Predicting Catamaran Resistance
A HydroComp Technical Report
Product link: NavCad
This report comments
on the use of NavCad version 4 (and prior) for the resistance
prediction of catamarans. It presents a discussion of two different
techniques. (Note: NavCad 2003 contains an explicit prediction
of catamaran resistance.)
is twice the individual hull resistance, plus an added drag due
to the interference of the hulls with each other. NavCad predicts
this system resistance (hulls and interference) in one of two
ways - a catamaran system solution and a modified monohull
The catamaran system
solution directly predicts the total system resistance. The prediction
algorithm combines both hull and interference resistances.
The modified monohull
solution predicts individual hull resistance just as if it were
a monohull. NavCad adds interference drag through correlation
to catamaran model tests via the aligned prediction feature.
With this approach, the effect of hull parameters and spacing
can be explicitly evaluated.
NavCad has one algorithm
for catamarans [Gronnslett, 1991]. The algorithm utilizes a set
of curves for residuary resistance. A random collection of full-scale
and model tests of high-speed displacement catamarans with slender
symmetric demi-hulls is the basis of this algorithm.
The method does
not take differences in hull separation into account. Differences
in interference drag are averaged to produce a generic result.
This algorithm exhibits surprisingly good accuracy, however. We
surmise that this is due to two characteristics of these types
First, the hulls
are long and slender operating in a high speed range (Fn from
0.6 to 1.6). A good portion of this resistance will be frictional,
which is directly calculated. Second, hull spacing has shown to
have the most effect on interference resistance in the lower speed
ranges near the principal wave-making hump speed (Fn from 0.3
to 0.7). Above this speed regime, there is little difference in
added interference drag due to different hull spacing [Insel,
The above system
solution is inadequate for lower speed ranges and hull types that
are not the typical "wave-piercer" or "high-speed displacement
catamaran". A modified monohull solution can be used for these
situations, and to improve prediction accuracy in general. This
approach requires the use of model tests or full-scale trials.
The key to this
approach is to work with half of the vessel. In other words, results
are shown "per hull". Total resistance will then of course be
twice the predicted result.
coefficients from catamaran model test results are the same for
one hull or two. Remember, the coefficient is a function of wetted
surface. As resistance and wetted surface are both divided in
half, the coefficient remains the same. Thus, Cr values can be
entered directly from model test reports or trial results without
correction. These Cr values include hull drag, as well as interference
The first step is
to choose a catamaran model test that has similar L/B and spacing
as the subject design. The aligned prediction then evaluates this
model and creates a correlation curve to go from predicted bare-hull
drag (as a monohull) to actual catamaran drag (including interference).
This correlation curve is then applied to the prediction of the
design (as a monohull with its own parameters of L/B or Cp, for
instance). A prediction of the demi-hull resistance, correlated
to a model with similar spacing is the final result.
model test files suitable for use in a modified monohull solution
[Insel, 1991]. These test are based on a transom stern, round
bilge hull form. Successful use of aligned prediction calls for
a broad range of L/B and spacings (S/L ratio). This series of
fifteen tests includes pure monohulls (for reference) and catamarans
of L/B from 7 to 11, and S/L from 0.2 to 0.5. Other tests can
be entered and archived in NavCad's model/parent file system.
A systematic procedure
is described below.
1. Review and select
a catamaran model test report that has similar L/B and S/L ratios.
2. Enter this data
into a NavCad model/parent file. Speeds and Cr values can be entered
directly from the report. If a slow speed form factor was determined,
this too can be entered as shown. Hull data, however, should be
for one hull. Especially remember to use the wetted surface and
displacement for only one hull (half of the ship).
3. Enter data for
the hull design into NavCad for one hull, just as was done for
4. Build a resistance
prediction. First, choose a prediction method that is suitable
for the range of hull parameters.
5. Choose aligned
prediction and a resistance parameter for alignment (Rbare,
Rr or Rw, if available).
6. Define the model
file name and run the calculation.
A slightly different
approach uses the extrapolation feature of NavCad in place
of the aligned prediction. Extrapolation simply uses a
non-dimensional resistance/displacement ratio correlation between
model and design to predict resistance. If a model and the design
are quite close in shape and parameters, then extrapolation can
be a successful approach.
a curve of resistance to displacement ratio versus Froude number.
It has the effect of scaling a model's resistance in suitable
proportion to size and speed. Total bare hull resistance can be
extrapolated, as can residuary (or even wave-making) if the frictional
or viscous portions are calculated from an accurate wetted surface.