i just had a sleepless night and thought about the Gertler-Shapes, got up and turned on the computer and tataaa

thanks for this great tool ðŸ˜‰

]]>great idea, I created a MANTIS Ticket for it here http://bugs.airshipworld.info/view.php?id=31 that way I wont forget it.

I also want to invite everyone to contribute in Mantis with bug reports and feature requests. If anyone wants to help with the development please contact me.

The bugtracker can be found at http://bugs.airshipworld.info/ ]]>

thank you again for this improved tool. I would like to add the text below as a basic description and “help file”.

Best Regards, Johannes

Airshipworld Gertler Series 58 Generator – Version 0.6 (27.03.2009)

(c) A. Grunewald & J. Eissing

http://www.airshipworld.info/software

Helpfile by Johannes EiÃŸing, 18.08.2009

General

The Series 58 hullforms were developed by Morton Gertler and Louis Landweber for the David Taylor Model Basin DTMB in 1950 [1], [2]. These shapes are described by five parameters such as slenderness ratio, prismatic coefficient, location of maximum thickness, bow- and sternradius. The series 58 shapes are well covered in literature because of their parametrics and reproducibility. Their value for research and development is comparable to the well known NACA four- and five digit profiles.

User Interface

– Render Profile

pretty much self explaining, klicking this button updates the plot window.

– Copy Values to Clipbord with TAB/semicolon

Points shown in the plot window are copied th the clipbord as x/y point coordinates. Only the coordinates for the upper shape are exported to the clipbord. The number of Points “n” is set in the dialogue box “Input Parameters”, see below. Coordinates are given nondimensionally, referred to the length of the body. Points are allocated in a full cosine distribution. The delimiting character can be chosen as TAB or semicolon. Chosing the TAB Character facilitates import to e.g. EXCEL by CNTRL+V

– Calculated Parameters:

– Cs

Surface Coefficient as introduced by Gertler [1]

Cs = Swet/(L*pi*D) where

Swet = wetted surface area,

L = Length of the body

pi is the ratio of perimeter to diameter of a circle with approximately 3.1416

D is the diameter of the body.

Reversely, wetted surface area is computed by

Swet = Cs*L*pi*D

Cs is calculated numerically, meaning it’s accuracy increases with the

number of points n (see Input Parameters). Already with 20 points the

error is less than 0.5%, with 50 points about 0.05%.

– CB

Centre of buoyancy. This is the volumetric center of the body referred to the body’s length.

– a1 to a6

are the computed polynomial coefficients for the shape function

y(x)=D*sqrt(a1*(x/L)+a2*(x/L)^2+a3*(x/L)^3+a4*(x/L)^4+a5*(x/L)^5+a6*(x/L)^6)

where

y(x) is the local radius (ordinate)

x is the abscissa

D is the maximum diameter

L is the length of the body.

– Input Parameters

– n – Number of steps

Here, the number of points to be computed for the shape can be set. For standard use, 20 to 50 points will do.

– m – Point of maximum thickness

This is the position of the maximum section, referred to body length. A typical value is 0.40.

– r0 – Dimensionless bow radius

Bow and stern radii are nondimensionalized by the following relationship:

r = R*L/D^2=(R/D)*(L/D) where

r is the nondimensional radius

R is the dimensional radius

L is the Length and

D is the diameter of the body.

A typical value for the bow radius is 0.5, being the bow radius of any prolate spheroid. A pointed bow would show a value of 0.0.

– rl – Dimensionless stern radius

See above r0. A typical value for a tail radius is 0.1. A pointed tail would show a value of 0.0.

– Cp – Prismatic coefficient

The overall prismatic coefficient is a measure of how good a slender body fits an enveloping prism, built from the maximum crossection extruded for the length of the body. In case of a body of revolution, this prism is a cylinder. An arbitrary ellipsoid shows a prismatic coefficient of 2/3. Typical values for airships and submersibles are in the range of 0.60 to 0.70.

– L2D -Length to Diameter ratio

This is the slenderness ratio of the body, typical values being in the range between four and ten. A typical value for airships is five.

References

[1] “Resistance Experiments on a Systematic Series of Streamlined Bodies of Revolution – For Application to the Design of High-Speed Submarines”

DAVID TAYLOR MODEL BASIN WASHINGTON DC

Gertler, Morton, APR 1950

[2] “Mathematical Formulation of Bodies of Revolution”

DAVID TAYLOR MODEL BASIN WASHINGTON DC

Landweber,L. ; Gertler,M., SEP 1950