTITUTE OF TECHNOLOGY
SCHOOL OF ENGINEERING SCIENCE

3. Abstract
This first level thesis focuses on the design of a human pow-
ered aircraft which theoretically can complete the Kremer In-
ternational Marathon prize. The competition awards the first
heavier-than-air aircraft human-power-driven aircraft that com-
pletes a circuit of 42 195 meter in less than one hour with £50
000.
The paper first introduces the reader to the basics of aircraft
mechanics. It continues with the presentation of the design pro-
cess with examples of evaluated airfoils and key aspects.
Our conclusion of the study is that the Kremer International
Marathon prize is fully feasible to complete with the technol-
ogy of today. However, the project is not economically viable
due to high prizes of selected composite materials and the rel-
ative small size of the prize money. An increment of the prize
would certainly increase the research into human powered high
performance aircraft, which could lead to a successful Kremer
International Marathon prize attempt.
The limitations of this thesis are to strictly stay within the aero-
dynamic field of study. Therefore, solid mechanics has not been
exactly calculated, but has been taken into account when di-
mensioning the aircraft in CAD, and neither has any calculated
turning performance due to academic level.

4. Referat
Detta kanditdatexamensarbete behandlar designen av ett m¨ansk-
ligt drivet flygplan som i teorin skulle kunna vinna Kremer Inter-
national Marathon prize. T¨avlingen bel¨onar den f¨orsta m¨anskligt
drivna och tyngre-¨an-luft farkosten som kan flyga runt en bana
p˚a 42 195 meter p˚a under en timme med £50 000, motsvarande
645 000 SEK (Maj 2015).
Uppsatsen introducerar f¨orst l¨asaren till grunderna i flygmeka-
nik. Vidare s˚a presenteras designprocessen tillsammans med ex-
empel p˚a unders¨oka vingprofiler och viktiga detaljer att t¨anke
p˚a i respektive steg.
V˚art resultat ¨ar att Kremer International Marathon prize ¨ar fullt
genomf¨orbar med dagens teknologi. Projektet ¨ar i dagsl¨aget dock
inte ekonomiskt f¨orsvarbart p˚a grund av de h¨oga byggkostnader-
na kontra den relativt l˚aga ers¨attningen fr˚an prispengarna. En
h¨ojning av prispengarna skulle definitivt ¨oka intresset f¨or forsk-
ning inom omr˚adet av h¨ogpresterande m¨annskligt drivna flyg-
plan, som i f¨orl¨angningen kan leda till att Kremer International
Marathon avklaras.
Begr¨ansningar har gjorts s˚a att vi endast unders¨okt de aerody-
namiska delarna av en m¨ojligt konstruktion. Till exempel har
inga exakta h˚allfasthetsber¨akningar gjorts ¨aven om enklare be-
r¨akningar tagits i beaktning vid CAD-designen, samt att ingen
sv¨angprestanda ber¨aknas p˚a grund av arbetets akademiska niv˚a.

5. Contents
Contents
List of Figures
List of Tables
Nomenclature
Nomenclature
I Introduction 1
1 Introduction to Human-powered flight 3
1.1 The Kremer prize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Human powered vehicles history . . . . . . . . . . . . . . . . . . . . . . . 3
2 Profile of Demands 5
2.1 Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Human Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
II Calculation model & Design process 7
3 Theory 9
3.1 Basics of Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1.1 The wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1.2 Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Basics of Propeller Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2.1 Basic design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2.2 Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Simplified Pitch Stability Analysis . . . . . . . . . . . . . . . . . . . . . . 15

6. 4 Design process 19
4.1 Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Thrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
III Results and Conclusions 21
5 Euler One 23
5.1 Feasibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2 Aeronautical properties of design . . . . . . . . . . . . . . . . . . . . . . . 23
5.2.1 Wings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2.2 Propeller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6 Future work 27
7 Conclusions 29
8 Division of labour 31
Bibliography 33
A Wing performances 35
B Kremer International Marathon Competition rules 37
C Clarification of rules 45
D MATLAB-code 49

7. List of Figures
3.1 An aircraft with the acting forces during steady level flight (Karlsson 2015a) 10
3.2 Wortmann FX 76 MP 120 (airfoils.com 2015a) . . . . . . . . . . . . . . . . . 11
3.3 Propeller blade geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.4 Forces acting on a propeller blade in motion . . . . . . . . . . . . . . . . . . . 13
3.5 Forces acting on a plane with canard configuration (FPVLab/Wikimedia 2015) 15
5.1 Simple CAD of concept human powered aircraft Euler One . . . . . . . . . . 23
5.2 Thrust, power and efficiency as function of the propeller diameter for three
different rotation speeds. The black vertical line represents the chosen diam-
eter of 1.2 metres. The four horizontal lines represent, from bottom to top,
the values of the total drag of 53 N, an estimation of the power ability of an
average human pedaling (150 and 250 W) and the average power output of
Tony Rominger (517 W). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
A.1 Lift as function of projected wing area at required speed . . . . . . . . . . . . 35
A.2 Lift as function of velocity wing selected projected wing area . . . . . . . . . 36
List of Tables
4.1 Airfoils analysed in early design stages with data from airfoils.com (2015b) . 19
4.2 Airfoils analysed in early design stages with data from airfoils.com (2015b) . 20

