 Hello viewers, I welcome you all in this today's session, analysis of overtaking side distance on roads. I am Ashok Kumar, Assistant Professor, Department of Civil Engineering, Walchand Institute of Technology, Swalapur. End of this lecture, students will be able to analyze and calculate the overtaking side distance on roads. In the previous session, we learned about how to calculate the distance of D1 and D3 and in this session, we will learn how to calculate the distance of D2. So, before we go into this one, we know that the overtaking side distance is a distance available in front of the driver for overtaking operation, minimum distance available to the driver for safe overtaking operation considering the opposite vehicle into the consideration. So, the total overtaking side distance is equal to D1, D2 and D3. So, this is we are also the understood the what is D1 here, it is the distance that is a the fastened vehicle A1 to A2 that is a distance D1 travelled by overtaking vehicle at the reduced speed of VB meter per second during the reaction time t. So, I know the what is the the small t and the VB I can calculate the D1 as VB into t here. So, here VB is meter per second and t is the your reaction time of the driver. Again from position A2, the vehicle start accelerating, now it has gone to position A2 and it start accelerating and overtakes the overtakes this slow moving vehicle B and occupies the position A3 during the overtaking time t. So, now after reaching to A3, it will observe that there is an overtaking opportunity is there, it will accelerate and occupies the opposite lane and the accelerate during the this one, this is the capital T, this is the overtaking time is taken t and it will accelerate on the opposite lane and occupies overtake the slow moving vehicle and occupies the position A3. So, during this time you can see the slow moving vehicle has distance moved from B1 to B2 and that is denoted by the that is small b and the total D you can write like this because there is a two spacing is involved that is the spacing between A2 and B1 that is one spacing and B2 and A3 that is another spacing S. So, overall you can write the equation of D2 that is S plus B plus S. So, here there is an empirical equation suggested by IRC that is how to calculate the S. So, S you can calculate like this that is 0.7 VB plus 6 it is in meter and here V is in meter per second. So, now I know the value of your the S value and how to calculate the this the B value that that also we will see and how to calculate the value of T also we will see. Now, how to calculate the value of B here we know that the B1 vehicle is traveling at an the speed of VB meter per second. I know the overtaking time T you can calculate the distance that is B that is B equal to your the distance that is speed VB into T. So, now your B also defined over here. So, now you can write B equal to VB into T again VB is here meter per second. Now the total distance D2 equal to B plus 2 S it is in meter. Now, the how to calculate the T we know that the T depends on the speed of the overtaken vehicle B and the average acceleration A. So, that is in meter per second square of overtaking vehicle A. Now, I am going to calculate the capital T using your second linear motion equation that is UT plus half AT square. Now, we can calculate the D2 equate this D2. So, now you can call this equation as equation number 1 and now equate this D2 to your linear motion equation that is UT plus half AT square. So, that is T is nothing but the overtaking time and A is your acceleration during the overtaking and T is the again overtaking time T. Now you calculate equate this D2 to UT plus half AT square. Now equating D2 equal to we know that D2 is nothing but B plus 2 S. So, equate B plus 2 S equal to UT plus half AT square. Now, you can write the what is your UT? U is nothing but the initial speed of the vehicle. During this position the initial speed of this vehicle is nothing but the VB that is the fast mean vehicle at this position it is VB. Now, I know the initial speed is VB and capital T you can replace this U by VB and T plus half AT square. Again, I know the value of B, the value of B is nothing but the VB into T. Now, you replace the B value as VB into T. Now, replace the B value as VB into T and now you calculate the distance of D2. Now, B plus 2 S equal to VB into T plus half AT square. Here you can put the B value as VB into T and now replacing B by VB into T on left hand side also VB into T and right hand side also VB into T both get cancelled the remaining will be 2 S plus half AT square. Now, I need the value of the capital T you take the T outside and it becomes square root of cross multiplying it is 4 S by A. Here, we know that the value of S equal to as the empirical equation it is 0.7 VB plus 6. Now, the D2 is VB plus VB into T plus 2 S. So, that is your this is VB into T nothing but the B that is B plus 2 S. So, T is nothing but your square root of 4 S by A. So, here A is in meter per second square. So, this is you have to use the equation when we we are using in meter per second. Now, you can if the in case the speed of overtaken vehicle that is VB or VB small VB or capital VB is not given at the same way it can be assumed that 4.5 meter per second or 16 kmph less than the design speed. Suppose, the design speed in the in your numerical if the slow moving vehicle speed is not given to you you can calculate the slow moving way the speed of the slow moving vehicle that is VB by deducting the 4.5 if it is in meter per second or 16 it is in kmph. So, you know the design speed deduct the 4.5 or 16 it is in kmph. So, like this you can calculate the value of VB that is speed of the overtaken vehicle. Now, D3 