3 - Power Requirement Estimation

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.