Fender Design Criteria:

Introduction:
The principal function of the fender system is to prevent the vessel or the dock from being damaged during the mooring process or during the berthing periods. Forces during the vessel berthing or anchoring may be in the form of impact, abrasive action from vessels, or direct pressure. These forces may extensive damage to the ship and structure if suitable means are not employed to counteract them. The amount of energy absorbed and the maximum impact force imparted are the primary criteria applied in accepted fender design practices. 

Selection of fender system type:
A variety of factors affect the proper selection of a fender system. These include, but not limited to, local marine environment, exposure of harbor basins, class and configuration of ships, speed and direction of approach of ships when berthing, available docking assistance, type of berthing structure, and even the skills of pilots or ship captains. It is considered impractical to standardize fender designs since port conditions are rarely identical. Previous local experience in the application of satisfactory fender systems should be considered, particularly as it applies to cost-effectiveness characteristics. Here is a good guide for selecting a fender system fit for your needs. We follow the PIANC 2002 and other Standards set forth by other manufacturers with a long history in the marine fender industry.

General Design Procedure:
The design of a fender system is based on the law of conservation of energy. The amount of energy being introduced into the system must be determined, and then a means devised to absorb the energy within the force and stress limitations of the ship's hull, the fender, and the pier. General design procedures are as follows:

1. Determine the energy that will be delivered to the pier upon initial impact. It is recommended to consider the heaviest/largest vessel capable or allowed to use your dock.

2. Determine the energy that can be absorbed by the pier or wharf (distribution of loading must be considered). For structures that are linearly elastic, the energy is one-half the maximum static load level times the amount of deflection. Allowance should also be made in cases where other vessels may be moored at the pier. If the structure is exceptionally rigid, it can be assumed to absorb no energy.

3. Subtract the energy that the pier will absorb from the effective impact energy of the ship to determine the amount of energy that must be absorbed by the fender.

4. Select a fender design capable of absorbing the amount of energy determined above without exceeding the maximum allowable force in the pier. Please contact us for our product catalogue. You can get specific performance information of our products.

 

I. Terminology:

Gross Tonnage(GT): Total Volume of vessel and cargo. This is derived by dividing the total interior capacity of a vessel by 100 cubic feet.

Net Tonnage(NT): Total Volume of cargo that is carried by the vessel.

Displacement Tonnage(DPT): Total weight of the vessel and cargo when the ship is loaded to draft line.

Dead Weight Tonnage(DWT): Weight of cargo, fuel, passenger, crew and food on the vessel.

Light Weight(LOW): Weight of Vessel.

Ballast Weight(BW): Weight of ship and the water added to the ballast compartment to improve its stability after it has discharged its cargo.

II. Calculation of  the Normal Berthing Energy or Effective Berthing Energy:

Side Berthing:

Side Berthing is the most typical case for docks. The Berthing Energy is calculated by the following kinetic equation:

Where E_B : Berthing energy (KJ, N*m, or Lb_F*ft)

W_D : Water displacement of the berthing ship (Tons, Kg, Lbs). - This is the Total Displacement Tonnage(DPT) of the vessel. If you do not have this information you may use our tables to view standard vessel's information by type and sizes. Please click here to view our tables.

V_B : Berthing velocity of the Ship at the movement of impact against the fender (m/sec, ft/sec) - Berthing velocity is an important parameter in fender system design. It depends on the size of the vessel, loading condition, port structure, and the ease of difficulty of the approach. Therefore the berthing velocity is preferred to be obtained from actual measurements or relevant existing statistical information. When the actual measured velocity is not available, the most widely used guide to estimate the berthing velovity is the Brolsma table, adopted by BSI, PIANC and other standards. To facilitate the calculations, designers can use tables, graphs or equations shown below.

V_a: Easy Berthing, sheltered.       V_b: Difficult Berthing, sheltered.    V_c: Easy Berthing, exposed.             V_d: Difficult Berthing, exposed.
        

