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Interactive Audio Lesson
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Rolling Resistance Calculation
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Let's begin with rolling resistance. Can anyone tell me what rolling resistance means?
Is it the resistance a vehicle faces when moving because of its weight?
Exactly! Now, if a vehicle weighs 50 tons and the rolling resistance is 28 kg per ton, how do we calculate it?
We multiply 50 tons by 28 kg per ton, right?
Correct! This gives us the total rolling resistance of 1400 kg. Great job! Now, remember this acronym: ROLL - Rolling Overcomes Lots of Load!
That’s a good way to remember it!
Now, can someone explain why we convert weight to tons in these calculations?
Because rolling resistance is expressed per ton!
Exactly! We're setting the stage for calculating penetration resistance next.
Penetration Resistance Calculation
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Now, let's dive into penetration resistance. What happens when tires sink into the ground?
They create more resistance that needs to be overcome, right?
Absolutely! If the tire sinks 6 cm with a resistance of 6 kg per ton per cm, how do we calculate the penetration resistance?
We calculate it by multiplying 6 cm by 6 kg per ton by the gross weight in tons?
Exactly! This results in 1800 kg of penetration resistance. Who remembers the total resistance calculation?
You add the total rolling resistance and penetration resistance!
That's right! And what is our total again?
3200 kg!
Perfect! Remember the mnemonic: DEPTH - Depth Equals Penetration's Total Hardship!
Grade Resistance
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Let's turn our attention to grade resistance. What do we mean by 'grade'?
Isn’t it just the slope of the ground we're working on?
Good! So how does a steep slope influence our tractive effort?
We need more tractive effort to go uphill because of gravity!
Correct! For example, how much tractive effort is needed for a 4% slope?
You multiply the percentage by 10 kg per ton and then the gross weight.
Exactly! So if we have a total machine weight of 50 tons for a 4% slope, what’s our grade resistance?
It's 600 kg!
Nicely done! Remember: SLOPE - Steep Lands Overtake Power Exertion!
Utilizing Power Ratings
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We need to make sure our machines can handle the calculated total resistance. How do we verify this?
By checking the power ratings the manufacturer gives us.
Right! What are the factors affecting the usable power on-site?
Altitude and temperature conditions can change the efficiency of the machinery.
Well done! Remember the acronym: POWER - Project Operations Will Evolve with Resistance!
That helps a lot!
Finally, if our machine has 7000 kg of maximum rimpull and we've calculated a 1500 kg resistance, how much usable power is left?
5500 kg for towing!
Excellent summary of our session!
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
The section outlines methods for calculating rolling resistance based on vehicle weight and specific resistance values. It also discusses grade resistance and how it impacts total resistance when a vehicle travels up or down a slope, allowing for a better understanding of the overall resistance that a machine must overcome at a project site.
Detailed
Detailed Summary
The calculation of penetration resistance is crucial in understanding the total resistance a vehicle must overcome in a worksite, particularly for off-road machinery. This section begins with the conversion of vehicle weight into tons, which is essential since rolling resistance is commonly expressed as kg per ton.
- Rolling Resistance Calculation: The gross weight of a machine is typically given, in this case, as 50,000 kg, equivalent to 50 tons. The rolling resistance for the specific haul route being analyzed is given as 28 kg per ton. By multiplying the gross weight by the rolling resistance (50 tons * 28 kg/ton), the total rolling resistance is calculated to be 1400 kg.
- Penetration Resistance Calculation: The section continues with penetration resistance, which occurs when tires sink into the ground. The problem specifies a penetration depth of 6 centimeters, with a resistance of 6 kg per ton per centimeter of depth. Thus, multiplying the depth by the resistance and the gross weight (6 cm * 6 kg/ton * 50 tons) yields a penetration resistance of 1800 kg.
- Total Resistance: The total resistance, the sum of rolling and penetration resistance, is calculated as 3200 kg (1400 kg + 1800 kg). This total is crucial to determine the required tractive effort needed to move the machinery across the project site, emphasizing the importance of selecting appropriately powerful machines for overcoming these resistances.
- Grade Resistance: The section also discusses grade resistance, which arises when a vehicle must move up a slope, requiring additional effort to pull against gravity. It highlights how the grade slope percentage directly influences the additional tractive effort needed. The relationship for grade resistance is simplified where 1% of grade resistance requires 10 kg/ton.
- Final Power Requirements: Finally, considerations about the available power ratings of machines are discussed, explaining that these must be compared against resistances to ascertain usable power at project sites.
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
In this step, we begin by converting the weight of the vehicle from kilograms to tons because rolling resistance calculations often require weight in tons. We take the gross weight of the machine, which is given as 50,000 kg. To convert this to tons, we use the conversion factor: 1 ton = 1000 kg. Therefore, we divide 50,000 kg by 1000 to find that the machine weighs 50 tons.
Examples & Analogies
Think of it like converting your body's weight into stones whenever you're discussing your weight with a friend from the UK. If you weigh 70 kg, you'd tell them you weigh around 11 stones (since 1 stone is approximately 6.35 kg). Just like that, converting to tons helps us use the right scale of measurement for our calculations.
Calculating Rolling Resistance
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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.
Detailed Explanation
After converting the vehicle weight to tons, we calculate the rolling resistance, which is a measure of the force resisting the motion when the vehicle rolls on surfaces. Here, the rolling resistance is provided as 28 kg per ton. To find the total rolling resistance, we multiply the weight of the vehicle (50 tons) by the rolling resistance value (28 kg per ton). The calculation looks like this: 50 tons x 28 kg/ton = 1400 kg. This means that to move the vehicle, a force of 1400 kg is required just to overcome rolling resistance.
Examples & Analogies
Imagine you're pushing a shopping cart (the vehicle) in a supermarket. If the cart is heavy (like our 50-ton vehicle), it requires more effort (rolling resistance) to move it. If the cart has flat wheels (good surface), it's easier to push than if it has wobbly or squeaky wheels (high rolling resistance). Here, the effort needed is quantified as 1400 kg of force in our calculations.
Finding Penetration Resistance
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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.
Detailed Explanation
Next, we calculate the penetration resistance, which is the resistance encountered by the tires as they sink into the surface. The problem states that the tires sink 6 centimeters and that each centimeter of penetration requires 6 kg of force per ton. We multiply the depth of penetration (6 cm) by the vehicle's weight (50 tons) and the specified resistance value (6 kg/cm/ton): 6 cm x 50 tons x 6 kg/cm/ton = 1800 kg. Therefore, the total penetration resistance is 1800 kg.
Examples & Analogies
Think of trying to walk on a sandy beach. The deeper your feet sink into the sand (like the 6 centimeters), the harder it is to walk (this is like the additional force needed). If someone weighs more (like our 50-ton vehicle), they'll sink deeper and have more difficulty moving compared to someone lighter, reflecting the calculation of 1800 kg that represents the effort needed for movement.
Total Resistance Calculation
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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
Finally, we arrive at the total resistance the vehicle must overcome, which combines both the rolling resistance and penetration resistance. We simply add the previously calculated rolling resistance (1400 kg) and penetration resistance (1800 kg) together: 1400 kg + 1800 kg = 3200 kg. This means that the total effort required for the vehicle to move is 3200 kg.
Examples & Analogies
Imagine trying to move a large box. First, it feels heavy because of the weight of the box (like rolling resistance), but then someone puts a small weight on the box (say, to represent penetration resistance). To move the box, you now need to account for both the weight of the box and the additional weight, which in this case is 3200 kg total effort required.
Tractive Effort Requirements
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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? Select a machine that can generate enough power to overcome this resistance.
Detailed Explanation
With the total resistance calculated, we determine the required tractive effort to overcome it. The vehicle needs a minimum of 3200 kg of tractive effort to start moving on the project site. This information is crucial for selecting the correct machine; we need to pick a machine that can produce this amount of power to successfully perform operations under these conditions.
Examples & Analogies
Consider it like using a bicycle on a steep hill. If you know the uphill part of the journey requires a lot of effort (3200 kg), you'd want to make sure you have a bike with enough gears (power) to get you up that hill without stopping. Choosing the right equipment ensures you can complete your task effectively without unnecessary struggle.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Weight Conversion: Converting vehicle weight to tons for rolling resistance calculations.
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Resistance Calculation: The process of calculating both rolling and penetration resistance for any vehicle.
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Grade Slope Impact: Understanding how different slope percentages influence the tractive effort needed.
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Power Rating Importance: The connection between the manufacturer's power ratings and the machine's ability to operate under specific conditions.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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A tractor weighing 15 tons has a rolling resistance of 60 kg/ton, resulting in a total of 900 kg resistance.
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For a 4% slope, the tractive effort required can be estimated at 600 kg using the guideline of 10 kg per ton of grade.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
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For rolling resistance we say, weight and grip lead the way!
📖 Fascinating Stories
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Imagine a truck struggling up a hill — the steeper it gets, the harder it spills, rolling down it's a thrill, but up it needs a power drill!
🧠 Other Memory Gems
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RAMP - Rolling And Moving Power: how to think about tractive efforts on slopes.
🎯 Super Acronyms
REPOWER - Resistance Equals Power On Weight and Resistance.
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 a vehicle's motion due to its weight, expressed in kg per ton.
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Term: Penetration Resistance
Definition:
The additional force required when a vehicle's tire sinks into the surface, typically dependent on depth.
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Term: Grade Resistance
Definition:
The additional effort required to overcome gravity when a vehicle moves up a slope.
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Term: Tractive Effort
Definition:
The force that a machine must exert to move itself forward, overcoming all forms of resistance.
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Term: Haul Route
Definition:
The designated path over which vehicles move, which can affect total resistance based on its characteristics.