1. Introduction & the three phases (5.1)
Source: HENSEN, Henk. Tug Use in Port: A Practical Guide. 4th ed. Rotterdam: STC Publishing, 2021. Chapter 5 — Bollard pull required.
Edital: Anexo 2-B, Área II (Arte Naval / Shiphandling), item 9 (Hensen) → Chapter 5 — Bollard pull required · Anexo 2-A, Área II, item 26 (Utilização de rebocadores portuários — cálculo do bollard pull necessário) com itens 4 (Emprego de rebocadores na manobrabilidade) e 31 (Métodos de utilização de rebocadores empregados no Brasil).
Chapter 4 asked what each tug type can do. Chapter 5 asks the quantitative question that follows: how much bollard pull is actually needed to handle a given ship safely? In practice tug configuration, number of tugs and total bollard pull are set by a pilot's experience, varying with port and circumstances, and the system generally works. But as ships grow, experience alone becomes too narrow a basis, so accurate data on wind, current and wave forces becomes essential — especially for large container ships, car carriers and deep-draught tankers or bulk carriers in confined ports and bad weather.
There is also commercial pressure: shipping companies try to minimise tug costs, which sparks disputes over the minimum number of tugs. A ship with bow and/or stern thrusters often uses one or two tugs fewer, but side-thruster power is limited and its effectiveness falls off very fast once the ship gathers headway. A pilot and master who understand the forces are in a far better position to settle these arguments and make the right call.
5.1 The three phases of an arrival or departure
Tug assistance generally falls into three phases as a ship arrives or leaves:
- Reasonable-speed phase. The ship still uses engine and rudder to compensate drift from wind, current and waves by steering a drift angle; tugs may assist.
- Intermediate phase. Reducing speed to enter a dock, basin or turning circle, or to approach a berth — and stopping within a set distance. As speed falls, steering performance drops, the propeller is stopped, wind and current bite harder, and tug assistance is needed more often and more fully.
- Final phase. The ship is practically dead in the water (turning circle, berthing): very restricted, unable to compensate wind and current itself, so tugs must assist fully.
2. Factors influencing total bollard pull & the two situations (5.2–5.2.1)
2.1 The main factors (5.2)
Five groups of factors govern the tug assistance needed:
- Port particulars — fairway and entrance restrictions, passage to the berth, turning circle, manoeuvring space, stopping distance, locks, bridges, moored vessels, water depths, speed limits. The port is a more or less constant factor that fixes a basic number, type and total bollard pull for a class of ship, from local experience (sometimes simulator studies).
- Berth construction — open (e.g. jetty) or solid; it affects the transverse approach speed (§ 2.5 here).
- The ship — type, size, draught and underkeel clearance, trim, windage, engine power ahead/astern, propeller type, manoeuvring performance, side thrusters and special rudders.
- Environmental conditions — wind, current, waves, visibility, ice.
- Method of tug assistance — towing on a line, operating at the ship's side, or a combination.
On top of the port layout, the varying environmental factors that drive the required total bollard pull for a particular ship are wind, current and waves — weighed against ship size, draught, windage and underkeel clearance. (Reduced visibility mainly concerns fog safety procedures, not the magnitude of bollard pull, so it is not pursued here; ice was covered in Chapter 3.) In theory tugs compensate the total force when bollard pull equals the combined wind + current + wave forces. In practice several things eat into that ideal:
- Tugs do not always pull or push at right angles — when the ship has fore-and-aft movement or there is a current with relative speed through the water, a tug spends power keeping pace, at the expense of useful pull or push.
- Available bollard pull may be below the original test figure because of wear and fouling.
- Forward and after tugs often cannot pull or push at full power at the same time: if the ship starts to swing, one end must reduce power to stop it.
- Propeller wash from a tug towing on a line can hit the hull and cut pulling effectiveness (correct towline length and angle help).
- Tugs need reserve power to push or pull against wind and current and to stop a drifting ship and bring it back to track.
2.2 The two basic situations (5.2.1)
To find the total required bollard pull, two fundamentally different situations must be separated, because each needs its own approach:
- External forces — wind, current and waves that tugs must compensate. This dominates for ships with high windage (container ships, car carriers, gas carriers, light tankers/bulkers). These forces can be calculated, and the required tug force follows from the result.
