The speakers discuss the importance of loading and hauling in construction equipment, including factors affecting cycle time, productivity, and cost. They also discuss the importance of resistance and tire flex in the process of loading truck, as well as the factors affecting the speed and efficiency of the machine. The speakers provide examples of various types of rock, including resistance, tire penetration, and soil conditions. They also discuss the factors affecting the speed, efficiency, and maximum speed of the tractor, including weight, traction, and resistance. They provide examples of performance curves and explain how to measure the performance of the machine and estimate the maximum speed. They also discuss the factors affecting the total production of the equipment and the importance of derating factors and preventing acceleration and deceleration during driving conditions.
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Steve, hello, into another lecture of construction equipment, and

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primarily in this lecture, we're going to learn about how to

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calculate the cycle time, and what are the elements affecting the

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cycle time, primarily, what kind of resistance is the equipment

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going to be subject to that can affect its performance. It can

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affect the duration of the cycle time and the number of cycles per

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hour.

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So the equipment productivity is affected by several things. Speed

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affects the cycle time. Speed of each cycle. The Cycle Time affects

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the production. Because, again, the production is determined by

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the number of cycles per hour times the production per cycle.

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And the number of cycles per hour is determined by the length of the

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cycle time, and production determines cost. So primarily, we

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can say that the speed of the performing the operation for each

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cycle affects the project cost for that piece of equipment.

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Each piece of equipment requires a certain amount of power to

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overcome the resistance that is going to be facing. So the

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required power is the power needed to overcome resisting forces and

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cause machine motion. So for example, imagine that you are

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driving in a muddy condition. There's going to be a certain

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resistance to the motion of the tires, so the equipment has to be

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able to overcome that resistance in order to move forward.

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The magnitude of the resisting forces determines the power

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required, the minimum amount of power required to overcome this

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resistance and to be able to move the vehicle or the equipment

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forward. The

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equipment cycle time. The Cycle Time for a piece of equipment is

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the time it takes to perform one cycle of its planned job. We

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mentioned in last in the last class, that one cycle is basically

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going to be, for example, for a loader is to position itself

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instead of the area to be excavated, or in front, in front

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of the soil to be removed, and then to load that soil in the

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bucket, to turn around and to move, to dump that soil, and then

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to come back, position itself and get ready for a new cycle. All of

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All of these are parts of the cycle time for the equipment. And

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each cycle consists of two components. One of them is called

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fixed cycle part, or fixed cycle time, or fixed component of the

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cycle time, and the other one is the variable component of the

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cycle time. The fixed time is the part of the cycle other than the

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So mostly the fixed time is done while the equipment is in its

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standing in place. Dumping is the same thing, whereas traveling back

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and forth, this is the hauling part of the cycle time, which is

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going to be part of the variable time. So the variable time

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represents the travel time from origin to destination and back,

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and it depends on equipment characteristics, like the weight

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and the power, the engine, power of that equipment, the road

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conditions, whether it's flat or bumpy, whether it's uphill or

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downhill, what kind of soil is it trolling on grade and altitude?

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Again, grade, which is the slope of the road, again, downhill or

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uphill altitude, as we have discussed in class, the higher

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from the sea level you're working, the thinner the air is going to

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be, which might affect the efficiency of the engine and the

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distance traveled. Of course, the farther the distance, the longer

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it's going to take to get to and from there, the longer the

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variable part of the cycle time.

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The loading time is a function of the capacity and cycle time of the

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the capacity of the truck or hauler and the skill of the

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excellent job conditions, above average, average, below average,

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etc. It had something to do with the angle of swing. For example,

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of the equipment, the larger that angle of swing, the longer it's

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going to take, which means it's going to take the cycle time is

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going to be longer, whether it's dumping on the ground or it's

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dumping in a truck, whether that truck is a large truck or a small

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truck, how skilled the truck driver is? How big is the bucket

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for the loading equipment, and how big is the bed of the truck where

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you're going to be dumping the soil? All of these are elements

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The type and condition of material, how easy it is it going

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to flow from the bed or from the bucket of that equipment,

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whether that material is going to be wet or dry, the Method of

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dumping or spreading, whether it's going to be end dump or bottom

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dump, or whether you're going to be dumping into a pile or you're

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going to be spreading it around, and the type and maneuverability

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of the truck or the piece of equipment, basically.

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So the haul and return time are a function of the haul road profile,

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including the great resistance, rolling resistance and distance to

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be traveled. We're going to talk about each one of these in more

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detail in a second, the altitude of the project site and the

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performance characteristics of the hodding equipment, which is a

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characteristic of the vehicle itself, or the equipment itself,

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number of loader cycles to load a truck. So if you have, let's say,

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a loader with a bucket size of two cubic yards, and you have a truck

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with a capacity of 15 cubic yards, how many cycles is it going to be

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needed to load the truck? The volume capacity of the truck

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divided by the volume capacity of the loader? So in this case, going

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to be 15 divided by two, which is seven and a half, which means it's

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going to take eight cycles. Now,

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that truck, you're going to need eight cycles of that loader. If

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each cycle takes, let's say, 35 seconds, then it's going to be

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eight times 35 seconds, that's going to be the duration of

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And here, for example, are some examples in this table about the

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job conditions, whether it's favorable, average or unfavorable,

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for the turn and done time and for the spotting time, which are

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basically all of these are part of the fixed time of the equipment.

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This is not the variable time. This is the fixed part. So in

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under favorable conditions, in end dump, it's going to take about one

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minute.

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The spotting time is going to be about 15 seconds. For the bottom

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dump is going to be less than that, only point four minutes, and

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the spotting time is going to be pretty much the same. So under

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favorable conditions, the fixed time for that piece of equipment

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is going to be for an end up is going to be a minute and 15

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seconds. Under unfavorable conditions, as you can see, that

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number is going to be much larger, one and a half to two minutes, and

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point eight minutes, so almost twice as much as the favorable

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conditions. Now,

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talking about the resistance, what kind of resistance is the

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equipment going to be facing while it's trying to move and to perform

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its function? Rolling resistance is the first type, and it's a

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measure of the force. The force is going to be expressed in pounds

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per ton

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that must be overcome to rotate a wheel over the surface on which it

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makes contact. So this is got friction is going to be part of

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that equation, one of the types of resistance and equipment faces

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while moving. So we have two types of resistance, the equipment Scott

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has to overcome. One of them is going to be running resistance,

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and the other one is going to be the grade resistance. It can be

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expressed either in power as a pounds per ton or of equipment

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weight, or just in pounds. So you can say either the rolling

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resistance going to be 20 pounds per ton of the equipment weight.

