# Higher Horsepower Cars Run Later Apexes And Apply Throttle Earlier

I was recently asked how I can tell whether an apex is early or late by looking at data. This is often a tricky question, especially when comparing different cars driven by drivers of different skill level and aggression. I will try to explain my thought process, starting with a simpler example - one of cars differing only in horsepower.

## Identical Weight And Grip

Consider two Miatas with the same weight, suspension and tires taking turn 10. Miata 1 has 100 hp, Miata 2 has 200 hp. Let's suppose Miata 1 drives turn 10 at the limit of traction and is flat out at the apex which is right in the geometric center of the turn. How would Miata 2 drive the same turn with the same driver? If Miata 2 had the same apex speed as Miata 1 (which is possible as cars have identical grip), once Miata 2 applied full throttle it would fly off track or spin at corner exit because it demands more forward grip while requiring the same amount of lateral grip. To stay on track, Miata 2 must run a later apex. A later apex involves:

Performing more rotation at turn in and opening steering earlier and more at corner exit. This way there is less lateral grip demand which leaves grip to be used for forward acceleration.

As Miata 2 is rotating more before the geometric center of the turn (which is the same as apex in Miata 1 but not in Miata 2, as we will see), Miata 2 requires more grip than Miata 1 between turn in and geometric center. As both cars have equal grip it follows that Miata 2 must be slower between turn in and geometric center.

Since Miata 2 is slower at the geometric center, i.e. at that track position Miata 2 is slower than Miata 1, and assuming Miata 1's lowest speed is at the geometric apex which would be accomplished with trailbraking, Miata 2 must have a lower minimum corner speed (the floor of the speed trace in a corner) than Miata 1.

These are all aspects where Miata 2 is slower than Miata 1. What does Miata 2 gain from a late apex?

Miata 2 is faster at corner exit than Miata 1. This is accomplished by accelerating harder from the point at which Miata 2 begins to accelerate (which is where Miata 1 is likely still trailbraking). This is the reason for running a later apex.

Miata 2

*might*be faster at geometric center - Miata 1's apex - but this is not required.Miata 2 applies power earlier than Miata 1. While this is not necessary to simply beat Miata 1 (better exit speed might be sufficient), as Miata 2 is traveling slower than Miata 1 at geometric center there is additional grip available for acceleration for Miata 2 - thus it would be wise for Miata 2 to make use of this grip.

Now, if we look at speed traces of these two Miatas, what would we see?

Both cars have the same speed slopes in braking zones (identical weight and tires).

Miata 2 will start braking earlier than Miata 1.

Miata 2 will decelerate to a lower speed.

Miata 2 will start accelerating earlier than Miata 1.

Speed slope during acceleration will be higher in Miata 2 than in Miata 1.

Speed trace for Miata 2 will cross through speed trace of Miata 1 at some point between turn in and corner exit.

## Differing Grip

In practice, higher horsepower cars often run larger tires, and therefore
have more grip. Continuing with the Miata example, suppose Miata 1
is on a 205 width tire and Miata 2 is on a 275 width tire.
Had both cars had the same horsepower, Miata 2 would have been able to take
turn 10 faster. As Miata 2 has more power than Miata 1, Miata 2 will
run a later apex as we already figured, but it may be the case that
at the geometric center of turn 10 *both cars have identical speed*.

It is important to keep the grip level separate from the line when reasoning about data. Miata 2 with the wider tires may have an apex that is too early or too late - for that car - while having a later apex than Miata 1.

## Differing Weight And Suspension

Weight and suspension also affect how fast a car can drive through a given corner, but in less straightforward ways. The most difficult comparison is one between, say, a Miata and a Corvette.

Tagged: advanced