1.2. Calculation of Total Rolling Resistance

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 chunk, we are focusing on converting the weight of a vehicle from kilograms to tons. The reason for this conversion is that rolling resistance is generally calculated in kilograms per ton. Since the vehicle's gross weight is given as 50,000 kg, we can convert this into tons by dividing it by 1000 (since 1 ton equals 1000 kg). Thus, 50,000 kg divided by 1000 equals 50 tons.

Think of it like converting your weight from pounds to stones for a weigh-in contest; it’s the same quantity expressed in a different unit. Just like 200 pounds can be converted to approximately 14 stones, here we convert vehicle weight for easier calculations in engineering.

Now the rolling resistance you need to calculate for this particular haul route it 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. So, now we are going to calculate for your particular vehicle what is the total rolling resistance? That is nothing but 1400 kg, so 1400 kg is your rolling resistance.

In this chunk, we are calculating the total rolling resistance using the value of rolling resistance per ton. With the previously calculated gross weight of 50 tons and a rolling resistance value of 28 kg per ton, we multiply these two values together: 50 tons multiplied by 28 kg/ton equals 1400 kg. Therefore, the total rolling resistance the vehicle needs to overcome is 1400 kg.

You can imagine this scenario similar to how much force you need to keep pushing a heavy cart on a flat surface. If the cart weighs 50 units and it requires 28 units of force for every unit of weight to keep it moving, your total required force will increase proportionately as you add weight.

Now we need to find the penetration resistance. It is given to you in the problem that the tyre is sinking to the depth of 6 centimeters into the surface. So, you know that for each centimeter of penetration the amount of effort needed is 6 kg per ton per centimeter. So, you multiply that by how much is the depth of penetration? It is nothing but 6 centimeter, and what is the gross weight of the machine? It is nothing but 50 tons. So, that gives you the penetration resistance as 1800 kg.

Here, we are determining the penetration resistance, which is the force required when the tire sinks into the ground. The problem states that each centimeter of penetration requires an additional 6 kg of force per ton of vehicle weight. The tire has penetrated 6 centimeters into the ground, so we multiply the penetration depth (6 cm) with the force required per ton (6 kg/ton) and the gross weight of the machine (50 tons), resulting in a total penetration resistance of 1800 kg.

Imagine if you’re trying to push a heavy object across a deep rug. The deeper the object sinks into the rug, the more effort you’ll need to exert to move it. The depth of the tire in the soil acts just like the depth of the object in the rug, requiring more force the deeper it sinks.

Now we can find the total resistance, that is nothing but add your rolling resistance and the penetration resistance. It is nothing but your 1400 kg + 1800 kg, so that gives me the answer as 3200 kg is the total resistance.

In this section, we are calculating the total resistance the vehicle must overcome while moving. The total resistance is the sum of the rolling resistance (1400 kg) and the penetration resistance (1800 kg). Adding these two values gives a total resistance of 3200 kg that the vehicle needs to counteract to move effectively.

Think of it like carrying heavy boxes while walking: if one box (the rolling resistance) weighs 1400 kg and another box (the penetration resistance) weighs 1800 kg, the combined total weight you will need to carry is 3200 kg. This is what the vehicle has to overcome to keep moving.

So, I need tractive effort of at least 3200 kg to overcome this resistance in a project site. So, the total tractive effort needed to overcome this resistance is 3200 kg. So, select the machine accordingly, that is the purpose of estimating all this resistance, so that we can know what is the required power for your machine? Select a machine that can generate enough power to overcome this resistance.

In this part, we summarize our findings by stating that the vehicle must produce a tractive effort of at least 3200 kg to move against the total resistance calculated earlier. This information is crucial for choosing a machine that can generate sufficient power to manage the identified resistance forces in real-world conditions.

Imagine selecting a backpack to carry your boxes. If you know that you have to carry a total weight of 3200 kg, you wouldn’t select a small backpack; you’d opt for something robust and durable that can comfortably handle the load without breaking, thus ensuring you can complete your task.

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