- The ship's mass — as with loaded tankers and bulk carriers. Currents usually play no role (apart from a cross current near a jetty) and wind has relatively little effect; what counts is the large mass.
3. Wind forces (5.2.2)
Wind force on a ship is computed from three formulae — lateral force, longitudinal force and yaw moment:
Longitudinal force: $F_{Xw} = 0.5\,C_{Xw}\,\rho\,V^2 A_T$ [N]
Yaw moment: $M_{XYw} = 0.5\,C_{XYw}\,\rho\,V^2 A_L\,L_{BP}$ [N·m]
where $C_{Yw}$, $C_{Xw}$, $C_{XYw}$ are the lateral, longitudinal and yaw-moment wind coefficients; $\rho$ is air density (kg/m³); $V$ is wind velocity (m/s); $A_L$ the longitudinal (broadside) wind area and $A_T$ the transverse (head-on) wind area (m²); $L_{BP}$ the length between perpendiculars (m). The coefficients depend on the ship's form, draught, trim, superstructure (bridge, deckhouses, masts, ramps) and the wind's angle of attack, and are found from wind-tunnel model tests. Deck cargo, as on container ships, must be included in the wind area.
For tankers the coefficients are tabulated in Prediction of Wind and Current Loads on VLCCs and OCIMF's Mooring Equipment Guidelines. Lateral forces are largest and so most important for bollard pull. For beam winds $C_{Yw}$ runs about 0.8 to 1.0, mostly 0.9–1.0. Taking $C_{Yw} = 1.0$, air density 1.28 kg/m³, and giving the result in kilograms instead of newtons, the beam-wind force simplifies to $F_{Yw} = 0.065\,V^2 A_L$ kgf. Adding 25 % to allow a 20 % safety margin gives Hensen's handy working formula:
($V$ in m/s; $A_L$ = longitudinal wind area in m²; graph in Fig. 5.2 is built on this.)
The graph (Fig. 5.2) is only valid for tugs towing on a line, or pulling at a ship's side on a fairly long towline. The included 20 % safety factor is sometimes effectively larger, because a $C_{Yw}$ of 1.0 is allowed where the real value may be only 0.8–0.85 (hard to judge in daily practice). The original graph was produced by the UK National Ports Council (Sept. 1977), modified for the book.
3.1 Wind from other directions, gusts and height
For winds not from abeam, the total bollard pull can be roughly read from the beam-wind figure: between abeam and up to about 30° each side of abeam, the requirement is nearly the same as for a beam wind. Yaw moment is generally largest for quartering winds (depending on ship type, loading, trim and deck cargo). Wind is never steady, so do not use only an hourly or 10-minute mean — allow for the higher winds over shorter periods (e.g. a 1-minute mean) and for gusts and squalls; a recording wind meter at a pilot or harbour station gives the best data, and PIANC gust factors can relate mean speeds to short-period maxima.
Wind speed also varies with height, per the graph (Fig. 5.4) built on $V_w = v_w\,(10/h)^{1/7}$, where $V_w$ is the velocity at 10 m, $v_w$ the velocity measured at elevation $h$ (m). For the formulae, use the standard 10 m velocity; speeds measured at another height are converted with this relation. For some ships the 10 m standard is too high or (for big loaded container ships, car carriers, gas carriers) too low — then transfer the 10 m value to the required height via Fig. 5.4. A wind meter on top of a ship's mast usually gives a safe approximation for lateral wind force.
4. Current forces (5.2.3)
Current forces are calculated like wind forces. For completeness the OCIMF formulae are:
Longitudinal force: $F_{Xc} = 0.5\,C_{Xc}\,\rho\,V^2 L_{BP}\,T$ [N]
Yaw moment: $M_{XYc} = 0.5\,C_{XYc}\,\rho\,V^2 L_{BP}^2\,T$ [N·m]
where $C_{Yc}$, $C_{Xc}$, $C_{XYc}$ are the current coefficients; $\rho$ = water density (kg/m³); $V$ = current velocity (m/s); $L_{BP}$ = length between perpendiculars (m); $T$ = draught. The coefficients depend on underwater shape, draught, trim and angle of attack — and are very strongly affected by underkeel clearance; they come from test-tank models and/or CFD.
