Log in or Sign up. Boat Design Net. How to make a GZ curve if you know GM? Is it possible to make just if you know GM or do I need some additional information? Can anyone explain me how to do it please. HaveANiceDayFeb 25, DCockeyFeb 25, Thank you very much for your help. HaveANiceDayFeb 26, I'll try again. The small angle metacenter, M, does not stay above the center of buoyancy, B, as the heel angle increase beyond a small angle. There may be confusion about terminilogy.

When I say "small angle metacenter" I mean the metacenter for very small angle of heel. The location of it is fixed relative to the hull and does not change with angle. However, as the heel angle increases it generally does not stay vertical perpendicular to the surface of the water above the center of buoyancy.

The term "metacenter" is sometimes considered to be a function of heel angle and used for the intersection of a vertical perpendicular to the surface of the water line from the center of buoyancy and the center plane of the hull. DCockeyFeb 26, Ad HocFeb 26, From the ITTC Dictionary of Hyrdromechanics, Version Metacentre, transverse M and longitudinal ML The intersection of the vertical through the centre of buoyancy of an inclined body or ship with the upright vertical when the angle of inclination approaches to zero as limitfor transverse or longitudinal inclinations respectively.

You must log in or sign up to reply here. Show Ignored Content. Similar Threads. KN curves shrijeet mishraMar 31,in forum: Stability. Replies: 13 Views: Freeship cross curves notation. Simon BootsOct 27,in forum: Stability. Replies: 2 Views: Simon Boots Oct 28, Replies: 4 Views: Kane24 Jul 11, Discussion in ' Stability ' started by claudiu01Jul 28, Log in or Sign up.

Boat Design Net. Help me to calculate area under GZ curve for a 8 m sail boat. If you already have the curve, trace or transfer the curve to graph paper and count the number of squares under the curve. A graph paper method is ok, but if you have the GZ curve in a form of a spreadsheet, you can let Excel preform the calculation for you.

As I understand that you already have the curve, the required area can be obtained through a simple integration. If you have the Gz curve, it would be easier to draw it in Autocad, then you can measure the area under the GZ curve. I suggest simpson's 1 4 1 rule. Divide the gz curve equally with a number of lines in vertical directions, if the number increases the result will be more accurate.

The total no of lines should be odd no. If your data points are equally spaced its very simple:The Trapezoid rule rules!

For any part of the curve you want the area under simply sum all the y data values and multiply by the x increment, the space between each x value. That will be close enough. If your data points are not equally spaced you can still use the Trapeziod rule. Just look it up it's simple arithmetic. If you want to play You can also run a curve fit program and derive and solve the definate integral between the ranges you are interested in, but that does need a knowledge of calculus.

Although it is easy. MikeJohnsAug 14, Planimeter Daniel. DCockeyNov 7, That sounds like a mathematician talking Trapezoidal will be perfectly accurate for this application, GZ curves are quite 'steady' as far as functions go and easily approximated by a constant slope over the sample interval. We don't want lots of decimal place anyway, that's a mistake often made in applied sciences; calculating something a little nebulous to far to many decimal places and imagining it's useful.

Even the Riemann Sums I described above add the Y values and multiply by the increment are accurate enough for design work and quite valid if the data point are not too far apart.

They do have the advantage of being very simple and can be performed manually quite quickly. If you calculate the Reimann sum for the mid point of the value within the range then you have implemented a trapezoid anyway. MikeJohnsNov 7, TeddyDiverNov 7, Just look up the error formula for the different methods and it becomes abundantly clear.

If you have a table of data from the PC with every 5 degrees then even Riemann will be accurate. Just sum and divide. If you plotted like skene by hand than you have a coarse data set and it would be more prudent to use simpsons for sure, but the accuracy is poor to start with and the real GZ curve will be a different shape to the Simpsons parabola approximation. If you really wanted to get carried away you could curve fit between 0 and degrees with a 6th order polynomial and integrate it between any limits you wanted.

In reality stability curves are not that precise to start with, boat design for example half tanks and no free surface allowance! To worry about a few percent error of the area under an interpolated curve is losing sight of reality. DCockeyNov 11, DC The 'formula' is not the Trapezoidal.

I didn't make it very clear, sorry.The intact stability analysis covers the basic ideas of applying stability limits and heeling moments. Then we discuss the various commands to evaluate these limits. How to construct stability limits in GHS.

Includes the basic command syntax and specific options on the following items. Homework covers how to develop limit statements. The homework includes several arbitrary limit statements that are created. Homework and solution files included in download.

The area limits require a minimum area of 0. Please adjust your limit requirements accordingly. Also called a righting arm curve in GHS. Includes instructions on how to apply stability limits to evaluate the stability criteria while constructing the righting arm. Homework works with the various ways to develop the GZ curve. There are several implementations of how to use the GZ curve and specification of the heel angles used to develop it. Download includes homework file and solutions.

This homework covers how to specify heeling moments in GHS. Includes the turning moments, wind moments, an arbitrary moment, and even tank heeling moments. You can also see how the heeling moment reports differ for each type of heeling moment developed. Download includes homework files and solution. This is a tricky criteria that requires an exact command sequence in GHS to work correctly. Homework covers the IMO severe wind and roll criteria. This is a tricky one that requires a specific sequence of commands to work correctly.

