Understanding gears

[citoyen]

From the On the commute today thread:

Maxed out at 56.7km/h on the descent into town, which is always fun on a 65" fixed gear.

Is it just me, or is that a quaint mix of units?

No, not just you - I actually felt quite uncomfortable writing it. But I've only ever learnt to understand gear sizes in terms of gear inches. Really need to overcome that (I've learnt to think of distances in km, and my height and weight in cm and kg, so I should be able to manage it).

What's the SI unit for gears?

It'd be metres development.

Development in Meters
In countries that use metric measurements, the usual system is "development" in meters. This is the distance that the bicycle moves with each revolution of the pedals. This system is a bit more cumbersome than the gear inch system, for two reasons. First, it is a little more difficult to calculate: wheel diameter in meters x front sprocket / rear sprocket x pi. Having to multiply by a constant (an irrational one, no less!) needlessly complicates things. Also, the resulting value is a less-convenient number to work with, a single digit plus two decimals. For example a road bike's 52/13 would be expressed: 8.64. A mountain bike's 24/28 would be: 1.78.

OK, I think I can work with that. I don't get why St Sheldon thinks having to use Pi makes things so complicated, especially as he then goes on to advocate his idiosyncratic gain ratio system, which I really don't understand at all...

I would like to propose a new system, which does take crank length into account. This system is independent of units, being expressed as a pure ratio.

This ratio would be calculated as follows: divide the wheel radius by the crank length; this will yield a single radius ratio applicable to all of the gears of a given bike. The individual gear ratios are calculated as with gear inches, using this radius ratio instead of the wheel size.

 

How does crank length affect gearing? Please can someone explain gain ratio in terms understandable by a Bear of Little Brain such as me.

And what system do you use to measure/understand gears, and why?

d.

[clarion]

Despite being a thoroughly metric person otherwise, frame sizing and gears make most sense to me in Imperial.

Simply because that's what I've learned to assess. 

I've tried to use metres dev, which is what British Cycling use for gear limits for kids, but I never got my head around it.  I think I just need to have a table of comparative figures, and learn from that.  It can be a sensible measurement, after all, rather than a calculation.

[Biggsy]

Cranks are levers.  Longer cranks effectively lower the gear.

Personally, I don't include crank length in gear calculations for the sake of simplicity.  I have no intention of changing my crank lengths anyway, so I can forget about this factor.

To compare gears of one bike to another with a different tyre size but the same crank length, I use gear inches.  Gear inches rounded to the nearest tenth give nice big chunky numbers that are easy to remember, and are easily understood by many other people.

[tatanab]

Gear inches.

It is what I grew up with and all the gear tables in Holdsworthy Aids, RTTC handbook etc used gear inches.  I am well aware that 48 by 20 on my fixed does not give the same gear on 700C as it did on 27" back in my youth, but I still call it a 65" gear because I only need a comparison with other gears, not an absolute measurement.

If forced I could adopt the continental system of development because that too makes sense, but again to be absolute it is tyre dependant.

[citoyen]

Cranks are levers.  Longer cranks effectively lower the gear.

If I understand levers correctly, a longer lever makes it easier to push a bigger gear, right? But what difference does a longer crank make to how far the bike travels per wheel revolution? I'm still unclear how that relates to bicycle gears in practical terms.

Gear inches rounded to the nearest tenth give nice big chunky numbers that are easy to remember, and are easily understood by many other people.

Yes, that's pretty much my reason for sticking with gear inches thus far in my life.

d.

[Cudzoziemiec]

Gear inches for me too.

I usually don't even bother to allow for different tyre size or the difference between 27" and 700c wheels - it is only a comparative system for me. I'd like to use development in metres as I think it's a far more directly applicable system - but I've grown up with our system of nominal wheel-equivalent inches and nobody I know uses development. I don't even recall anyone using it in Poland - people just tend to say 48 x 14 or whatever.

I also think of tyre pressures in PSI but everything else is metric.

[Biggsy]

The crank length doesn't really affect the gear at all, but the gear is no good on its own.  The gear is for the benefit of the rider.  The cranks (with pedals) are the link between the rider and the gear.  The cranks are like an additional gear - but you might as well combine the chain/sprocket gear and the cranks gear to call it "the gear".

[Panoramix]

Cranks are levers.  Longer cranks effectively lower the gear.

Kind off.

If you apply a constant force on a pedal, the work and thus the power will be greater with longer cranks as it is the (vectorial) product of the pedal linear speed (which is greater) by the force. It's not free energy as it will knacker you more!

Equally whatever the crank arm length at equal rpm, equal speed.


So the sheldown brown ratio is a way of knowing how much is transferred to the road at a set rpm, but the units are a bit weird for it to be intuitive. To me something like watts per force applied to the pedals and rpm would make more sense.

Edit: cross post with bigsy

[citoyen]

The crank length doesn't really affect the gear at all, but the gear is no good on its own.  The gear is for the benefit of the rider.

Good point.

Equally whatever the crank arm length at equal rpm, equal speed.

Yes, I think this is why I have trouble understanding how crank length affects gearing.

Thanks for the info, both - it makes a bit more sense now.

d.

