Aerodynamic Characteristics of the Portuguese Caravel
Nuno Jorge Jesus da Silveira
16/05/11
Abstract:
The Portuguese Caravel was extensively used as the main vessel on sea exploration during the XV
and XVI centuries, but technical and operational information have been lost. In order to re-acquire
knowledge, wind tunnel tests were conducted for a model of a Portuguese Caravel.
In the tests, the model faced different wind directions, the sails being adjusted for each direction
and data collected. For a given wind speed, the navigation speed in different directions was
estimated by the equilibrium between the aerodynamic and hydrodynamic forces acting on the hull.
The hydrodynamic resistance coefficient of the hull was estimated using an empirical formula. The
estimated navigation speeds were compared to an historic maritime record.
The present results suggest that the Portuguese Caravel had a uniform performance across the
navigation directions tested and that the estimated navigation speeds are in agreement with the
historic record information.
Keywords: Portuguese Caravel, Aerodynamics, Experimental, Navigation, Speed, Wind Tunnel
This study‟s purpose is to determine the
1. Introduction
Portuguese Caravel operability by evaluating
The Portuguese Caravel, namely the so
called “discovery model”, was extensively
used in the XV and XVI centuries. Its ability
to sail windward and out manoeuvre other
vessels in case of danger permitted the
Portuguese to gain the edge against other
nations in terms of sea exploration and
mercantile expansion.
expansions,
technical
and
operational information regarding it was
considered classified and so passed only by
oral transmission through generations of ship
builders
resulting
navigation angle (between the wind and the
sailing course) using the equilibrium between
the aerodynamic and hydrodynamic forces
action on the caravel. The aerodynamic force
is measured in wind tunnel tests performed
for a representative model whereas the
hydrodynamic
Due to its importance in the territorial and
economic
its sailing speed as a function of the
in
actual
scarce
information, the most available being the one
supported by artistic means (paintings and
force
is
estimated
from
empirical correlations based on the ship´s
geometry and weight.
Due to the lack of knowledge on the sails
behaviour
a
set
of
different
relative
sail-course sailed positions were tested. For
each of these positions, the sail form and its
aerodynamic angle of attack were varied in
order to obtain the best performance.
literature).
Understanding how these ships behave
sailing becomes a natural, but challenging,
2. Vessel’s Brief Description
task following an intense historical research
on construction techniques.
Historical references say that the Portuguese
Caravel could have two or three latin
(triangular) sails, although two masts were
common. It could sail windward, was fast for
its time and highly manoeuvrable.
Fig. 3 - Portuguese Caravel Bartolomeu Dias.
3. Sailing forces geometry
Fig. 1 - Artistic drawing of a three sail Portuguese
Caravel
Sailing forces are obtained according to
Fig. 4, where β is the apparent wind angle, λ
There is no absolute knowledge on what the
Caravel‟s real shape was, but even so, two
the yaw angle and the difference between
both, β-λ, is the navigation angle.
different Caravels real scale representations
were made, Figs. 2 and 3, with divergent
results.
Fig. 4 – Sailing forces and angles [1]
The
yaw
angle
is
originated
by
the
aero-hydrodynamic equilibrium, but during
aerodynamic essays λ was considered 0°.
4. Basic concepts
Fig. 2 – Spanish Caravel Niña III.
As all sailing vessels, the navigation force is
due to the aerodynamic force generated in
the
sails.
As
such,
aerodynamics
comprehension was required in order to
velocity. However the main issue of the
know the ship‟s behaviour and a brief insight
difference in Reynolds number (laminar or
is presented here.
turbulent flow) may be overcome using a
transition wire placed at the sail‟s leading
4.1. Dimension Analysis and Similarity
edge, according to Gibbings criteria [3] (5).
The aerodynamic force is dependent on the
air properties, body geometry and air-body
(5)
orientation (1)
Fortunately,
(1)
this
effect
is
by the
sail
supporting beam – the so called antenna and, adapting the transition wire‟s criteria to
and by conducting a dimension analysis [2],
the model‟s antenna dimension, it was
the resulting aerodynamic force coefficient is
possible to establish that the minimal wind
defined as (2).
speed in the wind tunnel tests to force
transition to turbulent flow should be 1.76 m/s
(2)
or Re = 52300, considering average sail‟s
chord as the characteristic length.
