The Skid Patch Calculator is an essential tool for fixed-gear (fixie) bicycle riders. It determines the number of unique spots on your rear tire where the wheel stops when you initiate a skid, a critical factor for maximizing tire lifespan and maintaining ride safety.
Skid Patch Calculator
Skid Patch Calculator Formula
The formula for calculating the number of unique skid patches ($S_{\text{unique}}$) is based on the gear ratio and the Greatest Common Divisor (GCD) of the number of teeth on the chainring and cog.
$$S_{\text{unique}} = \frac{P}{\text{GCD}(C, P)}$$
Source: Wikipedia – Greatest Common Divisor, Sheldon Brown – Skid Patches
Variables Explained
Understanding the inputs ensures you get an accurate result:
- Chainring Teeth (C): The number of teeth on the large chainring in the front, driving the chain. This is always a positive integer.
- Cog Teeth (P): The number of teeth on the fixed cog attached to the rear hub. This must also be a positive integer.
- Unique Skid Patches ($S_{\text{unique}}$): The final calculated number of distinct contact points on the tire where a skid can occur.
What is Skid Patch Calculator?
A skid patch calculator is a specialized tool that helps fixed-gear cyclists determine how many unique points on their rear tire are used as the contact point when they lock the pedals to skid. When a fixie rider skids, the wheel stops at one point relative to the crank’s position. If the gear ratio is a simple integer (e.g., 44/11 = 4), there is only 1 unique skid patch, which wears the tire out extremely fast.
The number of unique skid patches is directly proportional to tire longevity. The more unique patches you have, the longer your tire will last, as the wear is distributed across more surface area. Ratios where the chainring and cog teeth share a low GCD (like 48/17, where GCD is 1) yield the highest number of patches (17 unique patches), making it a desirable setup.
How to Calculate Skid Patches (Example)
Let’s calculate the unique skid patches for a common gear ratio: Chainring (C) = 48, Cog (P) = 16.
- Identify Inputs: C = 48, P = 16.
- Find the Greatest Common Divisor (GCD) of C and P: The largest number that divides both 48 and 16 is 16. So, $\text{GCD}(48, 16) = 16$.
- Apply the Formula: Divide the Cog Teeth (P) by the GCD. $S_{\text{unique}} = 16 / 16$.
- Determine the Result: The calculation yields $S_{\text{unique}} = 1$. This means this ratio is extremely poor for tire life, as the skid point is always the same.
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Frequently Asked Questions (FAQ)
Is a higher number of skid patches better?
Yes. A higher number of unique skid patches means the wear from skidding is distributed over more points on the tire, significantly prolonging the tire’s lifespan and reducing the risk of a blowout at a single worn-out point.
What is the best gear ratio for skid patches?
The “best” ratio is subjective, balancing skid patches with speed/effort. However, for maximum unique skid patches, you should choose a ratio where the Chainring (C) and Cog (P) have a Greatest Common Divisor (GCD) of 1 (coprime), such as 49/17 or 48/19. This maximizes $S_{\text{unique}}$ to P.
Can the skid patch calculator tell me my total skid spots?
This calculator provides the number of *unique* skid patches ($S_{\text{unique}}$). If you are proficient at switching your dominant foot forward (switching between two pedal positions), your total theoretical skid spots is $2 \times S_{\text{unique}}$, provided the chainring and cog are not both even (which would require a slightly more complex formula).
Do derailleur bikes need to worry about skid patches?
No. Skid patches are only a concern for fixed-gear bicycles that use the drivetrain to stop the wheel. Bikes with freewheels (derailleur bikes) can skid at any point on the tire, as the rear wheel is decoupled from the pedals when freewheeling or braking.