Space Sports – Sailing in Space

Maria Sundin

1,2

, Lars Larsson

1,3

and Christian Finnsgård

1,4

Centre for Sports Technology, Chalmers University of Technology, Gothenburg, Sweden

Dept. of Physics, University of Gothenburg, Gothenburg, Sweden

Dept. of Shipping and Marine Technology, Chalmers University of Technology, Gothenburg, Sweden

SSPA Sweden AB, Research, Gothenburg, Sweden

Keywords: Space, Titan, Sports, Sailing, Hydrodynamics.

Abstract: Titan is the largest moon of Saturn, and apart from the Earth it is the only body in our solar system where a

liquid exists on the surface. Within the last ten years a system of lakes and rivers have been discovered. The

climate and seasonal cycles of Titan are still not very well known, but the composition and pressure are fairly

well established. Perhaps in the future boats will sail the lakes of Titan for research purposes or even sport.

The purpose of this paper is to give an overview of the concept of space sports, the conditions of Titan and to

calculate important parameters of sailing such as floatability, stability, hull resistance and sail forces. This

paper shows that if a sailing yacht on Titan will have twice as large displacement as on Earth, it will be 2.6

times less stable for the same beam. Since friction will be smaller, it will be faster than on Earth at low speed,

but significantly slower at high speeds due to the wave generation. The same sail area is required to get the

same sail forces if the average wind is 3 m/s, while a 9 times larger sail area is required for if the wind speed

is only 1 m/s.

1 INTRODUCTION

Today the International Space Station has been

manned since the year 2000. Serious plans of sending

humans to Mars in the near future exist. The

European Space Agency is discussing having a

manned base on the Moon by 2030. Perhaps humanity

one day will colonize a large part of our solar system.

The idea of sports then being practiced in space is

probably not too strange. Space Sports would be

performed under very different conditions than Earth

Sports, and completely new possibilities would arise.

Sports research indicate new records being harder

and harder to obtain in some sports. Possibly, the

limits of human capability for certain sports will soon

be reached. But, one could argue, only on this planet!

On other planets it might be possible to jump higher

and patterns of locomotion and the motion of objects

will differ. Earth Sports could be adapted and new

sports could be created. Could interplanetary

championships exist? Could an athlete from Earth

compete against an athlete from Mars? How, and on

which planet in that case?

There are a large number of sports that could be

investigated using physics and technology. How high

could a horse jump on Mars? Can you sail on the lakes

of Titan, the largest moon of Saturn? How large

would a goal in soccer have to be on the moon? Can

you fly using muscular power on Pluto? What is the

pattern of locomotion when running in a different

gravity? Is The Jovian moon Europa the perfect place

for skating? How do you play ball in zero gravity?

Can you ski on Olympus Mons, the highest mountain

in the solar system?

The number of possible questions about space

sports are almost endless. This paper introduces one

concept study of space sports by looking at sailing on

Titan.

2 A BRIEF OVERVIEW OF OUR

SOLAR SYSTEM

Our sun is a medium sized yellow star, one of the

approximately 200 billion stars in the Milky Way

galaxy. Around the sun there are eight planets and

minor bodies such as dwarf planets, moons, asteroids

and comets.

The planets are usually divided into two separate

categories; terrestrial planets and gas giants. The

terrestrial planets are Mercury, Venus, Earth and

Mars in order from the sun and outwards. The gas

Sundin, M., Larsson, L. and Finnsgård, C.

Space Sports – Sailing in Space.

DOI: 10.5220/0006086701410146

In Proceedings of the 4th International Congress on Sport Sciences Research and Technology Support (icSPORTS 2016), pages 141-146

ISBN: 978-989-758-205-9

141

giants are Jupiter, Saturn, Uranus and Neptune.

Terrestrial planets are substantially smaller than the

gas giants with the diameter of Jupiter being 22 times

larger than the diameter of the Earth. Rocks and

metals are the main constituents of the terrestrial

planets, while the gas giants have large layers of

hydrogen, helium, ices and hydrocarbons in different

states surrounding rocky cores.