9. Nomenclature
Symbols
Symbols Description Unit
A Propeller blade area [m2]
α Angle of attack [°]
β Blade angle [°]
η Efficiency coefficient [-]
φ [°]
ρ Density [kg/m3]
CD Drag coefficient [-]
CD0 Zero-lift drag coefficient [-]
¯cc Mean aerodynamic chord canard wing [-]
¯cw Mean aerodynamic chord main wing [-]
CL Lift-coefficient [-]
CLc Lift-coefficient of canard wing (used in stability analysis) [-]
CLw Lift-coefficient of main wing (used in stability analysis) [-]
Cm Pitch moment coefficient [-]
Cmc Pitch moment coefficient of canard wing (used in stability analysis) [-]
Cmw Pitch moment coefficient of main wing (used in stability analysis) [-]
CP Power coefficient [-]
CQ Torque coefficient [-]
CT Thrust coefficient [-]
D Drag [N]
Di Lift-dependent drag term [N]
Do Propeller diameter [m]
J Advance ratio [-]
K Lift dependent drag factor [-]
L Lift [N]

10. Symbols Description Unit
lc Length AC canard wing to CG [m]
lw Length AC main wing to CG [m]
n Revolutions of propeller per second [rps]
NB Number of blades per propeller [-]
p Propeller pitch [m]
q Dynamic pressure [Pa]
Q Torque [Nm]
r Radial coordinate of propeller blade [m]
R Blade length [m]
sw Reference area of propeller blade [-]
S Reference area of wing [m2]
Sw Reference area of wing (used in stability analysis) [m2]
Sc Reference area of canard wing (used in stability analysis) [m2]
T Thrust [N]
V Velocity [m/s]
W Weight [N]
Abbreviations
Abbreviation Description
RoAS Royal Aeronautical Society
AC Aerodynamic Centre
CG Centre of Gravity
CP Centre of Pressure
CT Centre of Thrust
CAD Computer Aided Design

11. Part I
Introduction
1

13. Chapter 1
Introduction to Human-powered flight
1.1 The Kremer prize
Henry Kremer was an industrialist who in 1959 instituted a series of five money awards
to encourage innovation in the field of human powered aircraft. Today the awards are
administered by the Human powered Aircraft Group at the Royal Aeronautical Society
(RAeS 2015). The five parts of the Kremer prize are:
• Figure eight flight around two markers 1/2 mile apart, with start and ending 3m
above ground. £50000, claimed in 1977.
• Flight from England to France. £100000, claimed in 1979.
• Flight of a 1,5km triangle course for time under three minutes. £20000 + £10000
for each new record. Claimed in 1983. Removed in 1984 on the safety grounds.
• Marathon Course under one hour. £50000. Unclaimed.
• Sporting aircraft challenge. £100000. Unclaimed.
1.2 Human powered vehicles history
There have been several successful human powered aircraft projects since the prizes were
instituted. Paul MacGready and Bryan Allen are the true pioneers of human powered
flight as they claimed the two first Kremer prizes with the Grossamer Condor and
Grossamer Albatross.
During the 70s and 80s, the Massachusetts Institute of Technology had several stu-
dent projects designed, built and flew human powered aircraft with names like the
BURD, Chrysalis, Monarch and Daedalus. The projects were very successful. For ex-
ample, the Chrysalis was flown by over 40 different pilots, the Monarch B won the first
Kremer prize around the 1,5 km course under three minutes and the Deadalus managed
to fly from Crete to Santorini in 1988, which today still is the flight distance world record
for human powered vehicles.
3

14. CHAPTER 1. INTRODUCTION TO HUMAN-POWERED FLIGHT
The current world speed record is from 1985, when the Musculair 2 flew at 44,26
km/h. (Wikipedia 2015)
Since the 1990s, there has only been one new record set in the field of human powered
vehicles. In late 2014, the AeroVelo Atlas project of the University of Toronto managed
to hover a human powered helicopter for 64 seconds with an altitude exceeding 3 meters.
This feat was rewarded with the Igor I. Sikorsky Human Powered Helicopter Competition
prize of 250 000.(vtol.com 2015)
4

