Howard

What started me thinking ....
https://www.sheldonbrown.com/sliderule.html


Speed: time's hapless lacky
Once upon a time, the electronic speedometer was still a few years and many Benjies away, so we'd calculate speed in other ways. Such as ... you could calculate the gear inches and translate that to MPH at some cadence. Cadence was easy to calculate - count the number of left (or right) pedal strokes in however long it took the skinny hand on a watch to make a sweep (or a quarter sweep, if you're willing to multiply by 4).
Make a chart, tape it to the handlebars, and presto - a sort of OK speedometer. Digital watches made it lots easier to time miles in soybean country, and 3 minutes a mile cost only 20 imperial pain units (AKA MPH), 4 minute miles were a comparative bargain at only 15. Slew the ratios around in the grey matter mixmaster often enough and rough calculations of anywhere from 10 to 20 were pretty straightforward.

Gear inches * 0.002975 * cadence = speed. 0.002975? Nuts, shave it to gear inches * 3 * cadence then lop off enough zeros that the answer makes sense. The 0.002975 number is from memory, but I recall it having something to do with pi, tire diameter in miles, and converting cadence into units involving hours. Anyway, double check it if you like, here's the calculator I'm using for this post:
https://www.antiquark.com/sliderule/s...l-n909-es.html

Gear inches?
A long, long time ago, back before Prince was formerly known as anything other than either Prince or Rogers Nelson, the typical bike came with some typical gears: a 14-28 cog and a 40-52 crank. A triple crank was going to run another hundred bucks, which is like the cost of a Subaru in today's money. Anyway, this worked out to about a 40" low gear, and some of us, not knowing any better at the time, did a lot of riding around with those gears. Philosophically, maybe we expected to adapt to the world instead of the other way around, I dunno. That was a lot of cheesburgers ago.

So what? I mean other than the cheesburger thing. Well, that's kind of the point to this.

The sporting 3 speed

Well, I've been thinking - thinking about considering a single speed. Which I know is kind of nuts, because Henri Desgrange told us all "... that variable gears are only for people over forty-five." And danged if I don't qualify.

Let's sketch up some rough numbers. Maybe for a sporting bike a low gear of 40" isn't so bad. An AW gives us ratios of 3:4, 1:1, and 4:3 (see what I did there - none of that 1.3333333333 stuff, thanks). Sturmey, if I recall, suggests a chainring/cog ratio of no more than 2:1 ... so a 42/21 just fits, and that gives us a 54" 1:1 ratio.
Is a 54" gear fast enough? What kind of low gear does that give?

Well 54 * 3 * 100 (divided by enough 10's) comes out around 15-ish; 60 RPM gives around 11MPH and I'll confess to being happier these days at 100rpm than at 110, so for a middling gear, that's fine. But I've got a higher gear too, which is 4*54/3 ... not quite 75. 70 * 90 * .003 is around 2.1 * 9, ninteenish. Fine. Just fine. How about the low gear? 3*27/2 or 3*13.5 or 40.5: Spot on!

The bottom line, I guess, is that it's easy to over-geek the numbers, to over think the components. Bicycling isn't precise down to 4 decimal places, it isn't digital at all - at least I feel it shouldn't be. It should be the sweep of the analog second hand on a wristwatch, the tic-tic-tic of some sort of pawls on a race, it should to some extent be a slide rule, with the bezel set between two numbers, daring us to do better, to work it out for ourselves.
Or maybe it's just a bike. I don't know. That was a long time ago.

due ruote 

I see some question marks, but I can't tell if you're asking a question. I also couldn't quite follow the line from single speed to low gear, high gear, but to the question "is a 54" gear fast enough" I would say that for me, the answer would be an unequivocal "no," and I'm not terribly fast.

jyl

My daily ride has a low of 40" and a high of 108". Your proposed range is basically the small chainring of my bike (40" to 80"). Yes, that would be livable for around town and even longer rides at a relaxed pace. I can't say that I use the 108" much, ahem, barely?

old's'cool

After some study, I actually did follow your logic, but you may have some-uns scratching their heads. For me, 54" is a starting out gear, but then I like to stick to pavement. And I like to go fast, so I like to have at least 108" on tap for when conditions permit.