Gradeability of Commercial Vehicles

Commercial vehicles are used for transporting goods as well as passengers in the course of conducting business. Examples of commercial vehicles include pickup trucks, box trucks, semi-trucks, vans, cargo, coaches, buses, trailers, and travel trailers. The commercial vehicles being manufactured by automotive giants certainly feel the competitive essence because of the raised bar of expectation. But, the technology taking leaps and bounds every day, amelioration in performance. Currently, different commercial vehicles are running on Indian roads, but some of them stood out of the ordinary with their versatile excellence and satisfaction to both the businesses and the consumers. The demand for transport has been growing rapidly and the footprints of roads have been widespread to previously inaccessible areas, especially in hilly areas. Also, road inclinations are not always at zero, so the driver must be extremely vigilant while traveling through an inclined roadway. Here comes the essence of ‘Gradeability’.

The ‘grade’ (also known as slope, incline, gradient, main fall, pitch or rise) of a physical feature or landform refers to the tangent of the angle of that surface to the horizontal. Gradeability is a special case of the slope, where zero indicates horizontality. It is measured either in degrees(°) or percentage(%). A larger number indicates a higher or steeper degree of "tilt". Often slope is calculated as a ratio of "rise" to "run", or as a fraction ("rise over run") in which ‘run’ is the horizontal distance (not the distance along the slope) and ‘rise’ is the vertical distance. Grades are typically specified for new linear constructions (such as roads, landscape grading, roof pitches, railroads, aqueducts, and pedestrian or bicycle circulation routes). While aligning a highway too, the gradient is decided for designing the vertical curve.

Gradeability by definition is the ability of a commercial vehicle to negotiate a grade(slope/acclivity) in Gross Vehicle Weight (GVW) condition and it can vary from 0% to 45% (maximum). A 45° gradient is equivalent to 100%. In other words, gradeability is the highest grade a vehicle can ascend maintaining a particular speed. 

Example: A truck with a gradeability of 7% at 60 mph can maintain 60 mph on a grade with a rise of 7%.

Gradeability is dependent on engine power, drivetrain type, gear ratio, weight distribution, vehicle's center of gravity and traction. For off-road vehicles, gradeability equates to the steepest hill (grade) a truck can climb when running at peak engine torque in its lowest transmission gear (and lowest rear-axle ratio if the axle has a double reduction type gearbox). A double reduction gearbox system is one in which the engine output speed is reduced by two times.

Table 1: Vehicle Specification

Methods of gradeability measurement

 Gradeability is measured in multiple ways, mainly:

• As an angle of inclination to the horizontal (20˚, 30˚, 45˚, etc.). 
• As a percentage of rise over run. 
• As a ratio of one part run to some particular number of parts (1 in 20 meters, 1 in 50 feet, etc.) 

Normally, any vehicle is subjected mainly to three resistances and they are rolling resistance, gradient resistance, and aerodynamic resistance. If a vehicle has to start rolling, it has to generate enough tractive force at the wheels to overcome these opposing forces.

• Tractive force:
  

It is the net force available at wheels. To determine this force, we use the following formula: -

Te * ρt * gr   

Te: Torque at the engine(N)

ρt: Transmission efficiency

g: gear ratio

r: rolling radius(m)

• Rolling resistance:
  

This is the resisting force that opposes the rolling of the tires, which is caused due to non-elastic effects at the tire-road surface. It is given by the formula: 

Rr=k*Wcosϴ 

k:  coefficient of rolling resistance

W:  weight of the vehicle(N)

ϴ:  angle of inclination(°)

Table 2: Rolling Resistance Coefficients

*The values given in the above table do not take into account their variations with speed.

• Gradient resistance: 

When negotiating a slope, a component of weight(W) acts against the direction of motion, which is proportional to the angle of inclination of the road surface.

Rg=W*sinϴ

• Aerodynamic Resistance:
  

It is the resistance offered from the air in the direction opposite to the motion of the vehicle. It mainly results from two components: shape drag and skin friction. 

Calculated by:

Rd=1 2 *ρ*Cd*A*V2

ρ: Density of air (1.2 kg/m3) 

Cd: Coefficient of drag

A: Projected area (m2) 

V: velocity (m/s) 

• Total Resistance: 
  

It is the sum of the rolling resistance, gradient resistance and aerodynamic drag forces being applied on the vehicle.

Rt=Rr+Rg+Rd

Gradeability calculation

Consider a truck climbing a haul road with a 12% grade (rising 12 feet vertically in 100 linear feet) would need 12% gradeability to reach the top. And, for every inch the truck's tire penetrates the soft ground, an additional 6% gradeability is required. So, if the truck's tires sink 3 inches into loose gravel on the 12% grade, then the truck would need 30% gradeability (12 + 18) to get up the hill.

• The below-mentioned formula calculates the gradeability (G). We will use the variable ‘G’ to represent gradeability in our calculations.
  
• First, we need to know the values of tractive effort (TE) and gross weight (GW), which for our truck, respectively, are 10581 kg and 20185 kg (assumed).
  
• Hence, the resulting gradeability comes out to be nearly 52.42 %.
  

                           G=100 * TEGW

Traction-limited gradeability 

The formula for gradeability assumes that the truck can use all of its tractive efforts. But sometimes it can't because the drive wheels may slip before using all the available force. Usable tractive effort is determined by two factors: drive-axle weight and the coefficient of traction, which is akin to the coefficient of friction but has to do with rolling, not sliding, contact. Coefficients range from 0.80 on dry concrete to 0.10 on wet, ice-covered pavement.

For off-road, the determination of coefficients of traction can be tricky. For the sake of illustration, however, let us assume dry clay has a rating of 0.55. Thus, to find the theoretical amount of tractive effort our truck can apply before spinning its wheels in this material, multiply its weight on the drive axles (14969 kg) by the coefficient (0.55). The result is 8233 kg. Now, if we use this as the TE(tractive effort) number in the preceding gradeability formula, the result is nearly 41%.

If a truck comes up short on gradeability during the specifying process, then increasing tractive effort by increasing powertrain torque can be a solution. This can be done by choosing an engine with more peak torque, or by boosting the drive train's overall reduction ratio. The methods for accomplishing the latter include transmissions with deep low gears (both forward and reverse), auxiliary transmissions, and two-speed axles. 

To summarize, commercial vehicle designs are based on meticulous research done on road-load data patterns across a particular country and have been tested experimentally on various terrains before being launched in the market and sent to the manufacturer’s dealer networks. Since a vehicle should be ready to be driven on all types of terrains, tractive effort and tire grip become the predominant deciding factors. Superior trucks come with improved gear ratios to ensure maximum operating time spent by the vehicle on the higher gears. Better gradeability enables the vehicle to easily navigate the most hostile road conditions and climb gradients even with a full load. Hence, a vehicle with better gradeability can climb steeper slopes with lesser difficulty.