1.3. Penetration 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 step, we begin by converting the weight of the vehicle from kilograms to tons because rolling resistance calculations often require weight in tons. We take the gross weight of the machine, which is given as 50,000 kg. To convert this to tons, we use the conversion factor: 1 ton = 1000 kg. Therefore, we divide 50,000 kg by 1000 to find that the machine weighs 50 tons.

Think of it like converting your body's weight into stones whenever you're discussing your weight with a friend from the UK. If you weigh 70 kg, you'd tell them you weigh around 11 stones (since 1 stone is approximately 6.35 kg). Just like that, converting to tons helps us use the right scale of measurement for our 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, so 1400 kg is your rolling resistance.

After converting the vehicle weight to tons, we calculate the rolling resistance, which is a measure of the force resisting the motion when the vehicle rolls on surfaces. Here, the rolling resistance is provided as 28 kg per ton. To find the total rolling resistance, we multiply the weight of the vehicle (50 tons) by the rolling resistance value (28 kg per ton). The calculation looks like this: 50 tons x 28 kg/ton = 1400 kg. This means that to move the vehicle, a force of 1400 kg is required just to overcome rolling resistance.

Imagine you're pushing a shopping cart (the vehicle) in a supermarket. If the cart is heavy (like our 50-ton vehicle), it requires more effort (rolling resistance) to move it. If the cart has flat wheels (good surface), it's easier to push than if it has wobbly or squeaky wheels (high rolling resistance). Here, the effort needed is quantified as 1400 kg of force in our calculations.

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 you know that. 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.

Next, we calculate the penetration resistance, which is the resistance encountered by the tires as they sink into the surface. The problem states that the tires sink 6 centimeters and that each centimeter of penetration requires 6 kg of force per ton. We multiply the depth of penetration (6 cm) by the vehicle's weight (50 tons) and the specified resistance value (6 kg/cm/ton): 6 cm x 50 tons x 6 kg/cm/ton = 1800 kg. Therefore, the total penetration resistance is 1800 kg.

Think of trying to walk on a sandy beach. The deeper your feet sink into the sand (like the 6 centimeters), the harder it is to walk (this is like the additional force needed). If someone weighs more (like our 50-ton vehicle), they'll sink deeper and have more difficulty moving compared to someone lighter, reflecting the calculation of 1800 kg that represents the effort needed for movement.

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.

Finally, we arrive at the total resistance the vehicle must overcome, which combines both the rolling resistance and penetration resistance. We simply add the previously calculated rolling resistance (1400 kg) and penetration resistance (1800 kg) together: 1400 kg + 1800 kg = 3200 kg. This means that the total effort required for the vehicle to move is 3200 kg.

Imagine trying to move a large box. First, it feels heavy because of the weight of the box (like rolling resistance), but then someone puts a small weight on the box (say, to represent penetration resistance). To move the box, you now need to account for both the weight of the box and the additional weight, which in this case is 3200 kg total effort required.

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, we determine the required tractive effort to overcome it. The vehicle needs a minimum of 3200 kg of tractive effort to start moving on the project site. This information is crucial for selecting the correct machine; we need to pick a machine that can produce this amount of power to successfully perform operations under these conditions.

Consider it like using a bicycle on a steep hill. If you know the uphill part of the journey requires a lot of effort (3200 kg), you'd want to make sure you have a bike with enough gears (power) to get you up that hill without stopping. Choosing the right equipment ensures you can complete your task effectively without unnecessary struggle.

--