London Bike Kitchen - Gear Talk 1st October 2012
Gearing is the aspect of a bicycle's drivetrain linking cadence with the rate at which a drive-wheel turns.Human legs produce power optimally within narrow ranges so gearing is used to make a bicycle as efficient as possible.Gear ratio depends on the number of teeth of a drive/chain ring and rear sprocket (cog).Hub gearing also depends on interplanetary (epicyclic) gears!Shaft-drive bicycles depend on the bevel gears at the end of the shaft.For a bicycle to travel at a particular speed using a lower gear you need a faster cadence but less force. But too fast a cadence can be inefficient. To travel in a higher gear you need a lower cadence but more force. Too much force can cause knee damage and lower cadence usually makes the heart work harder. "Spinning vs Mashing".Four main methods of expressing gear ratios: gear inches, metres of development (roll-out), gain ratio and front/rear (aka 'racing style').Gear inches, gain ratio and development are all expressed as a single number which can be compared between bicycles. The larger the number, the higher the gear.Front/rear only really used for racing bicycles with specific wheel sizes such as 700C and only considers the size of chain ring and cog.Gear inches and meters of development take the real wheel into account. Gain ratio (proposed by Sheldon Brown) also takes the crank arm into account. Gear inches-----------The oldest system and even pre-date the bicycle chain. Gear inches really mean 'the size of wheel'. If an 'ordinary' bicycle, aka penny farthing, had a 60" wheel the GI would be 60". Gearing allows a wheel to be turned faster so a 28" wheel can be turned as fast as a 60" wheel with the same rotations of cranks. So a bicycle with 72 gear inches would be advanced the same distance as if it had a 72" wheel.Calculated by using (where gi = gear inches, dwd = drive wheel diameter, fct = front cog teeth, rct = rear cog teeth):gi = dwd x fct/rctUsually the lowest gear on a MTB would be around a gear inch of 20 and the higher gear on a road bike would be somewhere around 110 gear inches. Gear inches can be thought of as the 'wheel size'. A gear inch of around 16 gives an effective speed of around 3 mph so at this point it'd generally be faster to walk.Metres of Development (Roll-out)
--------------------------------Instead of expressing the relative wheel size, meters of development describes distance travelled during one rotation of the crank. Calculated by using (where md = metres of development, dwc = drive wheel circumference, fct = front cog teeth, rct = rear cog teeth):md = dwc x fct/rctThe drive wheel circumference is calculated using diameter x pi.Gain Ratio
----------While gear inches and meters of development relate to distance travelled per turn of the pedals, gain ratio relates to the 'mechanical advantage' of a drivetrain. GI and development do not take the crank arm into account. This can provide a misleading comparison as on a MTB a gearing of 46/16 is comparable to a road bike gearing of 53/19, but if the MTB had a crank length of 175 and a road bike of 170 then the MTB gearing would actually be around 3% lower.Calculated by using (where dwr is drive wheel radus, gr = gain ratio, fct = front cog teeth, rct = rear cog teeth):dwr / crank length = radus ratio...then:radius ratio x fct/rct = grExamples:
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| Gear | Gear Inches | Metre Development | Gain Ratio | Front/rear | MPH at 80 RPM |
|---------------|-------------|-------------------|---------------|---------------|---------------|
| Very high | 125 | 10 | 9.4 | 53/11 | 29.7 |
| High | 100 | 8 | 7.5 | 53/14 | 24 |
| Medium | 70 | 5.6 | 5.2 | 53/19 / 39/14 | 16.6 |
| Low | 40 | 3.2 | 3.0 | 34/23 | 9.6 |
| Very low | 20 | 1.6 | 1.5 | n/a | 4.7 |
---------------------------------------------------------------------------------------------------Gear inches and meters of development are closely related. To convert Gi into development you multiply by 0.08, or more specifically 0.0798 which is 0.0254pi.mph can be calculated using various methods, with gear inches it is:mph = gi x cadence in rpm / 336Relative gearing:On bicycles with multiple gears gears tend to have relative differences of around 15% for comfortable changes between gears. Moving from a 13 tooth cog to a 15 tooth cog (15.4% relative difference) feels similar to shifting from a 20 tooth to 23 tooth cog (15% relative difference) although 20 to 23 teeth is a larger absolute difference. Cassettes often have average step size of 15%: 14-16-18-21-24-28-32. Racing bikes often have a smaller step-size so cadence can be very finely tuned. The course is generally known before the race so an appropriate gearing can be pre-selected for the terrain.A 'derailleur' is used on some bicycles to 'derail' the chain from one ring to another, much like a train on tracks. Sheldon Brown proposed the correct word was derailer rather than the faux-French word derailleur.Gearing ranges
--------------180% - 3-speed hub
250% - 5-speed hub
300% - 7-speed hub
327% - 1 chainring derailleur
428% - 2 chainring derailleur
526% - 3 chainride derailleur / 14-speed Rohloff Speedhub)
698% - 3x10 Touring 3 chainringCompact and standard chainrings are often used for road bicycles. Compact chainrings help your legs in mountains! Compact would be a chainring pair of 34 and 50 teeth. Racing bicycles may use around a 53 / 39 pair.Derailleur gear system is around 87% to 97% efficient. Hub gears are around 86% to 95% efficient.Velodromes generally specify crank lengths of 165mm to 170mm although road bikes and MTBs are sometimes larger.There is not a huge difference in power output in crank length of 120 to 220mm although a shorter crank can provide a biomechanical advantage and allow the rider a more aggressive race position on the bicycle; a larger crank would close off the hip angle at the top of the pedal stroke.Sprinters on the track would use a gear inch of around 94" to 98".Endurance riders would use 92" to 96" indoor and 88" to 94" outdoor.Time-trial riders could use a gearing as high as 103" with the biggest gearing being on the persuit event. Maximum gearing is limited to rider's ability to start. If it takes two seconds to get started the advantage of the higher gearing is lost.Typical chainring/cog combinations are:50x15 (87.67") - Track
48x15 (84.16") - Novice track rider.
48x17 (74.26") - 'Spin to Win' average road gearing for faster starts and reasonable top speed.
48x19 (67.4") - More spinny road gearing for flatter roads and new fixed/single-speed riders.
42x19 (59") - Relaxed gearing for cruising or hills.
24x12 (53.4") - Freestyle gearing with smaller chainring.To work out an initial gearing for fixed-single speed find a single gear you can manage on a geared bike and then work out the gear size (in gear inches if the crank length and wheel size is the same between bikes). Then find a chainring / crankset and a matching rear cog with the right number of teeth to provide a matching gearing.