## Initial Hullform DefintionAlthough a rough estimate of resistance and speed/powering requirements, etc can be made using only overall gross dimensions (as shown on the page) in order to get a more accurate
estimate of these characteristics requires a better definition of a
ship's hullform, including such things as Block Coefficient, Midships
Coefficient, Waterplane Coefficent, Prismatic Coefficient, Waterline
Half Entrance Angle, LCB Location, and Transom Shape, etc (as defined
on the Tables & Figures for the
Pre-Processor page).
Additionally, these factors will also play a role in estimating a
vessel's stability and seakeeping capabilities. TerminologyIn general, many of these factors are inter-related, and a change in one factor (such as ) will have an
impact on many of the other factors (such as Half Entrance Angle,
Waterplane Area Coefficient, and Waterplane Inertia Coefficient).
As such, on this sheet, some guidance and recommendations are provided
for estimating many of these factors to allow the user to understand
how they inter-relate and also allow him or her to better experiment
with their impacts on the overall ship design. Block Coefficient
page, a vessel's Terminology is a general measure of how full its hullform
is. In general for conventional displacement hulls, the slower a
ship is intended to go the fuller its hullform can be. At higher
speeds, however, a decrease in Block
Coefficient
is desirable to keep power requirements from becoming excessive.
At the higher end of the speed range of conventional displacement hulls
though, the benefits of further reduction in Block Coefficient tends to
taper off. Block CoefficientWithin general Naval Architecture literature there are many rules of thumb for estimating recommended
versus the vessel's design Block Coefficient (or Froude Number). Several of these recommendations are plotted in
the graph below, along with a limited amount of data points for some
post WWII naval designs.Speed/Length
RatioIn this graph: - The
line represents a curve fit recommended by Towsin in a paper by Watson & Gilfillan [Reference 6], where;*Blue*- Cb = 0.70 + 1/8 atan ((23-100*Fn)/4), and
- the dashed lines above and below this cureve represent a band of +/- 0.025
- The
line represents a curve recommended by Schneekluth & Bertram [Reference 7], where;*Red*- Cb = -4.22 + 27.8*sqrt(Fn) - 39.1*Fn + 46.6*Fn^3
- The
line represents a curve fit recommended by Telfer for the Series 60 sysematic series of single-screw merchant type hullforms [Reference 8], where;*Green*- Cb = 1.18 - 0.69*Vk/sqrtL
- The
line represents a curve recommended by Alexander [Reference 9], where;*Orange*- Cb = K - 0.5*Vk/sqrt(L), and
- K = 1.33 - 0.54*V/sqrt(L) + 0.24*(Vk/sqrt(L))^2
As can be seen in this figure, based on the data points shown, typical design Froude Numbers for modern naval surface combatants appear to be > 0.35 . In general, the curve is the only curve that
covers this region. Typical values recommended by the Blue curve in this region range from
about 0.51 to 0.55 (+/- 0.025), however the data for actual ship
designs suggest that actual Blue may
range as low as about 0.45. As such, users may wish to
enter this data themselves. Block Coefficients
versus the vessel block coefficient, along with a
limited amount of data points for some post WWII naval designs.Midships
CoefficientAs shown in this figure, there are two general sets of curves provided. In general, as discussed on the page the midship
section of a vessel may be flat bottomed, with a curved radius at its
bilges, or it may have a similar shape, but with a small amount of Terminologydeadrise,
resulting in a slightly less full shape, or it may have a similar
shape, but with a higher degree of deadrise, resuling in an
even less full shape. The curve for Equation (1), which spans
from a Block Coefficient from 0.3 to 0.6 represents a
recommendation for a vessel's midship section with a high degree of
assumed deadrise. The curve for Equation (2) represents a
r ecommendation for a vessel's midship section with a low degree of
assumed deadrise and Equations (3) represents a recommendation
for a vessel's midship section assuming that the section is flat
bottomed, with no rise of floor (deadrise). Additionally, I
believe that Equations (4) and (5) represent vessel's either with no
deadrise or only a very small amount.
