Elevation Matters

Two circuits can look much alike by one obvious measure - and quite different from the cockpit. Two August race meetings provided a useful example: Super Formula visited Sugo, while the British Touring Car Championship went to Knockhill. Both circuits are known for their pronounced elevation changes. The figures seem to confirm the resemblance.

Sugo’s official difference between its highest and lowest points is 69.83 metres, over a lap of roughly 3.6 kilometres. Knockhill is considerably shorter - about 2 kilometres - with its operators quoting an elevation range of approximately 60 metres.

An almost ideal pairing, then, for testing our (another one!) proposed index. Put only elevation range in a table, and the two might appear to belong to the same family. Watch the racing, however, and the resemblance soon wears thin.

Sixty metres of difference

The trouble with the familiar “elevation change” figure is that it tells us only the difference between two extremes. Imagine a wholly artificial circuit: three kilometres of level running, followed by one gentle climb of 60 metres and a descent to the original level. Now imagine another, which climbs and falls ten times over those same three kilometres, with braking zones and corners between the climbs. Both entries in the circuit guide could read “elevation change: 60 metres”, leaving us thoroughly pleased with how much we know.

The first task for our proposed elevation index is therefore to stop treating the difference between the highest and lowest points as an adequate description of a circuit. Sugo and Knockhill make the reason apparent with scarcely a formula required.

Knockhill: elevation packed into two kilometres

Knockhill describes its international layout as approximately 2 kilometres long, with a succession of climbs, descents and corners, and an elevation range of around 60 metres. The lap length matters here: those 60 metres have to fit into just two kilometres of circuit.

For a first, deliberately crude approximation, divide the elevation range by the lap length:

Knockhill: 60 / 2.04 ≈ 29 metres of elevation range per kilometre.

Sugo: 69.83 / 3.586 ≈ 19.5 metres per kilometre.

A difference is already visible. Sugo has the greater absolute elevation range, but Knockhill packs its elevation changes much more tightly into the lap. For now, let us call this a working parameter rather than an index:

Elevation-range density: RD = ΔH / L

Here, ΔH is the difference between the highest and lowest points, and L is the lap length.

Sugo gives an RD of approximately 19.5 m/km; Knockhill, around 29 m/km. That tells us more than elevation range alone. Almost immediately, however, it becomes clear that it still does not tell us enough.

Sugo: a mountain built into the layout

Sugo arranges its elevation differently. Super GT’s official circuit description makes particular mention of the substantial height difference: the main straight climbs noticeably, while the back straight descends. After the descent towards the hairpin, the circuit begins climbing again. The Esses run uphill, High Point lives up to its name near the top of the lap, and the circuit then drops towards the back straight. Even the final corner changes character as the car travels through it: first downhill, then uphill towards the main straight.

Much of Sugo can therefore be understood as a succession of broad vertical waves. A climb lasts long enough to influence acceleration. A descent lasts long enough to influence the speed reached before braking. The driver does more than cross a crest: the car spends a sustained period working on a particular gradient.

That matters to several aspects of its behaviour: drive, braking, the aerodynamic platform and the distribution of load between the axles.

Knockhill gives a different impression. There, the terrain continually intervenes in the car’s work. A crest, a drop, a levelling of the road, a braking zone, another climb - all arrive within a very short distance.

Left to its own devices, our first parameter, RD, would run out of answers here. It notices that Knockhill has “more elevation per kilometre”, but cannot explain what makes that elevation so different in practice.

We need the shape of the profile, not just its height

Imagine the circuit’s vertical profile as a simple graph: distance around the lap on the horizontal axis, elevation on the vertical.

The difference between Sugo and Knockhill then begins to resemble the difference between two signals. One may have a large amplitude but long wavelengths. The other may have a similar amplitude, with much more frequent changes. This is where a meaningful index begins to take shape.

ΔH alone is insufficient. Even ΔH/L is insufficient. Our initial assessment suggests that we need to measure at least three further properties of the vertical profile.

First, how much height the car actually gains and loses over a complete lap. A circuit that climbs 30 metres and descends once presents one case. A circuit that climbs those same 30 metres five times, returning to its original level each time, presents another. The range between the highest and lowest points may remain unchanged, but the car and its suspension face much more activity. We therefore need a measure along the lines of cumulative elevation gain per lap.

Second, the magnitude of the gradients. Two climbs gaining the same 30 metres might occupy 300 metres and 1,000 metres of track respectively. To the car, these are quite different events.

Third, how rapidly the gradient itself changes. This is particularly relevant at Knockhill. The car responds to more than the climb or descent: it also responds to the transition from climbing to descending - a crest - and from descending to climbing - a dip. These transitions produce additional unloading or loading of the car. We are therefore interested not just in elevation, nor even just in its first derivative - the gradient - but in how that gradient changes with distance.

A first result

We have yet to build the index, but comparing Sugo with Knockhill has already allowed us to discard the simplest candidates.

Elevation range, ΔH, is useful but insufficient.

Elevation range per kilometre, ΔH/L, is better: it immediately shows how tightly that range is packed into the lap. Knockhill is substantially higher on this measure - approximately 29 against 19.5 m/km. Yet this figure, too, tells us nothing about the shape of the profile between the highest and lowest points.

Our proposed elevation index must therefore account for at least elevation range, cumulative elevation gain, gradient magnitude, and the frequency and sharpness of changes in gradient.

Only then will we have a measure capable of distinguishing two fundamentally different characteristics:

Sugo’s large, sustained vertical movements of the car;

and

Knockhill’s closely spaced succession of vertical events.

That is why sixty-odd metres in a circuit guide do not, by themselves, make two circuits alike.

In the next instalment, we will take an actual circuit elevation profile and try to turn this qualitative observation into numbers. The first candidate is cumulative elevation gain per lap. It should reveal something that the simple difference between the highest and lowest points misses altogether.

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