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So if the equipment weight is 20 tons, then the total resistance,

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running resistance going to be 20 pounds per tons, time per ton

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times 20, which is the weight of the equipment. That's 400 pounds.

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Or you can just express it as number of pounds again, as we did,

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by multiplying that factor in pounds per ton by the total weight

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of the equipment. Now that weight of the equipment is going to

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change because whether the equipment is empty or is loaded.

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So when it's going when it's loading and going to dump, it's

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going to be moving forward full. So it's going to be heavier,

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therefore the resistance going to be much more. When it's coming

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back is going to be empty, therefore the resistance is going

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to be less than the previous case, it is caused by internal friction

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and tire flexing. Tire flexing is very important, so as you know, to

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properly inflated tires are going to yield better fuel consumption.

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Same thing here. It's going to increase that rolling resistance

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going to increase by about 30 pounds per ton for each inch of

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tire penetration. Tire penetration into that soil.

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If it's if the tire is penetrating two inches, then that's going to

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add 60 pounds per ton of rolling resistance. Properly inflated

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tires reduce rolling resistance. What if the equipment is.

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Running over asphalt or concrete. Now, in this case, you're not

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going to have any tyre penetration, so you're not going

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to have much

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additional rolling resistance due to tire flexing.

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If the tyre penetration is known, then the rolling resistance is

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equal to, which is RR, that's the running resistance. It's 40 pounds

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per ton of the equipment weight, plus 30 pounds per ton per inch

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times inches of tire penetration. So again, if you're running on

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concrete or asphalt, where you're not going to have any tire

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penetration, that second part of the equation is going to be equal

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to zero. You're only going to have the 40 pounds per ton,

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the running resistance force. So this is the running resistance,

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but the running resistance force for the whole equipment is going

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to be the running resistance in pounds per ton, which we

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calculated from here the RR times the total weight of the equipment

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in tons. That's going to be a force

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represented by or expressed in pounds. If tyre penetration is not

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known, then the running resistance can be estimated from tables. So

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you don't know exactly. You can't measure the type penetration, but

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you know what type of soil that equipment is going to be working

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on. We can use that table. So for concrete or asphalt, the running

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resistance factor in pounds per ton is going to be 40 pounds per

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ton, which is basically this one, with the second component of the

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equation being equal to zero.

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For concrete is going to be 40. For asphalt is going to be 30.

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Firm, smooth, flexing slightly under load. So we're not talking

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road. For example, that's going to be up to 64 pounds per ton, rotted

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dirt roadway. One to two inches of penetration is going to be 100

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which is basically the 40 plus 30 pounds per ton per inch times two

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inches, which is going to be 60. So 40 plus 60, that's 100 pounds,

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pounds per ton, soft, rotted dirt, three to four inch penetration,

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loose sand or gravel is going to be up to 200 pounds per ton, soft,

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muddy, deeply rooted road conditions is going to be anywhere

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between 304 100 pound pounds per ton. You can see the big

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difference between a paved road, concrete or asphalt, 40 and soft,

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muddy, deeply rotted. 300 to 400 which is 10 times the rolling

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resistance. Therefore, these are things that you can control as a

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project manager. For example, you can build a temporary access road,

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or you can have compacted soil or crushed stone or gravel or

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something like that, to improve the working conditions of the

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equipment, therefore reducing the rolling resistance, which means

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you're going to get better cycle Time, which means higher

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productivity and lower cost

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the second type of resistance is the grade resistance, which is the

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component of a vehicle's weight, which acts parallel to an inclined

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surface. It can be positive when moving uphill. Contrary to our

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intuition, you might think that positive is something good that

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helps, and negative is something that impedes. Here we're going to

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use the opposite sign convention. It's positive when moving uphill,

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so you're going to add that resistance when when moving

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uphill, is going to be working against the equipment, which is

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adverse conditions, and negative when moving downhill, which is a

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favorable condition, also called grade assistance, not resistance.

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In this case, grade assistance, which means it can help reducing

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the rolling resistance, and it can be calculated exactly the same way

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as we did with the rolling resistance. The grade resistance

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can be expressed in pounds per ton, which is equal to 20 pounds

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per ton for each 1% slope times the percent slope. So if the grade

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is 5% moving uphill by 5% is going to be 20 pounds per ton for each

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1% which is 20 pounds per ton times five which means we're going

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to have a grade resistance of 100 pounds per ton. If the weight of

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the equipment is 20 tons. Again, 200 pounds, 100 pounds per ton,

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which is 20 times five times 20 that's going to give you the total

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resistance force is equal to grade resistance, the factor that we

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calculated from here, times the total weight of the equipment in

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tons. Again, in this case, the issue of whether the equipment is

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Can we express both resistances into one so? Can we express both.

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Is rolling resistance and grade resistance as a common number.

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resistance encountered by the vehicle. So you can say, for

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example, that a vehicle that's moving on a flat surface, but the

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road is rotted and is going to exert a lot of rolling resistance.

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That is as if the equipment is moving uphill on a certain slope.

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It's also called equivalent grade, or percent total resistance, and

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can be calculated as the effective grade percentage is equal to the

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actual grade if it's moving uphill at 5% so that's going to be five

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plus rolling resistance divided by 20. So if the running resistance,

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for example, is, let's say, 100 pounds per ton, then we divide

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that by 20. That's going to be 100 pounds per ton is going to be

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equivalent to moving uphill at the 5% slope, which is the 100 divided

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by 20. So in this case, if you already have a 5% slope plus

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running resistance of 100 pounds per ton, that's equivalent to

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moving to up to a 10% slope uphill.

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Of course, that also is affected by the type of soil that you're

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running on. Imagine if you're running on ice, you're not going

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to have any traction with that ice, so the tires or the wheels

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can turn without the equipment moving forward. So we're going to

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deal with something called a coefficient of traction, the power

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available to move the vehicle and its load can be expressed as

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either, if that equipment is running on wheels. It's going to

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be called the rim pull. RIM pull, which is the pull available at the

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rim of the driving wheels under rated conditions. The driving

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wheels, some equipment are four wheel drive. Some of them are two

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wheel drive. Some of them have more than two moving axles. So an

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equipment might have, might have three axles. For example, two of

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them are moving axles. So in this case, we're going to calculate

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that pull available a dream of the driving wheels, which is the

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moving axles. If that equipment runs on tracks,

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then it's going to be called draw bar. So we we're talking about

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dream pull in case of wheels, draw bar in case of tracks, which is

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the power available at the hitch of the crawler tractor operating

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under standard conditions, how much pull can it exert? How much

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weight can it pull? The traction depends on the coefficient of

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traction and the weight on the drivers. So the maximum usable

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pull.