15. Chapter 2
Profile of Demands
2.1 Rules
The rules of the Kremer International Marathon Competition are clearly defined by
the Royal Aeronautical Society. The prize of £50000 is awarded to the first ”successful
completion of a flight over an approved course within the United Kingdom in a specified
time of ONE hour or less” with an aircraft within the a set of rules. The course is set
to be flown in figure eight motions between two pillars. The distance between the pillars
can be to be chosen up to 4051 m, which is equivalent to 5 laps around the course.
The full conditions of entry are specified in Appendix B and are furthermore clarified in
Appendix C. As of 2015, no known attempts have been made to win the prize.
2.2 Human Limitations
All attempts at human-powered aviation have the human factor as their greatest lim-
itation. With the development of new materials, which are both lighter and stronger
than previously possible, the materialistic limitations will continue to decrease while the
human limitations stays the same. As for the feasibility of the design, it is assumed
that we can access a world-class cyclist. The cyclist will only be used as a way to have
a known energy limit before further calculations are made, and is therefore only used
in initial feasibility studies. Over long periods of time, professional athletes have had a
recorded power output as high as 400-500 W, compared to a reasonable power output
of 150-250 W for an average person. The cyclist used in this study Tony Rominger, a
former Swiss cyclist of 175 cm and 65 kg, who in 1994 broke the World Hour Record.
During the attempt, Rominger had a recorded average power output of 517 W during
his record attempt.1.
1
The rules for the World Hour record have since then changed
5

16. CHAPTER 2. PROFILE OF DEMANDS
2.3 Thesis
This thesis will answer two clearly defined questions.
• Is the Kremer International Marathon prize theoretically achievable?
• If yes, how can an aircraft be designed to gain the proper aeronautical properties?
6

17. Part II
Calculation model & Design process
7

19. Chapter 3
Theory
This chapter is intended for readers without previous aeronautical background. It also
provides the reader with an understanding of the level of knowledge that the project
is based on. The theory is completely based on the lectures and hand-out documents
held and written by our supervisor Arne Karlsson. The documents can be accessed
through the department of Aeronautical and Vehicle engineering at the Royal Institute
of Technology, references Karlsson (2015a)-Karlsson (2015e).
3.1 Basics of Flight
The absolute basics of steady level flight is to have force and moment balance. This
prevents the aircraft from unwanted rise, descend, curve or tilt. The aircraft’s movements
are categorized into three axis, lateral, longitudinal and vertical. Depending on which
axis the aircraft moves around, these movements are called pitch, roll or yaw. Forces
acting on the aircraft are the lift force generated by the wing, the gravitational force,
the thrust force and the resisting drag force. By looking at Figure 3.1 on page 10, we
see all forces acting on an airplane in steady level flight.
For steady level flight equilibrium among these forces are required. The force balance
in x-axis and y-axis are then easily calculated with small angles approximation.
→ : T − D = 0 ⇒ T = D (3.1)
↑ : L − W = 0 ⇒ L = W = mg (3.2)
where T is the thrust generated by the propeller, D is the drag force of the aircraft, L
is the lift from the wings and W is the weight of the aircraft.
The lift L is given from the equation
L = CL[α]
1
2
ρV 2
S (3.3)
where CL is a function of the wings angle of attack α, ρ is the density of the air, V is the
velocity of the aircraft and S is the surface area of the wing projected on the ground.
CL normally increases with an increase in angle of attack.(Karlsson 2015a)
9

20. CHAPTER 3. THEORY
Figure 3.1. An aircraft with the acting forces during steady level flight (Karlsson
2015a)
The drag force D is given from the equation
D = CD
1
2
ρV 2
S (3.4)
where CD is a non-dimensional drag coefficient. A simple and accurate approximation
of the drag coefficient is calculated through an equation called the drag polar,
CD = CD0 + KC2
L = CD0 + CDi, (3.5)
where CD0 and KC2
L are called the zero-lift drag coefficient and the lift-dependent drag
coefficient respectively. (Karlsson 2015a)
The K-factor in the lift-dependent drag coefficient above is called the lift dependent
drag factor. It is calculated with (3.6)
K =
1
πÆRe0
(3.6)
where the aspect ratio ÆR is given by
ÆR =
b2
S
, (3.7)
where b2 is the square of the wingspan, and e0 is calculated through the first empirical
method of Karlsson (2015d),
e0 = 1.78(1 − 0.045ÆR0.68
) − 0.64 (3.8)
10

