A truck does not roll over because it was going fast. It rolls over because, for the load it was carrying, it was going fast enough. The number that separates the two is the rollover threshold, and it is the one figure in a rollover case that the driver, the loader and the carrier each had a hand in and none of them wrote down.
The fraction. Picture the truck from behind, in a turn. The road pushes its tires toward the inside of the curve while the load, high in the box, keeps trying to go straight. Whether the truck slides or tips depends on how far apart the tires are and how high the load sits, and nothing else. The University of Michigan’s study of heavy-truck rollover, written for a truck maker and a university research center in 1999, defines the limit of a rigid vehicle as “the ratio of the half track (T/2) to the cg height (h)”: half the width between the tires, divided by the height of the center of gravity, which gives the sideways pull, measured as a fraction of gravity, at which the inside tires leave the ground. “The rollover thresholds of passenger cars are virtually always greater than 1 g,” which is why a car in a turn slides first, as Rolled explains through the federal rating built on the same fraction. “The rollover threshold of a loaded heavy truck often lies well below 0.5 g.” The typical five-axle tractor and van semitrailer, the study says, has a threshold perhaps as high as 0.5 g with a dense load carried low and as low as 0.25 g with the worst-case load, and “The typical U.S. five-axle petroleum semitanker has a rollover threshold of about 0.35 g” (UMTRI, 1999), the figure High and Heavy works through for a load that also moves. A quarter of a g is not much. It is the sideways pull a car gives its passengers on a freeway ramp taken without a thought.
The arithmetic. The pull in a turn is the speed squared divided by the radius of the curve. That is why speed matters more than it feels. Take an illustrative ramp with a 600 foot radius. At 40 miles an hour the sideways pull is about 0.18 g. At 50 it is about 0.28 g. At 55 it is about 0.34 g. Going 38 percent faster, from 40 to 55, nearly doubles the load on the trailer, and it carries a truck loaded to a 0.25 g threshold from well inside the line to well past it. The study puts the design standard next to that: the guidelines for highway curve design “result in lateral accelerations as high as 0.17 g at the advisory speed,” and “Drivers regularly maneuver vehicles at well over 0.2 g” (UMTRI, 1999). A curve is built so that a car at the posted advisory speed feels a sixth of its weight pushing sideways. A truck at the bottom of the threshold range has a quarter of its weight to give. The margin between the two is what the yellow sign Advisory describes, and it is not written for the truck.
The soft truck. The fraction assumes a rigid box, and a truck is not one. In a turn the tires squash, the springs lean, the fifth wheel between tractor and trailer has play in it, and the trailer frame twists, so the body moves outward before the tires lift and the center of gravity moves with it. The study adds them up: “All the compliances combined can reduce roll stability to as little as 60 percent of the rigid-vehicle stability” (UMTRI, 1999). A trailer that would hold 0.4 g if it were made of stone may hold 0.24 g as built, before anyone has loaded it badly. Worn springs, soft tires and a loose fifth wheel each take a piece of that margin, and each is a line in a maintenance file.
The load. The width of the axles is fixed. The height of the center of gravity is decided at the dock, which is why the people who never see the road are in a rollover case. Dense freight laid flat on the floor keeps the fraction high; bulky, light freight stacked to the roof pulls the center of gravity up and the threshold down, which is what a furniture load did, or did not do, in The Tall Load. The commercial driver’s manual teaches it as a rule of the trade: “A high center of gravity (cargo piled up high or heavy cargo on top) means you are more likely to tip over,” and “Poor weight balance can make vehicle handling unsafe” (CDL manual, Sections 3.2.3 and 3.2.4). A load that shifts in the turn is worse than one that is merely tall, because it moves toward the side the truck is already leaning to, and the federal rule is written for exactly that: cargo must be secured “to prevent shifting upon or within the vehicle to such an extent that the vehicle’s stability or maneuverability is adversely affected” (49 CFR 393.100).
The cliff. Here is why the driver is so often the last to know. The study describes the event in two sentences that belong in every opening statement about a rollover. “First of all, rollover is very much an either-or situation,” and “It is something like walking up to a cliff with your eyes closed.” Nothing in the cab changes as the sideways pull climbs from 0.2 g to the threshold; the truck is as stable at 0.24 g as at 0.1 g, and at 0.26 g it is gone. And the tractor is built in a way that hides the trailer’s lean: “the flexible nature of the tractor frame tends to isolate the driver from the roll motions of the trailer, which might act as a cue to rollover” (UMTRI, 1999). The trailer can be lifting its inside wheels while the seat under the driver tells him nothing. That is the physical fact behind the manual’s instruction to slow before the curve and not in it: “Tests have shown that trucks with a high center of gravity can roll over at the posted speed limit for a curve,” and “Braking in a curve is dangerous because it is easier to lock the wheels and cause a skid” (CDL manual, Section 2.6.3). Once the truck is over, what happens inside it is the subject of The Roll, Excursion and Crush.