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You might have a lot of power for the equipment. You might have a

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lot of RIM pull, lot of drawbar but especially lot of RIM pull in

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this case, but you're working on a very slippery soil, so the wheels

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turn in place, therefore it's not all translated into motion. So

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here we have a something called the coefficient of traction. For

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concrete that's dry, it's going to be point nine, which is 90% of the

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power is going to be translated into motion, whereas for tracks,

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it's only 45%

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concrete that's wet, 80% and 45% respectively. And you keep going

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down until we reach for example, ice is only 10% 90% of the power

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of the equipment is wasted. And in case of tracks, it's going to be

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85% of that power that's going to be wasted.

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So the maximum usable pull is the coefficient of traction, which we

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can obtain from such a table, depending on the soil conditions,

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times the weight on drivers, not the weight of the whole equipment,

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but the weight on the moving axles. That's going to be what

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affects the motion of the equipment. That's why, if you

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remember in the last lecture, when we were talking about that

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coefficient of traction, in case you are driving uphill on an icy

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road or where you have snow, it might, especially in a rear wheel

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drive car, putting a heavier weight on the rear axle, like

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having sandbags in your trunk, for example, in the trunk of Your car,

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might help overcoming that kind of resistance,

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the equipment available power is the engine, horsepower and

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operating the engine horsepower and operating gear are the primary

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factors in determining the power available at the drive wheels or

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the draw bar of a machine

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drawbar, in case of tracks, RIM pulled in case of wheels.

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Horsepower involves the rate of doing work, and one horsepower is

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equivalent to 33,000 foot pound per minute. Therefore the

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traveling speed of the machine should be considered when

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calculating the amount of.

00:20:00 --> 00:20:01

00:20:03 --> 00:20:06

per minute, so we're talking about speed, which is going to be a

00:20:06 --> 00:20:06

factor.

00:20:10 --> 00:20:14

Performance charts are provided by equipment manufacturers to enable

00:20:14 --> 00:20:19

the calculation of the estimated machine speed. So with each piece

00:20:19 --> 00:20:22

of equipment, you're going to have a manual that has some performance

00:20:22 --> 00:20:26

charts that tells you, under first gear, what's the maximum

00:20:26 --> 00:20:29

attainable speed on second gear, third gear, fourth gear, under

00:20:29 --> 00:20:31

00:20:31 --> 00:20:36

loaded or it's empty, it's gross weight or net weight and so on and

00:20:36 --> 00:20:41

so forth. The charts relate trim pull or draw bar pull to gross

00:20:41 --> 00:20:46

vehicle weight, speed and total resistance as a percent, which is

00:20:46 --> 00:20:48

00:20:51 --> 00:20:58

Here's an example of a performance curve. It shows both in kilograms

00:20:58 --> 00:21:02

or in pounds, so metric and imperial, and that's the drawbar

00:21:02 --> 00:21:02

pull.

00:21:03 --> 00:21:07

And this is the speed that the equipment can reach. And it tells

00:21:07 --> 00:21:09

you here under such and such

00:21:10 --> 00:21:16

speed under such and such gear. So under the first gear, your maximum

00:21:16 --> 00:21:20

speed is going to be about two and a half miles per hour. Under the

00:21:20 --> 00:21:22

00:21:23 --> 00:21:27

miles per hour, and the maximum overall maximum speed of that

00:21:27 --> 00:21:29

equipment is going to be less than seven miles per

00:21:31 --> 00:21:36

hour. So knowing the drawbar pull here, for example, 25,000 pounds

00:21:37 --> 00:21:42

is going we go horizontally, is going to interact, is going to

00:21:42 --> 00:21:46

intersect with two different gears. So under the first gear,

00:21:47 --> 00:21:52

with that 25,000 pounds of available drawbar, available pull,

00:21:52 --> 00:21:58

we're going to have about 1.4 miles per hour, and under the

00:21:58 --> 00:22:02

second gear, we're going to have only about one mile per hour.

00:22:05 --> 00:22:07

Here's another example of these sets of

00:22:08 --> 00:22:14

of performance curves. It shows at the top the gross weight of the

00:22:14 --> 00:22:18

vehicle, and it shows whether when it's empty, that's the weight, and

00:22:18 --> 00:22:23

this is when it's loaded. So we can do the same thing, the gross

00:22:23 --> 00:22:27

weight, the rim pool, the total resistance, which is grade plus

00:22:27 --> 00:22:31

rolling resistance. We converted the rolling resistance into grade

00:22:31 --> 00:22:32

by dividing it by 20

00:22:34 --> 00:22:38

and each that's going to be represented as percentage points.

00:22:40 --> 00:22:43

So here, for example, if that way, vehicles weight is

00:22:44 --> 00:22:51

about 100,000 pounds, and it's running over a surface with an

00:22:51 --> 00:22:53

00:22:54 --> 00:22:55

then

00:22:56 --> 00:22:59

in the fourth gear,

00:23:02 --> 00:23:03

it's going to give us

00:23:06 --> 00:23:13

a speed of about 14 miles per hour, and that's got the available

00:23:13 --> 00:23:16

rim pole is going to be or the available the required

00:23:18 --> 00:23:21

power To generate is going to be around 6000 pounds.

00:23:27 --> 00:23:32

Here we have something called a retarder curve. If that equipment

00:23:32 --> 00:23:37

is moving downhill, downhill again, the same piece of

00:23:37 --> 00:23:41

equipment, here's the weight and it's moving the effective grade is

00:23:41 --> 00:23:44

a favorable grade moving downhill 20%

00:23:46 --> 00:23:52

in the second gear is going to give us a speed of about maybe

00:23:52 --> 00:23:53

seven miles per hour.

00:23:57 --> 00:24:01

And if it's empty, this is when it's loaded. If it's empty, same

00:24:01 --> 00:24:07

equipment and moving again on the same slope, is going to give us

00:24:07 --> 00:24:07

also

00:24:10 --> 00:24:12

in the second gear, it's going to give us about the same speed,

00:24:12 --> 00:24:15

which is about 7% seven miles per hour.

