5. Working on the Problem for Balancing Machines

But the loading time will be number of bucket loads multiplied by the bucket cycle time. (Refer Slide Time: 19:46)

The loading time for a machine is determined by calculating the number of times a bucket is loaded (the number of bucket loads) multiplied by the time it takes to fill the bucket once (bucket cycle time). This means that if it takes a specific time to fill the bucket and you know how many loads are needed, you can easily find out the total loading time required for the machine to operate efficiently.

Imagine a person is filling buckets of water from a well. If it takes them 2 minutes to fill one bucket and they need to fill 5 buckets for a task, the total loading time will be 2 minutes multiplied by 5 buckets, resulting in 10 minutes of loading time.

Another important thing you have to keep in mind is, for any machine whatever maybe the mission we have discussed about different types of machines so far. All the machines we are concerned about the safe gravimetric capacity of the machine. For every machine what is this safe operating load in terms of weight is given by the manufacturer, so that we call it as a gravimetric capacity.

The gravimetric capacity of a machine is the maximum weight it can safely carry, as specified by the manufacturer. It is crucial to adhere to this capacity to prevent damage to the machine. Overloading can lead to structural issues, inefficiencies, and safety hazards. Before loading, you should always verify that the load weight does not exceed this gravimetric capacity.

Think of a backpack designed to carry a maximum weight of 25 lbs. If you load it with 30 lbs, it can tear or break. Similarly, each machine has its limits, and exceeding them can cause serious issues.

Check the load weight against the gravimetric capacity of the truck, how to check that? For that you need to know what is the unit weight of your material, if you know the density of your material you can multiply by the volumetric load you will get the actual weight of material in the truck, you will get the truck load.

To verify if the truck's load respects its gravimetric capacity, first, determine the unit weight of the material you're handling. If you have the density (mass per unit volume) and the volume of the load, you can compute the total weight by multiplying these two values. This ensures that the actual weight of the load does not exceed the truck's capacity.

Consider a container that holds 100 liters of water. If water has a density of 1 kg/L, the total weight would be 100 kg. Before moving this container, one needs to ensure that whatever vehicle used can handle at least 100 kg. If it can only handle 80 kg, the container cannot be safely transported at full capacity.

If the material is going to be denser like wet sand or other denser material, what happens is there are more chances that your machine may be overloaded. That means the weight of material in the truck will be above the safe gravimetric capacity defined by the manufacturer.

Using denser materials, like wet sand, increases the risk of exceeding the gravimetric capacity of the machine. When the load is heavier than what the manufacturer recommends, it can cause excessive wear and tear on the equipment, particularly stressing components such as tires, which can lead to increased maintenance costs and decreased lifespan.

Think of trying to ride a bike with a backpack filled with heavy stones. If the backpack exceeds your carrying capacity, you won't only struggle to balance; you risk damaging the bike's wheels and frame over time.

If you overload the machine it will result in abusing of tires and it will increase the tire cost significantly. So, if you keep on overloading your truck it will result in premature aging of the truck, and it will result in huge loss for you, it will result in yearly replacement of your truck.

Overloading machines not only accelerates wear on tires but can also result in frequent repairs and replacements. For trucks, tires can represent a significant portion of operational costs. Over time, consistent overloading leads to such damage that trucks may need to be replaced more frequently, which drives up overall costs and reduces profitability.

Imagine running a car on flat tires. While it might drive for a bit, it will cause severe damage to the vehicle. Over time, you will face much higher costs due to repairs and may even need a new car sooner than expected.

So, next is about the dumping time. So, as we discussed earlier the dumping time will depend upon the type of hauling unit whether it is going to be rear dump or it is going to be bottom dump or side dump accordingly the dump time will vary.

Dumping time is influenced by the type of truck being used—different designs like rear dump, bottom dump, or side dump have their own rates of unloading. Additionally, the material's nature, such as how easily it flows or adheres to surfaces, also plays a crucial role in how long it takes to unload.

Think of a toy truck designed to dump its load versus one that has to open a back gate. The toy truck with a simple tilt mechanism can empty its cargo faster than one that requires opening a flap, similar to how different dump designs impact real trucks.

And the congestion in the dumping area...so in that case there may be possibilities of a lot of congestion in the dump area then your machine may have to wait.