C_M : Virtual mass factor - As a vessel makes contact with the berth and its movement is suddenly stopped by the fenders, the mass of water moving with the vessel adds to the energy possessed by the vessel. This is called "Mass Factor" or "Added Mass Coefficient" and the weight of the water is generally called "Additional Weight". The added mass coefficient makes up for the body of water carried along with the ship as it moves sideways through the water. As the vessel is berthing a body of water is carried along with the ship as it moves sideways through the water. As the ship is stopped by the fenders, the momentum of the entrained water continues to push against the ship and this effectively increases its overall mass. CM is normally calculated with the following formula:  

where,
D: Full Load Draft(m, ft)
B: Molded Breadth(m, ft)

Another calculation method for the virtual mass factor is:

        where,
       D: Full Load Draft
       L: Ship Length
       ρ: Sea Water Density(1.025 t/m³)

C_E : Eccentricity factor - In the case when a vessel contacts a berth at a point near its bow or stern, the reaction force with give a rotational movement, which will dissipate a part of the vessel's energy.

To determine the Eccentricity Coefficient, you must firstly calculate the radius of gyration(K), the distance from the vessels center of mass to point of impact(R), the velocity vector angle() and berthing angle() using the following formulas:

Where K: Radius of rotation of the vessel (usually 1/4 of the vessel's length)
            R: Distance of the line paralleled to wharf measured from the vessel's center of gravity to the point of contact. Usually 1/4- 1/5 of vessel's length.
         C_B: Block Coefficient, which is related to the hull shape and is is calculated as follows:

Where, W_D: Water displacement of the berthing ship(Tons, Kg, Lbs)
          : Sea Water density(1.025 Tons/m³)
          L_BP: Length between perpendiculars. Please see sketch below for better explanation:

          x: Distance from bow to point of impact
          B: Beam(m, ft)

If the Length, beam and draft are not known, this table can be used to estimate the block coefficient:

You may also use the following formula to calculate the eccentricity coefficient:                 

Some designers prefer to calculate the eccentricity coefficient using the simplified formula above. Care should be used as this method can lead to an underestimation of Berthing Energy when the berthing angle() is greater than 10 degrees and/or the point of impact is aft of quarter-point(x > L_BP/4). To verify your calculations, the eccentricity coefficient values generally fall within the following limits:
                   

Case 1: Closed Dock
A Closed Dock would be a wharf, where you have a concrete wall going directly to the sea ground. In this case the quay wall will push back all the water that is being moved by the vessel. This creates a resistance factor that can be calculated as follows:

If K_C ≤  D / 2, C_C ≈ 0.8

If K_C >  D / 2, C_C ≈ 0.9

Case 2: Open or Semi-Closed Dock
A Semi-Closed Dock is a Dock that water can flow underneath the dock, but the depth changes below the dock. Open Dock is usually a dock with piles underneath and the water can flow freely underneath the dock. In such case we can assume the following value of 1.

C_C ≈ 1

C_S : Softness factor - This is the portion of berthing energy which is absorbed by the deformation of the vessel's hull and fender. When a soft fender is used, C_S can be ignored. Otherwise, we can assume a value for C_S ≈ 0.9

II. Fender Selection:

After the effective berthing Energy(E_B) of the ship is calculated as explained above, the selection of the fender system should be conducted in accordance with the fenders performance(Reaction Force, Energy absorption, and deflection curve). The fender system selection has the following requirements:

1. Energy absorption of the selected fender system exceeds effective impacting energy of ships(E_B).
2. Reaction force of the selected fender system is less than the ship's allowable reaction force.
3. Surface pressure of the selected fender system is less than the allowable hull surface pressure. You can meet the requirements by changing the dimensions of the frontal panel.
4. When the ship is berthing in a slanting direction, the fenders will bear a angular compression which will decrease the energy absorption at point of impact. Therefore the fender performance should be adjusted in accordance with the berthing angles when selecting the fender system.
5. The selected fender system should satisfy special requirements of extreme environments(high/cold temperature, strong winds, waves, high/low tides, etc.)
6. The selected fender system should be chosen wisely for the investment(performance/price). The price of maintenance  and installation should be considered in your investment. Fenders that have an easy installation and maintenance are a better option for your investment.

