9.1. Example Problem on Tractive Effort Calculation

Now, for better understanding, let us work out a problem on calculation of the tractive effort. So, calculate the tractive effort generated by a hauling equipment, it is gross weight is given as 50,000 kg, it is traveling on a haul route. It is rolling resistance is given to you directly you can take it from the literature for that particular haul route; it is given as 28 kg per ton. And another important thing to be noted is your tire is sinking about 6 centimeters into the travel surface. That means you have to take into account the penetration resistance also. Now we are going to find what is the total tractive effort needed to overcome this resistance is in the underfoot conditions in your project site.

In this section, we are introducing a specific problem that illustrates how to calculate tractive effort, which is essential for understanding the power required by hauling equipment. First, we identify the key figures: the gross weight of the equipment (50,000 kg) and the rolling resistance (28 kg per ton). We also note the tire's sinking into the ground (6 centimeters), indicating there will be additional resistance to account for, known as penetration resistance. To solve this problem, we will first convert the gross weight from kilograms to tons (50,000 kg = 50 tons), and then calculate the total resistance based on the rolling resistance and the additional resistance from penetration.

Imagine you are trying to push a heavy cart along different surfaces. If the cart weighs 50 tons, that's like trying to push a small car. On a smooth concrete surface, it moves easily, but push it on soft grass, and the wheels start sinking in, making it harder. This is similar to what we see here: depending on how deep the tires sink into the ground and what type of ground they are on, you'll need different amounts of force to keep the cart moving.

First step, calculate the rolling resistance based on the given values. Since rolling resistance is given as 28 kg per ton, for a gross weight of 50 tons: Rolling Resistance = 50 tons * 28 kg/ton = 1400 kg. Now, let's calculate the penetration resistance from the sinking of the tire into the surface. Given that the tire sinks 6 centimeters into the surface, we see from literature that the additional resistance increases by 6 kg per ton for each centimeter of penetration. Therefore, for 6 centimeters: Penetration Resistance = 50 tons * 6 kg/ton = 300 kg. Therefore, the total tractive effort required will be: Total Tractive Effort = Rolling Resistance + Penetration Resistance = 1400 kg + 300 kg = 1700 kg.

To calculate the total tractive effort needed, we first determine the rolling resistance. Since the rolling resistance per ton is provided, we multiply this by the total weight in tons to get the total rolling resistance. After that, we calculate the penetration resistance caused by the tires sinking into the surface, which is added to the rolling resistance to find the overall total tractive effort. This total is significant because it informs us about the power the equipment needs to function effectively without getting stuck or bogged down.

Consider trying to pull that heavy cart through sand. The heavier it is, the more strength you need. If it sinks deeper into the sand, it gets even harder to pull. Just like our calculation: first, we find out how hard it is to move on a firm surface (rolling resistance), then we see how much harder it gets when it sinks into soft ground (penetration resistance). Adding those two together gives us the total effort needed to keep it moving.

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