The Fool on the Hill: Recumbent drive trains

This is the fourth in a series of essays about the design of a tricycle; if it interests you you probably need to read the others for context. Most of the ideas I'm discussing in this essay, however, come from the design of bicycles, and little is tricycle specific.

What's the state of the project?

As I've explained earlier, I entered into this project at least partly as a distraction from some real turbulence in my personal life which I feared would tip me into serious depression. Fortunately, that turbulence has resolved itself very positively, so I now have less time (and shall, inevitably, have less money) to indulge in geeky projects. However, efficient lightweight personal transport is still something I'm very interested in, and I do intend to continue with this project. As discussed in my previous essay, I'm still focusing on the design of the Mosquito velomobile as my primary design influence, although this may change.

In brief summary: although most of my design influences are racing machines, what I'm trying to design here is a (fairly) pragmatic everyday single-person utility machine, with reasonable comfort and capable of carrying useful cargo. It's a tricycle because as I age my balance is deteriorating, and because it's easier to park if it doesn't fall over.

Finally, my idea of using a male mould doesn't seem to be advisable. It seems it's pretty difficult to get a smooth enough surface. Also, kevlar as an outside, anti abrasion layer, may not be advisable. I'll do a separate essay on thoughts about moulding and layup when I've got this clearer in my mind.

Transmission

If the rider is reclined on their back, facing forward, their feet must be at the front of the vehicle. To route drive from the front of the vehicle to the rear wheel is mechanically complex and there are risks of inefficiency. There are risks of inefficiency in all the potential solutions, of course, but for the time being I'm focusing on front wheel drive solutions because they just intuitively feel better to me.

For a pedal cycle used on ordinary public roads in hilly country, a wide range of gears is a necessity. The most efficient system of gearing available is the derailleur; however, to have a wide range of gears, a derailleur needs a fairly long cage, and the volume through which the pantograph and cage sweep is quite large. A derailleur is least efficient in its highest gear, because chains become less efficient the more they're flexed.

An epicyclic gearbox is much more compact, but slightly less efficient. From my point of view, an epicyclic also has the problem that it competes with a hub centre motor for a significant location in the drive train, but we'll come back to that because there is a workaround. Efficiency on epicyclics varies with the gear used in a non linear way, but generally a gear in the middle of the range is direct drive and has no internal losses. The enviolo continuously variable transmission suffers the same drawbacks as an epicyclic, and additionally is significantly less efficient.

The final possibility for a gear system is a 'car style' dual shaft gearbox, such as the pinion. The obvious position for this is by the crankshaft, where it competes for space with a 'bottom bracket' style motor system; but as I dislike those anyway because of their propensity to break drive chains, that does not feel like a problem for me. Another problem is that they're less efficient; efficiency of the Pinion is quoted as 90.5% vs the Rohloff (best of the epicyclics) 94.5%. More of a problem is the fact that, like good epicyclics, the pinion is expensive.

Packaging, and the cross-shaft

A lot of the design of any very aerodynamic pedal cycle is packaging. Beyond the general point that it's important to keep the whole thing as small and streamlined as possible, there are places in the design where there's just a lot going on, and multiple different systems need to be fitted round each other. In the particular case of front wheel drive bicycles, the triangle between the crankshaft axis, the front wheel axis, and the steering head is extremely busy. For bicycles, this is complicated by the fact that the pull on the drive chain, unless it is directed to the wheel via an idler close to the steering head, is going to bias the steering. The whole point of the Mosquito-style design is that the drive-train is fixed with respect to the front wheel, and so this problem is avoided. However...

Both Beano and Seventy Seven have a cross shaft located above the front wheel, close to the steering head, with a primary chain on the right hand side of the transmission driving the cross shaft, and a secondary chain on the left hand side taking drive from the cross shaft to the front wheel. On both Beano and Seventy Seven, the cassette (and consequently the derailleur) are mounted on the cross shaft. Because of the need for steering movement, both also have a sprung idler sprocket on the secondary chain to maintain tension.

The cross shaft has a significant disadvantage: it puts a great deal of transmission gubbins directly in the rider's eyeline. It's also going to add a small amount of mechanical drag. For these reasons, especially considering that using the Mosquito design I don't need the front wheel to turn relative to the transmission, I'd ruled it out as an option.