00:24:18 --> 00:24:21

Now what if that equipment? Imagine if the road is divided

00:24:21 --> 00:24:26

into different segments, part of it is uphill, part of it is flat,

00:24:26 --> 00:24:28

and part of it is downhill,

00:24:29 --> 00:24:32

depending on the length of the segment. If the equipment is going

00:24:32 --> 00:24:35

to move in very short segments, it's not going to gain enough

00:24:35 --> 00:24:42

speed to move faster, so the longer the segment,

00:24:43 --> 00:24:46

the better the factor that we're going to use here, and we're going

00:24:46 --> 00:24:50

to see how to use that factor in a minute. If the length of the

00:24:50 --> 00:24:54

segment is only 10 100 feet, it has to start and stop in 100 feet.

00:24:54 --> 00:24:59

It hasn't gained enough speed but, but if it's moving 5000 feet, is

00:24:59 --> 00:24:59

going to give all.

00:25:00 --> 00:25:05

Almost gain 96% of its maximum speed. Here is going to have only

00:25:05 --> 00:25:07

about 45% of its maximum speed.

00:25:08 --> 00:25:12

And then we're going to have to compare whether it's coming from a

00:25:12 --> 00:25:17

stop and going uphill or coming from a stop moving downhill. Is it

00:25:17 --> 00:25:20

increasing or decreasing speed? We're going to see all of these in

00:25:20 --> 00:25:22

the in a problem in a moment.

00:25:24 --> 00:25:28

If the truck stops at both ends of a segment, divide the segment

00:25:28 --> 00:25:32

length into two parts and determine the speed factor for

00:25:32 --> 00:25:34

each part. So if, for example, we have

00:25:35 --> 00:25:41

a flat road segment of, let's say, 700 feet, the equipment is going

00:25:41 --> 00:25:45

to travel the the truck is going to travel 700 feet,

00:25:46 --> 00:25:50

but it's gone. It's going to be standing still at the beginning to

00:25:50 --> 00:25:54

be loaded, and it's going to stop at the end of these 700 feet to

00:25:54 --> 00:25:59

dump that load. In this case, we're going to divide that 700 by

00:25:59 --> 00:26:02

two, so as if the segment's length is only 350

00:26:03 --> 00:26:07

and we're going to use that factor only once, which is we can

00:26:07 --> 00:26:09

interpolate between these two numbers.

00:26:13 --> 00:26:16

Effect of altitude. If the equipment operates at a higher

00:26:16 --> 00:26:20

altitude where the air is less dense, the air is thinner, the

00:26:20 --> 00:26:24

engine may perform at a reduced power output, the engine power is

00:26:24 --> 00:26:29

going to be decreasing approximately 3% for each 1000

00:26:29 --> 00:26:35

feet above sea level. So in increments of 1000 feet,

00:26:36 --> 00:26:39

for each increment of 1000 feet, you lose 3% of the engine power.

00:26:40 --> 00:26:43

Turbocharged engine are more efficient at higher altitudes

00:26:43 --> 00:26:47

because they are not affected by that equation. So if you have in a

00:26:47 --> 00:26:50

problem, or if you have in real life that you're using

00:26:50 --> 00:26:53

turbocharged equipment, this does not apply. You don't have to worry

00:26:53 --> 00:26:55

00:26:56 --> 00:26:59

a the rating factor is used to reduce the engine production based

00:26:59 --> 00:27:05

on the altitude. For from this equation, the rating factor as a

00:27:05 --> 00:27:10

percentage is equal to three times altitude minus 3000 divided by

00:27:10 --> 00:27:16

1000 3000 is going to be our benchmark. So working 3000 feet

00:27:16 --> 00:27:18

above sea level is going to be where we're going to measure the

00:27:18 --> 00:27:19

equipment performance.

00:27:21 --> 00:27:25

If you are working at 4000 feet. So in this case, the altitude is

00:27:25 --> 00:27:27

4000 minus 3000 that's 1000

00:27:28 --> 00:27:34

times three that's 3000 divided by 1000 so that the rating factor is

00:27:34 --> 00:27:34

3%

00:27:35 --> 00:27:41

if you're working at 5000 feet. So five minus three, 5000 minus 3000

00:27:41 --> 00:27:46

that's 2000 times three 6000 divided by 1000 so the rating

00:27:46 --> 00:27:49

factor is going to be 6% and so on. Now

00:27:51 --> 00:27:54

let's look at an example that can illustrate all of the things that

00:27:54 --> 00:27:55

00:27:56 --> 00:28:00

Using the performance curve determine the maximum speed of the

00:28:00 --> 00:28:05

vehicle, if its gross weight is 150,000 pounds, the total

00:28:05 --> 00:28:10

resistance, which is rolling resistance, plus grade resistance,

00:28:10 --> 00:28:13

both of them combined and translated into effective grade 4%

00:28:15 --> 00:28:18

altitude. The rating factor is point two, 520, 5%

00:28:19 --> 00:28:24

altitude. The rating factor is 25% so obviously this equipment is

00:28:24 --> 00:28:26

working at a relatively high altitude.

00:28:27 --> 00:28:31

So we're going to look at this performance table here. The first

00:28:31 --> 00:28:33

thing that we can detect is 150,000

00:28:34 --> 00:28:37

pounds. So the weight of the equipment is going to be under

00:28:37 --> 00:28:43

50,000 pounds, and we have an effective grade of 4% so we're

00:28:43 --> 00:28:43

going to look at 150,000

00:28:45 --> 00:28:46

and the intersection with the 4%

00:28:48 --> 00:28:48

here's the 150,000

00:28:49 --> 00:28:54

the interaction with 4% it means that for this equipment to

00:28:54 --> 00:29:00

overcome the resistance, it needs 6000 pounds of rimple, 6000

00:29:00 --> 00:29:05

pounds. But remember that at this higher altitude we're not going to

00:29:05 --> 00:29:09

be able all to use all of that 6000 pounds. So to overcome that

00:29:09 --> 00:29:12

resistance at the higher altitude, we need actually more than 6000

00:29:13 --> 00:29:18

6000 1000 that was not taken into consideration the effect of

00:29:18 --> 00:29:21

altitude. So we're going to derate that. So we're going to decrease

00:29:21 --> 00:29:22

that by 25%

00:29:25 --> 00:29:28

which means dividing by one minus 25%

00:29:30 --> 00:29:34

divide by one minus the derating factor, which is 25% so as if we

00:29:34 --> 00:29:39

are dividing 6000 6000 divided by point seven, five, which is one

00:29:39 --> 00:29:44

minus point two five, which gives a required rainfall of 8000

00:29:45 --> 00:29:48

pounds. So at a rainfall of 8000 pounds,

00:29:49 --> 00:29:56

we're going to check third gear is going to give us a speed of about

00:29:56 --> 00:29:59

10 miles per hour. So this equipment can operate.

