1.1. Conversion of Vehicle Weight

So, let us convert the vehicle weight into tons, because your rolling resistance is commonly expressed as kg per ton. So, let us convert the weight of the machine into tons. You know that the gross weight of the machine is given as 50,000 kg. So, 1000 kg = 1 ton, so divided you will get the gross weight of the machine as 50 tons.

In this step, we convert the weight of the vehicle from kilograms to tons to standardize the measurement for rolling resistance calculations. The gross weight of the machine is given as 50,000 kg. Since 1 ton equals 1000 kg, we divide 50,000 kg by 1000 to find the vehicle's weight in tons, resulting in 50 tons.

Think of converting weights similar to how you might convert currency. Just like you can convert dollars to euros based on the current exchange rate, converting kilograms to tons makes it easier to work with standard units in certain calculations.

Now the rolling resistance you need to calculate for this particular haul route is given as 28 kg per ton. So, you multiply the gross weight of the machine by the rolling resistance value. So, gross weight is 50 tons multiplied by the rolling resistance is 28 kg per ton for that particular haul route. This gives you the rolling resistance of 1400 kg.

Once we have the vehicle weight in tons, we can calculate the rolling resistance. The problem states that the rolling resistance is 28 kg per ton. We perform the calculation by multiplying the gross weight (50 tons) by the rolling resistance (28 kg/ton). Thus, 50 tons × 28 kg/ton = 1400 kg. This means the force opposing the vehicle's motion on the haul route due to rolling resistance is 1400 kg.

Imagine riding a bicycle. If you know how much weight you are carrying per kilometer and how much it slows you down, you can calculate how difficult it will be to pedal based on the weight, just like we calculated rolling resistance based on vehicle weight and resistance per ton.

Now we need to find the penetration resistance. It is given to you that the tyre is sinking to a depth of 6 centimeters into the surface. For each centimeter of penetration, the amount of effort needed is 6 kg per ton per centimeter. So, you multiply that by the depth of penetration (6 cm) and the gross weight of the machine (50 tons). This gives you the penetration resistance as 1800 kg.

In this step, we calculate the penetration resistance, which is the force needed to push the tyre down into the ground. The problem states that the tyre sinks 6 cm into the surface and requires 6 kg of effort per ton for each centimeter of sinking. We multiply the depth of penetration (6 cm) by the gross weight of the machine (50 tons) and the effort needed per ton (6 kg), resulting in Penetration Resistance = 6 cm × 50 tons × 6 kg per ton = 1800 kg.

Consider trying to push a toy car into the sand. The deeper you try to push it, the harder it gets because the sand resists the car's movement. Just like that, when a vehicle's tyre sinks into soft ground, it faces resistance that we can calculate by considering how deep it sinks.

Now we can find the total resistance, which is the sum of rolling resistance and penetration resistance. This leads to 1400 kg (rolling) + 1800 kg (penetration) = 3200 kg total resistance. Thus, the tractive effort of at least 3200 kg is needed to overcome this total resistance.

To find out how much total force (resistance) the vehicle must overcome to move, we add the rolling resistance (1400 kg) and the penetration resistance (1800 kg). The calculation gives us a total resistance of 3200 kg. This means that the vehicle needs to generate at least 3200 kg of tractive effort to effectively move along the haul route.

Think of a tug-of-war where both teams need to overcome the combined weight of the opposing team to win. Similarly, in this scenario, the vehicle's engine must produce enough force to overcome both rolling and penetration resistances combined to move forward.

So, select the machine accordingly, that is the purpose of estimating all this resistance, so we can know what is the required power for your machine. Select a machine that can generate enough power to overcome this resistance.

The aim of calculating the rolling and penetration resistance is to determine the appropriate machinery for the job. Estimating the resistance helps us understand how much power the machine needs to perform efficiently in a given haul route. This informs our decision about which machine to select based on its capabilities.

It's similar to choosing a vehicle for a road trip. If you know the distance and what kind of roads you'll be on, you can select a vehicle with enough power and fuel efficiency to handle those conditions, ensuring a smooth journey.

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