[citoyen]

Interesting poll results so far - 12 out of 12 voters going with gear inches.

No takers for gain ratios? Sorry, Sheldon!

d.

[Biggsy]

Yes I accept that my "longer cranks effectively lower the gear" isn't technically correct, as I use the word "gear" casually.

[tom_e]

I've got shorter cranks on the bent than uprights.  Gain ratio was helpful for this.  Gear inches were not. 

I can't get too excited about it beyond that - the basic mechanics is easily understood, this is just a handy measurement method.  In reality I compare an intended setup with existing ones I use for a similar purpose.

[mrcharly-YHT]

gear inches for me, too.

While crank length changes leverage, it doesn't change how far you travel with one turn of the crank. Gear inches allows direct comparison between bikes with different wheel sizes and is in easy-to-remember figures.

[Kim]

I've voted gain ratio, because although I have an intuitive 'feel' for gear inches, I have non-170mm cranks to account for when actually choosing sprockets.  The whole point in gears is to manage stress on the Stupid Knees, so you have to take that into account.

[MattH]

No option for crank revolutions per furlong?

[tonycollinet]

To convert gear inches to inches development, mulitply by PI (3.14). To convert to Meters development, divide inches development by 39.37 - or easier, but approx multiply gear inches by 0.08 (multiply by 8, divide by 100). To get:

Gear Inch   Inches Development   Meters Development
10   31                                   0.80
20   63                                   1.60
30   94                                   2.39
40   126                                   3.19
50   157                                   3.99
60   188                                   4.79
70   220                                   5.58
80   251                                   6.38
90   283                                   7.18
100   314                                   7.98
110   345                                   8.77
120   377                                   9.57
130   408                                   10.37
140   440                                   11.17
150   471                                   11.96
160   502                                   12.76
170   534                                   13.56
180   565                                   14.36
190   597                                   15.15
200   628                                   15.95


Column formatting is a bit wrong - sorry

[citoyen]

Thanks, Tony, that's very helpful. 

d.

[rower40]

As the difficult b*gg*r who started all this, I'm going to throw my 2p-shaped spanner in the works.

All my bikes have 3 groups of gears:

• too low
• just right
• too high

The gears themselves move between groups as the roadspeed and terrain alter.

As most of my riding is done on hub-geared bikes, "change-up" and "change-down" are instantly understandable, with no clever/confusing double-shifting needed.  So if I'm in a "too high" gear, as evidenced by volume of knee grumblage, then I apply operation "change-down".  If I'm in a "too low" gear, as evidenced by scorch marks on lycra or standing-waves forming on my beergut, I "change-up".

If operation "change-down" doesn't yield results, I apply "MTFU and get out of the saddle" or "get-off-and-walk".  If "change-up" does nothing, then I free-wheel and relax a bit.

If "get-off-and-walk" becomes too frequent, I search the catalogues for a rear sprocket with n+2 teeth.  Which was fun, when applied to the belt-drive Trek.

So the actual numbers are a needless distraction.  Not knowing them doesn't detract from enjoying the bike ride.

[citoyen]

A good point, well made.

I mainly use the numbers to work out equivalence/difference between different set-ups, eg to work out what sprocket is necessary to give the same gear for a different size chainring, but as you say, in practical terms, being in the right gear for a given situation is all that matters.

Of course, when you're on fixed, you're nearly always in the wrong gear and can do nothing about it until you get home.

d.

[orienteer]

Another incher here.

When specifying a Rohloff 14 speed hub for my Moulton tandem conversion, the basic requirement was a bottom gear of 20 inches, the lowest rideable gear without losing balance in my opinion. That gave a top gear of about 106 inches. On 20 inch wheels, ended up with a 58 tooth chainwheel (can't recall the sprocket size).  Direct drive gear 11 comes in at 70 something inches, around gentle cruising speed.

In practice it's all worked out well, in both solo and tandem configs.

[PaulF]

I just use the ratios, as I mainly ride single-speed it's the relative ratios that are important to me so I 'know' that, for me, 32:18 is about right off road and 48:16 on road.

I did however get a spreadsheet out when working out what chainring to use when I put an Alfine on my Peregrine so that I could compare ratios with the 3x10 it was replacing. It's helpful that all my bikes have the same sized wheels.

[Tigerbiten]

Another incher here as well.

One thing I like about inches is its dead easy to work out your speed in that gear at a given cadence.

3/1000 x cadence x gear inches = speed in mph.

[Ian H]

Another incher here as well.

One thing I like about inches is its dead easy to work out your speed in that gear at a given cadence.

3/1000 x cadence x gear inches = speed in mph.

That's nice'n'elegant. Inches here also.

[clarion]

tonyc, that's a very useful table.  I shall cnp and print it out for my own use

[Panoramix]

In metrics that would be 2/3 * cadence/10 * development

So pushing a 5 m gear at 100rpm gives you 2/3*10*5 = 1/3*100 = 33kph

Bizarelly (if that makes sense) I've switched from the metric way to gear inches without too much trouble but I can't relate one to the other mainly because Bristol hills are shaped differently to the ones I was used to before.