00:30:00 --> 00:30:04

In the third gear, at this altitude, with a speed of 10 miles

00:30:04 --> 00:30:04

per hour.

00:30:08 --> 00:30:13

So basically, that's what we're looking for determine the maximum

00:30:13 --> 00:30:16

speed of the vehicle. So we determine the maximum speed is

00:30:16 --> 00:30:18

going to be 10 miles per hour. Let's

00:30:20 --> 00:30:25

look at another example, a four wheel drive, wheel tracker. Four

00:30:25 --> 00:30:30

wheel drive, which means that both axles are going to be moving.

00:30:31 --> 00:30:33

It's wheeled. It's not on tracks.

00:30:35 --> 00:30:39

It weighs 41,000 pounds and produces a maximum rim pull of

00:30:39 --> 00:30:40

40,000 pounds.

00:30:41 --> 00:30:46

It is working at an altitude of 8000 feet on wet earth. Wet earth

00:30:46 --> 00:30:51

means coefficient of traction is going to decrease the performance

00:30:51 --> 00:30:54

of the equipment. 8000 feet means that we're going to have a

00:30:54 --> 00:30:55

derating factor.

00:30:56 --> 00:31:02

Operating conditions require a pull of 20,000 pounds to move the

00:31:02 --> 00:31:06

tractor and its load. Can the tractor perform under these

00:31:06 --> 00:31:11

conditions? That's the question. Now, we need a force or a power of

00:31:11 --> 00:31:16

20,000 pounds. Are we going to be able to generate that power, or is

00:31:16 --> 00:31:18

that equipment not going to be able to do that?

00:31:20 --> 00:31:25

So first of all, we look at the derating factor. We have 8000 feet

00:31:25 --> 00:31:30

minus 3000 times three, so five times three, which gives 15%

00:31:31 --> 00:31:35

so the percent rated power available is going to be the power

00:31:35 --> 00:31:37

that was given here, which is

00:31:38 --> 00:31:42

40,000 pounds times 85%

00:31:43 --> 00:31:46

therefore the available power is 40,000 times point eight five,

00:31:47 --> 00:31:52

which is 34,000 pounds. Now the coefficient of traction based on

00:31:53 --> 00:31:56

wet earth. Wet earth, we're going to look here,

00:32:00 --> 00:32:04

wet earth for rubber times is going to give us a factor of point

00:32:04 --> 00:32:05

four, five,

00:32:06 --> 00:32:11

so the available power is going to be the maximum usable pull.

00:32:11 --> 00:32:14

Remember, the maximum usable pull is point four, five,

00:32:16 --> 00:32:20

which is what we got from the table times the weight, because,

00:32:20 --> 00:32:20

again,

00:32:21 --> 00:32:24

we use the whole weight in this case, because

00:32:25 --> 00:32:29

you have two moving axles. If it were only a two wheel drive, we

00:32:29 --> 00:32:32

would look at the weight on the moving axle, which might be less

00:32:32 --> 00:32:34

than that. So it's equivalent to 18,450

00:32:36 --> 00:32:37

pounds.

00:32:38 --> 00:32:39

The usable power

00:32:41 --> 00:32:43

is less than the required pull.

00:32:45 --> 00:32:49

Less than the required pull. The required pull was the 20

00:32:50 --> 00:32:51

the 20,000

00:32:52 --> 00:32:56

pounds. So basically, the usable pool is less than the required

00:32:56 --> 00:33:02

pool. Therefore the tractor cannot perform under these conditions in

00:33:02 --> 00:33:07

order to work, increase the weight or the coefficient of traction. So

00:33:07 --> 00:33:10

again, improve the soil conditions, or increase increase

00:33:10 --> 00:33:13

the weight, because if you increase the weight times the low

00:33:13 --> 00:33:16

traction, factor of traction, or coefficient of traction, is going

00:33:16 --> 00:33:19

to give you something higher. So if that will, weight were to

00:33:19 --> 00:33:26

increase by about maybe 3000 pounds or 4000 pounds, when you

00:33:26 --> 00:33:29

multiply it by this is going to give you something more than the

00:33:29 --> 00:33:34

25 20,000 which would be able to pull the load behind the

00:33:38 --> 00:33:41

equipment. To estimate the travel time, we have to account for

00:33:41 --> 00:33:46

acceleration and deceleration, and not only for the maximum speed of

00:33:46 --> 00:33:49

the vehicle, as we just mentioned a couple minutes ago, the longer

00:33:49 --> 00:33:53

the stretch of the road, the longer the part where you're going

00:33:53 --> 00:33:55

to be moving at maximum speed, because you have to accelerate at

00:33:55 --> 00:33:58

the beginning and you have to decelerate at the end. If you're

00:33:58 --> 00:34:02

moving in a very short distance, by the time you accelerate, you

00:34:02 --> 00:34:05

have to decelerate. You haven't reached the maximum speed of the

00:34:05 --> 00:34:10

equipment. But the longer the stretch of the road, the longer

00:34:10 --> 00:34:15

part with a maximum seed you're going to be achieving. Using the

00:34:15 --> 00:34:18

average speed factor from tables, converts the maximum speed to the

00:34:18 --> 00:34:23

average speed. Remember that point nine, 5.96 etc. Let's go back

00:34:23 --> 00:34:24

here.

00:34:25 --> 00:34:30

So here, for example, under if you were moving only 100 feet,

00:34:31 --> 00:34:35

you're going to be moving at only 45% of the maximum speed. So the

00:34:35 --> 00:34:38

maximum speed that we calculate the from the performance tables,

00:34:38 --> 00:34:41

you're going to multiply that times point four, five, that's

00:34:41 --> 00:34:45

going to be the operating speed. Whereas if you are moving at a

00:34:45 --> 00:34:49

length of 5000 feet, you're going to be operating at 96% of the

00:34:49 --> 00:34:51

maximum speed, which shows a big difference

00:34:58 --> 00:34:59

the travel time.

