3.2. Usable Power 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 section, we start by converting the gross weight of a vehicle from kilograms to tons because the rolling resistance is expressed in kilograms per ton. Since the gross weight is provided as 50,000 kg, we divide this by 1000 (the conversion factor from kg to tons) to find that the weight is 50 tons.

Imagine you have a big box that weighs 50,000 grams. If you want to tell your friend how heavy it is in kilograms, you would divide it by 1000, saying it's 50 kilograms. This is similar to what we do with tons; it helps everyone understand the weight in a unit that's commonly used in the industry.

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.

The next step involves calculating the total rolling resistance for the vehicle. The rolling resistance is given as 28 kg per ton. To find the total rolling resistance, we multiply the gross weight of the vehicle (50 tons) by the rolling resistance value (28 kg per ton), which results in a total rolling resistance of 1400 kg.

Think of rolling resistance like the friction that slows down a toy car on the floor. If the toy car weighs more, it’s harder to push. In this case, for every ton of the vehicle's weight, there's a certain amount of force that resists motion, and we compute that to understand how much extra power is needed to keep 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.

Next, we determine the penetration resistance based on how deeply the tire has sunk into the ground. For each centimeter of penetration, 6 kg of effort is needed per ton. So, we multiply the depth of penetration (6 cm) by the weight of the vehicle (50 tons) and the effort per centimeter (6 kg). This calculation gives us a penetration resistance of 1800 kg.

Consider walking on a soft sandy beach. The more you sink into the sand, the harder it is to walk. Similarly, as the tire sinks deeper into the surface, more force is needed to push through, just like how we calculate the effort needed as the tire sinks.

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 faced by the vehicle, we simply add the rolling resistance and the penetration resistance together. This means 1400 kg (rolling resistance) plus 1800 kg (penetration resistance) equals a total of 3200 kg of resistance that the vehicle must overcome.

Imagine pushing a heavy furniture piece across a floor. If you need a certain amount of force just to keep it moving over the floor (rolling resistance), then you'll need even more force if it gets stuck in a carpet (penetration resistance). When combined, the total resistance is what you really need to push against.

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.

The total tractive effort calculated (3200 kg) is the minimum force required from the machine to overcome the total resistance. This informed decision will help you select a machine that has adequate power to function effectively under these conditions.

Think of a tug of war game. If you know the opposing team is pulling with a strength of 3200 kg, you need to gather a team that can pull with at least that much strength to win. Similarly, in machinery, knowing the resistance helps in choosing a machine that can do the job.

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 extra effort needed to move a machine uphill. When a vehicle climbs a slope, it faces a force opposing its motion due to gravity. Understanding this resistance is crucial for estimating how much power will be necessary for the equipment to operate efficiently.

Think of riding a bicycle uphill. It takes much more effort to pedal up a hill than it does to ride on a flat road due to gravity pulling you back. This increased effort against gravity mirrors the concept of grade resistance in machines.

So, there is a force opposing the movement of the machine when it is moving up the slope that is causing grade resistance. So, when the machine is moving up the slope, so the machine is encountering grade resistance, that is a force opposing the motion of the machine movement of the machine up a frictionless slope.

Grade resistance, as we mentioned, occurs when going uphill. In addition, there is a concept of grade assistance, which happens when moving downhill. The machine receives a helpful force from gravity that makes it easier to move, thus reducing the amount of power needed.

When you go down a hill on your bicycle, you can often coast without pedaling thanks to gravity helping you. This is like grade assistance in machinery which reduces the effort needed when going downhill.

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%. So, this is +5 that means upslope. If you say -5% it means down the slope that means you will have a fall of 5-meter vertical fall of 5 meters in a horizontal distance of 100 meter.

The grade percentage indicates the steepness of a slope. For example, if a slope is 5%, it rises 5 meters vertically over a horizontal distance of 100 meters. Understanding how slopes are measured helps in calculating the resistance your vehicle would face while traversing them.

Imagine a set of stairs. If every five steps (horizontal distance) you go up one step (vertical rise), that's similar to a 5% incline. Knowing how steep the steps are helps you understand how much effort you need to go up them.

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.

For every percentage of grade, a certain amount of force is required to overcome uphill resistance. Specifically, for each 1% incline, a vehicle requires 10 kg of force per ton of weight. This provides a straightforward method to estimate the tractive effort required based on the steepness of the slope.

Imagine pushing your friend up a slight hill. For every small incline, you find you need to push harder. In engineering, we quantify this effort: every 1% incline requires a definable amount of push (like 10 kg) to estimate the total force needed.

So, these guidelines will be valid for smaller slopes, say less than a 10% you can go by this guideline. 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.

The provided estimates for grade resistance are specifically accurate for slopes less than 10%. Engineers can refer to established literature for reliable tables that provide grade resistance values for various gradients, ensuring proper calculations can be made based on industry standards.

Think of it as a cooking recipe: if the recipe works well for small batches (less than 10%), it might be unreliable for larger ones. Just as you would consult reliable sources for good cooking techniques, engineers rely on literature for accurate resistance values.

So, 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, so how to convert it?

