Ship Stability, Theory and Practice • Volume One: Foundations of Ship Stability

Chapter 11 — Suspended Weights and the Use of the Ship's Lifting Gear

The weight that moves before it moves

Learning objectives

By the end of this chapter you will be able to:

  1. explain why a suspended weight acts at the point of suspension from the instant the wire takes the strain;
  2. calculate the virtual rise of G and the equal loss of GM when a weight is lifted;
  3. handle a lift from the quay as a weight added at the head of the gear;
  4. find the list while a load hangs outboard, using the GM of the lifted condition;
  5. work a complete lift stage by stage, and identify the worst stage on which the lift is judged;
  6. size the heaviest permissible lift against a list or GM limit;
  7. plan counter ballast for a heavy lift, and price its free surface honestly.

Twice already this book has met the strangest rule in ship stability. In Chapter 6 a 60 t lift sent KG upwards before the load had visibly moved; in Chapter 7 the same load, swung outboard, listed the ship with a GM that had already shrunk. Both times the treatment was a single worked example and a promise. This chapter is the promise kept: the suspended weight in full, and with it the safe use of MV Ninja's own cranes, the everyday heavy machinery of a geared bulker's trade.

11.1 The point of suspension

A wire rope can pull only along its own length. Hang a load from a crane and let it swing where it will: whatever the load does, the force it exerts on the ship is the pull in the wire, and that pull passes always through the point of suspension, the head of the crane or derrick. So far as the ship's stability is concerned, the load might as well be bolted to the head. This is true from the instant the wire takes the strain, while the load still rests apparently innocent on the deck or the quay, and it remains true until the moment the load lands and the wire falls slack.

The weight that moves before it moves ON THE DECK ON THE WIRE G acts at its own Kg G₁ the head a weight resting on the structure acts where it rests the instant the wire takes the strain it acts at the head The wire can pull only along its own length, so wherever the load swings, its line of action passes through the point of suspension. Before the load has risen a centimetre, G has already jumped towards the head. Nothing else in this book moves so much stability so fast, which is why the lift is planned before the strain is taken.
Figure 11.1   On the deck, a weight acts where it rests. On the wire, it acts at the head, however long the fall of wire below it.

11.2 The virtual rise of G, and the loss of GM

For a weight already on board, the lift is simply Chapter 6's shift formula applied all at once: the weight w moves, in effect, from its stowage to the head, a vertical distance d, the moment the wire goes taut.

GGV = (w × d) ÷ ∆ MCA formula sheet, September 2020 — d measured from the weight's stowage to the head of the gear

And since KM has not moved, every millimetre that G rises is a millimetre of GM lost: the loss of GM equals the virtual rise of G. The word virtual earns its keep: nothing physical has climbed to the head, yet the ship behaves in every respect as if it had, and behaves so until the wire is slacked.

The virtual rise of G: a shift from the stowage to the head Worked example 11.1: MV Ninja's 60 t lift of Chapters 6 and 7, seen whole head, Kg 21.50 m the load, Kg 3.00 m G G₁ d = 21.50 − 3.00 = 18.50 m the lift is a shift of w through d, made all at once, the instant the wire goes taut GGᴠ = (w × d) ÷ ∆ = (60 × 18.50) ÷ 26000 = 0.043 m MCA formula sheet, September 2020 — the shift form of the GG formula, applied vertically and the metacentric height falls by the same amount: the loss of GM equals the rise of G KG jumps from 7.300 to 7.343 m; GM falls from 3.106 to 3.063 m. When the load lands, G settles wherever the load now rests: the head only rules while the wire is taut.
Figure 11.2   The lift as an instantaneous shift: w through d, from stowage to head. The rise of G is the fall of GM.
Worked example 11.1

MV Ninja, displacement 26000 t, KG 7.300 m, booklet KM 10.406 m, lifts 60 t with her crane from the bottom of a hold, Kg 3.00 m. The crane head is at Kg 21.50 m. Find the loss of GM the instant the wire takes the strain, and the GM during the lift.

d = 21.50 − 3.00 = 18.50 m

GGV = (w × d) ÷ ∆ = (60 × 18.50) ÷ 26000 = 0.043 m, so KG = 7.300 + 0.043 = 7.343 m, exactly as Worked example 6.6 found.

GM before = 10.406 − 7.300 = 3.106 m; GM during = 10.406 − 7.343 = 3.063 m: a loss of 0.043 m, equal to the rise.

