The Coquihalla, the stretch of Highway 5 climbing out of Hope, British Columbia, is known for long, steep grades and hard winters. It is exactly the kind of road that invites a what if question: can a fully laden semi-truck/lorry climb it, and what changes when summer tarmac turns to packed snow?
Figure 1 - Trucks operate in all weathers, conditions and terrain; engineers ensure that capability. Donna Elliot/Unsplash
There's an important questions for design engineers, fleet operators and logistics planners to understand; questions a simulation model can answer without a truck, a mountain or a very patient test driver. In this post I take a heavy goods vehicle (HGV) model adapted from the Claytex VeSyMA suite for Dymola, point it at a series of mountain gradients, and vary the grip. Three things interest me:
A heavy vehicle on a long grade is a clearly defined physics problem. Gravity pulls it back down the slope, and the powertrain must answer through the drive wheels - which can only put down as much tractive force as the tyres will accept. On a dry road the limit is engine power; the truck settles at whatever speed the powertrain can sustain. Drop the grip and a second limit appears - traction - where the wheels slip before the truck can accelerate any further.
I ran three gradients, each within reach of a road like the Coquihalla, whose steepest sections approach 8%: 1:20 (5.00%), 1:17 (5.88%) and 1:14 (7.14%). Over each, I stepped the tyre-road friction (μ) down a ladder: 0.9 for dry tarmac; 0.5 and 0.4 for studded or chained tyres on packed and loose snow; and 0.375 and 0.3 for winter tyres on those same two surfaces. So which of the two ends up in charge on a climb like this - the engine, or the grip?
The vehicle is a 42 tonne (metric) HGV - a 4×2 tractor with a two-axle trailer - adapted from the HGV model found in the VeSyMA library, optimized for straight line studies like this. Working from a library like this means the architecture (chassis, powertrain, driveline, driver and road) is already built and physically structured, so the study becomes a matter of parameterizing models then sweeping variables rather than modelling physics from scratch.
The driver is deliberately blunt; it demands 100 km/h and holds the throttle wide open. On these grades it never comes close, so the throttle stays pinned and the truck simply settles at its flat-out best, giving a clean “maximum speed” for each run. Every run starts from rest on the grade and terminates automatically once the vehicle has climbed 5, so every scenario is judged over the same hill and the fuel and speed numbers compare fairly.
Figure 2: The top-level experiment. Gradient and μ in the road model are the two variables swept across the run matrix.
Five friction conditions across three gradients gives 15 runs, swept automatically in Dymola.
So how far short of that 100 km/h ambition does the truck fall? The headline result is the vehicle speed at the end of each 5 km climb - its sustained best on that grade and surface.
|
Gradient |
μ = 0.9 |
μ = 0.5 |
μ = 0.4 |
μ = 0.375 |
μ = 0.3 |
|
1:14 (7.14%) |
32.16 |
28.77 |
27.16 |
26.66 |
24.84 |
|
1:17 (5.88%) |
37.20 |
33.83 |
32.20 |
31.69 |
29.81 |
|
1:20 (5.00%) |
44.69 |
41.11 |
39.34 |
38.79 |
36.72 |
Table 1: End-of-climb speed (km/h). μ conditions: 0.9 dry tarmac, summer tyres; 0.5 studded/chained on packed snow; 0.4 studded/chained on loose snow; 0.375 winter tyres on packed snow; 0.3 winter tyres on loose snow.
Even on dry tarmac the truck is firmly power-limited: the best it manages is 44.7 km/h on the shallowest grade, dropping to 32.2 km/h at 1:14 - nowhere near the 100 km/h demand for comparable and moderate tyre slip ratios. Steepening the grade costs the most speed. On top of that, reducing grip peels off a further, consistent slice at every gradient: at 1:14 the truck loses close to a quarter of its speed going from dry tarmac (32.2 km/h) to loose snow (24.8 km/h). Both effects are visible in every row.
