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.

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.

Now we need to find the penetration resistance. It is given to you in the problem that the tyre is sinking to the depth of 6 centimeters into the surface. So, you know that for each centimeter of penetration the amount of effort needed is 6 kg per ton per centimeter 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.

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.

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.

Now so far, we have discussed about the rolling resistance, let us look into the other part of the resistance in your project site that is your grade resistance. Most often you can see that equipment has to climb up a slope. So, when the machine is climbing up the slope, obviously you need some additional efforts to make it move up the slope because it is pulling against the gravity.

Now similar to this, we should also know about what is grade assistance? So, we discussed about what is grade resistance, there is something called as grade assistance that means what? When your machine is moving down the slope, you can see that the amount of power needed gets reduced because it can easily move down by the gravity.

So, now let us see how to calculate the grade resistance. Grade resistance is nothing but by simple elementary I mean a mechanics people have worked out this the relations. Say for example, for 1% of grade so the amount of tractive effort needed to overcome this 1% of grade it is 10 kg per ton.

So, say for example, if your slope percentage is say 5%, it means what? In a horizontal distance of 100 meter you will have a surface rise of vertical surfaces rise of 5 meter that is 5%.

So, when you select your haul route, so we have to be very careful in the selection of your haul route. So, if there is a option that you can use the down slope, it is always preferable to use down slopes, because your power required gets reduced.

So, there are sufficient information’s in different literature which I have cited in the references towards the end of the lecture, you can go through. So, you can find the tables, which provide you the grade resistance for different percentage of gradient.

So, you know the rolling resistance in kg per ton, so you know that 1% of grade equal to 10 kg per ton. So, you divide it by 10 kg per ton, you will get the equivalent gradient percentage.

So, so far what we have discussed is about the required power. So, what is the total power required by the machine to overcome the different resistances in the project site, in the underfoot conditions.

So, the available power you can get the data easily, because the manufacturer would have done the horsepower rating of the machine. So, the available power is determined by the SAE rating.

Now let us see what is this usable power? So, out of the available power prescribed by the manufacturer, how much amount of power becomes usable to you? That depends upon your project condition.

So, we need to estimate this usable power of this particular machine. We are going to see how to estimate the usable power? Say for example, when we are using a tractor for towing the load.

So, the usable power you can express in terms of rimpull or drawbar pull. So, depending upon the mounting of your machine.

So, how to calculate this usable force? So, this usable force is going to depend upon the traction of your travel surface. So, as I told you how much amount of the total power becomes usable, it depends upon the degree of traction between your wheel and the ground.

So, another important thing to be noted is weight on the power running gear of the machine. So, in common equipment or the common wheels of the cars whatever we are using, you can see that all the wheels of the car are not driving wheels.

So, assuming your coefficient of traction is sufficient, if there is proper traction, sufficient traction between your wheel and the ground. In that case your rimpull can be taken as a function of your horsepower of the machine.

Using this simple relationship, you can directly estimate the rimpull if you know the horsepower of the machine given by the manufacturer, and you should know that it is a function of speed; inverse function rimpull and the speed of the machine are inversely related.

Now let us workout the problem on how to estimate the power requirements of the machine. So, a tractor weighing 15 tons is operating on a haul road, the gross weight of the machine is given as 15 tons.

First let us see what is the tractive effort needed to overcome the grade resistance? Grade resistance, you know the grade percentage it is nothing but 4%.

Now let’s calculate how to estimate a tractive effort to overcome the rolling resistance? It is nothing but for this particular haul route the rolling resistance value is given us 60 kg per ton.

Now the total power required to overcome all the resistances are given here as 600 kg. So, 600 kg is nothing but your grade resistance, the power needed to overcome this grade resistance plus 900 kg is your rolling resistance.

So, the maximum rimpull available for this machine as given by the manufacturer is 7000 kg. Now you need to know what is a grade resistance on the rolling resistance?

So, out of this 7000 kg, 1500 kg will be used for overcoming the resistances. So, for overcoming the different resistances in the project site, you are going to spend 1500 kg.