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Interactive Audio Lesson
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Understanding Rolling Resistance
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Today, we're starting our discussion on calculating usable force, beginning with rolling resistance. Who can tell me why we need to convert weights from kilograms to tons?
Is it because rolling resistance is often expressed in kg per ton, making it easier for calculations?
Exactly! In our example, if the gross weight of a machine is 50,000 kg, how many tons is that?
That would be 50 tons, since you divide by 1000.
Correct! Now, if we have a rolling resistance of 28 kg per ton, who wants to calculate the total rolling resistance for 50 tons?
That would be 50 times 28, which equals 1400 kg.
Awesome! So, rolling resistance can be calculated using the formula: Roll Resistance = Gross Weight (in tons) × Rolling Resistance (kg per ton). Remember, 'Roll Resistance = GR × RR', where GR is gross weight and RR is rolling resistance.
That gives us a good starting point for calculating usable force!
Great! In summary, we’ve covered rolling resistance calculations and their significance in selecting machines.
Calculating Penetration Resistance
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Moving on, let’s talk about penetration resistance. Can someone explain what it is?
It’s the resistance a tire faces when it sinks into the ground, right?
Correct! For our scenario, if a tire sinks 6 cm into a surface, and resistance is specified as 6 kg per ton per centimeter, how do we calculate the total penetration resistance?
We would multiply the penetration of 6 cm by 6 and then times the gross weight of 50 tons.
So, that’s 6 × 6 × 50 = 1800 kg.
Excellent! Now we can find the total resistance by adding rolling resistance and penetration resistance.
That would be 1400 kg + 1800 kg = 3200 kg total resistance.
Precisely! Remember our formula: Total Resistance = Rolling Resistance + Penetration Resistance.
That’s really helpful!
Let’s summarize: We've learned how to calculate penetration resistance and total resistance.
Understanding Grade Resistance
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Today, we’ll dive into grade resistance. Why do we need to consider slope in our calculations?
Because machines have to exert more effort when moving uphill, right?
Spot on! Referring to a 4% slope, can anyone calculate the grade resistance?
Using the guideline, it's 10 kg per ton for 1% gradient. So for 4%, it’s 10 times 4 times the gross weight, or 10 × 4 × 50 tons.
That gives us 600 kg for grade resistance.
Just right! So how does this grade resistance compare to rolling resistance when deciding on machinery?
Higher grade resistance means we need a machine that can provide more power to overcome it.
Exactly! To sum up, we've elaborated on grade resistance and its implications for equipment selection.
Calculating Usable Power
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Now, let’s connect what we’ve learned to usable power. Why is determining usable power important?
It's needed to understand how much power is actually available for work after accounting for resistances!
Perfect! Given a maximum rimpull of 7000 kg and resistance of 1500 kg, what’s the usable pull available for towing?
That would be 7000 kg minus 1500 kg, resulting in 5500 kg for towing.
Correct again! And what nuances must we consider regarding usable power?
Conditions, like altitude and surface traction, influence how much power we can effectively use.
Exactly! So, to conclude, we explored how to calculate usable power and its importance in machinery operation.
Introduction & Overview
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Quick Overview
Standard
In this section, the key calculations required for determining rolling resistance, grade resistance, and usable force in machinery operations are explained. The importance of these calculations in selecting the right machinery power for project sites is emphasized, along with the effects of different surface conditions.
Detailed
Detailed Summary
This section covers how to calculate usable force, focusing on two primary resistances: rolling resistance and grade resistance. The gross weight of the machine is converted into tons to simplify calculations, with a gross weight of 50,000 kg translating to 50 tons. The rolling resistance is specified as 28 kg per ton, leading to a total rolling resistance of 1400 kg.
Next, the section explains penetration resistance when the tire sinks 6 cm into the surface, which adds an additional 1800 kg of resistance to the initially calculated total. The total resistance is thus calculated as the sum of rolling resistance and penetration resistance, culminating in a total of 3200 kg of resistance that equipment must overcome.
The section further discusses grade resistance associated with machines climbing slopes. The explanation details how tractive effort required varies with the percentage of slope, illustrating the contrast between grade resistance and grade assistance when moving downhill. Specific calculations relate to 4% slopes, establishing a guideline of 10 kg per ton for grade resistance under 1% gradient, allowing students to translate these resistances into usable force for equipment selection.
Issues related to available power versus usable power, and how project conditions affect each, are also delved into, with calculations illustrating the reduction of usable power due to resistance from elements such as gradation and traction. This culminates in understanding usable power as what remains after overcoming resistance. The section finishes by exploring power requirements through real-world examples, guiding students through practical calculations to ascertain usable force in machinery scenarios.
Audio Book
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Conversion of Vehicle Weight to Tons
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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.
Detailed Explanation
To calculate the usable force, we start by converting the vehicle's weight from kilograms to tons. This is important because rolling resistance is typically expressed in kg per ton. Given that the gross weight of the machine is 50,000 kg, we divide this by 1000 (the number of kg in a ton) to get 50 tons.
Examples & Analogies
Imagine carrying a backpack that weighs 50 kg. To make it easier to understand how heavy it is, you might want to convert the weight into a unit that you’re more familiar with, like pounds. Just like how you convert your backpack's weight into a more familiar unit, we convert the vehicle's weight to tons for ease of calculation.
