1. Rolling Resistance Calculation

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 begin by converting the vehicle's weight from kilograms to tons to ease the calculation of rolling resistance, which is typically expressed as kilograms per ton. The gross weight of the machine is stated to be 50,000 kg. Since 1 ton equals 1000 kg, we divide 50,000 by 1000 to find that the weight of the machine in tons is 50 tons.

Imagine you are measuring ingredients for a recipe. If a recipe calls for 5 kilograms but your kitchen scale measures in pounds, you'd first need to convert that weight into pounds—just like you convert the vehicle's weight into tons for easier calculations.

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.

In this section, we focus on the calculation of rolling resistance. The rolling resistance is given as 28 kg per ton for the specific haul route. To find the total rolling resistance, we multiply the gross weight of the machine (50 tons) by the rolling resistance (28 kg per ton). Therefore, the total rolling resistance for the machine is 50 tons multiplied by 28 kg/ton, which equals 1400 kg.

Think of rolling resistance as the effort needed to push a heavy object across a rough surface. If you know how heavy the object is (in tons) and how difficult it is to slide on that surface (in kg per ton), you can easily estimate the total effort needed.

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. 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 centimeters, 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.

Next, we calculate the penetration resistance when a tire sinks into the surface. The problem states that the tire is penetrating 6 centimeters into the ground, and the required effort is 6 kg per ton of machine weight for each centimeter. Thus, we multiply the depth of penetration (6 cm) by the effort needed (6 kg/ton/cm), and then multiply that by the gross weight of the machine (50 tons) to find the total penetration resistance, which is 1800 kg.

Consider walking through mud. The deeper you sink (like the depth of penetration), the harder it is to walk (more resistance you feel). Just as you might need to exert more effort to lift your feet out of the mud, the machine's tires need to exert effort to push through the surface.

Now we can find the total resistance, that is nothing but adding 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.

Having calculated both rolling resistance and penetration resistance, we can now find the total resistance the machine encounters. We simply add the two values together: 1400 kg (rolling resistance) + 1800 kg (penetration resistance) equals 3200 kg as the total resistance that the machine needs to overcome.

Imagine hiking up a hill. You have to push against the weight of your backpack (rolling resistance) and fight against the mud that's slowing you down (penetration resistance). Your total effort to get to the top consists of both these parts combined.

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.

With the total resistance calculated at 3200 kg, we can determine the necessary tractive effort to move the machine effectively. Understanding this helps in selecting an appropriate machine that has the power output needed to overcome this resistance during operations on the project site.

Think of it like choosing a vehicle for a road trip. If you know the hills you'll encounter on your way (total resistance), you wouldn’t pick a small car that struggles uphill; instead, you’d choose a more powerful vehicle that can easily handle the required effort.

--