For bollard pull, the maximum transverse force of a crosswise current matters, given by $F_{Yc} = 0.5\,C_{Yc}\,\rho\,V^2 L_{BP}\,T$. The lateral coefficient for a cross current in deep water is about 0.6 (the OCIMF value for loaded tankers). With $C_{Yc}=0.6$, salt-water density 1,025 kg/m³, 25 % added for loss of tug effectiveness, and the result in kilograms, the approximate bollard pull for a cross current in deep water becomes:
This deep-water form is valid only where water depth is more than six times the ship's draught. But port underkeel clearances are often small, where current forces matter at least as much. As clearance falls the required bollard pull rises sharply (25 % for safety is included in every case):
| Underkeel clearance | Approximate formula | Relative to deep water |
|---|---|---|
| Deep water (> 6 × draught) | $F_c = 40\,V^2 L_{BP}\,T$ | ×1 (baseline) |
| 1.5 × draught | $F_c = 110\,V^2 L_{BP}\,T$ | ≈ ×2.8 |
| 20 % of draught | $F_c = 150\,V^2 L_{BP}\,T$ | ≈ ×3.8 |
| 10 % of draught | $F_c = 185\,V^2 L_{BP}\,T$ | ≈ ×4.6 (nearly five times) |
The graph (Fig. 5.5) is based on these formulae and OCIMF loaded-tanker coefficients (MEG, 3rd ed.), with a 20 % margin, and is valid only for towing on a line or pulling alongside on a not-too-short towline. Fig. 5.6 shows the same effect: starting from a 10-ton current force, the same current velocity produces a strongly rising force on the same ship as clearance decreases.
Small underkeel clearance does more than raise current forces: it enlarges the turning diameter, cuts rudder effectiveness and lengthens the stopping distance — so tug assistance may be welcome for safe handling. It also lengthens the time to swing a ship around: the transverse forces to overcome fore and aft of midships grow as clearance falls, so swinging takes longer unless more bollard pull is used.
5. Wave forces; mass & berth construction (5.2.4–5.2.5)
5.1 Wave forces (5.2.4)
Wave forces may also count when setting the bollard pull, depending on conditions in and around the port. Harbour tugs only work effectively up to a maximum wave height (Chapter 4), so only short beam seas are considered. Exact calculation is hard; it is assumed the ship's draught is large enough to reflect the waves completely, and that the short wave period causes no ship motion — i.e. the windy-but-sheltered case, short steep waves whose length is small relative to the ship (not open-water ocean swell that makes the ship heave, roll and pitch). The force per metre of ship length from such short-period waves is about $F_{wave} = 0.5\,\rho\,g\,\zeta^2$ N; since the hull is not flat over its whole length and draught, the total force is roughly $F_{wave} = 0.35\,\rho\,g\,\zeta^2 L$ N, where $\rho$ = seawater density, $L$ = waterline length (take $L_{BP}$), and $\zeta$ = wave amplitude = ½ × significant wave height $H_s$. Adding a 25 % margin and converting to kilograms with $H_s$:
($L$ = waterline length ≈ $L_{BP}$ in m; $H_s$ = significant wave height in m. Graph: Fig. 5.7.)
5.2 The effect of ship's mass and berth construction (5.2.5)
Tugs need reserve power to stop a drifting ship — and a comparable situation arises at berthing. An arriving ship is stopped parallel to the berth, then pushed, pulled or heaved alongside; wind, current and even waves may also push it onto the berth. The ship gains transverse speed that tugs must slow to "dead in the water" — or to a safe berthing speed when it touches the fenders. So tugs both oppose wind/current/wave forces and reduce the transverse approach speed, needing extra bollard pull. Even with no wind, current or waves, bollard pull is needed to control transverse speed.
