3.4. Calculating Usable Force

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.

To calculate the usable force, we start by converting the vehicle's weight from kilograms to tons. This is important because rolling resistance is typically expressed in kg per ton. Given that the gross weight of the machine is 50,000 kg, we divide this by 1000 (the number of kg in a ton) to get 50 tons.

Imagine carrying a backpack that weighs 50 kg. To make it easier to understand how heavy it is, you might want to convert the weight into a unit that you’re more familiar with, like pounds. Just like how you convert your backpack's weight into a more familiar unit, we convert the vehicle's weight to tons for ease of calculation.

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. 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.

Next, we calculate the rolling resistance using the formula: Total Rolling Resistance = Gross Weight (in tons) * Rolling Resistance (in kg per ton). Here, we know the gross weight is 50 tons, and the rolling resistance for the haul route is 28 kg per ton. Therefore, we calculate 50 tons multiplied by 28 kg/ton, which equals 1400 kg of rolling resistance.

Think of rolling resistance like the friction you feel when trying to push a heavy box across the floor. The heavier the box (similar to the vehicle weight), the harder it is to push. This calculation helps us understand how much effort is needed just to get the vehicle moving.

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.

Penetration resistance is calculated based on how deep the tire sinks into the ground. The formula for penetration resistance is: Penetration Resistance = Depth of Penetration (in cm) * 6 kg/ton/cm * Gross Weight (in tons). Here, we multiply the 6 centimeters of penetration by 6 kg/ton/cm and the gross weight of 50 tons to get a total of 1800 kg.

Imagine trying to walk through sand. The deeper your foot sinks into the sand (similar to the tire sinking), the more effort it takes to lift it out. In this example, we're calculating how much additional weight you're effectively 'carrying' because of that sinking.

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.

The total resistance encountered by the vehicle is the sum of both the rolling resistance and penetration resistance. We simply add the two values: 1400 kg (rolling resistance) + 1800 kg (penetration resistance) to get a total resistance of 3200 kg.

Think of total resistance like the total effort you need to pull two different weighted sleds attached to each other. First, you have the weight of the first sled (rolling resistance). Then you add the weight of the second sled (penetration resistance). Together, you have to account for the combined weight to understand how much force you'll need to pull them both.

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?

The tractive effort required is directly related to the total resistance calculated previously. In this case, the vehicle needs a tractive effort of at least 3200 kg to move effectively. By knowing this, we can select an appropriate machine that has sufficient power to overcome this resistance while working at the site.

Imagine trying to pull a heavy wagon with a horse. If you know the total weight of the wagon and its load (3200 kg), you can decide whether a horse can pull it or if you need a stronger horse. This decision-making process is crucial in selecting the right equipment.

Now so far, we have discussed about the rolling resistance, let us look into the other part of the resistance in your project site that is your grade resistance. Most often you can see that equipment has to climb up a slope. So, when the machine is climbing up the slope, obviously you need some additional efforts to make it move up the slope because it is pulling against the gravity.

Grade resistance is encountered when a vehicle must move uphill. This type of resistance works against the weight of the vehicle due to gravity, requiring additional tractive effort to overcome. The steeper the slope, the more resistance the vehicle will face, making it crucial to factor this into the calculations for total resistance.

Think of riding a bicycle uphill. The harder it is to pedal due to the incline, the more effort you need to exert compared to riding on flat ground. Similarly, in our calculations, we have to account for the effort required to overcome the uphill gradient.

Grade resistance is nothing but by simple elementary mechanics people have worked out this the relations. Say for example, for 1% of grade so the amount of tractive effort needed to overcome this 1% of grade it is 10 kg per ton. So, this is simple guideline which they are worked out which is worked out in the literature you can easily find it.

To calculate grade resistance, we use a guideline indicating that overcoming a 1% grade requires 10 kg of tractive effort per ton of weight. Therefore, to find the total grade resistance, we multiply the percentage of the slope by the gross weight of the machine, converting it into the required tractive effort.

Imagine climbing stairs with a backpack. If the stairs are steep (similar to a grade), you need to exert more force to lift yourself and your weight up each step. This analogy helps explain why equipment requires more effort to move uphill.

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