Modest here, because the ship is stiff and the load light. Scale w up towards a crane's full working load on a tender ship, and this same line of arithmetic is the difference between a routine lift and a dangerous one.

11.3 Outboard: the list during the lift

A lift is rarely straight up and down: the whole purpose of the gear is reach. The moment the load swings outboard of the centreline, the suspended weight pulls G sideways exactly as Chapter 7 taught, and the ship takes a list. Both effects of the suspension now act together, and both against her: G has risen, so GM is down; and GGH grows with every metre of outreach.

GGH = (w × a) ÷ ∆,   then   tan(List) = GGH ÷ GM MCA formula sheet, September 2020 — a is the outreach; ∆ is the displacement with the load on board; the GM is that of the lifted condition
Swung outboard: G rises and leaves the centreline at the same instant outreach a the head the load, hanging over the water G G₁ G₂ first the rise: KG up, GM down, the moment the wire goes taut then the swing: GGᴴ grows with the outreach, and she takes a list GGᴴ = (w × a) ÷ ∆, then tan(List) = GGᴴ ÷ GM MCA formula sheet, September 2020 — and the GM in the triangle is that of the LIFTED condition both effects of the suspended weight act together, and always in the ship's disfavour The list leans the load further out, the gear feels the list, and the whole lift is judged at this, its worst moment.
Figure 11.3   Swung outboard: the rise and the swing of G happen together, and the list is calculated with the reduced GM.
Worked example 11.2

MV Ninja, displacement 26000 t, KG 7.300 m, is to load a 120 t transformer from the quay on her port side using her heavy derrick, head at Kg 21.50 m. At the moment the derrick takes the whole weight off the quay, the load hangs 15.0 m outboard of the centreline, about 3 m beyond the ship's side (her breadth is 24.20 m). All tanks are pressed full or empty. The booklet KM at 26120 t is 10.400 m. Find the KG, GM and list at that moment.

Lifting from the quay, the weight comes on to the ship the instant it leaves the ground, acting at the head:

new ∆ = 26000 + 120 = 26120 t

KG = (26000 × 7.300 + 120 × 21.50) ÷ 26120 = (189800 + 2580) ÷ 26120 = 192380 ÷ 26120 = 7.365 m

GM = 10.400 − 7.365 = 3.035 m

GGH = (120 × 15.0) ÷ 26120 = 1800 ÷ 26120 = 0.0689 m; tan(List) = 0.0689 ÷ 3.035 = 0.0227, so List = 1.3° to port, towards the quay

Note the bookkeeping: a lift from ashore is a loading, done with the moments table at the increased displacement, with the weight's Kg taken as the head. Compare Worked example 11.1, where the 60 t was already on board and the lift was a shift. Same principle, different table entries.

11.4 The whole lift, stage by stage

A complete heavy lift is four different ships in the space of ten minutes, and the officer of the watch should be able to write down all four before the wire is bent on. The transformer of Worked example 11.2 tells the whole story.

One lift, four ships: the stages of Worked example 11.3 the 120 t transformer, from the quay to the bottom of No.3 hold 1. alongside, beforeKG 7.300 mGM 3.106 mupright 2. at the head, over the quayKG 7.365 mGM 3.035 mlist 1.3° towards the quay 3. plumbed over the holdKG 7.365 mGM 3.035 mupright again 4. landed low in the holdKG 7.278 mGM 3.122 mupright Stage 2 is the whole plan: highest G, least GM, and the listing moment, all at once the lift is approved or refused on the numbers of stage 2, never on the comfortable ones either side of it Notice the end state: the heavy load has gone LOW, so she finishes stiffer than she began; and notice stage 3, where the listing moment has gone but the virtual rise remains until the wire is slacked.
Figure 11.4   The four stages of the transformer lift. Stage 2 carries the highest G, the least GM and the listing moment all at once: the lift is judged there.
Worked example 11.3

Continue Worked example 11.2: the transformer is swung inboard until it hangs plumb over No.3 hold, then landed on the tank top at Kg 2.50 m. Find the ship's KG and GM at each remaining stage, and confirm the landed condition by two routes.

Plumbed over the hold: the weight still acts at the head, so KG remains 7.365 m and GM 3.035 m; but the outreach is gone, GGH = 0, and she stands upright again. The virtual rise outlives the list.