Fender Spacing:
This calculations are critical, due to the possibility of a vessel hitting the dock structure while berthing at an angle. As per British Standards, for continuous quay, the installation pitch is recommended to be less than 15% of the vessel. Minimum installation pitch of fender can be calculated with the following equation:

Where
S: Maximum spacing between fenders
R_B: Bow radius of board side of vessel(m, ft)
P_U: Uncompressed Height of fender including panel(m, ft)
C: Fender height in rated compression.
: Fender deflection(m, ft)
If the bent radius(R_B) is not known, we can estimate by the vessel's overall length(L_OA) and width(B) as follows:

For vertical orientation arrangement, the types and sizes of all ships berthing shall be considered. All possible tides vary scope. To assure safe berthing we must consider the height and draft of the smallest and largest vessels to determine the point of contact on the structure. Do not design your arrangements considering only the largest vessels berthing in your dock, since your design might not work for smaller vessels berthing in your dock. 

Fender Panel Design:

Hull Pressures:
Permissible hull pressures vary greatly with the class and size ship. The best guide to hull pressure is the designer's experience in similar cases. If this information is unavailable, then the following table may be used as an approximate guide for design:
 

Hull pressures are calculated using the frontal panel area(excluding lead-in chamfers) as follows:

Where
P: Hull Pressure(N/m², psi)
ΣR: Combined Reaction Forces of all rubber fenders
A₁: Valid Panel Width excluding lead-in chamfers(m)
B₁: Valid Panel Height excluding lead-in chamfers(m)
P_P: Permissible hull pressure(N/m², psi)

Approximate Hull Pressure for other fender types:

The above formula and table apply to berths fitted with frontal panel systems. However, many berths use Cylindrical and Arch fenders safely and without damaging the ship's hull, despite the fact that these fenders exert higher hull pressures. The Arch Fenders have hull pressures of 760~1300kN/m². Cylindrical Fenders have 460~780kN/m². Also bear in mind that when cylindrical fenders are used with large chains or bar fixings through the central bore, the hull pressure will be higher to approximately double the above figures. Again there is no evidence to show that this causes hull damage.

Selection and Calculation of Chain:

There are three types of chains in fender systems:
1. Tension Chain: The main function of the tension chain is to protect the fender from damage while it is under compression.

2. Weight Chain: The weight chained is used to support the weight of the frontal and face panel.

3. Shear Chain: This chain protects the fender from damage while in shear deflection.

The following should be noted in the chain design:
-Chain dimensions should be as exact as possible. Not too loose, not too tight.
-The chain can not be twisted as this reduces the load capacity.
-Open Link is preferred.
-The initial(static) angle of the chain is important. Normally weight chains are set at a static angle of 15 - 25° to the vertical and shear chains are set to 20 - 30° to the horizontal.
-All chains must be designed or selected with a safety factor of 2 to 3 times of the work load.
-The dimensions of the shackle is usually the same as the chain, but if the shackle is required to bear the same load with the chain, then a thicker shackle is preferred.

Where,
Ф₁: Static Angle of Chain(°)
h₁: Static offset between brackets(m, ft)
Ф₂: Dynamic Angle of Chain(°)
h₂: Dynamic offset between brackets at F(m, ft)
D: Fender compression(m, ft)
R: Reaction Force of rubber units behind the frontal panel(N, Lbs)
W: Weight of the panel face(N, Lbs)
F_L: Safe working Load of chain(N, Lbs)
L: Bearing length of chain(m, ft)
n: number of chains acting together
μ: Friction coefficient of face pad. Usually equals 0.15 for UHMW-PE facings.
F_M: Minimum Breaking Load(N, Lbs)
F_S: Safety Factor(2~3 times)

III. Other Berthing Scenarios:

Dolphin Berthing:

Passing Lock Entrance:


 

Ship to Ship Berthing:

 

End Berthing:

Please note that this information is only for reference. Please allow us to confirm your fender selection. Provide us with all the information needed to assure your selection. Please contact us. We will provide you with support for your fender system. We are committed to our clients from the design to the installation and even for future maintenance inspections and consulting. Please fill up our design condition form and send it to us. To download or access our design inquiry form, please click here.

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