The distance between the Earth and the sun is

some 150 million km, and this distance is usually

referred to as 1 Astronomical Unit (1AU). Mars is

located at 1.5 AU, so the four terrestrial planets are

fairly close together when it comes to astronomical

distances. Jupiter is at 5.2 AU from the sun and the

outmost planet Neptune is at 30 AU.

Most of the bodies of the solar system orbit the

sun in the same plane, the only exception being the

large spherical cloud of comets surrounding the sun.at

the outskirts of our solar system.

3 LIQUIDS ON PLANETARY AND

LUNAR SURFACES

Oceanus Procellarum – Sea of Storms, Mare Crisium

– Sea of Crises, Mare Tranquillitatis – Sea of

Tranquillity and Mare Imbrium – Sea of Rains

The names of the dark areas on the moon are most

likely exciting for any sailor. Indeed, their names

reflect a time when they were mistaken for being

oceans and seas instead of the dry lava plains we now

know them to be. No liquid water can exist on the

surface of the moon primarily due to the absence of

an atmosphere.

Large amounts of liquids on the surface of a

planet or a moon is in fact extremely rare in our solar

system. Titan, the largest moon of Saturn, is probably

the only place excepting our own Earth. The seas,

lakes and rivers of Titan are however not filled with

water but the hydrocarbons methane and ethane in

liquid state.

Since Titan then is the only other body in our solar

system with a liquid on the surface, it is also the only

other place where we could practice sailing. Will we

ever do that, and why in that case?

Most likely the first expeditions to Titan would be

for scientific purposes much like the way we are

exploring Mars today. The exploration of Mars is

partly being done using robotic rovers, and on Titan

robotic boats could be an option. A great advantage

of sailing is it being a form of transport without the

need of extra energy sources. In space exploration,

energy is always one of the limiting and costly

factors.

The research on autonomous vehicles on the Earth

is evolving rapidly, and autonomous boats on Titan

would be an enormous advantage since the

communication time between the earth and Titan is

an approximate hour. NASA is currently discussing

the possibility of sending a submarine to Titan.

Of course, the possibility exists of Titan being

colonized in the future. Manned sailing boats could

then become reality and apart from transport perhaps

even sailing could become a recreational pleasure as

well as a sport.

Why then are the Earth and Titan the only bodies

in our solar system with liquids on their surfaces? The

uniqueness of Titan is the conditions being right for

the existence of a relatively thick atmosphere. A

certain atmospheric pressure is necessary for the

existence of liquids instead of having a substance in

solid or gaseous state. The surface pressure on Titan

is larger than on the Earth, and the atmosphere of

Titan consisting mainly of nitrogen.

Our neighbor planet Mars has such a thin

atmosphere that liquid water can hardly exist on the

surface anymore. Large amounts of water are present

on Mars, but almost all the water is in solid state (ice)

with the transition to water vapour being very quick

when heated. The lack of atmosphere on Mars is due

to a weak gravity and no shielding magnetic field.

The solar wind is a stream of electrons and protons

from the sun, and it exerts a pressure on the Martian

atmosphere. On Earth our atmosphere is partly

shielded by our magnetic field. The weak Martian

gravity has not been able to hold on to the originally

much thicker atmosphere when battered by the solar

wind.

Jupiter and Saturn are our two largest planets and

they are called gas giants. Both have more than 60

moons each. Several of these moons are exciting

worlds in different sizes and with varied surfaces. A

few of the moons are actually larger than the planet

Mercury. A planet moves around the sun, and a moon

moves around a planet but planets and moons can be

of equal sizes. Titan is the second largest moon in our

solar system, but it is smaller than Mars in both radii

and mass. Why then has Titan not lost its atmosphere

when Mars has? The reason is it being much colder

out by Saturn at 9.5 AU than at Mars at 1.5 AU. The

average temperature on Titan is around -180 degrees.

This will lead to the velocities of the molecules in the

atmosphere not being as high. It is easier for the

gravity to hold on to a cooler gas than a hot one, since

fewer of the molecules reach the escape velocity.

Titan is also shielded from the solar wind by the

magnetic field of Saturn.