Berth construction also affects approach speed: solid berths reduce it (a water cushion builds up between ship and berth), while open berths or jetties do not (the water can flow away). Taking virtual mass as 1.8 × displacement and accounting for berth construction, a rough indication of the tug force to stop sideways movement is:
Solid berths: $F = \dfrac{0.07\,D\,V_i^2}{S}$ [tons]
($V_i$ = initial speed in m/s; $D$ = displacement; $S$ = stopping distance in m; based on zero final speed.)
Safe final approach speeds for VLCCs are generally a maximum of 6–8 cm/s. Three Hensen examples assume an initial 0.5 knots (0.25 m/s), tugs starting to pull 30 m from the berth, zero transverse speed at contact:
| Ship | Berth | Tug force to stop in ~30 m |
|---|---|---|
| 250,000 dwt ballasted tanker (LOA 340 m, beam 38 m, draught 9 m, displ. 124,000 t) | Open jetty | ≈ 23 tons |
| 250,000 dwt loaded tanker (draught 20.4 m, displ. ~300,000 t) | Open jetty | ≈ 60 tons |
| Container ship (LOA 294 m, beam 32.2 m, draught 12.2 m, displ. 80,000 t) | Solid berth | ≈ 12 tons (stop in ~one ship's width) |
These confirm experience: large-displacement ships need large stopping forces, and berth construction influences approach speed. Loaded tankers and bulk carriers need the most tug power for transverse speed and are less affected by wind; any current should ideally run in line with the berth (not always so), and tugs need reserve to compensate it. As draught decreases the bollard pull for transverse speed falls, while lateral wind area rises — so freed-up bollard pull can be used to hold the ship up into wind, current and/or waves. Newer tugs can run a limited time at 110 % MCR, giving extra bollard pull in critical situations. The transverse-speed need for loaded tankers and bulkers is included in the displacement formula of § 8 (5.3.1).
6. Tug wash effects (5.2.6)
In certain pulling situations a tug's propeller wash hits the ship's side, bow or stern and cuts pulling effectiveness. The smaller the ship's underkeel clearance, the worse the effect, and increasing revolutions or thrust makes it worse still, because the counter-effect grows with a larger, more concentrated wash. Proper towline length and angle reduce it: the less the underkeel clearance and the more power needed, the longer the towline should be.
6.1 Towing positions (Fig. 5.11)
For a ship stopped in the water, Hensen ranks towing positions by their loss to propeller wash:
- Positions 1f / 1a (right at the bow / stern) — high chance of losing pulling effectiveness, wash hitting bow and stern almost at right angles; hull form, bow/stern shape and a large bulbous bow all matter, and the wash can even turn the ship the wrong way.
- Positions 2f / 2a — somewhat less loss than 1f / 1a.
- Positions / directions 3f / 3a — the most effective regarding wash loss.
- Positions 4f / 4a (operating at the ship's side) — large loss when pulling; in push-pull mode, with short towlines, pulling effectiveness can drop below 50 %, depending on how close the propellers are to the hull.
6.2 Keeping the propellers clear
Tug propellers should be as far as possible from the hull. Conventional tugs towing on a line have their propellers closer to the hull than tractor, reverse-tractor and ASD-tugs; the latter two, towing or pulling over the bow, have them furthest away — important for tugs working at a ship's side or in narrow basins on short lines. VS tugs have a less pronounced wash than conventional or azimuth tugs (especially nozzled ones), so the negative effect on a ship's side is less; independently controlled azimuth thrusters can be set at a small angle to deflect the wash. So forward and aft line-tugs minimise the loss by appropriate towline length, towing angle and/or thruster setting — a towing winch is very useful for adjusting line length.
7. Bollard pull from environmental conditions (5.3–5.3.1)
In assessing the required bollard pull, equal power forward and aft is assumed — which is not always true. Yaw moments from wind depend on wind force, angle of attack and the ship's above-water profile (varying with draught, trim and deck cargo); from current they depend on velocity, angle of attack and the underwater profile, and increase as underkeel clearance falls. Yaw moments are generally largest with quartering winds and currents, and may demand more bollard pull at one end. A further point: pulling a ship off a berth brings in the lateral underwater resistance — on a ship with large stern trim the centre of that resistance lies aft of midships, so the after tug(s) must use more power than the forward tug(s) to pull it parallel off; a ship down by the head may need more forward. Because these moments vary so much, only the total bollard pull is considered; how much fore and aft must be judged case by case — so experience is indispensable.
