1 - Rolling Resistance Calculation
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Interactive Audio Lesson
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Introduction to Rolling Resistance
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Today, we will discuss how we calculate rolling resistance for vehicles. Rolling resistance is typically expressed in kilograms per ton. Can anyone tell me how we can convert vehicle weight into tons?
We need to divide the weight in kilograms by 1,000.
Correct! If a vehicle weighs 50,000 kg, what would that be in tons?
That would be 50 tons!
Exactly. Now, if the rolling resistance is 28 kg per ton, how do we find the total rolling resistance for our vehicle?
We multiply the gross weight in tons by the rolling resistance value.
Great! So, what is the total rolling resistance for a 50-ton vehicle?
It would be 1,400 kg!
Correct! Remember, rolling resistance is crucial to determine the effort required to move a vehicle. Let's summarize this part: we convert weight to tons and then multiply by the rolling resistance to find the total.
Understanding Penetration Resistance
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Next, let's talk about penetration resistance. If a tire sinks 6 centimeters into the surface, how do we calculate the penetration resistance?
We multiply the depth of penetration by 6 kg per ton.
Correct! Based on our previous example of a vehicle weighing 50 tons, what would the penetration resistance be?
It would be 1,800 kg!
Exactly right! Now, how do we find the total resistance when we combine rolling and penetration resistance?
We simply add both resistances together.
Correct! For our calculations, what is the total resistance?
It would be 3,200 kg!
Excellent! So the total resistance directly informs the power we'll need for our machine.
Exploring Grade Resistance
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Now, let's explore grade resistance. What happens when a vehicle moves uphill?
It needs extra effort to overcome the gravitational pull.
Exactly! The steeper the slope, the greater the grade resistance. What do we know about calculating grade resistance on a 1% slope?
It's 10 kg per ton!
Great! Using that, how much effort do we need to overcome a 4% grade for a 15-ton vehicle?
We would multiply 4% by 10 kg per ton and then by 15 tons.
Exactly! What would the grade resistance be?
It would be 600 kg!
That's right! Grade resistance is a key factor to consider for equipment operation, along with rolling resistance.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
The section details the calculation of rolling resistance based on vehicle weight and the specifics of the haul route, alongside insights into grade resistance that occurs when climbing or descending slopes. It illustrates the importance of understanding these resistances to select equipment that can effectively manage the associated power requirements.
Detailed
Rolling Resistance Calculation
This section focuses on the critical calculations for determining rolling resistance and grade resistance, which are vital for understanding the power requirements of vehicles operating on various terrains.
Key Calculations:
- Rolling Resistance Calculation: The section begins by converting vehicle weight from kilograms to tons, using a vehicle weight of 50,000 kg, equivalent to 50 tons. The rolling resistance for this machine is identified as 28 kg per ton, leading to a rolling resistance of 1,400 kg (50 tons x 28 kg/ton).
- Penetration Resistance: Additionally, if a tire penetrates the surface by 6 centimeters, the calculation for penetration resistance involves multiplying this depth by 6 kg per ton per centimeter, resulting in 1,800 kg of penetration resistance.
- Total Resistance: The total resistance, which combines rolling and penetration resistance, here amounts to 3,200 kg, representing the tractive effort required for the machine to operate efficiently in project conditions.
Grade Resistance Consideration:
The section also discusses grade resistanceβan additional force that opposes the movement of a vehicle on slopes. The tractive effort needed to overcome this resistance varies with the slope percentage, establishing that a steeper slope increases resistance.
The section emphasizes calculating grade resistance (10 kg per ton for a 1% slope), noting the importance of optimal haul route selection to minimize overall resistance and operating costs. The relationship between rolling resistance and equivalent gradients is also highlighted, enabling better assessment of total resistance dynamics.
In conclusion, this section illustrates the essential calculations necessary for estimating power requirements for vehicles, providing both theoretical and practical applications for road construction and other similar fields.
Audio Book
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Vehicle Weight Conversion
Chapter 1 of 5
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Chapter Content
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 chunk, we begin by converting the vehicle's weight from kilograms to tons to ease the calculation of rolling resistance, which is typically expressed as kilograms per ton. The gross weight of the machine is stated to be 50,000 kg. Since 1 ton equals 1000 kg, we divide 50,000 by 1000 to find that the weight of the machine in tons is 50 tons.
