TOO EASY: gear ratio explained

Basic maths for knowing your track bike better

Many of you curious peeps might have heard or read of what gear ratio someone is riding but without totally understanding what it’s all about. It’s a mystery, you’re craving to know more about what’s what with gear ratios, gear inches, skid patches, and all that semantic field beauty. So.. Read on!  A bit of easy geometry/physics of movement with the main aim to better understand your bike and ride more efficiently.

For having all these concepts automatized in a couple of button clicks, you can buy this app that Sanso recently reviewed. OR.. if, somehow, you want to lubricate your neurons a bit.. get into this.

1. The relationship chainring/cog is the number of times the rear wheel spins with one pedal revolution. This relationship is called GEAR RATIO and you can calculate it like this:

chainring teeth  ÷ cog teeth = GEAR RATIO

e.g : 44T ÷ 16T = 2,75 // every pedal revolution my rear wheel spins 2,75 times | RATIOS ARE ALWAYS UNITLESS NUMBERS.

– Knowing this, we can calculate exactly how many meters we cover with one pedal revolution:

The most common track wheel: 700c 23. The DIAMETER OF the tyres you’ll use is 668mm. (0,668m.)

For calculating the perimeter of a circumference, we need to use the following formula of basic geometry:

P=D x π ; 0,668m. x 3,14 =2,1m.

Every spin of the rear wheel your bike will be advancing 2,1 meters.

 

From here, we’re going to calculate the DEVELOPMENT:

(meters covered by 1 pedal revolution)

As you can imagine, now we just have to multiply the gear ratio (number of spins of the rear wheel per pedal rev.) for the perimeter of the wheel.

In the case of my gear ratio (2,75), every pedal revolution my bike will be covering 2,75 x 2,1m. = 5,77m.

¿NOT YOUR TYRE SIZE, not into cm.? Check out this table and find other tyre sizing options

WARNING:

KEEP UNITS TIDY. If you calculate with your wheel diameter given in inches, the perimeter, and later, the development will be in inches, too.

THE GEAR INCHES

You can easily find on the Internet extensive tables of correspondence CHAINRING/COG, expressed in terms of gear ratio but giving cyphers above 50, while gear ratio values will be under 5. These tables, although they can be found under the name of gear ratio, they refer to a different value, called GEAR INCHES:

Gear Inch Value = Number of Teeth on the chainring ÷ Number of Teeth on the Cog x Diameter of the Wheel IN INCHES!.

The diameter of our wheel in inches is 26.3″. (1 inch=2,54cm.)

MY CASE: 44T ÷ 16T x 26.3″ = 72.3″ (pansy?)

Click here for a chart of gear inches

The bigger the gear inches value, the harder the bike is to pedal and the further the distance it moves with each pedal revolution (only if you keep the same cog size, of course).

The common ratios for city commuting/ city riding go from 70″ to 75″, although these are only the standards. There are more powerful or speed demanding riders that spin out  at those ratios, and they’ll want to go up to 80″ for riding the city.

TRACK RACING?

By comparison, elite track racers commonly hit 60km/h, but would never use a combination larger than 50 x 14 (94”), and more likely would be riding a 49 x 14 (92”) or 51 x 15 (90”).  So, at 60kph, their cadence is between 134rpms (50 x 14) and 141rpms (51 x 15).

cogs feature

Australian track cycling team cog collection (super special shimano cogs collection worth around $10.000 AU) source

pendi track_cyclingweeklyuk

Victoria Pendleton’s track build at a 51/15 (91,2″)

meares-bt_stealth

meares driveline

Anna Meares’ track build with her SRM Power Meter

In cycling, cadence is the number of revolutions of the crank per minute; roughly speaking, this is the rate at which a cyclist is pedalling/turning the pedals. Cadence is related to wheel speed, but is a distinct measurement.  Recreational and utility cyclists typically cycle around 60–80 rpm. Us, we’re a bit tougher, so we’ll be normally doing around 90 rpm.

Knowing our cadence, we can easily know how fast are we riding, by doing this calculations:

RPM to KM/H

1. one of my pedal revolutions covers= 5,77m (development)

2. if I spin my pedal 90 times per minute = 90 x 5,77m = I cover 519,3m per minute

3. One hour has 60 precious minutes in it, so we’d need to multiply those meters per minute for 60 and we’ll get meters per hour

519,3 x 60= 31158 meters per hour

4. One kilometer has 1000 meters in it, so we’d have to divide those meters per hour by 1000 and we’ll be given km/h

31158 ÷ 1000 = 31,16 km/h riding at 90RPM : Not bad!

 SKID PATCHES

Calculating the SKID PATCHES is super easy, you just have to simplify the function N/D where:

N is the number of teeth of the chainring

D is the number of teeth of the cog

for simplifying my combination 44/16, I divide both numerator (N) and denominator (D) by the same number. We can do it by 2, but also easier by 4. Which gives me 11/4

11/4 is an equal expression of 44/16

THE MOST SIMPLIFIED DENOMINATOR (D) OF THE FUNCTION OF OUR CHAINRING/COG TEETH NO. WILL BE THE NO. OF SKID PATCHES IN CASE THE DENOMINATOR IS AN EVEN NUMBER OR YOU’RE NOT AN AMBIDEXTROUS SKIDDER.

More examples:

45/15 simplifies to 3/1 so there will only be 1 skid patch.

42/15 simplifies to 14/5, so there will be 5 skid patches.

43/15 can’t be further simplified, so there will be 15 skid patches.

This is based on the assumption that you always skid with the same foot forward.

If you are an ambidextrous skidder, and the calculation gives an even result, your number of skid patches will be the same.

If you are an ambidextrous skidder, and have an odd denominator, the number of possible skid patches will be doubled, so, in the second and the third cases, you’d have to multiply the number of patches for 2:

42/15 simplifies to 14/5, so there will be 5×2=10 skid patches for an ambidextrous skidder

43/15 can’t be further simplified, so there will be 15×2=30 skid patches: rippa!

 

 

 

 

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