Already in the 1980’s the speculations of lakes on

icSPORTS 2016 - 4th International Congress on Sport Sciences Research and Technology Support

142

Titan began triggered by data from the Voyager space

crafts. When the Cassini space craft arrived after a ten

year long journey in 2004 hopes were high of a rapid

detection of the lakes. But it took three more years

until the lakes were finally proved to exist in 2007.

Today we know that the largest lake of Titan Kraken

Mare has a surface of 400 000 square kilometers and

a depth of 160 m. Its surface is probably just a little

bit smaller than the surface area of Sweden and

possibly larger than the Caspian Sea. Titan has

several other lakes and rivers of different sizes and

depths and shows an intriguing landscape. Measure-

ments so far indicate flat lakes and low velocities of

the winds, but modelling of Titans climate shows

possibilities of strong winds and even hurricanes.

This has received support by other studies of the

landscape.

Saturn orbits the sun with a period of approxima-

tely 29 years. The seasons are therefore some 7 years

each. When Cassini reached Saturn in 2004 the

northern hemisphere of Titan was in deep winter.

Now, twelve years later the northern hemisphere is

approaching the summer solstice. This means that we

have not as yet had the opportunity to study the

climate of Titan during a whole “Titan-year”.

Therefore it is quite uncertain how valid the weather

observations are when it comes to average conditions.

4 THE POSSIBILITY OF SAILING

ON TITAN

So, what are the possibilities of sailing on Titan, and

how different would it be from sailing on Earth?

Would it be at all possible, and what would the boats

look like? To assess the possibilities we need to

consider aspects like floatability, stability, hull resis-

tance and sail forces. These properties are in turn

dependent on physical constants like the density and

viscosity of the atmosphere and the liquid, and on the

gravity. Wind speed is of course also an important

parameter. In Table 1 the physical constants are lis-

ted, based on data from Cassini. For comparison, the

corresponding values on the Earth are also presented.

Table 1: Physical constants (Hayes et al, 2013).

Constant Titan Earth

Atm. density,

[kg/m

]

5 1.2

Atm. viscosity,

/s]

1.3x10

-6

15x10

-6

Liquid density,

[kg/m

]

530-660 1030

Liquid viscosity,

/s]

0.3x10

-6

3x10

-6

Acc. of gravity, g [m/s

] 1.4 9.8

Let us start with the floatation, i.e. how deeply the

boat will float in the liquid. The gravity force F

(downwards) is obtained as





= (1)

where m is the total mass of the boat and g is the

acceleration of gravity. The buoyancy force, F

(upwards) is equal to





=



 (2)

Where

is the liquid density and D is the

submerged volume (displacement) of the hull. This is

according to Archimedes’ principle. At equilibrium





=



(3)

which yields

= 



⁄

(4)

Since g appears both in F

and F

it disappears

from the final equation, which says that for a given

mass the displacement is inversely proportional to the

fluid density. According to Table 1 the density on

Titan is about half of that on Earth. Therefore the

displacement will be twice as large on Titan as on

Earth for a given mass.

Stability is of fundamental importance for a

sailing yacht. As appears from Figure 1, it is achieved

through the sideward movement to leeward of the

centre of the underwater volume from B to B’ when

the yacht heels (Larsson et al, 2014). Since F

acts at

the centre of buoyancy, it will create a righting

moment with F

. A vertical line along F

will cut the

heeled center plane of the yacht at the metacenter, M.

The distance between this point and the centre of

gravity G is called metacentric height and is denoted





. It follows that the righting arm, RM, can be

computed as 



sin , where  is the heel angle, and

that the righting moment, RM, is

 = 







sin  (5)

To compute the righting moment we need the

metacentric height 



. This can be computed using

the distance from B to M, 



, which is obtained from

a fundamental formula in stability theory (Larsson et

al, 2014)





= 

⁄

(6)

where I is the moment of inertia around a

longitudinal axis of the area inside the waterline of

the hull.

For a sailing yacht, B and G are close together and





and 



are approximately equal. With this

approximation, and using (1) for the gravity, the

righting moment is

 =  sin  / (7)

Space Sports – Sailing in Space

143

Figure 1: Stability principle.