The count. The study opens with the stakes as it found them: about 50 percent of truck-driver deaths and 47 percent of incapacitating injuries occurred in accidents in which the truck rolled over, by the figures it cites, and it notes that a disproportionate number of commercial-vehicle rollover crashes occur on exit ramps, 17 percent by the count it relies on (UMTRI, 1999). A ramp is a curve a truck meets at highway speed with a sign written for cars. That is the geometry of The Ramp, and of a disproportionate share of the rollovers on the road.
What the numbers do in court. Each of them assigns a duty. The fraction belongs to the loader, who set the height of the center of gravity, and to the carrier, which dispatched the truck knowing what it carried; federal law makes the carrier answer for a load that is not “properly distributed and adequately secured” and makes the driver inspect it before he leaves and within the first 50 miles (49 CFR 392.9). The arithmetic belongs to the driver, because Texas forbids “a speed greater than is reasonable and prudent under the circumstances then existing” and requires “an appropriate reduced speed” when “approaching and going around a curve” (Transportation Code Section 545.351), the duty of Reasonable and Prudent; a driver who says the truck went over without warning will reach for Sudden Emergency, and the instruction does not cover an emergency his own speed created. The compliances belong to the maintenance file. And because a rollover usually has more than one author, Texas lets the jury divide it: the trier of fact “shall determine the percentage of responsibility, stated in whole numbers,” for each claimant, each defendant, each settling person and each responsible third party designated in the case (Civil Practice and Remedies Code Section 33.003), which is how a shipper that stacked a box to the roof ends up on the verdict form beside the carrier that sent it out, the allocation Comparative Fault explains. The evidence is the engine’s recorder, which kept the speed; the bill of lading and the loading photographs, which kept the height; the tires, springs and fifth wheel, which an expert reads for the margin they had given away; and the Logbook. All of it is in the company’s hands, and the first letter in the case asks that none of it be repaired, sold or overwritten (Spoliation).
The science is settled. A truck tips at a sideways pull set by its width and the height of its load, a soft truck tips sooner than the fraction says, speed raises the pull with its square, and the driver feels nothing until the trailer is already over. The question a Texas jury asks is who knew the fraction, and who sent the truck into the curve as though no one did.
The fraction, the soft truck, the cliff and the count: C. B. Winkler and R. D. Ervin, Rollover of Heavy Commercial Vehicles, UMTRI-99-19 (University of Michigan Transportation Research Institute, Aug. 1999; SAE RR-004), the record in the university’s Deep Blue repository, with the text as posted in the copy posted by Canada’s Council of Ministers Responsible for Transportation and Highway Safety (the definition; the car, heavy-truck, van-trailer and tanker thresholds; the 60 percent; the 0.17 g and 0.2 g figures; the either-or, the cliff and the tractor frame; the 50 and 47 percent and the 17 percent on exit ramps, each as the study cites them). The load and the curve: Commercial driver’s manual, Section 3, as posted by the Georgia Department of Driver Services (3.2.3, 3.2.4) and Section 2.6 (2.6.3). The rules: 49 CFR 392.9 (paragraphs (a)(1), (b)(1) and (b)(2)); 49 CFR 393.100 (paragraph (c)); Tex. Transp. Code § 545.351 (subsections (a) and (c)(2)); Tex. Civ. Prac. & Rem. Code § 33.003 (subsection (a)). The ramp figures are arithmetic for an illustrative curve, not measurements of any road: lateral acceleration is the speed squared divided by the radius, so on a 600 foot radius 40 miles an hour (58.7 feet a second) gives about 5.7 feet per second squared, or 0.18 g at 32.2 feet per second squared per g; 50 miles an hour (73.3 feet a second) gives about 9.0, or 0.28 g; and 55 miles an hour (80.7 feet a second) gives about 10.8, or 0.34 g. The 0.4 and 0.24 g pair is the study’s 60 percent applied to a round number. Figures and text as published at publication.