21. 3.2. BASICS OF PROPELLER PROPULSION
3.1.1 The wing
In order to determine a design for the main wing the total lift force needed for flight
must be known. Secondly for stability the design must include horizontal and vertical
stabilisers, either integrated with the main wing or as an external component of the
overall aircraft design.
Designing the wing is mainly with respect to the non-dimensional lift coefficient as
this determines the wings ability to generate lift force. For a human powered aircraft
with limited power, a lift coefficient CL as high as possible is desirable.
The lift coefficient is only dependent on the profile of the wing as the analysis can be
divided into two subsets including firstly the actual profile and secondly the dimensioning
of the wing.
3.1.2 Profile
The table 4.1 on page 19 displays a number of wing profiles designed for human powered
flight. As mentioned above a lift coefficient CL with a higher value is preferable.
[Karlsson (2015a) Karlsson (2015d) Karlsson (2004) Karlsson (2015h) Karlsson (2015f)
Karlsson (2015g) Karlsson (2015c) Karlsson (2015b) Karlsson (2015e)
Figure 3.2. Wortmann FX 76 MP 120 (airfoils.com 2015a)
3.2 Basics of Propeller Propulsion
3.2.1 Basic design
All human-powered aircraft are powered by one or several sets of propellers. The pro-
pellers are driven by the pedaling pilot and, similarly to the wings, consist of an airfoil
that generates lift when facing a fluid stream. The lift force generated by the propeller
is called thrust, and pulls or pushes the aircraft forward perpendicularly to the plane of
rotation of the propeller. The thrust has to overcome the drag force to make the aircraft
accelerate. The cost of generating thrust is called torque, which is the force moment
counteracting the propeller blades from rotating.
Figure 3.3 shows the general geometry of a propeller blade. As we can see, the
velocity component increases linearly with the propeller’s radial distance from the shaft
with the magnitude of Vres = 2πnr. The figure also introduces three angles: α(r), β(r)
11

22. CHAPTER 3. THEORY
Figure 3.3. Propeller blade geometry
and φ(r). These angles are respectively called the angle of attack and blade angle, while
φ(r) is the angle between the relative wind direction direction and the plane of rotation.
As seen in the figure, the angles have the relation
α(r) = β(r) − φ(r). (3.9)
The angle of attack of the blade is usually selected for the α that corresponds to the
highest value of CL/CD, but can contain smaller changes along the blade. However, the
blade angle must change a great deal since the blade must twist. The conclusion is that
the blade angle must be large close to the hub and decreases along the blade. β(r) is
calculated from (3.9) after the calculation of φ, which by geometry is given by
φ(r) =
V
2πnr
. (3.10)
With the introduction of a non-dimensional parameter called the advance ratio
J =
V
nDo
, (3.11)
with the propeller diameter as Do and rotational speed n, the angle φ(r) can be written
on the form
φ(r) =
J
π(r/R)
. (3.12)
12

23. 3.2. BASICS OF PROPELLER PROPULSION
Pitch is in the literature referred to as several different angle and blade pitches but
will in this paper only be used as the geometric pitch p, i.e. the distance the propeller
will advance in one revolution.(Karlsson 2015b)
p = 2π tan[β(r)] (3.13)
3.2.2 Forces
Figure 3.4 shows the forces acting on an infinitesimal thin piece of the propeller blade.
Figure 3.4. Forces acting on a propeller blade in motion
By integrating the thrust dT and torque dQ over the whole blade, the total thrust
and torque can be calculated. Their expressions are geometrically derived to
dT = dL · cos[φ(r)] − dD · sin[φ(r)] (3.14a)
dQ
r
= dL · sin[φ(r)] + dD · cos[φ(r)]. (3.14b)
From (3.3) and (3.4), the lift and drag forces are known as
dL = CL[α(r)] ·
1
2
ρV 2
resc(r) dr (3.15a)
dD = CD[α(r)] ·
1
2
ρV 2
resc(r) dr, (3.15b)
13

24. CHAPTER 3. THEORY
where c(r) is the chord of the blade as function of radial coordinate of the blade. By
inserting (3.15) into (3.14) and integrating over the whole blade T and Q are given as
T =
1
2
ρNB
R
0
V 2
res CL[α(r)] cos[φ(r)] − CD[α(r)] · sin[φ(r)] c(r) dr (3.16a)
Q =
1
2
ρNB
R
0
V 2
res CL[α(r)] cos[φ(r)] − CD[α(r)] · sin[φ(r)] c(r)r dr, (3.16b)
where Vres is geometrically derived from (3.3)
V 2
res = V 2
+ (2πnr)2
= V 2
1 +
π
J
r
R
2
(3.17)
and NB is the number of blades per propeller.
The performance of propellers has historically been presented with charts or ta-
bles of three non-dimensional coefficients for thrust, torque and power. Based on the
-theorem, a dimensional analysis of the n parameters affecting each one of the non-
dimensional coefficients can be grouped into (n − 3) non-dimensional groups since me-
chanical problems have three reference dimension (length, time, mass). This dimension
analysis results in the following set of non-dimensional coefficients.
CT =
T
ρn2D4
CQ =
Q
ρn2D5
CP =
P
ρn3D5
. (3.18)
The power P is known from the field of mechanics as P = ωQ with the angular velocity
ω = 2πn. At last, an expression for the propeller efficiency can be derived as the ratio
between thrust power and the power P.
ηpr =
TV
P
=
CT · ρn2D4 · V
CP · ρn3D5
=
CT
CP
V
nD
= J ·
CT
CP
(3.19)
The relation between CP and CQ is given through (3.18) as CP = 2πCQ. This finalizes
the efficiency expression to
ηpr =
J
2π
CT
CQ
. (3.20)
However, this calculation method only takes into account the viscous effects. For a
more correct efficiency factor, slipstream factors must be accounted for by multiplying
ηpr with a corectional factor (Karlsson 2015b). By evaluating the propeller moment
theory in Karlsson (2015e), this correctional factor ηideal is given by
ηideal =
1
1 + a
(3.21)
where a is derived in Karlsson (2015e) to
a =
1
2
− 1 + 1 +
S
NBA
CD (3.22)
14