what about the D3 here that is the vehicle C moving at a design speed V meter per second during the overtaking operation during time T and this way you can calculate I know the T and I know the the speed of the opposite vehicle you can multiply V into T again here V is in meter per second. Now, you calculate the overall distance of your OSD that is D1 plus D2 plus D3. Now, D1 is nothing but the the distance travel during the reaction time. So, this is your D1 and this is D2. So, that is a B plus 2s or B is nothing but VB into T and this is your D3 that is V into T it here V is in meter per second. The same equation you can convert into kmph we know that how to convert the meter per second equation to your kmph equation multiplying by 0.278 or you can round it up to 0.28. So, multiplying the this VB into T by 0.28 it can be converted into meter per second into kmph. So, now all this equation are converted into kmph now it becomes 0.28 VB V into T VB into T plus 0.28 VB into T plus 2s plus 0.28 V into T here both are this is also VB and this is also VB and here it is small t is nothing but reaction time of the driver and capital T is nothing but your overtaking time T. Now, how to calculate that T if it is in kmph and this is we know that this equation is in meter per second. So, now I am going to convert this meter per second into kmph per second. So, the the unit of the your acceleration is meter per second square I am going to convert into kmph per second. So, we know that how to convert the meter per second into kmph that is converting meter to kilometer that is 1000 and dividing second into minute and minute into hours. So, dividing by 60 into 60 so, that simplifies 1 by 3.6. So, you can multiply taking in the numerator that is multiplying 4 into 3.6. So, this the equation converts into square root of 14.4s divided by a here a is nothing but the kmph per second. So, many students will get confused sir it is meter per second square or kmph per second square you can see here out of this one I have converted only meter 1 meter per second only. So, one second another second is already left out like this. So, I have just converted meter per second into the kmph ok. So, for that we 1 more second is left out over here. So, out of this meter per second I have only converted into meter per second. So, another second is left out in the numerator that is it is taken in the kmph per second. So, unit is not changed here that is acceleration unit is still it is meter per second square only. Now, you pass over here and calculate the there is a speed of the overtaken vehicle is given as 50 kmph and spacing you are going to calculate the spacing of the vehicle you can calculate the spacing like this it is 0.7 bb plus 6 it is you know that the 0.7 multiplied by if it is in kmph you have to multiply by 0.278 and yeah it is speed you have to multiply that 50 kmph. So, we know that the equation is 0.7 bb plus 6. So, it is in meter per second if the equation is meter per second you can use directly you want to take the V value as kmph you have to multiply 0.7 by 0.278 to convert meter per second into kmph. So, now the value correct answer is 16 meter is the correct answer in this one. Now, overtaking acceleration you can take this ready made the table for calculating your acceleration. So, here all the values are meter per second if the equations are given in meter per second you can calculate the yeah this is your the speed in kmph and these are the speeds in meter per second. Now, you can use any your acceleration value if you are using in kmph you have to use this table and if you are using in a value in meter per second you have to use this value. So, these are the ready made table you can utilize for taking the acceleration value in meter per second or kmph per second. Now, another concept here the overtaking joint overtaking zones. So, whenever the if you observe the any the constraint of providing this overtaking in any particular alignment you can due to the land constraint you are unable to provide the overtaking in the particular alignment you can provide this overtaking zones for a smaller length by informing the driver in the next 1 kilometer you are going to receive the overtaking zone and you can overtake the slow moving vehicle in that particular zone. So, how to calculate that the overtaking zone that is the minimum length is given as a 3 times of the OSD whatever the OSD have calculated you can multiply by 3 you will go to get the minimum length and maximum length desirable it is 5 times the OSD. So, now you can able to draw the this overtaking zone here the in this this is the tool in section in this particular section you are going to overtake over from here to here. So, we need to inform the driver well in advance by providing the signpost at a distance of OSD from the overtaking zone right here the driver will understand there is a overtaking zone is available and he will come over here and overtake this moving vehicle again the end of the overtaking zone also to be informed by the another signpost that is SP2 we have to inform that there is a end of the overtaking the driver coming from the this direction same way we have to inform the driver which is coming from this direction also informing giving the signpost 1 and the end of the signpost that is the end of the overtaking zone. So, the desirable length it is 3 to 5 times of the your overtaking side distance. So, this is the signboards you have to inform the driver yes there is an overtaking zone is available in the next 1 kilometer or next 300 meter or 500 meter so that he will be get ready to overtake the slow moving vehicle these are the references I have used for this presenting this presentation. Thank you.