 I welcome you all for the today's session on Fundamentals of Traffic Flow. In this class we are going to discuss about the speed and travel time. I am Ashok Kumar, Assistant Professor, Department of Civil Engineering, Walchand Institute of Technology, Solapur. At the end of the session, students will be able to calculate time mean speed and space mean speed of a traffic stream. In the previous classes we have seen other macroscopic parameters. Now another macroscopic parameter is the speed. We know that the importance of the speed with the speed, we can control the traffic, we can regulate the traffic and we can also use the speed for a geometric design, accidental analysis and capacity analysis. Now we know that speed is defined as the rate of motion in distance per unit time. And travel time is the time taken to traverse a defined section of a roadways. It is given by s equal to d upon t, distance upon time, where s is the speed in kmph or meter per second, d is the distance in meter or kilometer and t is the time to traverse a distance in d in hours or seconds. Before we go for a detailed analysis of our speed, let us define some definitions. The first one is a spot speed. It is instantaneous speed of a vehicle at a particular location. It means at a reference point you are standing and finding out what is the speed at that particular location for that moment. That we call as a spot speed. And another one is the average speed. It is average of all the spot speed of all the vehicles passing at the given points on the highway. It means we are not unable to find out the speed of an individual vehicle and design our proposals. It means each individual vehicle we cannot measure the speed of the net traffic stream. So for that we have to take the average speed of a traffic stream. The average speed of a traffic stream can be computed in two ways. First one is a time mean speed and space mean speed. So let us discuss these two parameters in detail. Time mean speed is the average of all the vehicles passing a point over a duration of a time. It means here if you are standing at this particular reference point for a particular time duration and finding out what is the spot speed of all these vehicles. So it is a simple average of a spot speed or arithmetic mean of all the spot speeds. So it is given vt equals to 1 by n summation of uts. uts means a number of speeds you are counting, number of speeds you are measuring over here for n number of vehicles. Suppose you are counted at three spot speeds, it means it is just average of that three spot speeds. So three spot speeds divided by three gives the spot speed of that particular vehicle. So remember you are standing at that particular location and measuring this spot speed. How we measure this spot speed? Using a detector loops in this one, entry time is recorded and exit time is recorded. So we know the distance will be very very short distance say 10 meter or 5 meter less than that. So with this we can able to calculate the L distance upon difference of these two exit and entry time. Another one we use an anoscope method where the observer is standing over here and he start the stopwatch when vehicle crosses on this first line and stop the stopwatch when vehicle crosses on this. So we know the length and we know that time recorded we can calculate what is the spot speed. Another the versatile method we use it for measuring the spot speed is the radar gun with the radar gun also we can find out the what is the spot speed of the vehicle. So it is not the actual the speed of the vehicle we are measuring in this topic stream because we are not covering any kind of the vehicles which is travelling at high speed which is travelling at a slow speed. The time is recorded here but the inner traffic stream we unable to get all kind of the vehicles but this is only actual speed you are taken on that particular spot. This is not the actual speed we are expecting for the improvements. Another one is the space mean speed in this one you can find out what is the difference between the space mean and time mean speed. This is the average speed of all the vehicles occupying a given section of a highway. What is the meaning of given section of a highway? Within a section given for you say 1.5 kilometer or 2 kilometer within that 2 kilometer you are measuring the what is the specified time period and what is the time travel to cross that particular 1.5 kilometer or 2 kilometer. Earlier time mean speed you are just measuring the what is the spot speed of that particular vehicle on that particular reference point. Here within a section of a highway within a length of a highway we are measuring the various duration of a time. So in this one we can record all kind of the vehicle's movement slow moving fast moving so this is the one of the useful method for finding out the actual speed of the vehicles. So let consider a unit length of road and vi is the spot speed of ith vehicle and ti is the time the vehicle takes the complete unit distance