 best greetings of the time to all the students. This is an online educational resource on elements of simple circular curve being presented by me, Mr. Shashikant Gosavi, Assistant Professor, Department of Civil Engineering, Walchand Institute of Technology, Sulakpur. The learning outcomes of this OER are at the end of this session, the students will be able to explain need of design of simple circular curve. The student will be able to draw the sketch of simple circular curve and name its components. The student will be able to derive the formula for designing the components of simple circular curve. All of us are familiar with the curves in our day to day life. There are vertical curves as well as horizontal curves. The horizontal curves are defined as the curves introduced between two alignments or two directions to have smooth change in direction from one alignment to the other alignment. There are four types of horizontal curves. The simplest one is simple circular curve, the other one is compound curve, then combined curve and lastly there is reverse curve which is also a classification of horizontal curve. The curves are normally designated in two ways. One is radius of curve, other is by using the degree of curve. As is apparent from the sketches shown over here, there is something called as chord definition of a circular curve wherein the basic unit for derivation is this chord C1 C2 having a length 30 meter which is making an angle D at the center of curvature. The other one is the arc definition wherein this arc length is taken as the unit for consideration and at the center the degree of the curve is D. There are two derivations corresponding to each of these. See in the chord definition it is sin D by 2 is equal to 15 by r as is shown over here. This particular angle is 90 degree and therefore sin of D by 2 will be equal to this 15 meter divided by r which is sin D by 2 is equal to 15 by r. But because the angle is so small D by 2 will be taken equal to 15 by r and hence D will be equal to 1718.9 divided by r. As per the arc definition if we will go which appears to be more precise because we are measuring the arc length over here. As we know radius of curve r multiplied by angle subtended at the center D r into D will be equal to 30 meter. Second thing is if this particular arc length is 30 meter making an angle D at the center what will be the total perimeter of the circle 2 pi r making angle at the center it will be 360 degree. This relation is used for a derivation. So 30 by D is equal to 2 pi r divided by 360 which gives us D is equal to 1718.9 divided by r very important for us to do conversion from radius designation system to the degree of curve designation of the system. More importantly what is need of design of curves why at all it is needed? We know in transportation utmost importance is given to the safety. Safety of the passengers as well as safety of the vehicle both of them are equally important particularly on the curves because in a non-designed curve there are chances that because of the because of the centripetal force the vehicle will be thrown away from the center as well as passengers will find it discomfort. The other and obvious thing is economy when we will be designing a curve we will be ensuring that smooth transition from one alignment to other alignment will happen with least possible length and with safety as well. The third and pleasing thing is aesthetics when we introduce a curve into alignments the curves give us a pleasant feeling and natural beauty. The objective of this OER being explanation of elements of simple circular curve you can go through this particular sketch which I have picked up from a source civilengineeringterms.com. As you can see there is a back tangent starting from a chain H which is moving towards one direction as well as it is meeting another directional change for the forward tangent both of these are meeting at a common point called as the point of intersection P i. The curve is assumed to have a radius r which is of course a function of the speed of the vehicle and as per the transportation criteria radius will be known to us. So if the radius is r the respective arc which is introduced between two alignment is shown over here. This is the point at which the straight gets converted into the curve so B c is called as the point of curvature and this curve ends at this particular point which is called as point of tangency as the curve converts into the tangent. We know in advance what is the chain edge of this point and hence by measuring this particular distance we can find what is the chain edge of point of intersection and then with the help of the knowledge of radius, chain edge of point of intersection and this particular angle which is called as the deflection angle we can start deriving the different components of this particular curve. The first component is the central angle delta as has been shown over here this angle will be delta because this is isosceles triangle P i B c E c these two angles will be equal angles with the geometry of this triangle having the summation equal to 180 degree we can easily say that this is delta so this will be 180 minus delta and 180 minus delta plus this angle plus this angle being equal to 180 degree each of these angles work out to be delta by 2 half the deflection angle. Another important thing is this is radius and this is tangent which are supposed to make angle 90 degree at this particular point and therefore if we will consider a triangle P i B c and this particular center of curvature we can easily see that this particular angle will be this is 90 this being the delta by 2 this particular angle will also be delta by 2 and hence this whole angle can easily be derived to be delta same as that of the deflection angle while calculating the tangent length which is B c to P i again we can take the help of this particular angle delta by 2 so sin of delta by 2 is equal to t divided by r and hence sorry tan delta by 2 is equal to t divided by r and hence we can say t is equal to r tan delta by 2 the length of the curve can be calculated as r delta by 180 and thus we can derive these many components please pause the video for a while and answer following questions comment whether the degree of curve is directly or inversely proportional to radius of curve and what is the sequence of calculation of change in the elements of curve discussed earlier in this presentation the degree of curve is inversely proportional to radius of curve that is apparent from the previous discussion secondly sequence of calculation of change begins with change of intersection point minus tangent length gives us change of point of curvature plus curve length gives us change of point of tangency. I have referred to the NPTEL notes and the book of Carnet-Caribou-Carnier of serving and leveling as has been mentioned over here. Thank you very much.