For a given mass and heel angle the righting

moment is thus proportional to g and I/D. As seen in

Table 1, the gravity on Titan is seven times smaller

than that on Earth, so for the same stability I/D has to

be 7 times larger. Now, for a given length, the inertia

I is proportional to beam cubed, while the

displacement D is proportional to beam to the first

power. It the follows that I/D is proportional to beam

to the second power. For I/D to be 7 times larger than

on Earth beam has to be increased

√

7

times, i.e.

about 2.6 times.

A hull with the same length as on Earth, but twice

as beamy would satisfy the displacement criterion

above but it would be less stable. To remedy this, the

hull could be longer and it could carry more ballast.

The main parameter of interest may be the payload

the yacht can carry. For a given displacement this

depends on the weight of the yacht itself. The heavier

the yacht, the smaller the payload. The weight

increases with beam, but much more so with length.

So from this point of view it is better to make the hull

wider. This will however increase resistance, as we

will see. Another very interesting possibility is to use

a catamaran. Then stability is no problem and the

resistance low.

Having considered the most important properties,

floatability and stability, we now turn to the speed

potential of the yacht. This is determined by the

driving forces on the sails and the resistance of the

submerged part of the yacht. Let us start with the

latter.

There are two main components of resistance for

a body moving along the surface of a liquid: friction

and wave resistance. The former occurs because of

the internal friction in the fluid, its viscosity, while

the latter is caused by the generation of waves

transmitted from the body.

Similarity laws for scaling resistance (Larsson

and Raven, 2010) show that friction, R

, may be

computed as





=



0.5



 (8)

where 



is a friction coefficient,  the fluid

density U the fluid velocity and S the wetted surface

of the body. 



is determined by the Reynolds

number, 







= 

⁄

(9)

where L is a characteristic length of the body and

ν the kinematic viscosity of the fluid.

Table 1 gives a range of possible viscosities for

the liquid on Titan. The range is however centered

around the value on Earth (10

-6

/s). Since the

dependence of 



on 



is essentially logarithmic

(Larsson and Raven, 2010) it is enough for the present

discussion to note that the order of magnitude is the

same for the liquid viscosity on Titan and Earth. We

can thus assume the same C

. For a given speed,

friction is then proportional to . As we have seen

the density on Titan is half of that on Earth, but the

wetted surface is larger if the hull is made twice as

wide. However, not so much that it compensates for

the lower density. Friction may thus be assumed

somewhat smaller on Titan.

As shown in Larsson and Raven (2010) the wave

resistance is governed by the Froude number, F





=/



 (10)

Neglecting some higher order effects, a constant

Froude number will imply the same wave pattern

(scaled with length) and the same wave resistance

coefficient, C

, regardless of the speed, length and

gravity. The wave resistance, R

is obtained from the

coefficient in the same way as the friction in equation

(8)





=



0.5



 (11)

Unlike C

, C

will not be the same as on Earth.

This is for two reasons. A wider hull will give a larger

, and, more importantly, a given speed will give a

higher Froude number on Titan, thereby increasing

. The first effect can be roughly estimated as

proportional to beam, i.e. for double beam a twofold

increase for a given Froude number. But the second

effect is difficult to estimate. The relation between C

and F

. is very nonlinear, and also dependent on the

hull shape. For most standard yachts there is a

maximum Froude number around 0.45, where the

wave resistance gets so large that the driving force

icSPORTS 2016 - 4th International Congress on Sport Sciences Research and Technology Support

144

from the sails is insufficient for increasing the speed.

This limit will now occur at

√

7

times smaller speed

than on Earth, due to the 7 times smaller gravity (see

Equation 10). In fact the whole wave resistance/speed

curve will be compressed in the speed direction by a

factor

√

7

At low speeds friction dominates over wave

resistance and, as seen above, the speed may then be

somewhat larger on Titan, but at higher speeds the

total resistance depends mainly on the wave

resistance, and then the speed will be considerably

smaller due to the Froude number effect.

Finally, let us look at the sail forces. The sail is a

wing which generates a force with components in the

direction of motion, F

and at right angles to that, F

Both can be obtained in a similar way as R

and R





=



0.5











(12)





=



0.5











(13)

where C

and C

are coefficients

the density of

the atmosphere, V the wind speed and S

the sail area.