and it is given by 1 by vi that is the speed you are measuring. Time equal to 1 by distance is unit 1 and if there are n such vehicles then average travel time is a TS. So TS equal to ti by n so number of vehicles you have measured the time divided by the number of the vehicles. So put the TS value and 1 by n summation of 1 by vi. Put the ti value as 1 by vi so equation becomes TS equal to 1 by n to summation of 1 by vi. If t average is the average travel time the average speed vi is equal to 1 by TS. So this is the space mean speed is vi so this is distance upon time. So put the TS value as full this and the equation finally converts into vi is equal to n by summation of i equal to 1 to n into 1 by vi. So whatever the spot speeds you are measuring it is just simply the harmonic mean of the spot speeds. So whatever you are finding out the spot speed if you take the harmonic mean of that that becomes your space mean speed. So this is the actual measure we are trying to find out in this all kind of the travel time which is include fast as well as the slumming vehicles. The measurement of the space mean speed we can hear the distance is given for you so to say 2.5 kilometer and in this one entry time is recorded and exit time is recorded. So with this we can able to calculate what is the space mean speed of the vehicle. Let us consider the another example where 3 speeds are taken 20, 40 and 60 kmph traveling at the unit length d. We know that time mean speed is arithmetic mean of all the speeds. So taking the arithmetic mean of 20, 40 and 60 by 3 that gives you 40 kmph and space mean speed we know that it is a simply harmonic mean of the spot speeds you can take the harmonic mean is 1 by vi so number of observation is 3. So this gives you 32.72 kmph. Now with this explanation let us pause the video for a while and can you think why the space mean speed is always lower than time mean speed in the previous example we seen one is 40 kmph and another one is 32.72 why these two values are different why the space mean speed is lesser than your time mean speed. I hope you are able to give the answer for this the actual answer is this space mean speed is measuring in a length of say 1.5 km or 2.5 km but the main weightage is given for a slow moving vehicles for the reason always space mean speed is lesser than time mean speed. So another illustration over here we can observe we got two lanes lane a and lane b in this one lane a slow moving vehicles are observing 10 meter per second and 50 meter spacing and lane b 20 meter per second and 100 meter spacing. So what is the headway headway is measured from front of the vehicle to the front of the vehicle. So in this case so the vehicles are passing at 50 by 10 so 50 the spacing divided by the speed. So 5 second each vehicle is traveling taking 5 second to cross the 50 meter length and number of the vehicles observed in a per hour it is 60 by 5 it is 12 number of vehicles are observed in a one hour. So density is number of vehicles in a unit length say 1 kilometer how many number of the vehicles are occupied that is your density. So 1000 meter is the length and 50 is the spacing so 20 vehicles are occupied in a length of 1 kilometer that is the meaning of your density same way calculate for a lane b here 5 second and number also 12 for one hour and numbers are 10 because the spacing is larger here number of vehicles are 10. Let us calculate the what is the space means time means speed first so it is just arithmetic mean of your spot speeds it means a 12 number of vehicles are traveling at 10 and 12 number of vehicles traveling at 20 so 12 number vehicles in lane a and 12 number vehicles in lane b. So total vehicles are 24 so the total vt comes 15 meter per second. Now space means speed can be calculated in two ways one using a distance or one using a density we can calculate over here. So here in the first case a 20 number of vehicles moving at 10 kmph and second case 10 number of vehicles moving at 20 meter per second. So total number of vehicles occupied in a unit length that is in a 1000 meter is 30 that is 20 plus 10. So in this case our space means speed is 13.3 meter per second. If I take the harmonic mean of the spot speed again the value will be same. So in this case you can observe the 24 number of vehicles and 12 number of 1 by 10 that is a harmonic mean of a speed and 1 by 20 lane 1 by 10 in lane a and 1 by 20 lane b. So that comes 13.3 meter per second so both the values are same. So another speed we have is a running speed. Running speed is also a spot speed but this speed is measured while the vehicle is in motion but this excludes the delay. If we include the delay that becomes your journey speed. So if you are effective speed with the vehicle, if the vehicle travels a particular route between two terminals but it includes the delay and stoppages. So that is meaning of your journey speed excluding running speed including journey speed. These are the references I have used for presenting this presentation. Thank you.