00:35:01 --> 00:35:04

Is obtained by dividing the treble distance by the average speed.

00:35:06 --> 00:35:09

Travel distance by the average speed. The average speed factor

00:35:09 --> 00:35:13

applies twice, if starting from rest and ending at stop. So as we

00:35:13 --> 00:35:17

said, if you're going to be moving only 100 feet, you're going to

00:35:17 --> 00:35:23

divide that by two. And as if you're only moving 50 feet, and

00:35:23 --> 00:35:26

you apply that factor, or you apply the factor twice, because

00:35:26 --> 00:35:29

you're going to be starting from standstill and ending at the

00:35:29 --> 00:35:32

standstill as well at the end. Let's look at an example which

00:35:32 --> 00:35:35

might again explain this idea and illustrate the ideas.

00:35:37 --> 00:35:40

We are using a caterpillar, D, 6r standard.

00:35:42 --> 00:35:43

It weighs 39,800

00:35:45 --> 00:35:45

pounds,

00:35:46 --> 00:35:49

with a coefficient of traction of point six.

00:35:50 --> 00:35:55

What is the maximum speed when up when moving up an 8% slope.

00:35:57 --> 00:36:04

So the available pull is going to be the weight on the driving axles

00:36:04 --> 00:36:08

times the coefficient of traction here, by the way, we use the whole

00:36:08 --> 00:36:10

weight, which means that it's a four wheel drive.

00:36:13 --> 00:36:13

So 39,800

00:36:15 --> 00:36:18

times point six, which is equivalent to 23,880

00:36:20 --> 00:36:21

pounds. That's the available pool,

00:36:22 --> 00:36:23

00:36:24 --> 00:36:29

We are moving at 8% slope, which is 20

00:36:31 --> 00:36:33

times the weight in tons,

00:36:35 --> 00:36:42

times eight, which is the percent 20. That's a constant times 20

00:36:42 --> 00:36:47

pounds per ton times the weight in tons, which is 20 tons, which is

00:36:47 --> 00:36:48

this one, the 39,800

00:36:49 --> 00:36:54

almost 40,000 pounds, which is 20 tons. So 20 pounds per ton times

00:36:54 --> 00:37:00

20 tons times 8% the slope, which gives 3200 pounds. That's the

00:37:00 --> 00:37:07

grade resistance, 3800 pound. So the net drawbar pull that we want

00:37:07 --> 00:37:09

is going to be 23,880

00:37:11 --> 00:37:16

the available minus 3200 which is the resistance which gives 20,680

00:37:18 --> 00:37:22

pounds. That's the available drawbar pull. So we're gonna go

00:37:22 --> 00:37:23

here and look at

00:37:24 --> 00:37:28

this. By the way, either is a four wheel or it's on tracks. In this

00:37:28 --> 00:37:32

case, I believe it's on tracks because we're using drawbar pull

00:37:32 --> 00:37:35

and not trim pull. So the net drawbar pull is 20,680

00:37:37 --> 00:37:41

we're gonna go along this axle axis here, 2680

00:37:42 --> 00:37:48

which is about here, 20,006 80 that's going to intersect with the

00:37:48 --> 00:37:52

first gear and the second gear almost at the same point, which

00:37:52 --> 00:37:56

gives a speed of about two miles per hour.

00:37:58 --> 00:38:02

Now this is going to be the maximum speed, looking at the

00:38:02 --> 00:38:06

distance is going to be traveling, and the conditions of the road,

00:38:06 --> 00:38:10

we're going to multiply that by the factor that's going to reduce

00:38:10 --> 00:38:13

that to the actual speed, rather than the maximum speed.

00:38:15 --> 00:38:19

Looking at the third example here a contractor is to use a

00:38:19 --> 00:38:24

caterpillar, d7, G, crawler, tractor, crawler on tracks, the

00:38:24 --> 00:38:28

whole weight is going to be used and not part of the weight with

00:38:28 --> 00:38:33

the power shift transmission to excavate 1500 bank cubic yards for

00:38:33 --> 00:38:37

the foundation of a large house. The swell of the excavated

00:38:37 --> 00:38:38

material is estimated to be 25%

00:38:40 --> 00:38:43

remember now this problem, each word here has a meaning, so we

00:38:43 --> 00:38:46

have to break it down later on to look at the meaning of each one of

00:38:46 --> 00:38:50

this piece of information, the tractor must push the excavated

00:38:50 --> 00:38:55

material up a 12% slope where it will be stockpiled for later

00:38:55 --> 00:38:55

removal.

00:38:56 --> 00:38:59

The contractor has measured the pile of excavated material in

00:38:59 --> 00:39:03

front of the tractor, universal blade, just before spinach occurs,

00:39:04 --> 00:39:05

and has determined the pie. Length,

00:39:06 --> 00:39:12

12.6 feet. Width, 8.1 and height, four feet, if you remember the

00:39:12 --> 00:39:15

equation that we used in the previous lecture, point 375,

00:39:16 --> 00:39:20

wlh, this is something that we're going to be using here.

00:39:21 --> 00:39:22

The tractor weighs 44,400

00:39:24 --> 00:39:28

pounds, and the coefficient of traction is estimated to be point

00:39:28 --> 00:39:28

seven.

00:39:29 --> 00:39:34

The average haul distance is estimated to be 300 feet. What is

00:39:34 --> 00:39:38

the estimated productivity of the tractor? If the contractor plans

00:39:38 --> 00:39:43

to average 50 minutes of operation per hour, lots of information.

00:39:44 --> 00:39:49

Let's break it down to see what is given and what is needed. How are

00:39:49 --> 00:39:52

we use what's given into what's needed? What kind of equations are

00:39:52 --> 00:39:56

we going to use? So we're going to break that down into steps and

00:39:56 --> 00:39:59

look at each step is going to give us certain deliverable. We're

00:39:59 --> 00:39:59

going.

00:40:00 --> 00:40:02

Use that deliverable in the following steps. We're going to

00:40:02 --> 00:40:04

process it until we reach the finance

00:40:05 --> 00:40:10

so step number one, the volume of material that can be removed moved

00:40:10 --> 00:40:15

during one operation cycle, which is point 375, WHL. Remember that

00:40:15 --> 00:40:19

equation, but also remember that this equation gives us a volume in

00:40:21 --> 00:40:27

cubic feet in loose cubic feet. So we need to convert that into cubic

00:40:27 --> 00:40:30

yards. Therefore the number that we got 153.09

00:40:32 --> 00:40:37

cubic feet. We divide that by 27 which is equivalent to 5.67

00:40:38 --> 00:40:41

again, this soil, remember, is loose. So it's in loose cubic

00:40:41 --> 00:40:45

yards. We need to convert that into bank. Do we have the swell?