7.1 Worked example — container ship with wind, current and waves
| Source of force | Graph | Bollard pull |
|---|---|---|
| Onshore wind | Fig. 5.2 | 117 tons |
| Crosswise current | Fig. 5.5 | 42 tons |
| Waves (281 m × 30 kg) | Fig. 5.7 | 8 tons |
| Total bollard pull required | — | 167 tons |
To compensate wind + current + waves, four tugs of at least 40 tons are needed; the total already includes a safety factor of at least 20 % (= 33 tons), enough also to control approach speed. With no current or waves, four tugs of ~30 tons (or two of 60 tons) would handle the wind alone.
7.2 Crediting a bow thruster
Most container ships, car carriers and ro-ros have bow (or bow and stern) thrusters. For a ship dead in the water, 100 hp ≈ 1.1 tons force, 100 kW ≈ 1.5 tons force (stern thrusters somewhat less). A 2,500 hp (1,840 kW) bow thruster on the example ship gives about 28 tons less bollard pull forward — enough, against wind alone, to drop from four 30-ton tugs to three (one forward, two aft).
When tugs work in push-pull mode on short towlines, holding a ship up into wind, current and/or waves, increase the graph pull by at least 20 %. For the example container ship with a bow thruster and a 30-knot onshore wind, that is about 140 (117 + 20 %) − 28 (bow thruster) = 112 tons: roughly a 40-ton tug at the forward shoulder and two of 35 tons at the after shoulder.
8. Large displacements & tug use in ports (5.3.2–5.3.3)
8.1 Ships with large displacements (5.3.2)
As noted in § 2.2, large-mass ships need a different, experience-based approach. For loaded tankers and bulk carriers Hensen gives an empirical formula based on displacement:
This includes the transverse-speed control discussed in § 5. (Note 6: where tugs assist station-keeping at offshore installations — SPMs, F(P)SOs — the same bollard-pull logic broadly applies, with further guidance in the OCIMF publications Recommendations for ships' fittings for use with tugs and Mooring Equipment Guidelines.)
8.2 Number and bollard pull of tugs used in ports (5.3.3)
There is no uniform world system linking ship size to number and power of tugs. Calculations are mostly on length overall, but deadweight, displacement or gross tonnage are also used. Decisions rest mainly on experience: a standard number/bollard pull serves most ships and situations, while large ships and special cases are assessed separately by the pilot and/or port authority, in consultation with the master, sometimes with simulation.
In most ports masters or pilots are free to order the number and power of tugs they judge necessary. In some — a number of Far East and Australian ports, and some large oil terminals — a fixed (minimum) number and power is compulsory, depending on ship type, size and draught, conditions, berth location and berthing side; a reduction is sometimes allowed for side-thruster ships. Figures 5.15–5.17 plot tug use (minimum, maximum, average total bollard pull and average number of tugs) for general-cargo ships, container vessels, tankers and bulk carriers in a number of ports:
- Reading the graphs. The upper line is the requirement for more difficult situations; the lower line for normal and easier ones.
- Departures / part-loaded / ballast sometimes use fewer tugs or less bollard pull than shown.
- Thrusters. A bow thruster may (not in every port) allow one tug fewer; bow + stern thrusters sometimes two fewer.
- Cross-check. The average for bulk carriers and tankers (Figs. 5.15–5.16) roughly matches the displacement formula for deadweight up to about 230,000 tons.
9. Engine/rudder failures, stopping & summary (5.3.4–5.3.6)
9.1 Loss of propulsion and rudder failures (5.3.4)
One situation needing tugs may strike without warning: engine failure. In 2014, 88 loss-of-propulsion incidents were reported in the ports of San Francisco, Los Angeles/Long Beach and San Diego — of these 14 were fuel-switching related and 26 suspect-fuel related. Other possible causes of main-engine failure:
- Blackout; poor or contaminated fuel oil (fines, water, bacteria); inadequate fuel-changeover procedure entering or leaving a SECA.