The homework covers that sequence of commands. The criteria is developed, a wind heeling moment is applied, and then GZ curve is developed. This includes variation by draft or displacement. Also covers trim variation. Shows how to run this analysis for variation of draft and for variation of displacement. Also covers how to introduce different trim angles into the analysis.Initial transverse metacentric height shall not be less than 0.

For ship carrying timber deck cargo complying with athis may be reduced to not less than 0. Initial metacentric height — point of intersection of the tangent drawn to the curve at the initial point and a vertical through the angle of heel of Angle of contraflexure — the angle of heel up to which the rate of increase of GZ with heel is increasing.

Though the GZ may increase further, the rate of increase of GZ begins to decrease at this angle. These curves are provided for an assumed KG, tabulating GZ values for various displacements and angles of list. Same as the GZ cross curves and also used to get the GZ values for making the curve of statical stability. This solves the problem of a sometimes positive and sometimes negative correction, as now the correction is always subtracted.

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Add post Story Image Embed View all formats. This curve is for a particular displacement and KG. From this curve it is possible to ascertain the following: Initial metacentric height — point of intersection of the tangent drawn to the curve at the initial point and a vertical through the angle of heel of The range of stability — where all GZ values are positive.

The angle of vanishing stability — beyond which the vessel will capsize. The area of negative stability. The moment of statical stability at any given angle of heel GZ x Displacement of the ship.

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Maritime Professionals Club.

### CROSS CURVE OF STABILITY PART#1

Close Search for: Search. Log In Sign In. Forgot password? Enter your account data and we will send you a link to reset your password. Your password reset link appears to be invalid or expired. Log in Privacy Policy To use social login you have to agree with the storage and handling of your data by this website. Add to Collection Add new or search Public collection title.Having discussed the basics of intact stability of surface ships, we are now at a stage to analyze the same.

In fact, a ship designer or an officer on-board should be able to know the stability characteristics of a ship just by looking at the curves. Since the stability of a ship can be directly commented on by the nature and value of its metacentric height GMa direct method to track the stability of a ship for a range of heel angles would be, to generate a curve that relates this parameter to the angle of heel.

Since metacentric height is directly related to the righting lever GZ and angle of heel, the curve of static stability is a plot between the righting lever and angle of heel. The above graph is plotted assuming that the ship is in static condition. Some of the important information that can be derived from any GZ curve of a ship are discussed below:. Point of inflection does not play an important role in operational purposes, but it helps designers to make preliminary predictions regarding what changes in stability would be brought about if the design of a hull-form is altered.

The above theory implies, that steeper initial slope of the GZ curve would mean that the ship has more initial stability. However, larger initial stability does not imply larger values maximum righting lever and range of stability. This can be depicted by studying the nature of the GZ curves of two ships A and Bas shown below. It may so occur that the initial metacentric height of the ship becomes negative. As a result of this, the ship is not stable in its upright condition, leading to a heeling moment, as shown in part a of Figure 3 below.

As a result of the negative righting lever GZthe ship heels further upto an angle where the righting moment and righting lever, both, become zero.

This angle at which this condition is achieved is called Angle of Loll, as shown in part b of Figure 3. The important thing to visualize here is that a condition of loll can be treated as a shift of the GZ curve from the origin shown in Figure 4 below. Now, when the ship heels to an angle more than that of the loll angle part C of Figure 3a positive righting moment is generated, which brings the ship back to its equilibrium position.

However, as long as a condition of loll prevails, the equilibrium condition will not be achieved when the ship is upright. This results in a permanent angle of heel in the ship, which is an unwanted situation. There are many reasons behind a condition of loll.

One of the most commonly occurring ones is the free surface effect. We will study that, and the other causes of loll in later articles, and also see how they can be corrected. The important thing to note now, is the shape of the curve.

For a designer, it is very vital to observe the initial slope of the stability curve of a ship in all loading conditions, because often, the negative slope might not be as exaggerated as shown in the above figure. Though the values traced by the curve may be different in each case of loading, but the shape or curvature of the curve will hardly change, because it depends on the geometry of the hull.

So, the hull designer must always study the initial curvature of the GZ curve once it has been generated for a single load case.

## Ship Stability – Understanding Curves of Static Stability

Why and how? For each ship the GZ curves are plotted for:. In case of both the ships, if an identical rise in centre of gravity is considered which brings us to Loadcase 2 from Loadcase 1the GZ reduces due to reduction in metacentric height. But both the ships would respond very differently due to the initial curvature of their GZ curves.

**GZ CURVE & ITS CORRECTIONS, F3**

In case of Ship A, even when the initial metacentric height becomes slightly negative notice the initial slope for Loadcase 2the ship will heel upto a certain angle, but as the ship keeps heeling, due to the convex upward curvature of the GZ curve the righting lever becomes positive again.

