Matching sprocket and chainring to your cadence and heart rate

[Andre Jute]

If a cyclist has to push his bike up a hill because he has run out of puff, it is because his lungs can't supply the oxygen his muscles demand and/or because his heart can't circulate his blood fast enough to deliver the oxygen to his muscles. In all cases it is because something in his transmission was badly chosen, usually too optimistic.

All of this relates through the cyclist's maximum heart rate to his cadence. His theoretical maximum heart rate as a first approximation is roughly 220 minus his age, but that notional maximum is a number only professional athletes under medical supervision should approach. We generally speak in percentages because everyone's maximum heart rate is different. Ninety percent is possible for young men but you don't want to be in the 80 percents because there lactic acids are formed which will undo your good work. So for most of us, and especially for middle-aged cyclists, 75 per cent of age-related maximum is a reasonable heart-rate if you wear a heart monitor and pay attention to its output, otherwise lower still. If you're a careless rider, pick something even lower.

After heart surgery and physiotherapy, I found that the easiest way to relate this is through the cadence I could maintain on the flat for several hours. (I'm never on the bike for more than a couple of hours without a break.) Heavy tourers and cyclists who want to cross a small country in a day could pick that long day's best maintainable average cadence.

But all this knowledge will avail the cyclist nothing if the tooth counts on his sprocket or his chainring are optimistically chosen. The cyclist must start with a rationally and realistically chosen consistently achievable cadence and match the tooth counts on the gears to that cadence.

On this page-- 
http://coolmainpress.com/BICYCLINGHebieChainglider.html
you will find tables for
--60x622mm tyre at a cadence of 60rpm
--26x1.6in tyre at a cadence of 80rpm
--26x1.6in tyre at a cadence of 120rpm
--26inx50mm Schwalbe Dureme at a cadence of 65rpm

You can interpolate between the tables with only two facts: the circumference (standing in for the rolling length) of your chosen tyre and your cadence, if different from those used in the tables listed above. You don't want gears below your ability to balance the bike, and you don't want gears that force you to pedal faster than your reasonable cadence maximum. Coasting on the downhills is a wonderful opportunity to enjoy the surroundings.

After all that work, I found that on my preferred 622mm rims clad with 60mm Big Apples at my preferred cadence of 40rpm I liked the ex-factory default of 16T sprocket with a 38T chainring, super for hauling heavy easels and paint in my all-hills countryside in West Cork. Since fitting a torquey electric centre motor, I've moved up to a 42T chainring.

[martinf]

I have a different approach.

I reckon I can do without very high gears, but a very low gear is always useful on a bike used for touring with a load in hilly areas. So I specified the lowest permitted available option (38x17) on my Raven Tour when I bought it in 2012.

After Rohloff changed their lowest permitted input ratios, and as I got older, I changed the sprocket to 21T. This gives a lowest gear of 12.8 inches and a highest gear of 67 inches. The input ratio is just under the minimum now specified by Rohloff, but I don't think I will be putting out lots of power when I use the low gears. A bonus with 38x21 is that I can still have a ChainGlider, I simply changed the Rohloff-specific rear part for the standard rear part that I use on my Nexus Premium equipped bikes.

So speeds of 5.5 km/h to 29 km/h at a cadence of 90 rpm. That low gear is only really useful on steep inclines when I am tired, for example at the end of a long day in the saddle. In that scenario, my cadence also tends to drop so I can go as slow as 4 km/h, which is about my limit for keeping balance on a loaded bike on a reasonably good road surface.

At the other end of the scale, highest gear is rarely necessary. On a long ride I won't normally be going at 29 km/h. With a loaded bike on fairly flat terrain I reckon an average speed of 18-22 km/h is reasonable at my age (70). This corrresponds to gears 10, 11 and 12 on the Rohloff hub, where gear 11 (direct drive) is the most efficient in the range.
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For my utility bikes I just choose the lowest gear combination that still allows a ChainGlider. This is 38x22.

With a Nexus 8 Premium, that gives a range of 23 inches to 71 inches, so with my preferred cadence of 90 rpm that translates to 10 to 31 km/h. And a narrower range of 30 to 68 inches on my old Sturmey 5 speed.

These more limited gear ranges are still OK for the trips I do with these utility bikes, except when I am towing a loaded trailer. I recently did 3 trips to the local recycling centre carrying about 80 kg of rubble each time. As the centre is up a moderately steep hill I had to push harder than I would have liked.

The short-term solution is to fit the steel seatpost and towhook off my "new" utility bike to my Rohloff-equipped Raven Tour, the longer term solution will be an electrically assisted bike.

I have already sourced an old steel-frame ladies' style mountain bike that should be suitable for a conversion, but haven't yet decided whether I will start with a simple front hub motor conversion or go straight to a mid-motor, which is a bit more complicated and puts more stress on the hub gear. Ladies style in case I have trouble getting my leg over a diamond frame as I get older.   

[Andre Jute]

Thanks for reminding me, Martin:

I should've mentioned that the constraint behind my choices of chainring tooth counts is those that take Chaingliders, which are simply too useful to give up for some notionally "perfect" gear ratio; there is always another way to skin a cat.

And equally, I aim at cruising at my comfortable cadence of 40rpm on the level in gear 11, which is a 1:1 ratio, saving overdrive gears 12, 13 and 14 for fast downhills. Not that I'm on the flat all that often, but if you set up a Rohloff so that 11 is your most used gear, a lot of other possibilities fall into place -- for instance, after I fitted an electric motor, I could avoid the Rohloff's lower 7 gears by using the motor's software "gears" if I wanted to, though I don't.

You may ask why I worked up a complicated table for myself with a cadence of 60rpm when I'm comfortable at 40rpm. The answer is that 60rpm multiplied by 60 minutes in an hour has a red notch on a pilot's slide rule, and I'm comfortable working mental arithmetic on a base of 3600. For instance, 40rpm is 2/3 of 60rpm, so I eyeball a number, say a speed, on a different table and can instantly see how realistic it is; or I could argue that 2/3 of 3600 is 2400, which is pretty close to a quarter of 10,000, actually 9600, close enough for a first approximation or a check that you're working in the right direction; you can see that it makes mentally shifting the decimal point a lot easier. Martin's cadence of 90rpm is one and a half times 60rpm, so the result should run in the other direction, an easy division by two and then adding the product back to the base, result same as multiplying by 1.5. To be clear, I don't have the eyes any more for the small print on slide rules or the rotating slide rule bezel around a few of my watches, but I don't really need to see them; from long use I effortlessly picture them in my mind's eye. I fondled my pocket Pickett a bit and then slid it back into its leather sheath.

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BTW, Martin, a central motor installation isn't all that much more expensive than a front motor. It's the bigger battery you need when you go from a lower power front motor to a beefier mid-motor that raises the comparable cost appreciably. Also, the front motor that I had, despite its reputation as the Little Hill Climber, seemed more lightweight than the central motor, in every aspect but especially the control electronics, which were clearly not an in-house production in the case of the front motor. It might be that the front motor was built light to earn its title on the hills. Don't get me wrong. The front Bafang motor lasted lonhrt than any of my Nexus boxes, and the central Bafang motor seems likely to see me out, so I don't have any complaint about value received; I'll buy Bafang again, if necessary. But, if you're planning to make a permanent installation in the first instance, I suggest the central motor would be more satisfactory in the long term. The reason I made a sacrificial front installation was because there was very little known about these motors at the time (except for power-crazy Americans building electric motorbikes), so I was educating myself, but that no longer applies. There's a lot of experience of electrical motors on bicycles on this forum and elsewhere.