The arithmetic of spec’ing
When that dream truck you ordered turns out to be a wheezing, fuel-sucking disappointment that couldn’t pull a hill hauling potato chips, the likely culprit is failure to properly “do the math.”

By Paul Abelson, senior technical editor

Thinking about buying a new truck? If the truck is going to be a partner in your business, you need it to do certain tasks. And it needs to get good fuel economy, too. It takes more than guesswork to spec out the perfect truck for your trucking business; getting it right can be a challenge.

Math is involved in many aspects of trucking and nowhere more so than in the process of determining how variations in power-train components will affect performance and drivability. Fortunately, we have computers and programs to do the number crunching, but the savvy truck buyer needs to understand the basic arithmetic involved and why.

When you specify components for trucks, you learn about “tradeoffs.” It’s like a negotiation between what you would like to have, what you need to have, what you must give up and what you can afford. They are often at odds with each other.

Who among us wouldn’t want a truck with 550 or 600 horsepower, 2050 lb-ft of torque, an 18-speed double-overdrive transmission, tall 24.5-inch tires and a final drive ratio that will tie it all together?

Sounds great at first, but the result will be a heavy drivetrain and a very expensive one. It would also consume fuel at a higher rate than a smaller engine would, and its extra weight might keep you from getting some loads or it may limit the loads and revenue the truck can earn.

When you are spec’ing the truck of your dreams, you need to determine how components and gear ratios will work together. Back in the ’90s, the Technology & Maintenance Council had just started promoting the “gear fast, run slow” philosophy to improve fuel mileage. One driver spec’d a double-overdrive 18-speed behind a 550-hp engine with a sweet spot around 1,400 rpm. He wanted 11R24.5 rubber and a final drive of 3.08:1. The truck was a classic with a long hood and huge flat bumper. Needless to say it had the aerodynamics of a brick.

The truck could cruise all day at 95 mph, but the driver had to shift on every one-half percent grade increase. In practical terms, he rarely got out of 12th gear and his fuel mileage and hill climbing suffered. He could have had a much more drivable truck if he’d had some calculations done by his truck dealer. Speed in each gear, startability and gradeability can easily be computed by any dealer. Gradeability is the highest grade a vehicle can ascend while maintaining a particular speed and, yes, there’s a formula for that.

Rolling resistance
When a truck is traveling at a steady rate, the forces acting on the truck at the drive tires are rolling resistance (including internal engine and drivetrain losses and tire resistance to flexing), climbing resistance, acceleration resistance and aerodynamic drag.

Rolling resistance is related to truck speed, tire construction, tread design and inflation pressure. There isn’t much you can do about internal drivetrain friction loss. It is what it is, and component makers are working constantly to reduce it.

For low-profile tires, 24.5-inch wheels give 501 revolutions per mile and 22.5-inch wheels give you 515 revolutions per mile. Tire makers have the number for each tire they sell. This works directly with the drive axle ratio to determine top speed and climbing or starting ability.  If you want tall rubber, you’ll need more drive axle reduction to maintain performance up hills. If you want smaller tires, a “faster” ratio will give you cruising speed. The computer will tell you speed and climbing ability in each gear.

Grade resistance
Climbing or grade resistance is the vertical component of direction. A 1 percent grade means your truck climbs one foot vertically for every hundred feet of horizontal travel. For a 2 percent grade, that becomes two feet, and so forth. That’s like lifting your gross combination weight straight up every 100 feet.

On today’s interstate highways, 85 percent of the grades are 1.5 percent or less, so a truck should be spec’d to climb at least that without shifting.

Acceleration resistance
Acceleration resistance is where reserve horsepower enters the equation. If your truck can make 400 hp at 1,500 rpm and you are using only 210 hp, you have a potential 190 hp in reserve to help you increase speed or climb hills. As you go faster or climb more steeply, you use up your reserve. Then you stop accelerating or shift down to continue climbing.

Aerodynamic resistance
As your speed increases, aerodynamic resistance increasingly consumes power. It’s composed of three main components: frontal area, coefficient of drag, and velocity cubed.

Frontal area is determined by the height and width of your rig, provided the trailer is closely coupled to the tractor. With a large gap, you’re pulling an extra flat surface behind your truck.

Coefficient of drag is a measure of how easily your truck slips through the air. It’s reduced by devices that smooth air flow, like trailer tails, skirts or underbody fairings.

The first two come with the truck. Vehicle speed is the variable that you control.

The faster you drive, the more power you need, and at an increasing rate. Going twice as fast far more than doubles your need for power. Because the forces increase with the cube of the speed, you need to overcome eight times the aerodynamic resistance in order to double speed. Tripling your speed requires 27 times the power. Below 40 or 50 mph, depending on the truck’s aerodynamics, the forces are insignificant. At higher speeds, they can be very significant.

Because aerodynamics is such a factor, it takes about twice the power to cruise at 75 as it does to cruise at 60. Fuel use is higher and your power reserve is reduced.

The simplest ways to spec a truck are to use what has worked in the past or to take what a dealer has in inventory. Those specs have the broadest appeal. But there is newer technology today. The latest truck engines run slower than ever before, developing peak torque as low as 1,000 rpm. Many cruise at 1,200. Rear drive ratios below 3.00:1 let engines give maximum fuel mileage. The technology improves, but the math stays the same. LL