Calculating Rolling Resistance
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Now the rolling resistance you need to calculate for this particular haul route 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. 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.
Detailed Explanation
Next, we calculate the rolling resistance using the formula: Total Rolling Resistance = Gross Weight (in tons) * Rolling Resistance (in kg per ton). Here, we know the gross weight is 50 tons, and the rolling resistance for the haul route is 28 kg per ton. Therefore, we calculate 50 tons multiplied by 28 kg/ton, which equals 1400 kg of rolling resistance.
Examples & Analogies
Think of rolling resistance like the friction you feel when trying to push a heavy box across the floor. The heavier the box (similar to the vehicle weight), the harder it is to push. This calculation helps us understand how much effort is needed just to get the vehicle moving.
Determining Penetration Resistance
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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.
Detailed Explanation
Penetration resistance is calculated based on how deep the tire sinks into the ground. The formula for penetration resistance is: Penetration Resistance = Depth of Penetration (in cm) * 6 kg/ton/cm * Gross Weight (in tons). Here, we multiply the 6 centimeters of penetration by 6 kg/ton/cm and the gross weight of 50 tons to get a total of 1800 kg.
Examples & Analogies
Imagine trying to walk through sand. The deeper your foot sinks into the sand (similar to the tire sinking), the more effort it takes to lift it out. In this example, we're calculating how much additional weight you're effectively 'carrying' because of that sinking.
Calculating Total Resistance
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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.
Detailed Explanation
The total resistance encountered by the vehicle is the sum of both the rolling resistance and penetration resistance. We simply add the two values: 1400 kg (rolling resistance) + 1800 kg (penetration resistance) to get a total resistance of 3200 kg.
Examples & Analogies
Think of total resistance like the total effort you need to pull two different weighted sleds attached to each other. First, you have the weight of the first sled (rolling resistance). Then you add the weight of the second sled (penetration resistance). Together, you have to account for the combined weight to understand how much force you'll need to pull them both.
Estimating Required Tractive Effort
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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?
Detailed Explanation
The tractive effort required is directly related to the total resistance calculated previously. In this case, the vehicle needs a tractive effort of at least 3200 kg to move effectively. By knowing this, we can select an appropriate machine that has sufficient power to overcome this resistance while working at the site.
Examples & Analogies
Imagine trying to pull a heavy wagon with a horse. If you know the total weight of the wagon and its load (3200 kg), you can decide whether a horse can pull it or if you need a stronger horse. This decision-making process is crucial in selecting the right equipment.
Understanding Grade Resistance
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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.
Detailed Explanation
Grade resistance is encountered when a vehicle must move uphill. This type of resistance works against the weight of the vehicle due to gravity, requiring additional tractive effort to overcome. The steeper the slope, the more resistance the vehicle will face, making it crucial to factor this into the calculations for total resistance.
Examples & Analogies
Think of riding a bicycle uphill. The harder it is to pedal due to the incline, the more effort you need to exert compared to riding on flat ground. Similarly, in our calculations, we have to account for the effort required to overcome the uphill gradient.
Calculating Grade Resistance
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Grade resistance is nothing but by simple elementary 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. So, this is simple guideline which they are worked out which is worked out in the literature you can easily find it.
Detailed Explanation
To calculate grade resistance, we use a guideline indicating that overcoming a 1% grade requires 10 kg of tractive effort per ton of weight. Therefore, to find the total grade resistance, we multiply the percentage of the slope by the gross weight of the machine, converting it into the required tractive effort.
Examples & Analogies
Imagine climbing stairs with a backpack. If the stairs are steep (similar to a grade), you need to exert more force to lift yourself and your weight up each step. This analogy helps explain why equipment requires more effort to move uphill.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Total Rolling Resistance: Calculated by multiplying gross weight by rolling resistance value.
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Penetration Resistance: Resistance due to tire depth into the surface, calculated based on penetration depth.
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Grade Resistance: Varies with slope percentage, impacting machinery power needs.
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Usable Power: Determined by subtracting the total resistances from available power.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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If a tractor weighs 10 tons with rolling resistance of 40 kg/ton, total rolling resistance is 10 * 40 = 400 kg.
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For a slope of 6%, the grade resistance is 10 kg/ton, leading to an additional resistance of 6 * 10 * 10 = 600 kg.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
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When the tire sinks in, resistance is a spin; 6 kg per ton makes the effort begin.
📖 Fascinating Stories
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Imagine a truck on a slope trying to make way. Each kilogram of resistance is like a stone in the path, heavy yet stay. Rolling down seems easy with weight being light, but as it climbs higher, more effort feels right.
🧠 Other Memory Gems
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Remember 'RPG' for calculations: Rolling resistance, Penetration resistance, General resistance equals total needed!
🎯 Super Acronyms
R.U.F. - Remember Usable Force, as it guides us in power to tow!
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Rolling Resistance
Definition:
The force resisting the motion of a vehicle when rolling on a surface, typically expressed in kg per ton.
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Term: Penetration Resistance
Definition:
The resistance faced by tires when sinking into a surface, associated with the depth of penetration.
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Term: Grade Resistance
Definition:
The additional effort required for machinery to move uphill against gravity, dependent on the slope's percentage.
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Term: Usable Power
Definition:
The power available for performing work after accounting for resistances that oppose the machine's movement.