The efficiency of the dumping process can be adversely affected by congestion in the unloading area. If other machinery is operating simultaneously, such as bulldozers or graders, delays can occur. These waits can lengthen the overall cycle time for trucks, resulting in reduced productivity.

Consider a busy traffic intersection. If too many cars are coming from different directions, each car has to wait to get through the intersection. The same concept applies to construction sites: when multiple machines are trying to work in the same area, it can slow everything down.

Haul time depends upon your haul distance and the speed, speed you can get it from the performance chart.

To calculate haul time, you need to consider the distance that the material must be transported and the speed of the hauling vehicle. The speed can be derived from performance charts provided by truck manufacturers, which take into account factors like machine weight and terrain resistance.

Imagine you're walking to school. If it's a short distance and you walk quickly, you'll arrive faster than if the journey is long and filled with obstacles. Similarly, trucks need the right data to estimate their journey's duration based on distance and vehicle performance.

Now let us see how to balance the interdependent machines, trucks and the excavators...

Balancing the operations of different machines such as trucks and excavators is crucial for maximizing efficiency. This balance ensures that both machines work in harmony, reducing wait times and increasing overall productivity. The key is determining the optimal ratio of trucks to excavators based on their operational cycle times.

Think of a two-person team where one person prepares ingredients and the other cooks. If one person finishes their task much sooner than the other, efficiency drops, and they end up waiting. However, if they time their tasks to finish together, they optimize their workflow.

So, that depends upon the cycle time of your truck and the cycle time of your excavator. So, divide the truck cycle time by the excavator cycle time, you will get the balance number of trucks.

To determine the optimal number of trucks for one excavator, you can divide the cycle time of the truck (the time it takes to complete one round trip) by the cycle time of the excavator (the time it takes to load). This calculation yields the ideal number of trucks that can keep the excavator busy without excess waiting time.

If a student takes 30 minutes to complete a project while a classmate takes 15 minutes, the ideal ratio of students working together might be based on how many can work in the time it takes the first student to finish.

So, when they are compatible you can see that the cycle time will be less both will be working at maximum production.

The balance number may not always be a whole number. When faced with a fractional number, the decision on whether to round it up or down should be made based on economic analysis. Rounding down could result in inefficiencies (e.g., under-utilizing the excavator), while rounding up could mean extra trucks that may not be needed, leading to higher operational costs.

When baking, if a recipe calls for 2.5 cups of flour, you decide whether to use 2 or 3 cups. If you go with 2 cups, you might not have enough ingredients for the final product, but if you use 3, you might waste flour, leading to unnecessary costs.

In the case when I round it to the number greater than the balanced number…

When the number of trucks exceeds the balanced number, the excavator becomes the bottleneck because it dictates the pace of work. While there may be more trucks waiting, if they cannot load quickly enough, the overall productivity drops. Conversely, rounding down might leave fewer trucks, resulting in the excavator having idle time as it waits for trucks to arrive.

Imagine a workshop with too many apprentices but only one skilled craftsman. If the craftsman can only train one apprentice at a time, having too many apprentices waiting leads to wasted potential—akin to having extra trucks waiting when the excavator is too busy loading to keep up.

So, what is the volume of truck you are going to load in this case 9.9-meter cube, you are also supposed to check whether the truck payload is within the gravimetric capacity.

In this calculation, the truck's effective load capacity is derived based on the number of bucket loads calculated earlier, adjusted for fill factor. After determining this load, it’s essential to compare it to the truck's gravimetric capacity to ensure it’s safe to transport. This step is crucial for complying with safety standards and preventing equipment damage.

Consider an airplane that can carry a maximum weight of 20,000 pounds. If the passengers and cargo add up to 19,000 pounds, it’s within limits. However, if it hits 21,000 pounds, that may lead to serious safety risks, just as overloading a truck can lead to damage or accidents.

Truck production is nothing but your truck payload... truck production = truck payload divided by the truck cycle time.

To find the truck's production rate, divide the total payload (amount of material transported) by the total cycle time (including loading, hauling, unloading, and returning). This will provide the productivity in terms of volume per hour. Remember to adjust for job efficiency as well, which accounts for time when the machine is actually functioning vs. downtime.

Imagine a delivery truck that manages to deliver 50 cubic meters of flowers in 3 hours. To find out how much it delivers per hour, you’d divide 50 by 3, leading to a measure of how efficiently the truck is operating, which tells the company whether adjustments may be needed.

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