00:40:45 --> 00:40:50

Yes, we do. So to step number two is to convert the volume to bank

00:40:50 --> 00:40:54

cubic yards. The volume bank is equal to volume loose divided by

00:40:55 --> 00:40:58

one plus the swell factor, which gives us 4.54

00:40:59 --> 00:41:03

bank cubic yards. That's the volume of soil that's going to be

00:41:03 --> 00:41:05

moved into one cycle.

00:41:06 --> 00:41:09

Now we're going to look at the resistance for that crawler

00:41:09 --> 00:41:11

tractor. We do not have

00:41:12 --> 00:41:15

rolling resistance. We don't have any tire flexing. Therefore, all

00:41:15 --> 00:41:18

the resistance for the crawler tractor is going to be only the

00:41:18 --> 00:41:23

grade resistance, which is going to be 20 pounds per ton, per

00:41:23 --> 00:41:24

percent slope

00:41:26 --> 00:41:27

times 12%

00:41:28 --> 00:41:34

times the weight of the equipment, in tons, which was given here as

00:41:35 --> 00:41:36

44,400

00:41:37 --> 00:41:43

which is 22.2 tons. You know, 22,000 pounds per ton. So the

00:41:43 --> 00:41:49

total resistance is equivalent to 50 328 pounds.

00:41:53 --> 00:41:54

The usable power

00:41:55 --> 00:42:01

is going to be the maximum usable drawbar pull is the coefficient of

00:42:01 --> 00:42:05

traction point seven times the weight of the draw on the driving

00:42:05 --> 00:42:09

wheels or tracks. In case of tracks, we use the whole weight of

00:42:09 --> 00:42:10

the equipment. So 44,400

00:42:12 --> 00:42:15

which gives a maximum usable draw bar of 31,080

00:42:17 --> 00:42:17

pounds.

00:42:18 --> 00:42:23

The usable power that's available is greater than the required

00:42:23 --> 00:42:27

drawbar pull. Required drawbar pull is to overcome the

00:42:27 --> 00:42:29

resistance, which is the 5328

00:42:30 --> 00:42:33

so we have much more than that. Therefore, the

00:42:35 --> 00:42:38

equipment is going to be able to move without slip. So that's the

00:42:38 --> 00:42:41

first step. Yes, this equipment can move forward.

00:42:43 --> 00:42:46

Next we're going to look at the speed. At what speed can this

00:42:46 --> 00:42:50

equipment move? So to determine the maximum speed the track will

00:42:50 --> 00:42:53

operate in first gear, we're going to look here

00:42:54 --> 00:42:55

at

00:42:56 --> 00:42:58

the available drawbar pull,

00:43:01 --> 00:43:03

which is three, 3000

00:43:05 --> 00:43:06

something, and

00:43:08 --> 00:43:14

that's going to give us, in the first gear, a speed of 2.1

00:43:17 --> 00:43:22

about 2.1 miles per Hour. So the maximum speed to overcome the

00:43:22 --> 00:43:23

resistance, which is

00:43:25 --> 00:43:25

5328

00:43:28 --> 00:43:33

not 3053 28 pounds is going to be 2.1 miles per hour.

00:43:35 --> 00:43:36

Now, when returning,

00:43:38 --> 00:43:43

the tractor will return empty, going downhill, therefore we have

00:43:44 --> 00:43:45

no rolling resistance,

00:43:47 --> 00:43:50

and we have no great resistance either. It's actually going to be

00:43:50 --> 00:43:55

great assistance. So instead of using a negative number, we're

00:43:55 --> 00:43:59

just going to assume a zero, because we don't have any slopes

00:43:59 --> 00:44:03

here on this performance curve. So we're going to assume zero

00:44:04 --> 00:44:05

resistance.

00:44:06 --> 00:44:12

So the maximum speed available in second gear is going to be four

00:44:13 --> 00:44:14

miles per hour.

00:44:16 --> 00:44:21

So moving uphill, moving forward, loaded, we're going to operate at

00:44:21 --> 00:44:25

2.1 miles per hour, moving downhill backward. We're going to

00:44:25 --> 00:44:27

operate at four miles per hour,

00:44:28 --> 00:44:32

so the tractor will return empty, going downhill, no rolling

00:44:32 --> 00:44:36

resistance. Step number six is going to be determined the cycle

00:44:36 --> 00:44:42

time. Cycle time is going to be equal to fixed time plus haul time

00:44:42 --> 00:44:48

plus return time, fixed time. If you remember, here, it mentioned

00:44:48 --> 00:44:49

00:44:52 --> 00:44:56

shift transmission, power, shift transmission, if you remember,

00:44:56 --> 00:44:59

from the previous lecture, that was equivalent to.

00:45:00 --> 00:45:01

Three seconds, point oh, five

00:45:03 --> 00:45:08

so point o5, minutes. That's the fixed time. The hull time is going

00:45:08 --> 00:45:12

to be the distance, which is 300 feet, divided by the speed, which

00:45:12 --> 00:45:17

is 2.1 miles per hour. Now this is in feet, and this is in miles per

00:45:17 --> 00:45:22

hour. To convert that, we divide by a factor. Remember that that's

00:45:22 --> 00:45:26

going to be a constant to convert from feet to miles per hour. We

00:45:26 --> 00:45:27

divide by 288,

00:45:28 --> 00:45:31

so 88 feet per minute, per miles per hour,

00:45:32 --> 00:45:33

the return

00:45:35 --> 00:45:36

part of the cycle time,

00:45:37 --> 00:45:42

which is again a variable time, 300 feet, divided by the speed,

00:45:42 --> 00:45:45

four miles per hour. Again, we're going to divide by the same factor

00:45:45 --> 00:45:50

the 88 to convert from feet into miles per hour. So the total cycle

00:45:50 --> 00:45:53

time is going to be point oh, five. That's three three seconds

00:45:53 --> 00:45:58

plus 1.62 minutes, which is the number that we get from here, plus

00:45:58 --> 00:46:01

point eight, five minutes, which is the number that we get from

00:46:01 --> 00:46:06

here. So the total cycle time is 2.52 minutes to perform one cycle.

