Any idea of Mean of Mean of Mean Draught?

The term mean of mean of mean draught is also termed as Quarter mean draught. Commonly used in draught surveying. Lets see how the quarter mean draft is derived.

Consider,
Fwd draught  = Fd
Midship draught = Md
Aft draught = Ad

Mean draught = (Fd +  Ad) / 2

Mean of Mean draught or Half mean draught 
 = (((Fd +  Ad) / 2) + Md)/2 
= (Fd +  Ad + 2Md ) /4

Mean of mean of mean draught or Quarter mean draught 
 =((Fd +  Ad + 2Md ) /4) / 2
= (Fd +  Ad + 6Md) / 8

The mean of mean of mean is the draught that is used to refer the stability booklet or the hydrostatic tables with.

Ship Board Operations - Draft Survey 1

Draft Survey - 1

Introduction

Purpose: The purpose is of a draft survey is to determine the present amount (weight) of the cargo on board, thereby calculating the cargo loaded or discharged.

The formula -  Cargo weight = Present displacement - (Light ship + Ballast + Stores  + Fresh water + Constant)

Objective: Objective is to find the cargo weight presently on board. For that  Light ship, ballast, stores, constant are known. Therefore, finding the present displacement will solve the equation.

The method in brief:

1. Read the drafts at 6 points and correcting them for their respective perpendiculars. 

2. Using the corrected drafts above, obtaining the "Mean of mean of mean draft" or the "Quarter mean draft" (QMD)
3. Refer the hydrostatic table or the ship's stability booklet with the quarter mean draft and obtain the displacement.

4. Calculate the 1st trim correction or "Layer correction" and applying it to the displacement on step 3.

5. Calculate the 2nd trim correction and applying it to the displacement on step 4.

6. Correct the displacement above for sea water. (if the vessel is not floating in sea water)

7. Subtract all known wights onboard including the light ship displacement to get the present cargo weight on board.

Statical stability curve. (GZ curve)

Minimum stability requirements (as to the date)

Having a positive GM value alone is not sufficient.

 The minimum stability criteria for cargo ships as per the Load Line Convention

1. The area under the curve of righting lever (GZ curve) shall be not less than, 
1. 0.055 meter radians up to an angle of 30°
2. 0.09 meter radians up to an angle of 40° or the angle at which lower edges of any openings in the hull,superstructure or deck house which cannot be closed watertight, are immersed if that angle be less
3. 0.03 meter radians between 30° and 40° or the angle referred above

  2. The righting lever (GZ) should be 0.20m at an angle of heel equal to greater than 30°.
  3. The maximum righting lever (GZ) should occur at an angle of heel not less than 30°.
  4. The transverse meta-centric (GM) height should not be less than 0.15m.

IMO recommended general criteria for cargo ships  (IS code 2008)

(The only difference from the Load line rules above is that the maximum righting lever should occur at angle of heel not less than 25°. Others are the same.)

1. The area under the curve of righting lever (GZ curve) shall be not less than, 
1. 0.055 meter radians up to an angle of 30°
2. 0.09 meter radians up to an angle of 40° or the angle of down flooding if that angle be less
3. 0.03 meter radians between 30° and 40° or the angle referred above
   

  2. The righting lever (GZ) should be 0.20m at an angle of heel equal to greater than 30°.
  3. The maximum righting lever (GZ) should occur at an angle of heel not less than 25°. If this is not practicable, an alternative criteria based on an equalant level of safety may be applied to the approval of the administaration.
  4. The transverse meta-centric (GM) height should not be less than 0.15m.

 

 

 

Statical stability curve. (GZ curve)

Introduction

The Statical stability curve or the GZ curve is drawn by plotting the GZ values against the angle of heel. It is drawn for each voyage condition for a particular displacement and KG.

Illustration 1: GZ curve - Source - http://thenauticalsite.com/NauticalNotes/Stability/MyStability-Lesson06-CurvesofStatStab.htm

 Following data can be extracted from a GZ curve,

1. Initial metacentric height (GM). Its the point of intersection when a tangent drawn at the origin and the purpendicular at 57.3° or 1 radian meets. The scale on the GZ shows the value of initial GM.
2. Point of contra fexture. Point of Contra flexture means the point on the curve where the direction of bending. Angle of heel at this point represents the angle of deck edge immersion (DEI).
3. Maximum GZ and the angle of heel it occurs.
4. The range of piositive stability.
5. Angle of of vanishing stabitlity.
6. The moment of stability for a given angle of heel. (GZ x Displacement = FLM)
7. The dynamical stability for a given angle of heel. (Dynamical stability at Ɵ° = Ship's displacement in tonnes (W) x Area between the GZ curve and the baseline upto the angle of heel in im meter-radians. (A))

Navigation - General formulas

General Navigation Formulas. 

Topics Covered:

1. Plane Sailing

2. Parallel Sailing

3. Mercator Sailing

Plane sailing formula can be used generally up to 600 nautical miles, there after mercator sailing should be used. Sums are not presented as these are some basics in navigation.


1. Plane Sailing

N.1 - Plane Sailin

As these are right angles triangles,

Tan Co. = Depature / D.Lat
Sin Co. = Departure / Distance


The formulas above are sufficient to solve any given problem of plane and parallel sailing.

Cos Latitude = Departure / D.Long










2. Parallel Sailing.

The name itself gives the idea. It is sailing parallel on a particular latitude. The course will be due east (090) or due west(270).


The parallel sailing formula is,

• Cos. mean Lat = Dep / D.Long

when sailing parallel mean latitude is referred as Cos Latitude.





3. Mercator Sailing.

N.3 - Mercator Sailing

DMP = Diffence between Meridional Parts. Meridional Parts (MP) can be read from Traverse tables. Difference of Meridional parts can be calculated by either subtracting MPs or adding MPs.

Following fomulas can be derived,

• Tan Co. = DMP / D'Long

• Dep. = D'Long x Cos mean. Lat