- Failure of starting air — too many engine starts and stops while manoeuvring depletes the start bottles, so the engine may fail to start at a critical moment (e.g. docking); monitor start-air pressure and tell the bridge team the maximum consecutive starts available.
- Loss of control air or lubrication; automated engine shutdown or slowdown at a critical time.
Planning tug assistance for such failures is almost impossible, but awareness lets precautions be taken in tug type and positioning so the ship can be kept under control — e.g. after tugs with omni-directional propulsion that can brake speed and assist steering.
9.2 Stopping by tugs (5.3.5)
A loss of propulsion may need tugs to stop a ship with headway. The safest preparation is to have tugs that can immediately generate full braking power even as speed drops or is already low (e.g. 6 knots): tugs with omni-directional propulsion (ASD, ATD, Rotortug, Voith) as a stern tug, or carrousel tugs turned to the most effective braking position, or tugs with one azimuth thruster forward and aft oriented for full braking. The stopping distance can be approximated by:
($V_{kn}$ = speed in knots; $S$ = stopping distance in metres; $BP$ = bollard pull in metric tons.)
9.3 Summary (5.3.6)
- For wind-affected ships (container, ro-ro, car carriers, gas carriers, tankers/bulkers in ballast), approximate the bollard pull with the cross-wind graph; add current and wave graphs as needed.
- Account for the assisting mode: for tugs alongside on short towlines, increase the wind/current/wave graph results by roughly 20 % when pulling.
- For large-displacement ships, use the displacement formula; for a rough check of transverse-speed control, the § 5 (5.2.5) formula serves.
- The port-use graphs indicate the bollard pull for more difficult vs more normal situations; ships with side thrusters, part-loaded or departing may use less.
- Arrange tug placement so that, on an engine failure, the ship can still be kept under control. (Note 8: for FPSOs see the OCIMF FPSO Heading Control Guidelines and Static Towing Assembly Guidelines.)
10. Tariffs, fleet efficiency & powerful vs varied tugs (5.3.7–5.3.8)
10.1 Influence of tariffs on tug availability (5.3.7)
Shipping companies pay for tugs (sometimes within port dues). Tariffs are usually based on ship size and the number or total bollard pull of tugs; many ports charge extra for assistance in adverse weather (strong wind, ice, fog), at night, at weekends, or when assistance runs over a basic time. Because tariffs affect how many tugs are used, they deserve attention — though circumstances and tariffs differ by port.
Ship arrivals and departures are irregular (dock-labour hours, wind and tidal windows), so ships cluster at peak hours (slack or high water). The number of tugs a port keeps is set partly by peak traffic, and tugs busy at the peak sit idle outside it — peaks hurt efficient fleet employment. A company could cut tug numbers for efficiency, but that erodes peak-hour availability, causing waiting time or fewer tugs per move — a safety concern. Ships with side thrusters, twin screws, high-lift rudders and large windage (big container ships, cruise ships, ferries, car carriers, ro-ros) often use no tugs, or a minimum — except when wind rises (possibly after weeks of calm), straining availability just when several ships suddenly need tugs.
Depending on traffic, a more efficient fleet — without hurting availability — can use fewer but more powerful units, so fewer tugs per ship (e.g. for large tankers or bulkers) and fewer idle outside the peak. Where availability and tug power become a problem, a review of fleet and tariffs may be needed, possibly toward fewer high-power units. Regular meetings between port authorities, towing companies, shipping companies and pilots help keep service acceptable without raising tariffs too far; a basic tug tariff inside the port tariff could be considered to ensure minimum availability. Pilots should be free to assess the minimum tug requirement to handle a ship safely; it is reasonable that cost is a factor for the shipping company, but economy must never come before safety. A good contract stating the number and bollard pull of tugs — and covering when extra power is needed (adverse weather) — is strongly recommended, so the required tugs are available without extra cost.
10.2 Powerful tugs, or a variety of tug power? (5.3.8)
Several ports trend toward fleets of only powerful tugs (e.g. 60–100 tons bollard pull), understandable with rising ship size. But there are drawbacks. Fewer, more powerful tugs (say two 60-ton tugs instead of four 30-ton tugs) carry a redundancy risk: