3.5. Estimating Power Requirements with a Problem Example

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. 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.

Firstly, we need to convert the weight of the vehicle from kilograms to tons to make it compatible with the units of rolling resistance, which is expressed in kg per ton. Given that the machine weighs 50,000 kg, we divide this by 1000 to find that it weighs 50 tons. Next, we need to calculate the rolling resistance, which is given as 28 kg per ton. To find the total rolling resistance, we multiply the gross weight (50 tons) by the rolling resistance (28 kg per ton), resulting in a total rolling resistance of 1400 kg.

Think of rolling resistance like how hard it is to push a heavy cart. If the cart weighs more (like our vehicle), it becomes harder to push it just like a heavier truck has more rolling resistance. By converting weights into piles of bricks (tons), we can see how much harder it is based on how much we are trying to push.

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.

The penetration resistance is determined by how deeply the tyre sinks into the surface—in this case, 6 centimeters. For every centimeter of penetration, it requires 6 kg of effort per ton of weight. Therefore, we multiply the depth of penetration (6 cm) by the effort per cm and the gross weight of the machine (50 tons), which gives us the penetration resistance of 1800 kg.

Imagine trying to push a toy car into soft sand. The deeper you push it, the harder it becomes to move because you're fighting against the sand that gets packed in. Similarly, when a tyre sinks into the ground, it increases the force needed to pull the vehicle forward.

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. So, I need tractive effort of at least 3200 kg to overcome this resistance in a project site.

To determine the total resistance a vehicle must overcome, we simply add the rolling resistance (1400 kg) to the penetration resistance (1800 kg). This gives us a total resistance of 3200 kg. Therefore, the machine must generate at least 3200 kg of tractive effort to move.

You can liken this scenario to dragging a heavy box across a floor with some obstacles inside. If the box has to overcome a weighted hurdle (penetration) and has friction with the floor (rolling resistance), you need to use a combined amount of strength to lift and move it over both hurdles.

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 occurs when a machine has to move up a slope, requiring extra effort to overcome the force of gravity acting against the movement. This means the steeper the slope, the more tractive effort is needed to get the vehicle moving upwards.

Imagine riding a bicycle uphill. The steeper the hill, the more effort you need to pedal. This additional effort required to combat gravity is what we refer to as grade resistance in vehicles.

Now similar to this, we should also know about what is grade assistance? So, we discussed about what is grade resistance, there is something called as grade assistance that means what? When your machine is moving down the slope, you can see that the amount of power needed gets reduced because it can easily move down by the gravity.

Grade assistance is the opposite of grade resistance, occurring when a machine is moving downhill. In this case, gravity helps the vehicle move, reducing the amount of power needed to do so.

Picture yourself on a skateboard going down a hill. You gain speed easily and do not need to work hard. Here, gravity is assisting you, just as it does for machines on a downhill slope.

So, let us see how to calculate the grade resistance. 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.

Grade resistance is calculated based on the percentage of the slope. For every 1% grade, you need 10 kg of effort for each ton of weight to overcome the incline. This relationship helps in estimating the additional power required when climbing slopes.

It's like adding weights to a weighted vest when you try to climb up a staircase. The heavier you are (or the steeper the stairs), the more effort you need to exert to move effectively.

So now let us see what is this usable power? So, out of the available power prescribed by the manufacturer, how much amount of power becomes usable to you? That depends upon your project condition that depends upon the altitude of your project site and the temperature at your place.

Usable power refers to the portion of the total power output that can actually be converted into effective work. This is influenced by external conditions such as altitude and temperature, as these can reduce the effective power output of a machine compared to its manufacturer's rating.

Think of a car engine rated to produce 200 horsepower at sea level. If you're driving at a high altitude, the air is thinner, and the engine can't perform at full strength. Therefore, even though it has the capacity for 200 horsepower, the usable power might only be 150 horsepower.

So, another important thing to be noted is weight on the power running gear of the machine.

The weight placed on the power driving gear of a machine (such as the drive wheels) is crucial because it determines how much traction the vehicle can achieve. More weight typically increases traction, leading to higher usable force.

This is similar to how you would walk better on a firm surface when wearing shoes that grip well. If you're too light or the surface does not allow for good grip, you might slip. The more weight pressing down on the grip (wheels), the better the traction.

So usable force is nothing but weight on the paver running gear multiplied by the coefficient of traction of the travel surface.

Usable force can be determined by multiplying the weight on the driving gear (the part of the machine that drives it) with the coefficient of traction, which is the measure of how well the tires grip the surface. A higher coefficient of traction means more usable force, resulting in better performance.

Think of trying to pull a heavy wagon. If the ground is muddy, it’s hard to get a grip and pull it along the surface. If the wagon has more weight, say with additional luggage, you can pull it better if you're on a solid path, akin to how usable force operates between the tires and the ground.

Now let us workout the problem on how to estimate the power requirements of the machine. So, a tractor weighing 15 tons is operating on a haul road, the gross weight of the machine is given as 15 tons. It means it includes it is empty weight as well as the load it is carrying, with the rolling resistance of 60 kg per ton, it is given you can take it from the literature also for this particular haul route. For this particular mounting, what is the rolling resistance? The tables are available you can take it. And this machine is climbing a slope of 4% the gradient is given, the maximum rimpull in the first gear is 7000 kg.

To solve the problem, we start with the tractor's gross weight (15 tons) and the rolling resistance (60 kg per ton). First, we use these figures to calculate total rolling resistance and grade resistance, especially given that the tractor is climbing a 4% grade. Then, we can determine the total resistance and analyze whether the maximum rimpull (7000 kg) is sufficient to complete the task.

Consider a scenario where you're planning to transport a heavy load in a truck up a hill. Before starting, you want to understand if the truck can handle both the weight it's carrying and the incline of the road. You would calculate just like we did for the tractor to determine if the truck has enough power to make the trip.

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