In this graph: - The
line represents a curve fit recommended in the book*Blue*__Practical Ship Design__by D.G.M. Watson [Reference 10] for vessels with high deadrise, where;- Cm = 0.40 * Cb + 0.58,
- The
line represents a curve from the same book for vessels with a low degree of deadrise, where;*Red*- Cm = 0.05 * Cb + 0.935
- The
line represents a curve fit recommended by Benford based on the Series 60 sysematic series of single-screw merchant type hullforms [Reference 9], where;*Green*- Cm = 0.977 + 0.085 * (Cb - 0.60)
- The
line represents a curve recommended by Kerlen [Reference 9], where;*Orange*- Cm = 1.006 - 0.0056 * Cb ^ -3.56,
- The
line represents a curve based on an HSVA series of vessels [Reference 9], where;*Purple*- Cm = ( 1 + ( 1 - Cb ) ^ 3.5 ) ^ -1
Block Coefficients of the vessels
for which data is presently available tend to fall between 0.40 and
0.56 and for the most part the midship sections of these vessels appear
to fall closer to the Curve for Equation (1). As such, Equation
(1) is recommended for use in estimating the Midship Coefficient
of a Surface Combatant design. However, if the users wish they
can always enter their own estimates for use in a design.
The next graph gives some
guidance on Because the wave patterns that a vessel develop while underway are dependent on the vessel's length, speed, and fullness, at different speeds a vessel may end up with its stern resting either at a peak or trough of the developed wave pattern. According to a theory outlined in the book by Saunders, when the speed of a vessel is such that the wave train it develops will result in the vessel's stern falling into a trough in the waves, the vessel will have a relative hump in its resistance curve. If the speed of the vessel is such that the wave pattern developed results in a peak at its stern, then the vessel will be closer to even trim and overall it will have a relative hollow in its resistance curve. As shown in this graph,
for the vessels that data is currently available most, though not all
of them, fall into a blue shaded region of the graph and most fall at
least relatively close to the suggested desing lane. Because a
vessel's - adjust the design's
**Prismatic Coefficient**, which may provide small adjusts to where the design falls with respect to the humps and hollows, or - reconsider the selected length and/or design speed, such that the proposed design speed/length ratio no longer falls on a hump, or
- the users may just decide to accept the current dimension of the design and accept that at design speed their vessel may be operating at a penalty with regards to total installed power required.
The next graph shows
similar guidance on a vessel's
This next curve shows
guidance on In this graph: - The
line represents a curve fit recommended for conventional hulls, where;*Blue*- Cwp = 0.73 * Cp + 0.29,
- The
line represents a curve fit recommended for lengthened high-speed hulls, where;*Red*- Cwp = 0.73 * Cp + 0.32
- The
line represents a curve fit recommended for vessels that are to have good seakeeping, where;*Green*- Cwp = 0.73 * Cp + 0.35
- The
line represents a curve based on the Series 60 family of single-screw merchant type hullforms, where;*Orange*- Cwp = 0.180 + 0.860 * Cp,
- The
line represents a curve fit from a paper by Eames on the "Concept Exploration of Small Warship Designs" (check title) for small transom sterned warships, where;*Purple*- Cwp = 0.444 + 0.520 * Cp
- The
line represents a curve fit recommended for single-screw cruiser stern hullforms, where;*Light Blue*- Cwp = 0.175 + 0.875 * Cp,
- The
line represents a curve fit recommended for single-screw cruiser stern hullforms;*Gray*- Cwp = 0.262 + 0.760 * Cp,
- The
