3. Power Requirement Estimation

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 estimate power requirements, we first need to convert the weight of the vehicle from kilograms to tons since rolling resistance is typically calculated in kg per ton. By dividing the total weight (50,000 kg) by 1000, we find that the vehicle weighs 50 tons. This conversion is crucial for understanding subsequent calculations concerning rolling resistance.

Imagine you have a bag that weighs 50,000 grams, which can be cumbersome to think about. If you convert this weight to kilograms (50 kg), it's easier to visualize carrying it. Similarly, converting the vehicle's weight to tons simplifies 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.

Next, we need to estimate the rolling resistance, which is given as 28 kg per ton for this specific route. To find the total rolling resistance, multiply the gross weight of the vehicle (50 tons) by the rolling resistance value (28 kg per ton). This calculation gives us a total rolling resistance of 1400 kg, which indicates how much force is needed to keep the vehicle moving at a constant speed.

Think about pushing a heavy box across a rough surface. The force you need to keep it moving is akin to the rolling resistance. In this case, you would need to push harder if the box is heavier or if the surface is rougher.

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 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 next step is to calculate the penetration resistance. The problem states that the tire sinks 6 centimeters into the surface, and it requires 6 kg of effort per ton for each centimeter of penetration. To find the total penetration resistance, multiply the depth of penetration (6 cm) by the gross weight (50 tons) and then by the effort required (6 kg per ton). This results in a penetration resistance of 1800 kg, which adds to the overall resistance faced by the vehicle.

Imagine walking on soft sand; the deeper you sink, the harder it is to walk. Similarly, as the tires sink further into the ground, more effort is needed to keep moving 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.

To understand how much effort is needed from the machine, we must add the rolling resistance (1400 kg) and the penetration resistance (1800 kg). Thus, the total resistance encountered by the vehicle is 3200 kg. This is the total opposing force the vehicle needs to overcome in order to operate effectively.

Think of it like a team of horses pulling a wagon: if one horse can pull 1400 kg easily on flat ground but encounters a muddy patch that needs an additional 1800 kg of pull, then as a team, they must exert a total force of 3200 kg to move the wagon forward.

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 now known to be 3200 kg, we determine that the machine must generate at least this amount of tractive effort to move effectively at the project site. This estimation guides the selection of a machine that can produce the required power to overcome the resistance.

When you go to buy a car, you want one that can handle the conditions you will face, like hills or heavy loads. Similarly, here we need to choose a machine that has enough power to move effectively against the total resistance.

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 force required when the machine climbs a slope, as it works against the force of gravity. When climbing, machines require more power because they have to lift their weight vertically, making it harder to move. Understanding grade resistance is important for ensuring that the selected equipment can efficiently handle the terrain.

When you walk up a hill, you know it takes more effort than walking on flat ground. Just as we adjust our speed or take breaks when hiking up a steep slope, machines need more power to handle grade resistance when climbing.

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.

While we discussed how machines face additional challenges when climbing slopes, grade assistance refers to the reduction of required power when moving downhill. The weight of the machine works with gravity, thus requiring less energy to continue moving downward, presenting a contrast to the uphill effort previously discussed.

Consider riding a bike down a hill. You might need to pedal hard going up, but when going down, gravity helps you and you can coast with little effort. This is akin to how machines benefit from grade assistance when moving downwards.

So, now let us see how to calculate the grade resistance. Grade resistance is nothing but by simple elementary I mean a 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.

To calculate grade resistance, we use a simple guideline that states for 1% of slope, the force needed is 10 kg per ton. This means as the slope percentage increases, the tractive effort required increases accordingly. Understanding this relationship helps us to estimate the machinery required for various grades.

Think about driving a vehicle: the steeper the hill you need to ascend, the harder you have to push the gas pedal to maintain speed. This mirrors how the more steeply a machine must climb, the greater the force needed to move it.

So, say for example, if your slope percentage is say 5%, it means what? In a horizontal distance of 100 meter you will have a surface rise of vertical surfaces rise of 5 meter that is 5%.

Slope percentage provides a specific way to quantify how steep an incline is. A 5% slope indicates that for every 100 meters traveled horizontally, the elevation increases by 5 meters. Understanding slope percentages can improve route planning and machinery selection as steeper grades require machines with greater tractive effort.

Picture a ramp. If the ramp rises 5 meters over a horizontal distance of 100 meters, that slope is 5%. Knowing this helps you decide how much power is needed to climb it. It's like understanding the steepness of a hill on your way to a destination.

So, when you select your haul route, so we have to be very careful in the selection of your haul route. So, if there is a option that you can use the down slope, it is always preferable to use down slopes, because your power required gets reduced.

Carefully selecting a haul route is crucial because it can significantly impact the power requirements. Using downhill routes can minimize the power needed, leading to reduced operational costs and increased efficiency. Therefore, route planning should prioritize keeping resistance as low as possible.

Just as you would prefer a downhill path for a bicycle to conserve energy and increase your speed, heavy machinery also benefits from operating on favorable slopes to reduce power requirements.

So, there are sufficient information’s in different literature which I have cited in the references towards the end of the lecture, you can go through. So, you can find the tables, which provide you the grade resistance for different percentage of gradient.

Resourceful literature is available, providing tables that outline the grade resistance for various slopes. These can be helpful when planning operations, as they quantitatively express the resistance associated with different gradients, enhancing the decision-making process when selecting equipment.

Think of these resources like a weather forecast providing essential information about different conditions for travel - using the right data can help ensure you choose the best route and equipment for your task.

So, you know the rolling resistance in kg per ton, so you know that 1% of grade equal to 10 kg per ton. So, you divide it by 10 kg per ton, you will get the equivalent gradient percentage.

It's also beneficial to convert rolling resistance expressed in kg per ton into an equivalent gradient percentage. This allows for a better comparison between rolling and grade resistance, providing a more accurate assessment of the overall resistance for a vehicle.

Imagine wanting to compare distances in miles against kilometers. Converting units helps clarify which distance is greater. Similarly, converting resistance to gradients gives a clearer picture of what to expect on the route.

So, 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, in the underfoot conditions.

Up to this point, we've assessed the total power required for the machine to overcome all resistances. It is essential for operational planning to know this value as it dictates the capacity of the machinery we need. Understanding total power requirements ensures that we select machinery that meets operational needs.

Just like a student needs to know how many textbooks they need to carry for a semester, knowing the total power requirement helps in selecting the correct machinery capacity for their load.

So, the available power you can get the data easily, because the manufacturer would have done the horsepower rating of the machine. So, the available power is determined by the SAE rating.

Available power is defined by the horsepower rating provided by the manufacturer, which undergoes standardized testing by organizations like SAE (Society of Automotive Engineers). This rating provides guidance for understanding what machine can deliver under optimal conditions.

When you purchase a new car, the horsepower rating gives insight into how powerful the engine is. Similarly, understanding the available power of machinery is crucial for matching tasks with suitable equipment.

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.

Usable power refers to the portion of power derived from the manufacturer's available power rating that can be effectively employed in actual work situations. Its effectiveness can vary based on environmental factors like altitude and temperature, which can affect equipment efficiency.

It's like how a smartphone battery might last longer in cool temperatures but drain quickly in heat. Similarly, environmental conditions impact how much power you can actually use from your machinery.

So, we need to estimate this usable power of this particular machine. We are going to see how to estimate the usable power? Say for example, when we are using a tractor for towing the load.

To find the actual usable power of a machine, we assess the total available power and subtract the energy necessary to overcome resistances specific to the project's conditions. This helps quantify how much power is genuinely available for load towing or other tasks.

Think about budgeting money: if you earn a salary (available power) but have expenses like rent and groceries (resistances), the remaining amount (usable power) is what you can spend on leisure or savings.

So, the usable power you can express in terms of rimpull or drawbar pull. So, depending upon the mounting of your machine.

Rimpull and drawbar pull are terms used to describe usable power depending on whether the machine is wheel-mounted (rimpull) or track-mounted (drawbar pull). These values are crucial for understanding equipment capabilities in specific applications.

Imagine a truck (rimpull) compared to a bulldozer (drawbar pull). Each has different capacities for pulling loads based on their design; knowing these terms helps in selecting the right machinery for the task.

So, how to calculate this usable force? So, this usable force is going to depend upon the traction of your travel surface. So, as I told you how much amount of the total power becomes usable, it depends upon the degree of traction between your wheel and the ground.

The usability of a machine's power is directly influenced by traction, or the grip between the wheels and the ground. The better the traction, the more of the total power can be effectively translated into usable force, ensuring operational efficiency.

If you're trying to sprint on ice (low traction), you'll struggle to run fast. Conversely, running on a solid track (high traction) allows more of your energy to be effectively used - this illustrates how traction impacts usable power.

So, another important thing to be noted is weight on the power running gear of the machine. So, in common equipment or the common wheels of the cars whatever we are using, you can see that all the wheels of the car are not driving wheels.

Only specific wheels or axles are powered in many machines, meaning the weight distribution affects usable power. The weight on the driving wheels is the critical factor because it determines how much force can be exerted for traction on the surface.

When pushing a heavy shopping cart, the more weight you place on the wheels that are being pushed, the easier it is to move. This is similar to how the weight on the driving wheels of machinery can enhance traction and usable power.

So, assuming your coefficient of traction is sufficient, if there is proper traction, sufficient traction between your wheel and the ground. In that case your rimpull can be taken as a function of your horsepower of the machine.

Rimpull calculation is influenced by the available horsepower and the coefficient of traction on the surface. If traction is adequate, you can derive a direct relationship where higher horsepower leads to increased rimpull, directly affecting how effectively a machine can tow loads.

Just as a strong person can lift more weight if they have a solid grip versus a slippery handle, similarly, the more powerful the machine (higher horsepower) and the better the traction, the greater the rimpull they can achieve.

Using this simple relationship, you can directly estimate the rimpull if you know the horsepower of the machine given by the manufacturer, and you should know that it is a function of speed; inverse function rimpull and the speed of the machine are inversely related.

The relationship between rimpull and speed indicates that as the speed of the machine increases, the rimpull it can exert decreases. This inverse relationship is critical for operators to understand as it affects operational strategies.

Think of a runner: when they sprint at high speed, they can't exert as much force to push against the ground as they can when they run slower. Similarly, for machines, maintaining the right speed is key to maximizing power output.

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.

To consolidate our understanding, we can apply these principles to a specific problem. The scenario is set with a tractor weighing 15 tons and we will calculate the power needed using the same resistances discussed earlier. By analyzing these factors, we determine the tractor’s ability to operate effectively on the haul road.

Solving a math problem often requires multiple steps. Similarly, estimating power requirements involves using various known values, combined through calculations, to arrive at a useful conclusion.

First let us see what is the tractive effort needed to overcome the grade resistance? Grade resistance, you know the grade percentage it is nothing but 4%.

In our problem, we calculate the tractive effort necessary to overcome grade resistance. Knowing that the slope is 4%, we apply the earlier mentioned guideline that relates slope percentage to tractive effort (10 kg per ton). This step focuses our calculation strategy on meeting the demands of the terrain.

When preparing to climb a hill, knowing its steepness helps you gauge the energy needed to reach the top - similarly, understanding grade resistance shapes our approach towards overcoming inclines with machinery.

Now let’s calculate how to estimate a tractive effort to overcome the rolling resistance? It is nothing but for this particular haul route the rolling resistance value is given us 60 kg per ton.

Next, we compute the rolling resistance needed for our tractor scenario. Using the given rolling resistance value for this haul route (60 kg per ton) and multiplying it by the gross weight of our machine allows us to derive the total force the machine needs to exert against rolling resistance.

Consider driving a vehicle: the force needed to keep moving forward varies by how heavy the load is. In this case, it's similar; heavier tractors experience greater resistance, thus requiring a precise calculation for effective operation.

Now the total power required to overcome all the resistances are given here as 600 kg. So, 600 kg is nothing but your grade resistance, the power needed to overcome this grade resistance plus 900 kg is your rolling resistance.

After computing both grade resistance (600 kg) and rolling resistance (900 kg), we sum these values to understand the total power required for this tractor to function effectively. Knowing this total helps guide equipment selection and operational planning as it determines how much power the machinery will use.

Think of a football game: each team works together to tackle both offense and defense. Similarly, our power calculations require a combined effort (both grade and rolling resistance) to understand the total force needed for the tractor to operate successfully.

So, the maximum rimpull available for this machine as given by the manufacturer is 7000 kg. Now you need to know what is a grade resistance on the rolling resistance?

Identifying the maximum rimpull available helps us understand the tractor’s capabilities based on the manufacturer's specifications. This value is essential to see how much of this total capacity will be consumed by resisting forces (grade and rolling). This evaluation is paramount for ensuring that the equipment can operate in required conditions.

Much like knowing a vehicle’s towing capacity can inform you of what load you can safely transport, understanding the maximum rimpull available allows for informed decision-making regarding the loads the tractor can handle.

So, out of this 7000 kg, 1500 kg will be used for overcoming the resistances. So, for overcoming the different resistances in the project site, you are going to spend 1500 kg.

Finally, we determine that after accounting for the power used to overcome resisting forces (1500 kg), the remaining rimpull which can be interpreted as usable power for towing loads is 5500 kg. This final assessment is crucial in understanding how effectively the machine can perform its intended work.

Think of it like having $7000 in your budget: if you spend$1500 on bills (used for resistances), you are left with $5500 for savings or shopping. Similarly, the usable power left signifies what's available for performing actual work after meeting necessary resistance.

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