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raise exponentially. As we can see, Z excursion
needs to be higher than X and Y. This is a
consequence of the absence of sustained X and Y
accelerations, and also a consequence of sea tide,
which lifts the boat whenever a wave passes under
it, creating a short but more sustained Z motion.
The same can be done with peak-to-peak angles.
In this case, pitch (X) and roll (Y) angles do not
need to be larger than (approximately) 20° and the
yaw angle (Z) is unbounded. This means that pitch
and roll movements could be simulated directly
without filtering provided that the motion platform
withstands those limits (Nahon, 1990). Z turns have
to be filtered because yaw motion is not constrained
but the motion platform usually is. This is consistent
with the measurements of Section 3 and with the
nature of the motion. Following with the analysis,
with a 3 Hz cut-off frequency, the excursion needed
is (12.18, 10.9, 9.4)° (X, Y, Z). With a 5 Hz limit,
the excursion needs to be (10.8, 9.7, 6.6)°, and with
a 10 Hz limit, we need (8.52, 8.53, 3.87)°. Here, an
increase in the cut-off frequency does not change as
much as it did with the translational limits (with the
exception of yaw) and the 3 Hz limit is totally
feasible without losing much information.
4 CONCLUSIONS
Some conclusions can be drawn from our study. On
the qualitative side, we can affirm that the four
major cues when sailing a speed-boat are pitch, wind
speed, roll and heave. Pitch is the major cue because
it is directly linked to the throttle and, at full speed,
considerable pitch angles are reached. Wind speed is
quite important because, unlike in a car, no
windshield protects you from the air, and the feeling
of the wind is fairly intense. Roll is less significant
at high speeds but when the boat is turning or
stopped, it is also quite noticeable. And heave is also
important when the boat hits a wave. These
qualitative conclusions are consistent with our data.
On the quantitative side, the most important
conclusion is that sustained accelerations (low
frequencies) are rather small and that water, and not
the propeller, is the main cause of inertial cues. This
is a significant result because it means that it is more
important to be able to produce fast but sharp
movements than long accelerations. Therefore, the
motion platform excursions do not have to be very
long. However, the engines should be strong enough
to move the platform as quickly as possible. Another
conclusion that can be extracted is that motion along
Z axis is the most important of the linear motions.
As aforementioned, pitch and roll rotations also
reveal very important, because they change sharply
and they define the behaviour of the boat. On the
contrary, yaw rotations tend to be less important
compared to the former. Thus, if we were to choose
a motion platform design, we would build a 3-DoF
pitch-roll-heave motion platform. In our opinion,
this is the minimum necessary to reproduce the
major inertial cues of the boat.
Figure 3: Cut-off peak-to-peak maximum linear
displacements.
Future work includes, of course, building a
suitable motion platform and a real-time simulator to
use it. Some of the future work is already published
in (Casas et al., 2012).
REFERENCES
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Nahon, M.A. and Reid, L.D., 1990. Simulator Motion
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Nielsen Kellerman (Kestrel official site), 2009. Kestrel
4000 Data Sheet. http://www.nkhome.com/
pdfs/Kestrel_specs.pdf. Visited: 07/2011.
Ocean Server Technology Inc. ,2007. OS3000 Features.
http://www.oceanserver.com/download/Release_OSI_
060107.pdf. Visited 07/2012.
Reid, L.D. and Nahon, M.A., 1985. Flight Simulation
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Reymond, G. and Kemeny, A., 2000. Motion cueing in the
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Dynamics, pp. 249-259.
Casas S. et al., 2012. On the Real-time Physics Simulation
of a Speed-boat Motion. In GRAPP 2012, pp. 121-128
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