You can convert rolling resistance expressed in kg per ton into an equivalent gradient percentage. Knowing that 1% grade equals 10 kg per ton simplifies comparisons between rolling resistance and grade resistance, providing a consistent basis for calculations.

It's like converting different currencies: knowing that 1 dollar is a certain amount of another currency allows us to easily compare prices. Similarly, converting rolling resistance to a gradient percentage allows clearer comparisons between different types of resistance.

So, what is the power requirement that is what we have estimated so far. Now we are going to look into the estimation of the available power. So, the available power you can get the data easily.

After understanding resistance calculations, the next step is to estimate the available power, which can be easier to obtain since manufacturers provide data on their machinery's horsepower ratings. This sets a foundation for determining usable power.

Just like checking your car manual for engine power helps you understand how fast it can go, accessing manufacturer data on a machine's power gives insights into its potential performance on a job site.

The available power is determined by the SAE rating. So, there is an organization called as SAE Society of Automotive Engineers, it is a US based organization. So, in India also we have an organization SAE India.

The Society of Automotive Engineers (SAE) establishes standards for how machinery power ratings are determined, offering a reliable baseline for expected power performance of equipment. Similar organizations in various regions also contribute to standardizing these ratings.

It's like going to different restaurants that follow certain food safety guidelines; you know they meet a standard when they prepare and serve food. Similarly, machinery power ratings follow established guidelines ensuring reliability.

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 is that portion of the available power from manufacturers that can realistically be converted into work based on specific project conditions, like altitude and temperature that affect machine efficiency.

When baking, if you can't find the right temperature for your oven, your cookies may not come out properly, even if you have all the right ingredients. Similarly, machine performance can be impacted by environmental factors, affecting how much power is truly usable.

Say for example, when we are using a tractor for towing the load. So, how much power is actually available for the towing the load? That we need to calculate, so you know what is the total power available for the tractor, you know from the manufacturer what is the maximum power possible you know that for the particular tractor.

To determine the usable power for towing, you must first know the total available power and then subtract the power needed to overcome any resistances faced during operation. This provides insight into how much power remains for actual work.

Imagine you have 100 dollars but need to spend 30 dollars to pay off a bill. You’ll find that you have 70 dollars left to spend on anything else. Similarly, the usable power for towing is what's left after accounting for the power used in overcoming resistance.

So, this usable power you can express in terms of rimpull or drawbar pull. So, depending upon the mounting of your machine. So, if it is going to be wheel or tyre mounted machine, we call it as rimpull.

Usable power can be expressed in terms of 'rimpull' for wheeled equipment or 'drawbar pull' for tracked systems. Rimpull represents the force available at the tire-ground contact point, showing how much effort can be effectively exerted for towing.

Consider how a good pair of running shoes can give you better grip and pulling power. Just as your shoes help you run better, the type of machinery mounting determines how well the machine can exert force on the ground.

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 amount of usable force available is influenced significantly by the traction of the surface on which the machine operates. The better the traction, the more of the total power can be utilized effectively; poor traction results in less effective power conversion.

Think of riding a bicycle on a smooth road versus on wet grass. On the smooth road, you can go faster because your tires grip well. On the grass, you might slip and struggle to gain speed. Similarly, in machinery, the surface affects how much force can be applied effectively.

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 certain wheels in a vehicle contribute to the driving force, as not all wheels are powered. In the context of estimating usable power, understanding the weight distribution on driving wheels is crucial since only the weight on those wheels affects traction and usable force.

If you’ve ever tried to push a heavy shopping cart, you’ll notice it’s easier when you push down on the cart’s handle. The weight you apply at one point can change how easily it moves. In machinery, the more weight on the driving wheels, the easier it is to generate traction.

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

To determine usable force, multiply the weight resting on the powered wheels (or running gear) by the coefficient of traction for the surface. The coefficient of traction reflects how well the surface resists slipping, thus affecting how much usable power is available.

It’s like making pasta. If you have heavier flour (weight) on a clean surface (high coefficient of traction), you can easily roll out dough. However, if it's on a slippery surface, the dough will slip around more, just like how weight and surface type affect force on machinery.

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.

Usable force directly relates to the horsepower of the machinery when adequate traction is present. This relationship allows us to estimate rimpull based on the manufacturer's horsepower rating, indicating how effectively the machine can perform its intended tasks.

Think of how a powerful car engine allows you to speed up quickly. If you understand the horsepower, you can predict the vehicle's performance, similar to how knowing rimpull gives insights into the machine's effectiveness based on its power rating.

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.

You can estimate the rimpull using the manufacturer's horsepower data, noting that rimpull decreases as speed increases. This inverse relationship means that if a machine moves faster, it has less pulling power available for towing.

When walking faster, you might find it harder to pull a wagon behind you compared to walking slowly. Similarly, in machinery, as speed increases, the ability to exert pulling force decreases due to the physics of motion.

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.

In this section, we outline a practical problem to apply what we've learned about calculating usable power and resistance. By analyzing a tractor's weight, rolling resistance, and gradient, we can estimate the total power needed for effective operation.

Think of it as a math problem where you calculate how much strength you need to climb a hill while carrying a backpack. In this case, we're trying to determine the power needed for a tractor working under specific conditions, uniting formulas and real-life scenarios.

--