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The Racing Line Explained: Outside, Apex, Outside, and Why It Is Faster

Why the racing line is fastest: the outside-apex-outside arc, the physics of radius and speed, late versus early apexes, linked corners and trail braking.

By Published 3 min read

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Key takeaways

  • The racing line uses the whole track: start wide, clip the inside at the apex, and run wide again on exit.
  • For a given amount of grip, a wider radius allows a higher speed: cornering speed rises with the square root of the radius.
  • A late apex sacrifices some entry speed for a faster exit onto the next straight; Wikipedia notes an early apex is largely considered a beginner mistake.
  • In a sequence of corners, Wikipedia notes a driver may sacrifice the line through the early ones to exit the last one fastest.
  • Trail braking, carrying some brake into the turn, shifts weight to the front tyres to help the car rotate.

The racing line is the optimal path around a circuit. Wikipedia notes that in most cases it uses the whole width of the track to lengthen the radius of a turn: in from the outside edge, touching the apex on the inside, and back out to the outside. The reason is simple physics. This guide explains its shape, the arithmetic behind it and the main variations, drawing on Wikipedia's articles on the racing line and trail braking.

The basic shape

Wikipedia describes the optimal line into a corner as an arc of continuously changing radius:

  1. Turn-in from the outside. The line starts at the outside edge of the track.
  2. Tighten to the apex. As the car slows, the radius decreases towards a clipping point on the inside, the apex.
  3. Unwind to the outside. After the apex, the radius increases as the car accelerates, ending at the outside of the track.

In short: outside, apex, outside. Wikipedia adds that the line can often be glimpsed on the asphalt as tyre skid marks.

Why a wider arc is faster

A car following a curve needs a sideways acceleration, and Wikipedia's article on centripetal force gives its size: speed squared divided by the radius of the curve. Tyres can only supply so much grip. So, for a fixed grip limit, the maximum speed through a curve rises with the square root of the radius: double the radius and you can go about 41% faster, because the square root of 2 is about 1.41.

Worked example. Suppose a car can sustain 1.5 g of cornering grip, about 14.7 m/s².

Radius of the path Maximum speed
50 m about 27 m/s, 98 km/h
100 m about 38 m/s, 138 km/h
200 m about 54 m/s, 195 km/h

Using the full width of the track straightens the path and enlarges the radius, which is the whole point of going wide.

Late apex versus early apex

Wikipedia describes two common variations:

Apex How it works Effect
Late apex Turn in later, reaching the inside later in the corner Slower entry, but a longer radius on exit and more speed onto the straight
Early apex Turn in early Faster entry, but a tighter, slower exit; largely considered a beginner mistake

The reason exit speed usually wins: speed gained on exit is carried down the whole of the following straight, while speed lost on entry costs only a short distance. Wikipedia quotes the racing driver Ross Bentley's rule of thumb: the faster the corner, the closer to the geometric line you should drive; the slower the corner, the more you need a later apex.

Corners in sequence

When corners come in quick succession, the exit of one becomes the entry of the next. Wikipedia's example is the Maggots and Becketts complex at Silverstone. The driver's goal is then to exit the final corner onto the following straight as fast as possible, even if that means "sacrificing the line" through the earlier ones.

Wikipedia adds that finding the exactly optimal line is a hard mathematical optimisation problem, trading average speed against the curve's total curvature and distance, and that one common approximation, an Euler spiral whose radius changes at a constant rate, is close to the best but can usually be beaten.

Trail braking

The racing line is not only steering. Wikipedia describes trail braking as using the brakes past the turn-in point and gradually releasing them, instead of finishing all braking in a straight line. It transfers weight to the front tyres, increasing their traction and reducing understeer, so the car rotates better into the apex. The brake pressure is fully released somewhere between turn-in and the apex, depending on the situation. It is a fine balance: Wikipedia cautions that too much braking effort can make the car understeer heavily or, with the brake bias set close to neutral, lock the rear wheels and spin it.

When drivers leave the line

In a race, the ideal line is not always available: traffic, battles for position and rain all change it; wet-weather racing covers racing in the wet. A strong exit also sets up a pass using the slipstream on the next straight, as slipstream and drafting explains, and the car's setup decides how much grip there is to use; see racing car setup basics.

In Car Racing - Pro Career Racer, one of our sports career games, choosing whether to brake early, trail-brake or risk a late move, and which line to take through a hairpin or chicane, are among the decisions you make; the game guide explains how.

Good to know

Frequently asked questions

What is the racing line?
The path round a circuit that minimises lap time. Wikipedia describes the general shape through a corner as an arc of continuously changing radius: it starts at the outside of the road, tightens towards a point on the inside, the apex, as the car slows, then widens again as the car accelerates out to the outside.
Why is a late apex faster?
Because it lengthens the radius the car turns on at the exit, allowing more speed out of the corner onto the following straight, at the cost of a slower entry. Extra speed at the exit carries down the following straight, which is why a slower entry can be worth it.
How does the radius of a corner affect speed?
The acceleration needed to follow a curve is speed squared divided by radius. With a fixed amount of grip, the maximum speed therefore rises with the square root of the radius: doubling the radius allows about 41% more speed.
What is trail braking?
Using the brakes past the turn-in point and gradually releasing them. Wikipedia explains it transfers weight to the front tyres, increasing their traction and reducing understeer, so the car turns better.

Sources

  1. Racing line (opens in a new tab)Wikipedia — accessed
  2. Trail braking (opens in a new tab)Wikipedia — accessed
  3. Centripetal force (opens in a new tab)Wikipedia — accessed

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