New app: Pilot´s Tug Assist Tool PTAT - Bollard Pull Calculation for Marine Pilots

by Capt. M. Baykal Yaylai - published on 19 February 2020 5438

photos, graphics and article by Capt. M Baykal Yaylai

1.0 Introduction

Required tug power and number of tugs needed in variable conditions of wind, current and waves isin most cases an assessment made by pilots based on their professional experience. However, assessments will raise questions by lawyers if something goes wrong. They will use tools to calculate what really is needed with respect to tug power and number of tugs. They have furthermore the advantage of time.
A pilot has not so much time. For a pilot, if tugs are needed, it is hard to calculate the required tug power just before or during ship manoeuvring. Furthermore, the more extreme the weather conditions become the less accurate assessments are and the higher the risk of too little tug power.
A handy and simple tool to determine in a minimum time what is really needed as tug assistance, is the Pilot’s Tug Assist Tool(PTAT) which calculates in an approximate way the total required tug power for ships in various conditions of wind, current and waves. This tool can be loaded as an app on the smart phone.
The tool is based on the calculations and graphs as explained in chapter 5 of the book “Tug Use In Port”, written by Captain Henk Hensen FNI; first published in 1997 by The Nautical Institute, London, UK, with a 3rd edition published by The ABR Company, UK, in 2018 ( In this book is also explained why a safety margin of 20% is included in the calculations.
The program has been tested for more than 2 years and it has been observed that it works in a satisfactorily way.
The various possibilities of the PTAT are addressed on the following pages.
Much of the information can also be viewed by selecting the "ⓘ" symbol of each section on the app.

2.0 The Various Sections


i. Calculations for required tug power in case of cross winds

Ship Height: The value to be written in this box is critical.
It is the height from sea level to the average maximum height of the vessel, or in case of deck the average maximum height of cargo loaded on deck, including deckhouse.
It can be difficult to assess the sideways wind area. With container vessels it is rather easy.
When you keep in mind that the height of one container is about 2.60m, then it is easy to calculate the total height of the containers on deck. Between the lowest container and the main deck is also about 2 meters space. Height of container can furthermore be used to assess other heights as well, such as the height of main deck above water.

Wind force: Another important box in the same section.
As wind does not blow at constant speed, the highest wind speeds are important.
Therefore, it is recommended to use the estimated wind force in gusts.
Wind speeds given in Beaufort scale are average wind speeds during a 10 minutes
period and therefore too low and not suitable for calculation of required bollard pull.

Wind is commonly treated as steady-state static force and this force is calculated using the well-known drag force equation:
F = 0,5*C(yw)* ρ*V²*A(l) Newton
V = Wind velocity in m/sec
C(yw) = Lateral wind force coefficient
A(l) = Longitudinal (broadside) wind area in m²
ρ =Density of air in kg/m³

The wind force coefficients can be determined in wind tunnel tests and from computations. For several ship types the wind coefficients are known for all angles of attack and certain loading conditions.
For tankers and gas carriers they can be found in for instance, OCIMF publications. Lateral forces are largest and most important for calculating bollard pull required. C(yw)varies between approximately 0,8 and 1,0 for beam winds, depending on ship's type and loading condition, but lies mostly between 0,9 and 1,0.
This coefficient (C(yw)) is accepted as 1.0 in the program.

Note: The formula above is based on a density of air of 1.28kg/m3 which applies to dry air of 00 Celsius and 1 atmosphere (1000kPa) air pressure.
If for an actual situation a more accurate outcome is needed, density of air should be calculated based on the actual atmospheric air pressure (if needed taking into account height), temperature and humidity. Density of air increases with air pressure and for the same air pressure decreases with higher temperatures en humidity. It means that with a high pressure the required bollard pull calculated with the mentioned formula is somewhat too low, particular with low temperatures and dry air.

