TWL: Re: Displacement Hulls vs. Semi
This is why any planing boat can be used as a displacement vessel but not
vice versa.<<
To try and clear up some of the confusion surrounding this discussion. Lets
take a look at from the point of view of boat speed. Warning I am doing this
without the aid of illustrations.
Boat speed depends on friction resistance, wave-making resistance, induced
drag, eddy-making resistance, air resistance and power available to drive the
boat.
While waterline length has a major effect on all of the resistances the most
important are frictional, wave-making and air resistance.
Frictional resistance is the major resistance for boats going at low speeds.
Frictional resistance is a function of the wetted surface of the boat.
Therefore, the length of the boat and the lateral cross section of the
immersed portion of the hull control the magnitude of this resistance.
Whereas frictional resistance is essentially constant for a given hull,
wave-making resistance starts at zero when the boat is not moving and
increases gradually as the speed increases. At higher speeds this resistance
is greater than 90 percent of the total resistance and forms somewhat of a
barrier for displacement type hulls. This barrier is very similar to the
sonic barrier for airplanes.
Wave resistance is generated because as the boat moves through the water it
pushes (displaces) the water out of its way, which creates a bow wave. Once
a single wave is created it creates a third, fourth, etc., which trail out
behind the boat and are called its wake. Since wave height is related to
wave length, the second wave peak is created some distance behind the bow.
The faster the boat moves the more water piled up at the bow, the higher the
wave, the greater the distance between the first two waves.
Now we get mathematical for those few who like that sort of thing. The rest
of you can skip this part and go to the next line. Superscripts don't work
so the bold numbers are superscripts
The distance between the troughs (Lt) in feet can be found by using the fact
that wave length (Lt) is equal to the speed of a wave (Vw) multiplied by the
period (T)
Lt = VwT
In deep water wave the wave speed is five times the period therefore;
Vw = 5T or
T = Vw/5 and
Lt = (Vw)2 / 5 = 0.2(Vw)2
Now when wave speed is equal to boat speed (Vb ), then Vw = Vb and;
Lt = 0.2(Vb)2
By converting units to velocity in knots while leaving length in feet;
Lt = 0.56(Vb)2 Eq 8.4
The number of waves (N) occurring along the boat water line (LWL) can be
expressed as;
N = LWL / Lt Eq 8.5
With a little though it can be seen that once the wave length equals the
waterline length, or N equals 1, the boat is just supported at the bow and
stern by the wave crests it has created, with a deep trough at the center of
the boat. Any increase in speed will increase the wave length and the stern
of the boat drops down into the trough and now must literally power up the
back of the bow wave. The velocity at which this condition occurs can be
calculated from equations 8.4 and 8.5, by letting N =1.
N = LWL / 0.56(Vb)2
(Vb)2 = LWL / 0.56N = 1.78LWL / N
Vb = (1.78LWL / 1)1/2
= 1.34 (LWL)1/2 Eq 8.6
Behold the legendary 1.34 times the square root of water line length.
Therefore, a boat with a waterline length of 36 feet, would have a
theoretical speed of 6 x 1.34 or 8.04 knots.
It is possible for a boat to reach higher speeds for short periods of time if
it is surfing down a wave front. Although, if your own boat seems to be
going faster than this limit, discounting surfing, you had better recalibrate
your speedometer. In truth, these optimum speeds are only rarely reached and
then only in ideal conditions with good winds and relatively no
wind-generated waves.
However, lest you get too enthralled with theory, a duck has a waterline
length of about a foot; therefore according to the above theory, its top
speed should be about 1.34 knots. I would estimate that most ducks can swim
about twice that fast. The obvious conclusion is to put feathers on your
hull, or to take a closer look at the theory. To do this we will generalized
Equation 8.6 into;
V = k (LWL)1/2
If this equation is solved for k and plotted against resistance of hulls, a
sort of "S" shaped curve is developed.
Which shows that the energy required to move the boat through the water
increases more or less linearly until k is equal to one. At that point the
power required increases rapidly until the boat is supported by only two
waves, (k equals 1.34). Now the energy curve turns upward at an every
increasing rate.
To climb out of this self imposed trough large amounts of energy must be
added to the system. To go from 1.34 to 1.5 requires roughly a 100 percent
increase in power. In fact to transcend this barrier it would require thrust
approaching 5 percent of displacement.
Even though, the commonly accepted upper limit for boat speed based on
generalizations is 1.34, the actual upper limit of your boat speed maybe
quite different. For example, this upper limit of k can vary between 1.0 for
full keel, heavy displacement hulls that are under powered to 1.5 for ultra
light displacement canoe shaped hulls. Its value depends upon hull shape and
available power.
Suppose more energy is added, then the boat moves progressively up the bow
wave. Most power boats have sufficient power to push them part way up this
wave front. Eventually the center of gravity of the boat passes the peak of
the bow wave. At this point the boat now tips and begins to run down the
wave front. With gravity now assisting the boat down the wave front, the
speed of the boat can be maintained with reduced power. This behavior is
called planing.
Thus if you take a couple of aircraft jet engines and tie them to your full
displacement type hull it will also plane. Thus the quote at the beginning
is technically untrue, because all of the variables (power) are not being
considered.
At low speeds where fluid friction controls, the boat with the lest wetted
area will be the easiest driven. At higher speeds things get a little more
fuzzy. At displacement speed, i.e., where the hull is just supported on the
two crest of the wave, water line length controls the speed. However other
factors play a small roll and changes the (k) factor a few decimal points one
way or the other. Once you fall off the aft wave then displacement or more
accurately weight becomes the dominant factor.
Hope this adds to the confusion.
Don Dodds
North Pacific Research