This causes the ship to return to a condition of positive stability. But in case the initial metacentric height of Ship B is even slightly negative, even a slight heeling moment will capsize the ship. Because as the angle of heel increases follow Loadcase 2 for Ship Bthe righting lever remains negative due to the convex downward curvature of the GZ curve.

When such a GZ curve is obtained during design phase, the designer must iterate the design of the hull. Probable methods of correcting the shape is by increasing the beam, or adding a flare, etc. The vertical position of centre of gravity G of the ship is not always fixed.

It changes with every voyage, depending on the loading conditions and the amount of ballast.The G-LOC curves are based on a theoretical understanding of how acceleration affects underlying physiological mechanisms affording tolerance to acceleration, their limits, and what happens when they are exceeded. The two new G-LOC curves differed significantly from previous curves in temporal characteristics and key aspects underlying neurologic response to acceleration. G-LOC did not occur earlier than 5 s for any acceleration exposure.

These G-LOC curves alter previous temporal predictions for loss of consciousness and advance the understanding of basic neurophysiological function during exposure to the extremes of acceleration stress. Understanding the acceleration kinetics of the loss and recovery of consciousness provides the characteristics of uncomplicated and purely ischemic causes of LOC for application in medical diagnosis of syncope, epilepsy, and other clinical causes of transient loss of consciousness.

The curves are applicable to education, training, medical evaluation, and aerospace operations. Current understanding of the cause of the loss of consciousness LOC is based on acceleration producing an environment in which the cardiovascular system is unable to supply an adequate amount of oxygenated blood to the cephalic nervous system CPNS regions that support conscious function. When the specific neurologic areas responsible for supporting consciousness are functionally compromised, LOC occurs.

Fluctuations in cardiovascular function heart rate, blood pressure, and vascular tone occur regularly in normal environments, but are usually not of sufficient magnitude or duration to induce neurologic functional compromise.

The nervous system has a buffer period that allows transient ischemia to be tolerated without symptoms or signs occurring.

### Area under GZ curve

Fortunately, it is only when acceleration stress applied in a specific direction, over a long enough duration, and at a sufficiently high magnitude, that neurologic function is embarrassed. Tolerance to acceleration is therefore defined by the stress envelope that will induce LOC. A clear description of the human acceleration tolerance envelope is therefore a component of understanding who we are and what environments we are able to safely enter without the threat of LOC.

Thus, aeromedical research programs were developed to understand and improve acceleration tolerance. An excellent description of the components of acceleration tolerance was developed by Burton [ 2 - 6 ].

The physiologic alteration induced by acceleration underlying loss of consciousness is considered to be the critical reduction of perfusion to cephalic regions of the nervous system for a specific period of time. These areas of the nervous system have the capacity to tolerate inadequate energy supply resulting from altered perfusion for a short period of time.

The functional buffer period FBP is the time that the integrated neurologic function supporting consciousness is maintained following the loss of adequate energy necessary for sustaining normal function [ 18 ]. Their tolerance curve described a hyperbola without any indication of a dip related to cardiovascular response time. Accurate, more operationally applicable G-time tolerance curves are needed [ 21 ].

An essential aspect of accurate G-LOC curves and one that applies to operationally important rapid onset profiles is the use of adequate data describing the LOCINDTI associated with the rapid onset acceleration left side arm of the curves.

This study was conducted utilizing G-LOC data retrieved from a centrifuge data repository describing the response of completely healthy humans to acceleration stress in a human centrifuge. The data are from volunteer research subjects, aircrew undergoing training to improve G tolerance [ 13 ], students in various aerospace medical disciplines, and aircrew undergoing medical evaluation [ 22 ].

All individuals successfully completed military physical examinations or the equivalent, with many having additional medical evaluation procedures to ensure normal health. The repository did not identify the individual experiencing the G-LOC episode; therefore, the total number of individual subjects was approximately For this study, the data included all G-LOC episodes that occurred.

There was no separation of relaxed subjects, subjects performing an anti-G straining maneuver AGSMsubjects wearing or without anti-G suits AGSor other combinations of anti-G protection methods or devices. A variety of acceleration profiles existed in the data repository: 1 gradual onset rate GORramp linear rise profiles, 2 rapid onset rate RORramp to plateau profiles, 3 simulated aerial combat maneuvering profiles, 4 closed loop-centrifuge target tracking profiles, and 5 other complex experimental profiles.Discussion in ' Software ' started by mallia.

Log in or Sign up. Boat Design Net. GZ curve Discussion in ' Software ' started by mallia. Unfortunately in the Demo, or the academic version, this is not a feasible option. Thanks Steve. As with all computerized analysis, the GIGO rule applies garbage in, garbage out - the analysis won't mean much until you take the time to go through the program and figure out exactly what each parameter and option means.

Hi, Thanks for your help. But how can I import the model I have already drawn from Maxsurf? Is there a particular format?

## Curves of Statical Stability

Hi all, I did all you said, and I did import it in Archimedes. What am I doing wrong? You are practically there. The Kn curves are the stability curves for a VCG height of zero. You must log in or sign up to reply here. Show Ignored Content. Similar Threads. Rhino: make a curved bow on a developable plank Renaud ChileJul 2,in forum: Software.

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