line represents a curve fit from the book "Ship Design for Economy and Efficiency" by Schneekluth, where;*Blue Gray*- Cwp = Cp ^ 2/3,
- The
line represents a curve based on U-Form (need to define) hulls, where;*Light Orange*- Cwp = 0.95 * Cp + 0.17 * ( 1 - Cp ) ^ ( 1 / 3 ),
- The source of the
line is currently unknown, where;*Black*- Cwp = 0.23667 + 0.8333 * Cp
The next curve shows some
recommendations for a vessel's
The next curve shows a
recommendation for the location of a vessel's
The next curve shows an
estimate of For reference the Holtrop & Mennen equation is; WS = L * ( B + 2 * T ) * Cm ^ ( 0.5 ) * ( 0.453 + 0.4425 * Cb - 0.2862 * Cm + 0.003467 * B/T + 0.3696 * Cw )+ 19.65 * ABT/Cb Where ABT = the transverse area of the bulbous bow (which for now I have assumed to be zero) The range of validity of the Holtrop & Mennen equation is listed as - 0.55 <= Cp <=0.85
- 3.90 <= L/B <=14.9
- 2.10 <= B/T <=4.00
I have found several other equations relating Wetted Surface to other hullform parameters but have not yet tried plotting them. For reference these include; - WS = L * ( 1.7 * T + B * Cb ), which is attributed to Denny & Mumford
- WS = 1.7 * L * T + Vol / T, which is described as a revised Denny & Mumford equation
- WS = Vol ^ ( 2/3 ) * ( 3.3 + L / ( 2.09 * Vol ^ ( 1/3 ))), which is attributed to Haslar
- WS = Vol ^ ( 2/3 ) * ( 3.4 + L / ( 2 * Vol ^ ( 1/3 ))), which is attributed to Froude
- WS = ( -0.906385E-5 * (Displ / ( L /100 ) ^ 3) ^ 2 + 0.954632E-2 * ( Displ / ( L / 100 ) ^ 3 ) + 0.776457 ) * L ^ 2 / 10, which is attributed to Baier & Bragg
- WS = C * ( L * Displ ) ^ ( 0.5 ), which is attributed to Taylor
- WS = C / 5.916 * ( L *
Vol ) ^ ( 0.5 ), which is described as a revised Taylor equation
- where C is defined as .... (need to look up)
This next curve shows a
plot of recommended In this graph: - The
line represents a curve fit attributed to D'Arcangelo, where;*Blue*- Cit = 0.1216 * Cwp - 0.0410,
- The
line represents a curve fit attributed to Eames for vessels with small transom, where;*Red*- Cit = 0.0727 * Cwp ^ 2 + 0.0106 * Cwp - 0.003
- The
line represents a curve fit attributed to Murray (+4%), where;*Green*- Cit = 0.04 * ( 3 * Cwp - 1 )
- The
line represents a curve fit attributed to Normand, where;*Orange*- Cit = ( 0.096 + 0.89 * Cwp ^ 2 ) / 12
- The
line represents a curve fit attributed to Bauer, where;*Purple*- Cit = ( 0.0372 * ( 2 * Cwp + 1 ) ^ 3 ) / 12
- The
line represents a curve fit attributed to McGlochrie (+4%), where;*Light Blue*- Cit = 1.04 * Cwp ^ 2 / 12 ,
- The
line represents a curve fit attributed to Dudszus & Danckwardt, where;*Gray*- Cit = ( 0.13 * Cwp + 0.87 * Cwp ^ 2 ) / 12,
These next three curves show plots of suggested transom configuration parameters. Unlike most of the other data on this sheet which include recommendations based on equations found in general naval architectural literature, these next three graphs are currently based solely on curve fits I have tried to make through data that I have on existing ships. As such, the curves are a little rough, but are the best that I have to go on for now. As I collect and review more data I hope to update and revise these graphs. The first graph shows a
rough suggestion of
These next three curves show plots of suggested values for propeller diameter and rpm based on known data for similar vessels. Similar to the transom geometry graphs above these next three graphs are currently based solely on curve fits I have tried to make through data that I have on existing ships. As such, the curves are a little rough, but are the best that I have to go on for now. As I collect and review more data I hope to update and revise these graphs. The first graph shows a
rough suggestion of
Finally, these last curve
show plot of a vessel's |