Like for the liquid, the coefficients depend on the

Reynolds number





= 



⁄

(14)

where C is the mean chord of the sail and 



is the

kinematic viscosity of the atmosphere.

The wind speed on Titan is not well known. There

are indications of occasional hurricanes, but the

normal wind speed should be quite low. According to

Habib (2015) the average speed is estimated to about

3 m/s. Other sources quote lower speeds, around 1

m/s (Hayes et al., 2013, Bird et al 2005). On Earth the

average wind speed is 6.6 m/s (Habib, 2015).

Let us first assume a wind speed of 3 m/s. As seen

in Table 1, the atmospheric viscosity on Titan is about

1/10 of the viscosity on Earth, so the Reynolds

number according to equation (14) is about five times

larger for a given sail. This yields a slightly lower

friction coefficient on the sails, but this will have a

very small effect on the forces, which are almost

exclusively caused by pressure differences between

the two sides of the sail. We can thus assume that both

and C

are the same on Titan and Earth for a given

sail. Equations (12) and (13) then show that the forces

are proportional to

. Table 1 shows that the

atmospheric density on Titan is about four times that

on Earth, but on the other hand, the wind speed is only

about half in our assumption. So

turns out to be

the same! The sail forces will thus be unchanged.

The other scenario with an average wind speed of

1 m/s will yield 9 times smaller forces! To get the

same sail forces on Titan as on Earth the sail area has

to increase 9 times!

A factor speaking in favour of the lower wind

speed is that no waves have been observed on the

lakes of Titan. This may however be a matter of

measurement accuracy (Hayes et al., 2013). If the

wind speed is only 1 m/s very small waves will be

generated and they will not influence performance.

However, if the speed is 3 m/s the waves could be

significantly larger than the average on Earth. This is

due to the fact that the forcing of the waves, pressure

variation in the atmosphere, is the same, as we have

seen, but the gravity and density of the fluid lower.

Such large waves will slow down a sailing yacht

considerably, at least sailing upwind.

5 CONCLUSIONS

Titan is the largest moon of Saturn, and apart from the

Earth it is the only body in our solar system where a

liquid exists on the surface. Within the last ten years

a system of lakes and rivers have been discovered.

The climate and seasonal cycles of Titan are still not

very well known, but the composition and pressure

are fairly well established. Perhaps in the future boats

will sail the lakes of Titan for research purposes or

even sport. This paper addressed some of the issues

that will have to be considered before sailing on

Titan, or even designing a boat for sailing on Titans

lakes. A sailing yacht on Titan will have twice as

large displacement as on Earth, it will be 2.6 times

less stable for the same beam. Since friction will be

smaller, it will be faster than on Earth at low speed,

but significantly slower at high speeds due to the

wave generation. The same sail area is required to get

the same sail forces if the average wind is 3 m/s, while

a 9 times larger sail area is required for if the wind

speed is only 1 m/s. To avoid the stability problem a

catamaran seems to be a good choice!

ACKNOWLEDGEMENTS

The authors wish to acknowledge the support from

Chalmers Area of Advance Materials Science, and

the Department of Physics of University of

Gothenburg. And Västra Götalandsregionen via

Regionutvecklingsnämnden for its financial support.

REFERENCES

Bird. M.K et al, (2005). The Vertical Profile of Winds on

Titan. Nature 438, pp.800-802

Space Sports – Sailing in Space

145

Habib, M., (2015). Let’s Put a Sailboat on Titan,

www.universetoday.com/111216/lets-put-a-sailboat-

on-titan

Hayes, A. G. et al, (2013). Wind driven capillary-gravity

waves on Titan’s lakes: Hard to detect or non-existent?

Icarus 225, pp. 403-412.

Larsson, L., Eliasson, R.E., Orych, M., (2014). Principles

of Yacht Design. Adlard Coles Ltd, London

Larsson, L., Raven, H.C., (2010). Ship Resistance and

Flow, PNA Series, Society of Naval Architects and

Marine Engineers, Jersey City, USA.

icSPORTS 2016 - 4th International Congress on Sport Sciences Research and Technology Support

146