00:46:06 --> 00:46:08

It's 2.52 minutes.

00:46:10 --> 00:46:15

Step number seven, the productivity in each cycle,

00:46:16 --> 00:46:22

each cycle is going to take 2.52 minutes. And we have 50 minutes of

00:46:22 --> 00:46:26

operation per hour. So how many cycles in the 50 minutes? 50

00:46:26 --> 00:46:27

divided by 2.52

00:46:28 --> 00:46:34

almost 20 cycles per hour. Each cycle is going to be 4.54 bank

00:46:34 --> 00:46:38

cubic yards. So almost 20 times 4.54

00:46:39 --> 00:46:41

is going to give us a total of 91.3

00:46:42 --> 00:46:47

bank cubic yards per hour. That's going to be the total production

00:46:47 --> 00:46:49

of that piece of equipment. Another

00:46:52 --> 00:46:55

example. As you can see in the previous example, we broke it down

00:46:55 --> 00:46:59

into steps, processed the information for each step, and it

00:46:59 --> 00:47:04

led to additional elements of the problem. We combine all of these

00:47:04 --> 00:47:07

elements at the end to get the final answer. A wheel tractor is

00:47:07 --> 00:47:12

being operated on a soft roadway. Wheel operate wheel tractor so it

00:47:12 --> 00:47:17

has wheels soft roadway, which means we're going to have tire

00:47:17 --> 00:47:21

penetration. The tire penetration is five inches. The tractor weighs

00:47:21 --> 00:47:26

five tons. What is the total resistance and the effective

00:47:26 --> 00:47:31

grade? If the tractor is going uphill, ascending a slope of 4% or

00:47:32 --> 00:47:34

if the tractor is descending a slope of 6%

00:47:35 --> 00:47:40

let's look at it this way. Now we have rolling resistance because of

00:47:40 --> 00:47:43

the time penetration, and we have a grade resistance that's coming

00:47:43 --> 00:47:47

from that slope that we're talking about. So we need to combine these

00:47:47 --> 00:47:51

to calculate the total resistance, which is the effective grade,

00:47:51 --> 00:47:55

total resistance, as in pounds per ton, and translate that into an

00:47:55 --> 00:47:57

00:47:59 --> 00:48:03

So the running resistance factor is going to be 40 plus. That's the

00:48:03 --> 00:48:09

constant 40, as if you're moving on asphalt plus 30 pounds per ton

00:48:09 --> 00:48:13

times the tire penetration. So 40 plus 30 times five, that's 190

00:48:14 --> 00:48:18

pounds per ton. That's the rolling resistance factor. The total

00:48:18 --> 00:48:22

rolling resistance is the total resistance factor times the weight

00:48:22 --> 00:48:28

of the equipment. The weight is 20 tons. So 190 times 20, which gives

00:48:28 --> 00:48:30

a total of 3800 pounds.

00:48:32 --> 00:48:37

The grade resistance going uphill is equivalent to point oh four.

00:48:37 --> 00:48:44

That's the slope times 20, which is 20 pounds per ton, per 1% of

00:48:44 --> 00:48:45

slope times

00:48:47 --> 00:48:52

to convert that into times 2000 pounds per ton. 20,000 that's the

00:48:52 --> 00:48:56

weight of equipment, 2000 pounds per ton for the

00:48:58 --> 00:49:02

to convert the total into pounds. So the total resistance is

00:49:02 --> 00:49:06

equivalent to 1600 pounds. Descending is going to be

00:49:06 --> 00:49:10

negative. Remember that going uphill is positive, downhill is

00:49:10 --> 00:49:14

negative. So the resistance going downhill is negative, 2400

00:49:15 --> 00:49:16

pounds.

00:49:17 --> 00:49:21

So the total resistance if you're moving uphill, is rolling

00:49:21 --> 00:49:28

resistance plus grade resistance, 3800 plus 1600 that's the total of

00:49:28 --> 00:49:29

5400 pounds

00:49:31 --> 00:49:35

going in the opposite direction, descending downhill is going to be

00:49:35 --> 00:49:43

the same 3800 minus, in this case, 2400 which gives only 1400 pounds.

00:49:44 --> 00:49:49

Now to convert this resistance into effective grade, we're going

00:49:49 --> 00:49:54

to divide by the weight of the equipment and 20 pounds per ton

00:49:54 --> 00:49:59

for each percent of slope. So 5400 divided by 20.

00:50:00 --> 00:50:03

Times 20, that gives an effective grade of 13.5%

00:50:05 --> 00:50:09

uphill. So converting the rolling resistance into

00:50:10 --> 00:50:11

a

00:50:12 --> 00:50:18

a grade resistance is almost nine and a half percent, which is the

00:50:18 --> 00:50:24

difference between 13 and a half and four and for the downhill

00:50:24 --> 00:50:26

trip, is going to be that 1400

00:50:27 --> 00:50:31

divided by 20 by 20. So it reduced the

00:50:33 --> 00:50:34

the

00:50:36 --> 00:50:38

the total to this is going to be 3.5%

00:50:39 --> 00:50:44

remember, we had negative 3.5 so it's exactly the same 9.5 if you

00:50:44 --> 00:50:50

notice here, 9.5 is the rolling resistance. When added to the 4%

00:50:50 --> 00:50:57

gave a total of 13 and a half. When you subtract the six, it

00:50:57 --> 00:51:01

gives three and a half. So nine and a half plus 413, and a half,

00:51:02 --> 00:51:05

nine and a half minus six. That's the three and a half

00:51:07 --> 00:51:08

when descending.

00:51:10 --> 00:51:13

This is basically an introduction about how to calculate the slopes,

00:51:13 --> 00:51:18

how to calculate the resistances, how to calculate the speeds and

00:51:18 --> 00:51:21

how to calculate the cycle, the cycle time. We have posted online

00:51:22 --> 00:51:25

a more comprehensive example that shows different segments of the

00:51:25 --> 00:51:29

road uphill, downhill, and it follows the same procedure to

00:51:29 --> 00:51:33

calculate the different segments into different steps, and then we

00:51:33 --> 00:51:37

combine that at the end to get the total cycle time, and therefore

00:51:37 --> 00:51:40

the total production of that equipment. I'll see you in the

00:51:40 --> 00:51:40

next lecture so.

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