But...

The cross shaft essentially gives you a third axis on which gubbins can be put. By putting the gearing system on the cross shaft, you keep it further away from road dirt, make it easier to service, and (if a derailleur system is being used) you move the swept volume of the pantograph and cage up from the front hub to the steering head, so the bottom of the hull at the front wheel can be narrower, increasing lean angle (and thus cornering ability) and contributing to a decrease in frontal area.

However — especially if you're using conventional length cranks — it also puts that transmission gubbins close to the rider's knee.

Again, using the Mosquito design concept, if I do, I don't need to do that. I can put a motor and a derailleur transmission in the front wheel hub. I do have to ensure that the movement of the derailleur arm won't foul anything, but I don't think it will. Nevertheless, there is more merit to the cross shaft than I originally thought, and I am now seriously considering it.

Packaging, and crank length

The axis of the crankshaft obviously has to be in front of the arc of the front wheel. If your front wheel can turn (and currently I'm hoping that mine won't have to, but I'm not fully committed to that), then overlap between the front wheel and the chain ring is also going to at best greatly limit steering. The fact that the rider's feet need to rotate around the crankshaft and that the rider's crotch needs to be behind the front wheel then constrains the size of the front wheel. Consequently, most front wheel drive recumbents have nominally 'twenty inch' front wheels; but there are two sizes of nominally twenty inch wheels, ISO 406 or ISO 451.

Seventy Seven uses the smaller of these two sizes, partly because it has a huge (80 tooth) chain ring. The crankshaft axis is substantially in front of the front wheel. It's obvious that the closer the crankshaft axis is to the front wheel, the more the rider's seat can be moved backwards, and consequently the bigger the front wheel you can fit.

Many competitive fully faired bicycles use shorter than conventional cranks — the conventional length is around 172-177 mm, but I think that all of Beano, Soup Dragon, Snoopy and Woodstock use 140mm cranks and Seventy Seven uses 120mm — and the reasons given for this are usually that

1. it makes the footbox smaller;
2. the rider's feet protrude less far into their sight line;
3. it's argued by its proponents to be more efficient.

Making the footbox smaller is really important because the footbox — the swept volume within which the feet move while pedalling — is a large volume very close to the front of the vehicle, and consequently greatly affects the aerodynamic entry.

However, there is one further advantage: since the rider's leg is at its fullest extension when at the further limit of the pedalling circle, shortening the cranks also allows you to move the rider's seat back by an equivalent amount. Russell Bridge, designer and rider of Snoopy, Seventy Seven and Woodstock, comments that learning to ride on short cranks is quite painful at first, as new muscles are being used.

Moving the rider's seat back means that the knee, at the highest point in its cycle, can be substantially behind any gubbins that is above the wheel.

I'm skeptical of arguments regarding pedalling efficiency, as nothing in the UCI Technical Regulations specifies the length of cranks, and British Cycling — notorious for seeking marginal gains — aren't using 140mm cranks. In this video Phil Burt, their head of physiotherapy, talks of using shorter cranks to improve aero position on upright bikes. But by 'shorter', he's only meaning dropping from 177 mm to 170 mm, or from 172 to 165. In the same video the reporter, who is used to riding 177 mm, tried 170, 155 and 145mm cranks in rapid succession, and his speed declined on each change. However, everyone who advocates short cranks says you need a period of weeks riding them to acclimatise, so this is not a valid test.

Regardless, if I can learn to use them efficiently (I haven't yet tried), shorter cranks give me more room to play with around the front wheel. This is especially important if I'm using a cross shaft, since there's also a potential conflict between the swept volume of a cross shaft mounted derailleur and that of the rider's left knee. But this brings up another issue.

Packaging, and Q factor

When people walk, our thighs viewed from the front or rear move either in parallel to one another or even to some extent around one another. People who walk with splayed legs are unusual, and it's usually thought of as bad for the hips. But a bicycle puts considerable lateral distance between our feet, and modern gear systems and bottom bracket motor systems tend to increase this. This lateral distance is known as 'Q factor' or 'stance width'. People who care about pedalling efficiency tend to feel that the Q factor on modern bikes is too great for many people, even tall people; and that pedalling efficiency can be improved for those people be limiting Q factor.

