3.1. Determining Available Power

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 work with rolling resistance, we first need to convert the weight of the vehicle from kilograms to tons. Since 1 ton equals 1,000 kg, we can convert the gross weight of the machine (50,000 kg) into tons by dividing it by 1,000. Therefore, the gross weight in tons is 50 tons.

Think of it like converting a distance from meters to kilometers. If you live 5,000 meters away from school, you can easily say you live 5 kilometers away by dividing by 1,000. Similarly, converting vehicle weight helps us use a standard measure that is often easier to work with.

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.

To find the rolling resistance, we take the gross weight in tons (50 tons) and multiply it by the rolling resistance value, which is 28 kg per ton. This calculation gives us the total rolling resistance of the vehicle: 50 tons × 28 kg/ton = 1400 kg.

Imagine pushing a heavy box on the floor. The heavier the box, the more force you need to use to push it. In this case, the 'box' is the vehicle, and the 'force' is the rolling resistance. The rolling resistance represents the extra effort needed just to keep moving, based on the vehicle's 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 you know that. 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.

Penetration resistance relates to how much weight the tire sinks into the surface. For every centimeter of penetration, the machine requires an effort of 6 kg per ton. With 6 centimeters of penetration and a gross weight of 50 tons, we calculate the penetration resistance: 6 cm × 6 kg/ton/cm × 50 tons = 1800 kg.

Think about wading in mud. The deeper you step in, the harder it is to lift your feet out. Similarly, penetration resistance accounts for the added effort needed due to how deeply the tires sink into soft surfaces.

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.

To find the total resistance the vehicle faces, we simply add the rolling resistance and the penetration resistance together. So, 1400 kg (rolling) + 1800 kg (penetration) = 3200 kg, which is the total force the machine needs to overcome during movement.

Imagine carrying two bags of groceries, one weighing 1.4 kg and the other 1.8 kg. If you're asked to carry both, you would simply add their weights together to find the total weight you have to lift. Similarly, calculating total resistance integrates different opposing forces.

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?

Tractive effort is the force needed by the vehicle to overcome resistance and move forward. In this case, we determined that 3200 kg of tractive effort is required to push through the identified resistances, thus informing our choice of machinery based on its capability to provide this force.

Think of it like planning a trip uphill with your bicycle. If the hill is steep (i.e., high resistance), you need a stronger bike or more energy to pedal. Identifying the necessary tractive effort helps you choose the right 'bike' (machine) to complete your task effectively.

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 refers to the additional effort required when a machine must ascend a slope. As the steepness of the slope increases, so does the grade resistance, as the vehicle needs to exert more force to work against gravity.

Consider walking uphill versus walking on a flat surface. It takes more effort to climb a hill because you are working against gravity. Similarly, machines deal with this extra effort when they have to move up a slope, which contributes to the total resistance they face.

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, so the gravitational force will help you to easily move the machine.

Grade assistance is the opposite of grade resistance. When a machine descends a slope, gravity assists its movement. This results in reduced power requirements compared to climbing uphill. Understanding grade assistance can influence decisions on machine use based on the terrain.

Riding a bicycle downhill is much easier than going uphill. You naturally move faster with less effort while descending due to gravity. This concept helps to understand how machines can benefit from downhill movements, reducing energy use significantly.

Grade resistance is nothing but by simple elementary mechanics people have worked out this relations. ... So, for every 1% of grade, so your grade resistance is 10 kg per ton.

To calculate grade resistance, we utilize a basic guideline where 1% of a slope requires 10 kg of force for every ton of weight. This serves as a method for estimating how much additional tractive effort is necessary when moving uphill.

If you're hiking up a hill with a 5% grade, each step requires effort. Just as we relate effort to the steepness of a hike, machines relate grade percentages to the additional force needed to move loads up slopes.

You can convert a rolling resistance also into equivalent gradient. The rolling resistance which you have expressed in kg per ton, that you can converted into gradient percentage equivalent gradient I can convert it...

Rolling resistance values, often shown as kg per ton, can be converted into an equivalent gradient percentage. By understanding both formats, it becomes easier to assess the overall impact of both rolling and grade resistances on machine performance.

Think of how distances can be represented in different units (like miles vs kilometers). Just as this makes distance more manageable in travel plans, converting resistance values aids in assessing machine capabilities on varying terrains.

So far what we have discussed is about the required power. So, what is the total power required by the machine to overcome the different resistances in the project site...

After determining all necessary resistances, we now focus on how much power the machinery can actually provide, termed as usable power. This involves understanding the power rating given by manufacturers and the impacts of site conditions on actual power delivery.

Consider a smartphone with a battery life of 12 hours according to specifications. However, in real-world usage (like gaming), that battery power may last only 6 hours. Like the smartphone’s usage scenario, a machine's power rating may differ when applied to real conditions.

Now let us see what is this usable power? ... which can be realized at the point of contact between the tire and the ground, this is what is of our major interest?

Usable power refers to the effective power available for tasks after deducting power used to overcome resistances. This measurement is crucial for determining if machinery can perform the required work in a given scenario.

Consider a train that has a total power output but uses a portion of that power to overcome friction on the tracks. The remaining power can be used to pull freight. Understanding this gives insights into how much load can be carried.

The usable power you can express in terms of rimpull or drawbar pull. ... So, the usable tractive force developed at the point of contact between the tyre and the ground is called as a rimpull.

Rimpull refers to the tractive effort available at the tires of a wheeled vehicle. Understanding rimpull allows us to assess how well a vehicle can perform tasks, as it accounts for contact and traction between the tires and the ground, essential for effective operation.

Think of rimpull like the grip of your shoe on the ground when you run. If you have excellent grip, you're more likely to run faster and jump higher, versus slipping on a wet surface. Rimpull helps predict how well machinery can operate on different terrains.

So, another important thing to be noted is weight on the power running gear of the machine. ... So, usable force is nothing but weight on the power running gear multiplied by the coefficient of traction of the travel surface.

Various factors influence how much usable force a machine can produce, primarily the weight over the driving gears and the traction coefficient of the surface. Understanding the relationship allows for better efficiency and effective power use in operation.

Imagine how much better a heavy truck can grip a wet road compared to a light bicycle. Just like the weight of the truck can enhance grip, the weight on a vehicle’s wheels influences its ability to generate usable force effectively.

If you have sufficient grip sufficient traction between the tire and the ground...If the traction is sufficient, you can take the rimpull as a direct function of the horsepower of the machine.

When traction between tires and ground is optimal, we can directly relate usable force (rimpull) to horsepower. Thus, knowing machine specifications aids in calculating how much effective force is available during operation.

Again, think of a race car. If it has enough grip and is equipped with a powerful engine, it can accelerate smoothly and maintain high speeds. Traction translates horsepower into real usable force on the race track.

Now let us workout the problem on how to estimate the power requirements of the machine. ... So, out of this 7000 kg, 1500 kg will be used for overcoming the resistances.

Engaging in a practical example helps emphasize the concepts of power requirements and resistance calculations. Breaking down values confirms understanding and indicates the power available for actual work after resistances.

If you work part-time and earn $700, but have$150 in expenses, the amount you actually save and can use is $550—a direct reflection of understanding total income vs. value spent on necessary applied forces in a work scenario.

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