The cable of a reaction ferry is loaded sideways by the current, and the tension it must carry is T = D ÷ (2 sin α), where D is the current’s force on the ferry and α the angle each half of the cable is pushed off the straight line. For a loaded 6 x 2.4 m scow drawing 0.30 m in a 2 m/s current, D is 3,600 N, and holding the ferry within 2 m of the straight line across a 40 m span takes 18.1 kN, a verified breaking load near 181 kN at a safety factor of 10, and anchors that hold that pull; a cable sagging 3-5% of its span carries only about 0.9-1.6 kN of tension from its own weight and would let the ferry swing far downstream.
Part of River Navigation & Ferry Systems
Cable installation is the work of spanning a river with a cable above flood level, anchoring it at both banks and tensioning it to carry the load of a ferry in the current.
The Cable Carries A Sideways Load That Grows As The Cable Straightens
A ferry in a current pushes the cable downstream at the point where it is attached. The cable bends into a shallow V in plan view, and each half pulls back with tension T at an angle α off the straight line. Resolving across the stream: D = 2 T sin α, so T = D ÷ (2 sin α). The flatter the V, the larger the tension: halving the deflection roughly doubles T. The tension is the same at both anchors, because the load is shared by two halves.
The carrier lists the options. Cable: salvaged steel cable 12-20 mm in diameter for most crossings, or heavy rope (manila, nylon, polypropylene) that needs more sag and stretches. Anchors: wrap round large trees with protection against the cable cutting the bark; a deadman, a large log or steel beam buried horizontally 1-2 m deep, attached by a vertical post or rod; or a rock anchor, bolted into solid rock. Sag: 3-5% of the span. That figure describes the vertical clearance of a cable carrying only its own weight; the calculation below shows that it is unrelated to the load a ferry puts on the cable.
What You Need
- Cable with a known breaking load, from its tag or a proof test (see Rope Strength Testing); weigh a measured length to get its mass per metre
- Anchors as in the options above, and an anchor load-test method
- A tensioning device: windlass or block and tackle (see Windlass and Block and Tackle)
- A measured span and heights from a survey (see Surveying)
- A flood mark for the highest water you have records of (see Flood Planning)
Method: Compute, Build, Prove
Step 1: Compute the current force D from the scow’s side area below the waterline and the highest current you will operate in (see Reaction Ferry).
Step 2: Choose the allowed midspan deflection y. Then α = arctan(y ÷ (span ÷ 2)) and T = D ÷ (2 sin α).
Step 3: Choose the breaking load with the safety factor: 10:1 where people are aboard, as the corpus gives for life safety.
Step 4: Size and build the anchors to hold T, in a direction along the cable.
Step 5: Install with the cable above flood level and hang it so the trolley reaches both banks.
Step 6: Proof-test. Load the anchors to 1.5 times the design load before use, the practice in Construction Methods for bridges, and measure the deflection under a known sideways load at midspan.
Worked Example: A 40 m Crossing
Ferry: 6.0 m long and 2.4 m wide, drawing 0.30 m when loaded to the 30 cm freeboard of the barge in Ferry Platform Design. Side area 6.0 × 0.30 = 1.8 m². At 2 m/s with a drag coefficient of 1 (an assumed order of magnitude), D = ½ × 1,000 × 2² × 1.8 = 3,600 N.
| Midspan deflection y | α = arctan(y ÷ 20) | T = 3,600 ÷ (2 sin α) | Breaking load at 10:1 |
|---|---|---|---|
| 1 m | 2.86° | 36.0 kN | 360 kN |
| 2 m | 5.71° | 18.1 kN | 181 kN |
| 4 m | 11.31° | 9.2 kN | 92 kN |
18.1 kN is the weight of 18,100 ÷ 9.81 = 1,845 kg: it is a force, not a mass. At 3 m/s in flood, D = ½ × 1,000 × 3² × 1.8 = 8,100 N and T for y = 2 m is 40.7 kN, with 407 kN for 10:1: the 2.25-fold rise of force with the square of speed, which is why the operating limit exists.
Now the carrier’s sag. Weigh a metre of your cable; suppose it is 0.95 kg/m (an illustrative input). Its weight per metre is 0.95 × 9.81 = 9.32 N/m. For a sag d the horizontal tension is H = wL² ÷ (8d). At 4% of 40 m, d = 1.6 m and H = 9.32 × 1,600 ÷ (8 × 1.6) = 1,165 N, and at 3% and 5% it is 1,553 N and 932 N. That is 0.9-1.6 kN, 5% to 9% of the 18.1 kN the ferry needs. With only 1.2 kN of tension, the small-angle deflection formula y = D × L ÷ (4H) gives 3,600 × 40 ÷ (4 × 1,165) = 31 m, which means the formula no longer applies: the cable would form a deep V and the ferry would drift to the bank. A cable that holds the ferry within 2 m has a vertical sag of only 9.32 × 1,600 ÷ (8 × 18,100) = 0.10 m, which is 0.26% of the span. Use the carrier’s sag as a check on clearance, not as the design.
Anchors: a gravity anchor block resists by friction under it, so size it from the friction coefficient and not from a flat multiple of the tension — see Suspension Bridge, which gives W ≥ 2T ÷ μ for a factor of safety of 2, i.e. 4T at μ = 0.5 and 5T at μ = 0.4. For T = 18.1 kN that is 72 to 90 kN, the weight of roughly 7,400 to 9,200 kg. An earlier version of this page cited a 1.5T rule from that article giving 27.1 kN; the rule was wrong and has been corrected there, because at μ = 0.5 a 1.5T block resists only 0.75T and slides; the 1.5 times load test above is the real check. To pull a cable to 18.1 kN with a windlass of 6.7:1 (from Windlass), the crank rope needs 18,100 ÷ 6.7 = 2,700 N, and with a 3:1 tackle added 900 N, so tensioning to full design load by hand is not practical; the cable reaches that tension only when it is loaded, which depends on its stretch, which you must measure.
Common Mistakes
- Using the carrier’s sag as the tension target — it gives about 1-1.6 kN against 18 kN.
- Anchoring to a living tree at height — the moment at the root is T × height; attach low.
- Sizing for average current — size for the flood limit.
- Skipping the proof test — it is the only check on anchors in unknown soil.
Safety
A parted cable whips and the ferry is swept away
A cable carrying 18 kN stores a great deal of energy, and a cable or anchor failure sends the loaded ferry downstream broadside. Stand clear of the line of the cable during tensioning and testing, mark the cable with floats or flags for boaters, keep the cable above flood level, and stop the ferry before the river reaches the limit.
What’s Next
- Learn next: Ferry Platform Design — the hull that goes on the cable
- Combine with: Landing & Dock Construction — where the cable ends