I shall edit this ongoing sage in the light of further research as ordered items arrive in the post.
I had covered the trike in defensive cardboard, foam rolls and large sheets of plywood in case a tree fell on the shed. Time to survey the damage. The Danish news is full of fallen trees, delayed trains and crashing ferries. The traffic seems to be moving normally. It continued blowing for most of the day. No walk and no ride. Lazy git!
An image of the filthy 11-32 11sp cassette and Athena rear changer in bottom gear. It changes onto and runs perfectly on the 32T sprocket with the B-screw [worm] fully tightened. Whether it will accept a 36T sprocket is another matter entirely. I will have to lengthen the chain to avoid damage on the large/large, sprocket/chainwheel. 4 extra teeth x 1/2" pitch adds 2" in length but makes only a little difference in diameter. Which must be halved again since we are only dealing with radius as the changer works below the largest sprocket.
I exercised my fingers with an order for a Sram PG1170, 11 speed, 11-36tooth cassette at a very favourable price even including tracked postage from the UK. Meanwhile my order for tyres and 11 sp chain was dispatched within a couple of hours of ordering and I will receive them today if the Danish Post Office does its thing. [Which it duly did.]
I put the trike up on the work stand to examine the geometry of the Athena rear changer. The expense of a new rear derailleur will hopefully be avoided. The Athena 11sp uses a worm and wheel to rotate the changer away from the sprockets. This has considerable limitations compared with the ease of adjusting or even extending a simple B-screw. We [I] can only see what happens when the cassette turn up.The manufacturers are very conservative with their maximum sprocket limitations probably to avoid claims for damage by those who insist on pushing the limits. My present 32T bottom gear is well beyond Campag's suggestion. Yet it works perfectly in practice despite the gap between the chain and largest sprocket seen in the image.I do need a lower bottom gear but have no desire to return to a triple chainwheel. I am also limited to a 33T minimum chainwheel size by the PCD of the Spa double chainwheel crank.
I have also ordered an IRDM8000 XT11 rear derailleur because it has the necessary sprocket range. [UP to 42]Then discovered it [probably] has a pull ratio of only 1.1. Aaargh!!!
The pressure on manufacturers to allow greater cross compatibility must surely be increased as more and more information is published online. Indexing has made life much more difficult for those who wanted to go outside the very narrow range of gears offered by manufacturers. Tourists and cyclo-cross riders wanted much lower gears using MTB components but still wanted their dropped bars and "brifters". [Combined brake and gear levers.] The dictatorial major manufacturers insisted that every buyer of "road" equipment was a cross between Arny and the Hulk. So they were easily able to turn massive gears more suitable for land speed record attempts! 52x11 anybody? 34mph @ 90rpm cadence. I must get me one of those!
The following websites offer an excellent insight into the simple "geometry" of bicycle gear changers, sprockets and levers.
Art's Cyclery Blog » Science Behind the Magic | Drivetrain Compatibility
Bicycles/Maintenance and Repair/Gear-changing Dimensions - Wikibooks, open books for an open world
The problem is finding a way to drop my Athena 11sp rear changer enough to make room for the 36T dinner plate. Ideally I need a 1.4-1.5 shift ratio changer. Not a 1.1 MTB! Shimano Road rear changers would work just as well as Sram. I'll just have to try the Campag Athena to see how it copes.
Or go back to using the JTek Shiftmate. It tended to fray cables so I gave up using it. Though this problem may have been my own fault through incorrect set up. I found that the initial cable lay across the flat on the double pulleys quickly slipped out of place. Further research suggests that the very small pulley diameters of the Shiftmate stress the cable causing early breakage. So I can't really blame myself for this one.
My earlier idea of a simple lever [or bellcrank] to change the cable pull ratio [via differential radius anchor points] produces increasing errors of pull at each end of the lever movement. Only a long lever with very limited movement would help to reduce the pull error. Otherwise the indexing would run out of sufficient cable movement at each end of the cassette. I wonder whether a parallelogram would solve that problem at the price of increased complexity but allow reduced size? Perhaps a longer lever is not really a disadvantage? The question is where to fit the lever [and its pivot] to avoid conflicts of cable run, pull angle and a moving chain flopping about in the same area.
Scale image of bellcrank dimensions set against an image of the Trykit frame. By careful selection of the pivot point the arcs of cable anchor travel can be arranged as tangents to the original cable runs. This avoids distortion of the 1:1.36 ratio required for matching the cable anchor movements.
At first I thought there was a complication in my theory because the M8000 rear changer has a total movement of 26mm with the stop screws are fully screwed in. Fortunately the gap between the cable stop and the clamp easily exceeds 36mm when the stop screws are backed off to achieve the correct pull-per-click cable movement.
The Campag Ergo 11sp lever pulls a total of 26mm of cable from high to low. [10 clicks] With a 1.1 pull ratio rear changer I need to increase this by 1:1.36 to to achieve the correct indexing at the rear changer. An bellcrank pivoted in front of the seat tube will achieve this. The anchor points are arranged on the two radii in front of the bottom bracket and behind it just below the chain stays. The down tube cable will parted and clamped to the bellcrank with a pinch screw. A similar cable clamp bolt will fixed to the bellcrank to carry the final leg of the rear, gear cable inner.
The arcs of the cable clamping bolts will ensure the correct cable angle is maintained to avoid complication of the normal gear cable run. Now I just need a suitable clamp which fits the over-sized downtube on which to support the bellcrank pivot. A front changer gear hanger clamp is in the shed somewhere. That should be ideal.