Here the text of the word document accompanying the diagrams
Cascaded downhaul
Most catamaran downhaul systems today are of the uncascaded type. Meaning that the overall purchase is equal to the number of loops around the blocks of the system. Often this limits the purchase of these downhaul systems to 1:8 as a result of friction and the overall size of the setup.
Cascaded purchase systems, as often used in monohulls and yachts, are more efficient in friction as well as overall size of the setup. The Taipan 4.9 catamaran and A-cats use a simple (1st order) cascaded system for their downhaul. Often these are fully fitted inside the mast sections of these catamarans. The first stage boosts the force from 1 to 6 (purchase 1:6). This force is than boosted again by a simple 1:2 setup to an overal purchase of 1:12 . See the drawing.
The system used on the Typhoon F16 achieves the same 1:12 overall purchase by adding another stage. This 2nd order cascaded system first boost the force by a simple 1:2 which is followed in series by a 1:3 and the same 1:2 that was used in the Taipan 4.9 system. 2 times 3, times 2 equals 12.
The advantages of the Taipan / A-cat system are increased purchase for reduced size and the use of less blocks. The advantages of the Typhoon F16 system are yet again reduced size and the use of even less blocks combined with reduced friction as the line in the second stage can have a much smaller diameter than the others as this line isn’t held in the hand or subject to wear against the boom and fittings. Also the total number of 180 degrees loops around blocks have been reduced from 9 to just 7. Together this will result in reduced friction and therefor lower downhaul line loads on the hands to achieve the same net downhaul force.
An added advantage of the Typhoon F16 setup is that is uses less hardware and therefor is less expensive than the Taipan setup. Even more so with respect to the non cascaded systems. The reduction is respectively from 11 to 8 and 13 to 8.
A drawback is that a cascaded systems requires the room to allow longer travelled lengths of individual blocks. It is less square like than a non-cascaded system.
Example :
The 1:12 non-cascaded systems lets 66 units of length turn a corner around a block for each unit travelled length on the luff of the sail. (not counting the 90 degree corners)
The 1:12 single-cascaded systems let 45 units of length turn a corner around a block for each unit travelled length on the luff of the sail. The total line friction is now 68 % of the non cascaded system.
The Typhoon cascaded system lets 27 units of length turn a corner around a block for each unit travelled length on the luff of the sail. The total line friction is now 41 % of the non cascaded system if the Typoon system used the same 5 mm diameter line for all the stages as is required in the non cascaded 1:12 system.
If the 2nd and 3rd stages used 3 mm line instead and the 1st stage uses an oversized block than the total line friction is even further reduced.
An assumed difference in line friction of 5 kg’s is transferred to 12*5 = 60 kg loss in downhaul force by a 1:12 system.
The Typhoon cascaded system must be at least 6 times the require travelled distance of the mainsail luff tall. Otherwise the block of the first stage will jam against the bottom plate or block of the 2nd stage. External systems often don’t allow such stretched setups. Internal systems do.
In case of a 200 mm required downhaul distance the Typhoon setup must at least be 200 * 6 = 1200 mm tall. In principle there is no reason why a mutli-cascaded system inside the mast profile is limited in length below the full length of the mast.
Wouter Hijink Formula 16 NED 243 (one-off; homebuild) The Netherlands