Landed, route A (shift from head to tank top): GGV = 120 × (21.50 − 2.50) ÷ 26120 = 0.087 m down; KG = 7.365 − 0.087 = 7.278 m

Landed, route B (moments from scratch): KG = (26000 × 7.300 + 120 × 2.50) ÷ 26120 = 190100 ÷ 26120 = 7.278 m

GM = 10.400 − 7.278 = 3.122 m. Two routes, one answer; and she finishes stiffer than she began, because 120 t now lies deep in the ship. The dangerous stage was never the destination: it was the journey through the head.

Worked example 11.4

Port regulations limit MV Ninja's list during cargo work to 2°. With the ship at 26000 t, KG 7.300 m, head at Kg 21.50 m and full outreach 15.0 m, what is the heaviest single lift she may take from the quay? (Booklet KM by interpolation at each trial displacement.)

The condition to satisfy is tan(2°) = 0.03492 = GGH ÷ GM with every quantity depending on w, so the equation is solved by trial. Try w = 180 t:

∆ = 26180 t; KG = (189800 + 180 × 21.50) ÷ 26180 = 193670 ÷ 26180 = 7.398 m

KM at 26180 t (interpolated) = 10.398 m, so GM = 10.398 − 7.398 = 3.000 m

GGH = (180 × 15.0) ÷ 26180 = 0.1031 m; tan(List) = 0.1031 ÷ 3.000 = 0.0344, List = 1.97°: just inside the limit.

Try w = 185 t: ∆ = 26185 t; KG = 193777.5 ÷ 26185 = 7.400 m; KM = 10.398 m; GM = 2.997 m; GGH = 2775 ÷ 26185 = 0.1060 m; tan(List) = 0.0354, List = 2.03°: just outside.

Interpolating between the two trials, maximum lift ≈ 183 t (a direct check at 183 t gives KG 7.399 m, GM 2.998 m, GGH 0.1048 m, tan(List) = 0.0350, List = 2.0°). Notice why the answer is not simply proportional: every added tonne raises G and thins GM even as it adds listing moment, so the list climbs faster than the load; had GM stayed at its unlifted 3.106 m, the same 183 t would have listed her only 1.9°. Figure 11.5 draws the curve.

How heavy a lift may she take? The list grows with the load Worked example 11.4: outreach 15.0 m, head Kg 21.50 m, from ∆ 26000 t, KG 7.300 m; booklet KM at each ∆ + w 0.51.01.52.5 2.0° limit 183 t 04080120160200240 lifted weight w in tonnes; list in degrees while the load hangs at full outreach The curve steepens because every added tonne raises G and trims GM even as it adds listing moment: 183 t meets the ceiling.
Figure 11.5   Worked example 11.4: list against lifted weight at 15.0 m outreach. The curve steepens as GM thins; 183 t meets the 2° ceiling.

11.5 Preparing the ship: counter ballast, and its price

The professional lift begins hours before the wire is bent on. The GM of the lifted condition is calculated and checked against the booklet; slack tanks are pressed up or stripped so the free surfaces of Chapter 9 do not gnaw at a GM already thinned by the lift; and, for a heavy lift at reach, ballast is often run to the off side beforehand, so the ballast moment stands ready to meet the lifting moment and the ship works nearly upright through the worst stage. A transfer between a pair of double bottom tanks at the same height leaves KG untouched, but it usually leaves both tanks slack, and their free surface moments, i × density of the liquid for each tank from the booklet tank tables, must be priced before pumping.

Trimming her for the lift: counter ballast, and what it costs Worked example 11.5: the 120 t lift to port, met by ballast run to starboard beforehand No.3 D.B. (P) No.3 D.B. (S) 119 t run to starboard across 15.12 m 119 × 15.12 = 1799 t m of moment to starboard, ready and waiting for the lift's 1800 t m to port but two tanks now slack: booklet i = 2669 m⁴ each, FSM = i × 1.025 = 2736 t m, and Chapter 9 sends its invoice FSC = ΣFSM ÷ ∆ = 5471 ÷ 26120 = 0.209 m: fluid GM 3.035 falls to 2.826 m still ample here, but on a tender ship the cure can cost more than the disease: always price the free surface The seamanlike compromise: run the counter ballast, take the lift, then press one tank full and strip the other.
Figure 11.6   Worked example 11.5: counter ballast sized to meet the lift's moment, and the free surface invoice that comes with it.
Worked example 11.5

Before the 120 t transformer lift of Worked example 11.2 (moment at full outreach 120 × 15.0 = 1800 t m to port), ballast is to be run from No.3 D.B. (P) to No.3 D.B. (S). From the booklet the centres of the two tanks are 7.56 m either side of the centreline, both at Kg 1.12 m, and the free surface inertia of each is i = 2669 m4; the ballast is salt water. How much should be transferred to hold her upright at the worst stage, and what does the transfer cost if it leaves both tanks slack?