(3)
CF depends also on the wind-sails relative
position, angle of attack α and sails camber
Therefore, CF is dependent on the Reynolds
number (3), angle of attack and camber, Fig.
θ.
Sails are flexible wings but once they take a
stable form, they resemble thin wings and
5.
aerodynamics studies can be conducted with
identical procedures to those applied to thin
wings.
Fig. 5 – Angle of attack and aerodynamic
force. [1]
In order to obtain representative coefficients,
similarity laws have to be respected and tests
Re should be equal to the real one. The
equality of Reynolds number is impossible to
achieve because it would require a wind
velocity larger than wind tunnel top wind
Fig. 6 – CL and CD variation with α and θ.
From
those
studies,
coefficients
of
aerodynamic force decompositions, CL and
CD increase at first with α and then CL
decrease while CD keeps increasing due to
the occurrence of flow separation, Fig. 6
With θ increase, CL and CD results with α are
(8)
anticipated (results translation movement in
α‟s axis, Fig. 6)
(9)
5. Wind Tunnel Facilities and Model
The aerodynamic tests were performed at a
the LNEC‟s open circuit 9 m long wind tunnel
2
that has a 3.1 x 2.0 m cross section. The air
flow is established by a set of six 1.1 kW fans
providing velocities up to 18 m/s.
The flow velocity [2] (6) was determined from
the dynamic pressure acquired by a Pitot
tube connected to a Betz type manometer,
with atmospheric pressure and temperature
correction.
Fig. 7 – Balance, aerodynamic and
course-sailed referential.
(6)
The aerodynamic forces generated in the
model were measured by a previously
calibrated balance made of a deformable
column, equipped with strain gauges, rigidly
fixed to the model and a base by top and
bottom rigid plates under the wind tunnel.
The model used for testing was adapted from
Fig. 8 - Model in the wind tunnel.
an already existent one, assembled by Dr
Amaral Xavier [4] to [12], at a scale of aprox.
1:40 and showing only the dry part of the hull,
The model adaptation consisted mainly on
the reinforcement at the main mast base and
on the elimination of the gap between the hull
Fig. 7 to 9.
Due to the balance assembling and fixation
geometry the measured force had to be
translated from the balance reference axis
(YY-ZZ) to both aerodynamic referential (DDLL) and course sailed referential (SS-HH), as
seen in Fig. 7, according to equations (7) to
(9).
(7)
bottom and the wind tunnel floor. Extra
lashing points for sail‟s “loose” end were also
provided outside the hull and a compensation
weight to balance the mass centre position.
Fig. 9 - Applied adaptations
6. Wind Tunnel Tests
Fig. 10 - Trimmed sail.
Latin sails in the XV/XVI centuries did not use
a boom at the sail´s bottom chord (as
Once the mainsail‟s position is determined,
nowadays ships). Therefore, they require a
the secondary sail was hoisted while the
way to fix the sail‟s “loose” end. This fact
main was kept untouched. Except sail trim,
makes the identification of the best sail
all secondary sail procedures were the same
position troublesome. To overcome this
as those applied to the mainsail.
difficulty, the tests were divided in two
In phase 2, the navigation angle was varied
phases:
as well as the sails‟ angle of attack in relation
1. For a given navigation angle, the sails‟
best position (angle of attack) was
determined via the highest measured
upon
air interference. A total of five angles of
attack were tried out for each navigation
angle and for each angle of attack nine
sailing force;
2. Based
to the reference values due to the sails-hull
that
“reference”
sails‟
position, the aerodynamic forces were
recorded varying the navigation angle.
velocities were tested.
The required test parameters were navigation
angles, angles of attack, velocities, forces
and sail chords.
In phase 1) reaching the best angle of attack
requires the sail to “cross” the ship‟s deck
7. Results
taking the antenna leading edge to stay
7.1. Forces Coefficients Determination
outboard, Fig. 10, and also requiring trimming
the sail.
From phase 1. results it was possible to
Actually such sail position is often seen in
establish the range of valid Re to ensure
paintings and illustrations, as well as in
similarity conditions (elimination of Reynolds
present ships still using that kind of sails.
number influence) – Re > 53200, Fig. 11 and
12.
The force coefficients CL, CD, CFs were then
evaluated by linear regression applied to the
pairs force versus dynamic pressure, Fig. 12.
Tab. 1 – Errors from used equipment.