Why does grip cost speed even when the truck still climbs? Because as μ falls, the drive wheels begin incurring significant amounts of wheelspin during the climb. The truck becomes traction limited, not power limited.
Figure 3: The amount of wheelspin on the driven wheels tells the story regarding lost tractive effort due to road conditions (NB: the plot has been truncated for clarity. The truck has reached steady state).
As the grip level drops, wheelspin becomes progressively more impactful on the performance of the truck. On a dry road, the gradient is already curtailing the grip the tyre can generate, due to the reduced vertical load on the drive wheel caused by the climb, inducing not insignificant wheelspin (slip ratio >0.15). With slipperier tyre/surface combinations, this becomes severe wheelspin (slip Ratio >0.3). Greater wheelspin means the engine’s torque is used to accelerate the wheel itself rotationally, versus pulling the mass of the truck uphill, as the amount of tractive force the tyre can impart onto the road is progressively reduced. Not only is this observed during pull away from rest, but also as the truck has settled into a steady state climb.
There is a second story in the driveline, and it raises a question of its own: while the wheels are scrabbling for grip, what is the transmission quietly getting up to? Under these sustained high loads, the torque converter’s lockup clutch stays disengaged throughout the climb. That is entirely expected; an open converter is doing exactly the job it exists for, multiplying torque at low road speed under heavy load. But an unlocked converter means the impeller and turbine turn at different speeds, and that difference shows up as slip across the fluid coupling, and slip means heat generation.
Figure 4: Rate of power loss occurring within the torque converter due to slip between the impeller and turbine causing sheer in the Torque Converter Fluid. Almost 4kW more energy is being generated by the torque converter during the lowest grip/steepest climb.
The torque converter model currently is unimpacted by heat, but with Dymola this can be incorporated easily. Given the wide operating range of ambient conditions the truck must endure on this climb - +30°C to -20°C – ensuring that there is adequate cooling capacity is vital. Otherwise, excessive heat generation will adversely impact the performance of torque converter, and its reliability.
Two findings fall out of the sweep. First, a laden semi-truck on a mountain grade is power-limited even in the dry - it climbs, but slowly, and steeper grades cost speed fastest. Second, reducing grip takes a further, repeatable bite out of that speed through drive-wheel slip, and keeps the torque converter running unlocked throughout. None of this needed a real truck or a real mountain: a single VeSyMA model, a parameter sweep and a distance-terminated stop gave the whole picture.
The obvious next step follows straight from that unlocked converter. Because the low-μ cases here stand in for cold, snowy conditions, the truck generates the most converter slip. Whether that heat becomes a problem depends on how fast it builds and how well the transmission sheds it, and that is a genuinely multi-physics question, dependent on the mechanical characteristics of the truck and ambient conditions. Dymola is well suited to it: we could enable the thermal port on the torque converter, coupling the mechanical model to a thermal boundary and/or sink, and simulate transmission-fluid temperature over a long climb. Making the torque converter’s performance temperature dependent closes the loop on the physics.
That would tell us whether sustained slip on a winter ascent risks overheating the transmission. Given Canada’s weather patterns, maximum heat generation can be at 0°C as the snow begins to fall and we haven’t fitted studded chained tyres, or as low as -20°C during a sustained cold spell and we’re caught out in a similar tyre choice quandary.
Other interesting avenues this type of simulation can be used to look at:
Further detail can be added to the truck model with the VeSyMA – Suspensions library, equipping it for lateral dynamics. This opens the door to investigating other factors such as differential action and effect, or stability analysis under hard traction in difficult conditions.
Any commercial vehicle must be engineered for reliability in all weather conditions it will face. With climate change, weather patterns are becoming more erratic and variable. Dymola paired with VeSyMA enables you to future proof your designs and engineering decisions as much as feasible for all eventualities, making your products stand out in the market as the dependable choice for these challenging times.
Written by: Theodor Ensbury – Senior Project Engineer