Example 2.1;  Influences of the angles α and β on the fluke blade forces

The vertical fluke Force:

 

When investigating the vertical fluke force (Fv) as a function of the angles α, β, a 3D plot has been made.

 

In this plot it’s interesting to look at the influence of the angle α on Fv. As can be seen in the figures, when α reaches 1.1rad or +/- 60deg, the vertical fluke force becomes negative.

 

 

 

 

 

 

 

 

                                                           



Vertical fluke force 3D


A negative Fv represents an upward force, or in other words the fluke makes an up going movement. We want the fluke to go down and this negative Fv will not give penetration.

 

Other things which can be seen, are an increasing Fv between α = 0 rad and α = 0.75 rad for a maximum angle β, and between α = 0 rad and α = 0.9 rad for a minimum angle β.

 

First conclusion will be that the angle α lies between 0 and 60 deg.








Vertical fluke force as a function of alpha




When investigating the vertical fluke force as a function of β, the following conclusions can be made:

β doesn’t influence the Fv when looking at α = 0, this due to the horizontal orientation of the fluke in the sand. β lies between 10 and 50 deg and its influence on Fv is small.

 










Vertical fluke force as a function of beta


The horizontal Fluke force:

 

When looking at the 3D representation of the Horizontal fluke force (Fh) as a function of the angles α and β, a relative flat figure will occur.

Except, when looking at a high α and β, Fh reaches a high value then.

This result is as expected; with a high value of α  and β, it becomes hard to shear the sand over the shear zone and therefore a high Fh is necessary.













Horizontal fluke force 3D

 


















    

Horizontal  fluke force as a function of alpha


















Horizontal  fluke force as a function of beta