Examples & Analogies
Imagine you are measuring ingredients for a recipe. If a recipe calls for 5 kilograms but your kitchen scale measures in pounds, you'd first need to convert that weight into poundsβjust like you convert the vehicle's weight into tons for easier calculations.
Calculating Rolling Resistance
Chapter 2 of 5
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Chapter Content
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.
Detailed Explanation
In this section, we focus on the calculation of rolling resistance. The rolling resistance is given as 28 kg per ton for the specific haul route. To find the total rolling resistance, we multiply the gross weight of the machine (50 tons) by the rolling resistance (28 kg per ton). Therefore, the total rolling resistance for the machine is 50 tons multiplied by 28 kg/ton, which equals 1400 kg.
Examples & Analogies
Think of rolling resistance as the effort needed to push a heavy object across a rough surface. If you know how heavy the object is (in tons) and how difficult it is to slide on that surface (in kg per ton), you can easily estimate the total effort needed.
Calculating Penetration Resistance
Chapter 3 of 5
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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. 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 centimeters, 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 when a tire sinks into the surface. The problem states that the tire is penetrating 6 centimeters into the ground, and the required effort is 6 kg per ton of machine weight for each centimeter. Thus, we multiply the depth of penetration (6 cm) by the effort needed (6 kg/ton/cm), and then multiply that by the gross weight of the machine (50 tons) to find the total penetration resistance, which is 1800 kg.
Examples & Analogies
Consider walking through mud. The deeper you sink (like the depth of penetration), the harder it is to walk (more resistance you feel). Just as you might need to exert more effort to lift your feet out of the mud, the machine's tires need to exert effort to push through the surface.
Total Resistance Calculation
Chapter 4 of 5
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Chapter Content
Now we can find the total resistance, that is nothing but adding 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
Having calculated both rolling resistance and penetration resistance, we can now find the total resistance the machine encounters. We simply add the two values together: 1400 kg (rolling resistance) + 1800 kg (penetration resistance) equals 3200 kg as the total resistance that the machine needs to overcome.
Examples & Analogies
Imagine hiking up a hill. You have to push against the weight of your backpack (rolling resistance) and fight against the mud that's slowing you down (penetration resistance). Your total effort to get to the top consists of both these parts combined.
Determining Tractive Effort
Chapter 5 of 5
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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 at 3200 kg, we can determine the necessary tractive effort to move the machine effectively. Understanding this helps in selecting an appropriate machine that has the power output needed to overcome this resistance during operations on the project site.
Examples & Analogies
Think of it like choosing a vehicle for a road trip. If you know the hills you'll encounter on your way (total resistance), you wouldnβt pick a small car that struggles uphill; instead, youβd choose a more powerful vehicle that can easily handle the required effort.
Key Concepts
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Rolling Resistance: It is derived from the weight of the vehicle and the surface type, influencing the energy required for mobility.
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Grade Resistance: Additional energy required to overcome gravitational forces while ascending slopes, directly related to the steepness of the incline.
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Total Resistance: The sum of rolling resistance and penetration resistance that must be overcome to maintain vehicular movement.
Examples & Applications
A truck weighing 30 tons on a flat road with a rolling resistance of 25 kg/ton results in a total rolling resistance of 750 kg.
When climbing a 10% slope, the same truck would face an additional grade resistance of 300 kg based on the guideline of 10 kg per ton for each percent of grade.
Memory Aids
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Rhymes
To find rolling resistance, don't be shy, divide by a thousand, give it a try.
Stories
Imagine a truck named Tommy that weighed 50 tons. Every time it rolled over a road, it had to push against a force named 'Rolling.' Tommy learned that every hill made him work even harder, needing extra energy based on how steep the hill was.
Memory Tools
RPG: Resistance Comes from Penetration and Grade! Use this to remember that rolling resistance and penetration affect total movement.
Acronyms
RICE
Remember
it's Calculations for Effort! This helps to recall how to calculate total resistance.
Flash Cards
Glossary
- Rolling Resistance
The force that opposes the motion of a vehicle when tires roll over a surface, usually measured in kilograms per ton.
- Penetration Resistance
The resistance faced when tires sink into the surface, calculated based on how deep the tires penetrate.
- Grade Resistance
The extra force needed to move a vehicle up an incline, which increases with the steepness of the slope.
- Tractive Effort
The force required to move a vehicle forward, overcoming resistance.
- Payload
The load carried by a vehicle, including both the cargo and the weight of the vehicle itself.
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