25. 3.3. SIMPLIFIED PITCH STABILITY ANALYSIS
where A is the propeller area A = 2πR2.
The final efficiency factor is therefore given by
η = ηprηideal. (3.23)
3.3 Simplified Pitch Stability Analysis
The aircraft must be designed in favor for steady-level flight to prevent unwanted rise,
yaw or roll. What this means is that the aircraft’s total lift must balance the weight
and that the total pitching moment about the Centre of Gravity must be equal to zero.
This can be achieved with either a conventional aft-tail design or a canard configuration
as a stabilizing wing. To break new ground within the field of human powered aircraft,
a canard configuration will be analyzed.
Figure 3.5. Forces acting on a plane with canard configuration (FPVLab/Wikimedia
2015)
Firstly a simplified configuration is presented in Figure 3.5 with the aerodynamic
centre of the main wing and the canard. The centre of gravity is located between the
canard and the main wing, with the distance lw to the main wing’s aerodynamic centre
and the distance lc to the aerodynamic centre of the canard wing.
The lift generated by a wing known from (3.3) and the moment about the centre of
gravity also depends of the mean aerodynamic chord and the pitch moment coefficient
Cm instead of the lift coefficient.
15

26. CHAPTER 3. THEORY
L =
1
2
ρV 2
∞SCL (3.24a)
M =
1
2
ρV 2
∞ScCm. (3.24b)
Since the lift must balance the weight, (3.3) can be rewritten with L = W cos γ, with
γ being the angle of the fuselage reference line relative to the horizontal line. Further
on the moment is expressed in the same way but with the chord as the lever arm and a
moment coefficient instead of the lift coefficient.
Regarding the two basic criteria for stability with total lift balancing the weight and
total pitching moment about centre of gravity to be zero, (3.3) can be written as
L =
1
2
ρV 2
∞SCL = W cos γ
M =
1
2
ρV 2
∞ScCm = 0 → Cm = 0.
(3.25)
Equation (3.25) gives that to achieve stability the moment coefficient must be zero
and the lift coefficient must be positive in the equilibrium point. Considering the en-
tire aircraft with contributions from both the canard and the main wing the following
relations can be derived
CLw +
Sc
Sw
CLc =
Wcosγ
1
2 ρV 2
∞Sw
(3.26a)
Cm = Cmw +
Sccc
Swcw
Cmc −
lw
cw
CLw +
Sclc
Swcw
CLc . (3.26b)
As the two last terms in equation (3.26b) have been rewritten as the moment gener-
ated by the lift from the wing and the distance from the centre of gravity to the current
wing’s aerodynamic centre as a lever arm. Since the lift coefficients are set as well as the
weight and true air speed, (3.26b), the relation between the reference area of the canard
wing and the main wing is revealed. Given that the total pitch moment coefficient must
be equal to zero in the equilibrium point one can solve (3.26b) for the a relation between
the distances lw and lc since the other parameters are set for the main wing. Solving
(3.26b) for the lift on the main wing the lift coefficient can be presented in mathematical
terms as
CLw =
cw
lw + lc
Cmw +
Sccc
Sw(lw + lc)
Cmc +
lh
lw + lc
Wcosγ
1
2 ρV 2
∞Sw
, (3.27)
which verifies the centre of gravity’s placement between the wings since CLw is positive
and all lengths are hereby defined correctly.
For pitch stability the total pitching moment coefficient with respect to the angle of
attack requires to be zero. The pitch moment coefficient for the canard and the main
16