Q factor also (obviously) affects the width, and therefore frontal area, of the footbox. So limiting Q also improves aerodynamics. But if we've got a derailleur arm projecting into the natural path of the rider's knee, then it doesn't really matter from a biomechanical point of view how narrow the Q factor is in the footbox, the movement of the rider's hip is still going to be badly sub-optimal.

Additionally, both Beano and Seventy Seven are unable to select the lowermost gears of their derailleur systems, because to do so would create an intersection between the swept volume of the derailleur cage and that of the front wheel as it turns.

Thoughts about packaging

Both Beano and Seventy Seven base their cross shafts on adapted bicycle hubs, with the consequence that both need their cross shafts supported at both ends. If a custom shaft were used, it could be supported by bearings between the ends (i.e., like the bottom bracket of a conventional bicycle), making the transmission narrower by about 20 mm. However, the only standard bicycle gear system which could be used in such a position is the Pinion, which is expensive. Again, the only conventional bicycle motor system you could use in such a position would be a bottom bracket motor such as a Bosch. Using either the Pinion gearbox or the Bosch motor in place of a cross shaft would require the primary chain to be on the left hand side of the transmission and the secondary chain on the right, but I think this would work.

The narrowest Rohloff hubs have an over locknut dimension (essentially the width between the fork dropouts) of 135 mm. An off the shelf axle with a freehub shell for a modern derailleur cassette with a similar range of gears has an over locknut dimension of 148 mm. The Q factor of modern road bikes is pretty much the same as the overlocknut dimension, so 148 mm.

It doesn't have to be this wide. Track bikes and other single speeds can have an over locknut dimension of 114 mm - 120 mm. The width of an old fashioned bottom bracket shell is 68mm. The width of a 12 speed chain is 5.25 mm (11 speed about 5.5 mm).

The Q factor — measured over the outer faces of the cranks at the pedal axis — cannot I think practically be shorter than the bottom bracket axle (I'm not absolutely sure of that). But it is in essence the sum of the width of the bottom bracket shell, plus the width of the chain used, plus clearance to ensure that the chain doesn't rub against or interfere with any other component, plus the thickness of at least one crank arm. If the chain ring is smaller in dimension than the crank length, then both crank arms must be accounted for because the chain ring side crank arm has to pass the chain; however, if the chain ring diameter is bigger than twice the crank length (plus twice the depth of the chain (2 x 8 = 16 mm), plus the diameter of the pedal spindle (14.2 mm)), then the pedal can simply be screwed in to one of the arms of the spider and we lose (at least most of) the width of the arm.

For practical purposes, that means that for 140 mm crank length, you would need at least a 76 tooth chain ring. Note that a chainset with no chain ring-side crank would be very much a custom component!

Thus the narrowest total transmission system I can see working would have a chainset as follows:

This would then drive a primary chain on the left hand side of the bike to a custom cross shaft supported between, not outside, the sprockets, which could be as narrow as 80 mm. The secondary chain would then run down the right hand side to a 135 mm OLD Rohloff offset to the left of the bike by 27 mm, with the wheel built onto it dished so that the rim was brought back by that 27 mm to run on the centre line of the vehicle (yes, I know it's not conventional to dish a wheel with an epicyclic hub, but there's technically no reason why a relatively shallow dish such as this should not work perfectly well).

Such a hub will be about 160mm minimum width over the forks and securing hardware. This means that the front fork, at hub level, would protrude left 107 mm from the centre line of the vehicle, but only 80 mm right. In any case the total width at the hub is less important since it should be below the swept volume of the rider's legs. Because both chains would run straight from sprocket to sprocket without any lateral deflection, they should be subject to less than normal wear. If a it is possible to adjust the position of the cross shaft both vertically and fore and aft, and thus to set it to have both chains in optimal tension, there would be no need for tensioning idlers, slightly reducing drag.

All this needs a lot of custom parts and therefore isn't affordable to me. But, if one were production engineering this design, or if one were adapting it for racing or speed record attempts, it would be possible to get a very low Q factor.

Finally, although an off-the-shelf motor could not be used on a cross shaft in the configuration I've described, if one were production engineering it, a custom motor could be built around the cross shaft.

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