The transfer distance is 2 × 7.56 = 15.12 m. Counter moment required = 1800 t m, so w = 1800 ÷ 15.12 = 119 t to starboard (119 × 15.12 = 1799 t m against the lift's 1800 t m). Both tanks are at the same Kg, so KG is unchanged; but before the strain is taken the ballast alone lists her 1.4° to starboard (GGH = 1799 ÷ 26000 = 0.0692 m against a fluid GM of 2.895 m).

The price: two slack tanks. The booklet lists the free surface inertia i, and FSM = i × ρ = 2669 × 1.025 = 2736 t m per tank of salt water; ΣFSM = 2 × 2736 = 5471 t m; FSC = 5471 ÷ 26120 = 0.209 m; the fluid GM at the worst stage falls from 3.035 to 2.826 m. Without the counter ballast, but with the two tanks slack, the same stage would list her 1.4° to port (tan(List) = 0.0689 ÷ 2.826 = 0.0244) against the 1.3° of Worked example 11.2 with solid tanks.

Ample, on this stiff ship in this condition. But the lesson generalises: the cure has a cost, and on a tender ship the free surface bill can exceed the listing problem it was meant to solve. Price both sides before pumping, with the booklet tank data (FSM = i × density of the liquid), exactly as Chapter 9 taught; and when the lift is over, press one tank full and strip the other.

Worked example 11.6

A small general cargo ship, displacement 8000 t, breadth 18.0 m, KG 7.20 m, KM 7.95 m, is to lift 45 t from the quay with her derrick: head at Kg 17.0 m, the load 11.0 m outboard of the centreline at lift off. Find her list at the moment of lift off, and comment.

∆ = 8045 t; KG = (8000 × 7.20 + 45 × 17.0) ÷ 8045 = 58365 ÷ 8045 = 7.255 m

GM = 7.95 − 7.255 = 0.695 m (taking KM as unchanged for so small a weight)

GGH = (45 × 11.0) ÷ 8045 = 0.0615 m; tan(List) = 0.0615 ÷ 0.695 = 0.0885, so List = 5.1°

A smaller sideways shift of G than the transformer gave MV Ninja (0.0615 m against 0.0689 m) gives this ship a list four times greater, five degrees against 1.3°, because her GM in the lifted condition is under a quarter of the bulker's. The gear does not know or care how stiff the ship is; the officer must. The GM check comes first, always, and a lift that a big ship shrugs off can put a small one's deck edge towards the water.

11.6 Onwards

Every calculation in this chapter leaned on one number read from the booklet: KM at the working displacement. Chapter 12 asks where that column really comes from, and answers with a picture, the metacentric diagram, in which KB and KM are drawn as curves against draught and the ship's initial stability can be read straight from her geometry.

Looking ahead: the ship's geometry drawn as two curves KM against draught KB against draught 3579 5101520 draught in metres; heights above the keel in metres Chapter 12 draws the hydrostatic table as a picture, and explains why KM falls, flattens, and rises again.
Figure 11.7   Looking ahead: MV Ninja's own KM and KB drawn against draught, the metacentric diagram of Chapter 12.

Interactive: conduct the lift yourself

Set the load, take the strain, and swing it outboard. G climbs the ladder the instant the wire goes taut; the ship settles to her calculated list as you swing; the verdict panel judges the lift. The drawn heel is exaggerated four times.

Load on the tank top. Take the strain to begin.
a = 0.0 m
KG = – m GM = – m list = – —

Interactive: the four stage calculator

The whole of Section 11.4 as a live table, preloaded with the transformer lift. Change any figure and watch all four stages follow. The lift is from the quay; the load lands at the hold Kg.

Stage∆ (t)KG (m)GM (m)List
1. alongside, before–––upright
2. at the head, over the quay––––
3. plumbed over the hold–––upright
4. landed in the hold–––upright

Chapter summary

Self test questions

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Chapter 11: Suspended Weights and the Ship's Lifting GearSelf test score: 0 / 10