27. 3.3. SIMPLIFIED PITCH STABILITY ANALYSIS
wing are relative to the aerodynamic centers and do not change with angle of attack.
Differentiating (3.26b) gives the stability condition as
∂Cm
∂α
= −
lw
cw
∂CLw
∂α
+
Sclc
Swcw
∂CLc
∂α
< 0. (3.28)
The same wing profile used for both the main wing and the canard wing gives the
variation for the angle of attack to be same, the first term in (3.28) must be larger than
the second term. With numbers for the current configuration this requirement is not
fulfilled, making the aircraft unstable. Analysing (3.28) one can find that varying the
values in the quotient terms before the derivatives is not enough for ∂Cm to be negative.
Continuously either a higher value of ∂CLw or a lower ∂CLc is needed to achieve stability.
In other words the same wing profile can not be used for the canard wing and the main
wing for this current configuration.
Since the lift slope is always positive for angles of attack below stall Equation (3.28)
also shows that a canard wing always has a destabilizing effect on the airplane. Further
for the change in lift coefficient of the main wing also requires lw to always have a positive
value, meaning the center of gravity must always be in front of the aerodynamic center
of the main wing. On the plus side, in trimmed flight both the canard wing and the
main wing will always contribute with a positive lift. (Phillips 2009)
This conclusion requires a new wing profile for the canard with a lower variation of
the lift coefficient with respect to the angle of attack. Research shows that Eppler E399
is a sufficient wing profile for the canard wing.
17

29. Chapter 4
Design process
The aircraft design process of a human powered vehicle consists of a three step iteration
process. The first step is to select a wing and design it to exceed a series of specifications
and requirements. The main requirement for all aircraft wings are to generate enough
lift force. The second step is to design the propulsion system to generate the required
amount of thrust to accelerate to the desired airspeed. At last, the geometry of the
aircraft can be set using the stability theory. It is also during this last step that the
canard or tail wing’s dimensions are set. The design process then repeats itself until
it has converged to a optimal value. In the study, an approximation of five iterations
where made to reach the resulting design.
4.1 Lift
For the purpose of this project, a maximized lift and minimized drag is required. A large
CL/CD ratio is therefore optimal. Looking at Table 4.1 of analysed airfoils, it is clear
that two foils have competitive values.
Table 4.1. Airfoils analysed in early design stages with data from airfoils.com (2015b)
Eppler Lissaman Worthmann Worthmann Worthmann
E399 7769 FX 63-137 FX 76 MP 120 FX 76 MP 160
Smoothed
CL at α = 0 0.66 0.32 0.92 0.95 0.80
CD at α = 0 0.0075 0.01 0.009 0.009 0.008
Max thickness 14.8% 11% 13.7% 12.1% 16.1%
at % of chord 29% 30% 30.9% 33.9% 33.9%
Max camber 5.1% 4.4% 6% 7.6% 6.1
at % of chord 51.4% 30% 53.3% 46.7% 50%
The Worthmann FX 63-137 Smoothed and the Worthmann FX 76 MP 120 have the
highest CL and CL/CD as well as a low CD and thickness. The specific man-powered
airfoil (MP) has a slightly higher CL and a smaller thickness giving it an advantage.
19

30. CHAPTER 4. DESIGN PROCESS
4.2 Thrust
Determination of the propeller airfoil is a similar process to the wing’s. The absolute
priority for a human powered vehicle is to have an efficient propeller blade due to the
lack of available power. A maximized CL/CD is therefore key in choosing a propeller
airfoil. Three different airfoils were analysed for the propeller and are presented in Table
4.2
Table 4.2. Airfoils analysed in early design stages with data from airfoils.com (2015b)
Gottingen Eppler Worthmann
795 Smoothed E193 FX 60-100 Smoothed
Thickness 8% 10.22% 10%
max(CL/CD) at Re = 5 · 105 101.5 114.1 112.7
α for max(CL/CD) at Re = 5 · 105 3.25° 5.5° 3.75°
max(CL/CD) at Re = 1 · 106 116.2 138.4 120.1
α for max(CL/CD) at Re = 1 · 106 2.75° 4.75° 4.75°
As seen above, the Eppler E193 is highly favourable, while the Worthmann FX 60-100
Smoothed is a good contender.
20

31. Part III
Results and Conclusions
21

33. Chapter 5
Euler One
5.1 Feasibility
The study has shown that the Kremer International Marathon prize is theoretically fully
feasible. The work name for the project has been Euler One and its design is presented
below. The simulated unconventional canard wing design achieves the aeronautical re-
quirements for the prize to be completed.
Figure 5.1. Simple CAD of concept human powered aircraft Euler One
5.2 Aeronautical properties of design
5.2.1 Wings
The selected wing is the Worthmann FX 76 MP 120. Given a aircraft weight of 30 kg
from CAD-program Solid Edge and assuming a pilot weight of 80 kg, the wing achieves
23

34. CHAPTER 5. EULER ONE
lift-weight balance with a 14 metre wingspan at minimum ground speed for the Kremer
International Marathon Competition. The straight wing has a chord of 1 metre giving
the whole wing a cross-sectional reference area of 14 m2. The wing features downward
winglets for vertical stabilisation and integrated landing gear.
The simplified stability analysis gives the canard’s wing cross sectional area to 2.8
m2 with a mean aerodynamic chord of 0.575 m. The distance from the centre of gravity
to the main wing’s aerodynamic centre is 0.4 m and the distance from the centre of
gravity to the canard wing’s aerodynamic centre is 5.2535 m. This configuration gives a
total pitch moment coefficient that equals 0 at 0 angle of attack and a stability criteria
with a negative slope of the moment coefficient up to angle of attack of 8.
The pilot is to be seated in front of the main wing, between the connecting beams
with them at about chest height. The pedalling drives a chain that drives a shaft located
inside that main wing that drives both propeller shafts, each one in a different direction.
The total gearing in the propulsion system is set to 9.
Plots of the wing performances are found in Appendix A and on airfoils.com (2015a).
5.2.2 Propeller
The result of a trial and error iteration process of the propeller propulsion theory resulted
in two, 1.2 metre in diameter, propellers with the Worthmann FX 60-100 Smoothed
airfoil. The propeller diameter was chosen by studying Figure 5.2. As seen in the
middle plot, with a 1.2 metre propeller diameter, the pilot is not generating enough
thrust to overcome the drag. The last plot of Figure 5.2 does however show that if
the pilot pedals at 80 rpm, the propellers will generate more thrust than drag, without
requiring more than 220 W of power. This shows that there is more speed to be gained
than the calculated 42.195 km/h! The total propeller efficiency is 90-95 % depending
on rotation speed. The reason for the Worthmann airfoil being selected over the Eppler
193 is that it has higher values of CL at the optimal angle of attack.
The propeller analysis conclusion is that several smaller propellers rotating at a
higher speed are more efficient than one larger propeller rotation at a slower speed. The
result contradicts all known constructions of human powered vehicles. As seen in Figure
5.2, a smaller propeller at higher speed gives a more advantageous power-to-thrust ratio
than a larger propeller at slower speed.
24

35. 5.2. AERONAUTICAL PROPERTIES OF DESIGN
0.5 1 1.5 2 2.5 3 3.5 4
0
Diameter of propller [m]
Thrust[N]andPower[W]
Thrust and Power as function of D while n=1[rps].
0 0.5 1 1.5 2 2.5 3 3.5 4
−50
0
50
100
PropellerEfficiency[%]
Thrust
Power
0.5 1 1.5 2 2.5 3 3.5 4
0
Diameter of propller [m]
Thrust[N]andPower[W]
Thrust and Power as function of D while n=6[rps].
0 0.5 1 1.5 2 2.5 3 3.5 4
0
50
100
PropellerEfficiency[%]
Thrust
Power
0.5 1 1.5 2 2.5 3 3.5 4
0
Diameter of propller [m]
Thrust[N]andPower[W]
Thrust and Power as function of D while n=12[rps].
0 0.5 1 1.5 2 2.5 3 3.5 4
0
20
40
60
80
100
PropellerEfficiency[%]
Thrust
Power
Figure 5.2. Thrust, power and efficiency as function of the propeller diameter for
three different rotation speeds. The black vertical line represents the chosen diameter
of 1.2 metres. The four horizontal lines represent, from bottom to top, the values
of the total drag of 53 N, an estimation of the power ability of an average human
pedaling (150 and 250 W) and the average power output of Tony Rominger (517 W).
25

37. Chapter 6
Future work
The field of study for this thesis has only been straight and level flight and several sub-
jects of interest have therefore been left untouched due to either irrelevance or academic
level.
Fields such as solid mechanics of construction and construction details are not consid-
ered a part of the main topic and are not calculated exactly but have been a part of the
decision making process and dimensioning in CAD. Both above-mentioned are critical
aspects if an aircraft should be constructed and must be thoroughly investigated.
Another critical subject needed to be studied is the turning performance. For the
Kremer International Marathon prize, turning is critical as the course is in a figure eight
pattern. This field of study has been left out due to the subject being on a higher
academic level than reachable during the short time period of this study. In addition,
control and testing of propeller results as well as further optimization of design is required
before a finalized design can be presented.
27

39. Chapter 7
Conclusions
The Kremer International Marathon prize is theoretically feasible with the proposed
design. Breakthroughs have been made on the section of human powered propulsion
as well as the canard wing design. The conclusion from the propeller analysis of the
greater effectiveness of small versus large bladed propellers is unique and contradicts
known aircraft designs. Future work is needed to confirm these results, but it is an
interesting step forward for the field of human powered flight.
The design only takes into account the aerodynamic properties of straight, leveled
and stable flight. Key features such as turning performance, solid mechanics of different
parts and construction have not been included in the study and are a part of the future
work.
The results of this thesis should be considered as a evaluation of the possibilities of
human powered aircraft. It features several new research results and opens new doors to
the field of human powered flight in general. Hopefully, several of the ideas and results
presented can be confirmed by others as well as implemented into future constructions
of aircraft.
29

