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PCSail Velocity Prediction
Program

VPPs operate by the principle that a sailing vessel is in equilibrium.
Therefore, the summation of forces and moments on the vessel must be zero. In
this way, a VPP is divided into two parts: hydrodynamic and aerodynamic. The
hydrodynamic forces are a hull form's reaction to the vessel being driven
through the water. These forces include hydrodynamic drag, side force, yawing
moment, and righting moment in Figure 1 and Figure 2. The hydrodynamic
forces resist the aerodynamic forces on the boat due to sails. These forces are
aerodynamic drive, side force, yawing moment, and heeling moment. When each of
the hydrodynamic forces equals the opposite aerodynamic forces, the boat is in
equilibrium and is considered a possible sailing condition. After a VPP solves
for possible sailing conditions, the VPP finds the sailing conditions which are
fastest around a course and considers them the optimum conditions.

Fig. 1 : Z-plane force and moments diagram[1]

Fig. 2 : X-plane force and moments diagram[1]

PCSail was supplied as freeware at the 15th annual Chesapeake Sailing Yacht
Symposium. PCSail is a spreadsheet for Microsoft Excel which predicts the forces
on the boat and the optimum sailing conditions.[3]

PCSail predicts the hydrodynamic forces on a vessel from the Delft series of
sailing yacht model tests. The Delft series is a set of hydrodynamic data taken
from a series of different sailing hull forms. By giving key hull parameters,
PCSail interpolates through the Delft series to predict the hydrodynamic
qualities of a given hull form.[3]

The Hazen method documented by Larsson and Eliasson calculates the
aerodynamic forces generated by the sailing rig. The characteristic lift and
drag of sails for PCSail were found via experimental data as well as theoretical
calculations. After giving sail shape inputs, PCSail predicts the lift and drag
on the sails specific to a vessel. Finally, lift and drag in the sail-axis are
corrected to aerodynamic drive and lift in the vessel-axis.[2]

PCSail only solves to equate aerodynamic drive to hydrodynamic drag and
heeling moment to righting moment. Forces which are ignored included
hydrodynamic side force and yawing moments. Aerodynamic side force is considered
only for calculating heeling moment.[3]

PCSail Setup

Designer David Pedrick supplied the IMS VPP predictions for the Mk II Navy
44' STC. The IMS VPP serves as the standard of performance prediction and a
rating tool for racing yachts. However, since the IMS VPP output did not give
sailing characteristics such as sail forces and heel angles, the PCSail VPP was
used. The boat characteristics from the IMS VPP were used as inputs to the
PCSail VPP.

The initial inputs into the PCSail program were very straightforward as in
Figure 3.
Some modifications had to be made to the program so that the IMS VPP and PCSail
VPPs agreed in their output.

Fig. 3 : PCSail sample hull characteristics input

Modifications to PCSail

One modification was that of GM, the metacentric height. The metacenter is a
calculation which helps define initial stability in a vessel. PCSail computed GM
as:

(1)

While acceptable for trend studies, this approximation did not provide the
righting moment accuracy within the tolerance needed for this study. The
hydrostatics program FASTSHIP evaluated the stability of the Mk II Navy 44 STC.
GM was calculated for use in the VPP, and 4.94 ft was used instead of the PCSail
calculated GM of 4.27 ft. This indicated that the vessel was more stable than
predicted by the trend from PCSail.

Secondly, yaw angle and rudder angle determinations were added to the VPP.
PCSail had already calculated the total aerodynamic lift from each sail. From
the supplied rig diagrams, the longitudinal center of effort of each sail was
approximated at the geometric center of the sail. From these two values, the
yawing moment on the boat due to aerodynamic forces was found. From the lines
plan, the center of effort on each appendage was approximated so that the lift
force required on each appendage could be found. From these values, the
necessary angle of attack of each appendage was found.

Another small modification was that the VPP used the average freeboard height
as the height of the base of the mast. PCSail initially calculated that the
total height of the rig was approximately 6 inches less than the true height.
This made the righting moments and wind speeds at the height of the sails lower
than they should have been. The height of the base of the mast was modified to
reflect the true base mast height.

VPP Results

The VPP was run at wind speeds ranging from 6 to 24 knots. The PCSail output
corresponded extremely well with most of the IMS VPP output. There was a fairly
consistent discrepancy at low-wind speeds. This was expected since the PCSail
aerodynamic algorithm is not as rigorous as the IMS algorithm at these low wind
speeds. Figure 4 shows this
discrepancy in light air especially for heel angles at reaching angles (120-170
degrees). This sailing condition is very sensitive to apparent wind effects as
the sails are often stalled and requires more complex wind calculations for more
accurate results. However, most of the range had to be checked against their
respective velocities-made-good (VMG), which is the speed of the vessel on the
wind-axis. For instance, if leeway is neglected at a true wind direction of 90
degrees, the VMG is zero. By choosing the maximum absolute value of
velocity-made-good, the wind angle at which a boat can most optimally travel
upwind or downwind can be found. Most of the deep-reaching angles were at angles
past the best VMG, and therefore were out of the range of the optimum sailing
angle.[3]

Fig. 4 : PCSail VPP compared to IMS VPP at 6-knots wind
speed

The PCSail VPP seemed to disagree with the IMS VPP for heel around a true
wind angle of 90 degrees. This disagreement was based on the two algorithm's
different interpretations on when to raise and lower the jib and spinnakers.
Therefore, the heel angle was not a continuous function of true wind angle since
a spinnaker and jib have much different effects on heel. Velocity for jib and
spinnaker, however, was nearly equal at the point which the VPP chose to switch
sails. Velocity was considered continuous as a function of true wind angle even
while performing sail changes.

For medium to high wind speeds as in Figure 5, the PCSail's
data came very near the IMS VPP's data. Even heel angle showed much better
correlation between the two VPPs.

Fig. 5 : PCSail VPP compared to IMS VPP at 12-knots wind
speed

References
1.
Claughton, Andrew. "Developents in the IMS VPP Formulations."   14th
Chesapeake Sailing Yacht Symposium.  1999: 1.

2.  Larsson, Lars and Rolf E. Eliasson. Principles
of Yacht Design.  2nd Ed.  International Marine.  Camden,
ME.  2000.

3.  Martin, David.
"PCSAIL, A Velocity Prediction Program for a Home Computer."   15th
Chesapeake Sailing Yacht Symposium.  2001: 100.

About Me | Contact Me | | ©
Jon Silverberg 2005 | Modified 19MAR2005

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