7.3. Navigation Velocity Estimation
For each navigation angle the highest sailing
force coefficient, CFs, was taken out of five
tested sail positions, taking into account the
evaluated uncertainties.
Fig. 11 – Line mark (black) from Gibbings criteria.
F (N)
4
2
1
0
1
2
3
(Pt- Pe).A (N)
equilibrium
4
is
needed to estimate the ship‟s speed (11) and
had to be evaluated.
L
D
y = 0,4631x + 0,1243
R² = 0,997
0
aero-hydrodynamic
CFhydro and
y = 0,9537x + 0,1373
R² = 0,999
3
The
(11)
The hydrodynamic force coefficient had to be
empirically estimated by (12) to (15) [13], due
Fig. 12 - Measured force vs wind dynamic force
to the lack of model„s full hull geometry and
hydrodynamic tests.
and linear regression.
7.2. Uncertainties
(12)
An uncertainty analysis was performed to the
(13)
measured results by applying equation (9) [2]
to all the equations used in the force
coefficients determination. The measuring
equipment error values are given in Table 1.
Being unable to determine the force balance
error, a t-Student test [12] within a confidence
interval of 95% was applied to the balance‟s
output signals.
(14)
(15)
(9)
The necessary geometry information allowing
Equipment
Force balance
Protractor
Ruler
Betz manometer
Atm. manometer
Thermometer
Error (Δxi)
mV/V
0,5 ⁰
0,5 mm
0,5 Pa
0,05 mmHg
0,05 ⁰C
the use of equations (14) and (15) was
estimated by CAD software and the model‟s
emerged hull:
 Submerse Area, AW - 200 m2;
 Longitudinal Buoyancy’s Centre, LCB - 0%;
Vaerorel, Vnav (m/s)
10
 Draft, Tc – 2,7 m;
 Transversal Máx. Area, Ax - 17 m2;
 Volumetric Displacement,
3
- 290 m .
An iterative process allows solving (16) in
order to obtain the needed value of
setting a
1,5
8
1,2
6
0,9
4
0,6
2
0,3
0
0
30
70
Vnav
CFs
 Mass, mc - 250000 kg;
Vaer
o rel
CFs
110 150 190
β-λ (°)
by
value.
Fig.14 - Navigation coefficients as well as ship‟s
and apparent wind speeds as function of apparent
wind direction.
(16)
It is now possible to perform a final analysis
on the obtained values from the gathered
information
(angles
of
attack,
chords,
Measured CFs values were plotted against
navigation angles, CFs, vessel‟s speed,
navigation angles, Fig. 16, as well estimated
apparent air speed).
vessel‟s speed and apparent wind speed,
CFs values for the navigation angles 72°, 78°
Fig. 14.
and 90° were considered under evaluated
due to separation on the sails that was not
eliminated nor reduced with angle of attack
adjustment along the sails span.
At navigation angle 57°, the CFs value was
possibly
under-evaluated
too,
but
no
reasonable cause was found.
Looking into the vessel‟s speed of about 6
knots, Fig.14, it can be said that performance
appears to be uniform across the navigation
angles range due to the apparent air speed
and CFs inverse variation trends.
In order to check the estimated vessel‟s
Fig. 13 - Navigation coefficients as function of
course sailed (relative to the apparent wind)
speed, we have considered the journey made
by Caravel Niña III [14], Fig. 2, from the
Canarias Islands to the Lisbon Expo 98
where an average speed of 2.31 m/s or 4,5
knots and a top speed of 3.14 m/s or 6.1
knots were registered.
the hydrodynamic force it is possible to
estimate the navigation speed as a function
of the navigation angles – course sailed
relative to the apparent wind direction. The
wind tunnel tests also gave information about
the sail angles of attack for each navigation
angle.
It could be observed an almost uniform
performance across the tested navigation
angles. Such performance could enable the
Caravel to overcome other vessels by speed
Fig.13 - Path followed by Niña III.
8. Conclusions
or
route
wideness
choice
without
performance drop as reported in Historical
references.
A study on the aerodynamic behaviour of the
XV/XVI century Portuguese Caravel was
A comparison with the Caravel Niña III
performed using a set of wind tunnel tests on
voyage from Canarias Islands to Lisbon, in
a ship model.
1998, shows that the estimated velocity of 6
knots is within the ship‟s real achievements.
Combining the aerodynamic force obtained in
these tests with the empirical estimation of
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