Analysis of Vessel Acceleration
with NavCad
A HydroComp Technical Report
Report 118
Product link: NavCad
NavCad
is a program for the prediction and analysis of resistance and
propulsion. NavCad version 4 and newer can explicitly evaluate
vessel acceleration.
Overview
Hydrodynamic acceleration
of a marine vehicle is based on the principal of F = ma.
In hydrodynamic terms, the force (F) and mass (m) components
can be expressed as:
F
= T (1t)  R
m = (1+k) W/g


where, 
 T
= propeller thrust
t = thrust deduction
R = total resistance
k = added mass coefficient
W = vessel weight (displacement)
g = gravitational constant 
In other
words, the force available to overcome the vessel inertia is the
possible thrust less the vessel's resistance. Mass is the vessel
weight with a multiplier for the added mass of entrained water
that moves with the hull.
Analysis
A timestep
technique is at the heart of the analysis. Given a known weight
and added mass coefficient, the following procedure is performed
at incremental steps:
 Given speed at start
of the time step.
 At the speed, determine
thrust, thrust deduction and resistance.
 Calculate acceleration.
 Calculate speed at end
of time step.
 Redo the process for
the next time step with the new starting speed.
The precision
of the results are dependent on the value of the time step used,
small values leading to more accurate results. Then you can plot
speed, RPM and acceleration versus time.
NavCad
can be used to predict resistance and propulsive coefficients
(e.g., wake fraction, thrust deduction, relativerotative efficiency),
as well as vessel acceleration. Accurate results are critical
to the reliability of the acceleration model. The results can
be easily placed into a spreadsheet for the further analysis.
The calculation
of thrust is a difficult step that is made very easy with NavCad's
unique equilibrium torque ("towing") analysis. The thrust applied
to acceleration is not the freerunning thrust, but is the maximum
thrust that the propulsion system is able to produce at that speed.
In other words, this analysis determines the thrust that can be
generated until the engine has no more torque (along its torque
curve) to spin the propeller any faster.
The magnitude of the added
mass coefficient (k) is typically about 0.05 for displacement
modes, becoming zero at planing speeds.
Additional considerations
This is
a fairly simple, but quite effective, acceleration model. A few
additional calculations could be added to make the model more
realistic in the first few time steps.
At start
up, there can be a negative pressure region caused by propeller
suction under planing hulls. This can have the effect of causing
the vessel to trim or "squat". This effect could be modeled as
an additional increase in the added mass coefficient or as an
increase in thrust deduction at low speed.
Improvement
in the model would be gained by accounting for the initial torque
required to overcome the rotational moment of inertia (wr^{2})
of the engine, gear and propeller at start up. The above model
assumes that the RPM of the engine is allowed to reach its potential
RPM using a maximum rotational "acceleration".