A safety margin of 20% is included. Therefore 25% has been added to the outcome of previous formula. The reasons why a safety margin is needed are explained in the book `Tug Use in Port’.

ii. Calculations for required tug power in case of cross currents

Current force considerations are similar to those of wind force. The magnitude of current forces on a ship depends on the velocity of the current, the hull form andarea exposed to the current and the under keel clearance (UKC) of the vessel. Again lateral current forces experienced e.g. during berthing are most important.
The current forces acting on a ship can be calculated in the same way as the wind forces.
Formula for lateral current force:
F = 0,5*C(yc)* ρ*V²*LBP*T Newton
V = Current velocity in m/sec
ρ = Density of water in kg/m³
LBP =Length between perpendiculars in m.
T = Draft in m.
C(yc) = Lateral current force coefficient

When the UKC decreases, the forces due to currents increase. The magnitude of current force can be three times as great on vessels with very small UKC as for vessels in deepwater.(Fig.3)
Current force increases, as with wind, with the square of the velocity. If the current velocity doubles, the current force is four times larger. If the velocity triples, the force is nine times larger.

The program interpolates the ratio draft-depth for the correct lateral current force coefficient.
Again for reasons explained in `Tug Use in Port’ a 25% have again been added to the outcome of the formula to create a safety factor of 20%

It should be well understood that when pulling on a short towline, for instance at a distance of one tug length between tug and ship, there can be a large loss in pulling effectiveness of even up to 60% of the bollard pull of the tug, depending on direction of tug propeller wash and UKC of the ship. The shorter the distance the larger the loss. The negative effect of a pulling Voith tug will be less. As situations of distance and UKC varies, this loss can not be included in the program. (Fig.4-operational info)

iii. Calculation of forces created by cross waves

Although jetties, terminals and harbour basins are usually located well sheltered from waves, certain terminals and jetties may be located such that they can be under influence of waves. Wave action may become important when wave conditions exceed certain threshold values. Wave forces are essentially dynamic in nature and it is important to understand the nature of wave loading and vessel wave motion response and when a more rigorous dynamic analysis may be required.
In this program, only short beam waves are considered. The forces per metre of ship’s length due to these short period waves then amount to approximately:
Fwave = 0,35 ρ g LBP ζa² Newton
ρ = Density of water in kg/m³
LBP =Length of waterline, take length between perpendiculars in m.
ζa = Wave amplitude, equal to 0,5 * Wave height. (Hs)
Hs = Significant wave height from through crest, as indicated by an experienced observer when estimating visually

Again, 25% has been added to the previous formula for a safety margin of 20%. (Fig.4)


It is possible to convert in the “CONVERT” section:
kW and HP to metric tons thrust for bow and stern thruster, and knots to m/sec for wind.


In this section the user can calculate the required tug power to stop a sideways moving ship which has at 30m distance from the berth a certain transverse speed. This could be helpful for certain ships, such as those loaded with dangerous or hazardous cargo. Calculations can be performed for open as well as for solid berths.
Calculations apply to approximately 10% UKC


Loaded tankers and bulk carriers have a large displacement. For this type of ships the following empirical formula is used which is based on the displacement of the ships:

Required Bollard Pull (M/T) = {(Displacement of vessel x 10‾³) x 60} + 40

For such loaded ships wind effect is not so important, it is the mass of the vessel that has to be controlled, for which the total required tug power can be based on the empirical formula.

As with all large ships for which strong tugs are needed, such as container ships in high winds and large loaded bulk carriers, care should be taken that the deck equipment of the ships to be handled are strong enough for the powerful tugs.
For smaller tows, requiring less than 40 tons of Bollard Pull, this formula is not applicable.

3.0 Finally

I hope that all will use the app and that it may help you to bring ships alongside in a safe way particularly during adverse weather conditions, but preferable during good days and calm seas. Any suggestion for improvement of the app is welcome.

I would like to thank Capt. Henk HENSEN for his advice and consultancy on the system, which has been invaluable.

Web link to free download the mobile application "Bollard Pull Calculation For Marine Pilots”;

Bollard Pull Calculator for Android

Bollard Pull Calculator for iOS

Important note: Please note that data provided by the application are based on theoretical calculations. The calculations give an indication of the required bollard pull and should always be handled with care.


Tug Use in Port. A Practical Guide. 2nd.Edition by Cpt.Henk HENSEN FNI OCIMFMooring Equipment Guidelines (MEG4) 4th Edition 2018
OCIMF Recommendations for ship´s fittings for use with tugs [2002]

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