41. Chapter 8
Division of labour
The division of labour between authors has been fairly equal. Both took part in the
initial analysis to test several airfoils and set a dimension for the main wing that gave a
vertical force stability. The work was then split up, with Axel doing the propeller design
and Marcus the stability analysis.
As for the writing of the report however, Axel has done slightly more. As an expe-
rienced LaTeX-writer, Axel has setup the official KTH-template and tweaked it to work
properly. He has also written the vast majority of the text in the background, theory
and results except for everything concerning stability, as well as completing the CAD of
the proposed design. This division was due to Marcus having problems with the stability
analysis of the canard configuration and therefore spent more time on that part.
31

43. Bibliography
airfoils.com (2015a).
URL: http://airfoiltools.com/airfoil/details?airfoil=fx76mp120-il
airfoils.com (2015b).
URL: http://airfoiltools.com
FPVLab/Wikimedia (2015).
URL: http://bit.ly/CanardPic
Karlsson, A. (2004), ‘Lift to drag ratios’, Hand-out available through the Department
of Aerospace and Vehicle engineering at the Royal Institute of Technology.
Karlsson, A. (2015a), ‘The aeroplane - some basics’, Hand-out available through the
Department of Aerospace and Vehicle engineering at the Royal Institute of Technology.
Karlsson, A. (2015b), ‘Airplane propeller basics’, Hand-out available through the De-
partment of Aerospace and Vehicle engineering at the Royal Institute of Technology.
Karlsson, A. (2015c), ‘Airplane weight, balance and pitch stability’, Hand-out available
through the Department of Aerospace and Vehicle engineering at the Royal Institute
of Technology.
Karlsson, A. (2015d), ‘How to estimate the zero lift and drag-due-to-lift factors in simple
parabolic drag polar’, Hand-out available through the Department of Aerospace and
Vehicle engineering at the Royal Institute of Technology.
Karlsson, A. (2015e), ‘Momentum theory for aircraft propellers’, Hand-out available
through the Department of Aerospace and Vehicle engineering at the Royal Institute
of Technology.
Karlsson, A. (2015f), ‘The standard atmosphere’, Hand-out available through the De-
partment of Aerospace and Vehicle engineering at the Royal Institute of Technology.
Karlsson, A. (2015g), ‘Steady climb performance with propeller propulsion’, Hand-out
available through the Department of Aerospace and Vehicle engineering at the Royal
Institute of Technology.
33

44. BIBLIOGRAPHY
Karlsson, A. (2015h), ‘Steady flight with propeller propulsion’, Hand-out available
through the Department of Aerospace and Vehicle engineering at the Royal Institute
of Technology.
Phillips, W. F. (2009), Mechanics of Flight, John Wiley Sons.
RAeS (2015).
URL: http://aerosociety.com/About-Us/specgroups/Human-Powered
vtol.com (2015).
URL: http://www.vtol.org/hph
Wikipedia (2015).
URL: http://en.wikipedia.org/wiki/Human-poweredaircraft
34

45. Appendix A
Wing performances
0 5 10 15 20 25 30
0
500
1000
1500
2000
2500
Lift as function of projected wing area S at v =11.7208.
Projected wing area [m
2
]
Lift[N]
Lift
Selected area
Weight
Figure A.1. Lift as function of projected wing area at required speed
35

46. APPENDIX A. WING PERFORMANCES
0 5 10 15
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Lift as function of of velocity with S =14.
Velocity [m/s]
Lift[N]
Lift
Required velocity
Weight
Figure A.2. Lift as function of velocity wing selected projected wing area
36

47. Appendix B
Kremer International Marathon
Competition rules
37

55. Appendix C
Clarification of rules
45

59. Appendix D
MATLAB-code
All MATLAB-modelling code can be found and fetched from our Dropbox folder by
following the link:
http://bit.ly/KremerInternationalMarathonKTH2015
Where input values.m contains the basic values of nature, pilot and aircraft.
complex iterative model.m contains calculations of lift and drag.
Propeller.m computes the propeller thrust and torque for given diameter and rotation
speed.
PropLoops.m creates plots of thrust, torque and efficiency as function of diameter for
different rotation speeds. Be sure to comment the variables D and n in Propeller.m for
full functionality.
stability.m computes the different dimensions of the aircraft to achieve stability given
different initial criteria.
49

60. www.kth.se