Bicycle Gear Calculator

The "size" of a bicycle gear is a function of many factors:

• Radius of the wheels
• Radius of the crank arms (that the pedals are mounted on)
• Radius of the front chain ring (proportional to the number of teeth)
• Radius of the gear in the back (proportional to the number of teeth)

Problem

• It can be difficult to determine how different configurations of cranks, chain rings and gears will compare in terms of final gearing.
• This can be important, for example, when deciding how to configure the drivetrain of a bike.

Creates a visual comparison of two different drivetrain configurations on the same graph

Input:

• Crank length
• Frong chain ring size (two values: small and large (according to number of teeth))
• A choice from several common 10-cog rear gear clusters

Output:

• A graph showing the GAIN RATIO as a function of chain ring and sprocket

• A measure of the size of a gear: a higher gain ratio is a 'bigger' gear that will carry the bike further with each pedal stroke but which requires more force to turn
• For example, if the gain ratio is 5.58:
  • "...for every inch, or kilometer, or furlong the pedal travels in its orbit around the bottom bracket, the bicycle will travel 5.58 inches, or kilometers, or furlongs." - Sheldon Brown http://www.sheldonbrown.com/gain.html
• Calculated as:
  • {(radius of wheel)/(radius of crank arm)} * {(teeth in chain ring/teeth in rear sprocket)}
• Note: in this app, wheel radius is kept constant at 340 mm (standard wheel size for road bikes)
• Source code for the shiny app can be found at
  • https://github.com/jleslie17/BicycleGearCalculator

WheelR <- 340; CrankR <- 175 ##Standard for 'road' bikes
FrontVector <- rep(c(42, 52), each = 10)
RearVector <- c(11,12,13,14,15,16,17,19,21,23)
GainRatio <- WheelR/CrankR*FrontVector/RearVector
Gears <- data.frame(Config = rep("Configuration 1", 20), Front = FrontVector,
                    Ring = rep(c("small", "large"), each = 10),
                    Rear = RearVector, GainRatio = GainRatio)
head(Gears)

##            Config Front  Ring Rear GainRatio
## 1 Configuration 1    42 small   11  7.418182
## 2 Configuration 1    42 small   12  6.800000
## 3 Configuration 1    42 small   13  6.276923
## 4 Configuration 1    42 small   14  5.828571
## 5 Configuration 1    42 small   15  5.440000
## 6 Configuration 1    42 small   16  5.100000