Lecture 51: Intersection Layouts - 9

IIT Roorkee July 201
61 followers
Dec 1, 2023
This lecture discusses the warrants for interchanges, feasible options for different combinations of roads, the geometric features of interchanges, design challenges and the concept of ramp terminals.
00:00 Recap of Previous Interaction
00:48 Presentation Overview
1:13 Warrants for Interchanges
3:06 Feasible Conditions for Interchange
6:31 Geometric Features
23:09 Typical Design Challenges
27:58 Ramp Terminals
Dear students, let us restart our discussion on intersection layouts. In the previous interaction,
we have talked about the pedestrian refuse islands and then we took the various design
guidelines which was followed by the warrants for signalized intersections and then we had
a look on the types of interchanges. In today's interaction, we are going to move forward
and we will be first talking about the warrants for interchanges and then what can be the
feasible combinations under which we have to provide an interchange when we have different
type of roads and then related to the interchanges and specifically the ramps, we are going to
talk about the various geometric features and finally, we will be discussing the ramp
terminals.
So let us start with the warrants which are required and under what conditions the interchanges
should be provided. Now, these are related with the same conditions as we have discussed
before that means they are related with the traffic volume, they are related with the
conditions in terms of the type of mobility which needs to be ensured or it may be an
outcome of the topographic features. So in this sense, the very first point which is
there is that if the total traffic on all arms is in excess of 10000 PCUs per hour,
then this is one case where the interchanges are warranted.
The another condition is that if we have to maintain a total access control that means
there are limited locations from where the entry and exit can be provided to a system,
then that is also a case where the interchanges needs to be considered. The another case can
be and which has been also taught in terms of the various types of interchanges where
we said service interchanges and system interchanges. So if the major crossings of highways are
to be developed with say the expressways or the expressways standards, then in that case
also the interchanges are going to be there or there are major arterials of similar category
which are carrying lot of traffic, then also we have to ensure the mobility and the smooth
movement and this is the case where interchange has to be there.
The another case can be related to the crashes. If lot many improvements have been done at
grade intersections so as to eliminate or reduce the number of crashes which are happening
at that location and that is not resulting fruitfully, then probably the now solution,
next solution which is going to be there is interchange and as I said the topography is
one another thing which may also warrant that we have to provide an interchange. Now if
we try to talk about the feasible conditions, then here in this case what you can see is
that we are talking about urban roads.
So we have collector streets, sub arterials, arterials and urban expressways and when we
are looking at this matrix what it tries to tell is that when you have a collector, then
in the case that is crossing with the expressway, then it is recommended on the basis of the
site conditions, but in rest of the cases usually it is not going to be there. When
we talk about the sub arterial, then if it is coming with arterial, then it is on the
basis of site condition, but if it is coming with the expressway, then it is generally
recommended.
If you talk about the arterial and then its crossings with the different other type of
road systems, then it is shifting by one towards the left and that what we found is now if
it is a crossing with a sub arterial, so it is on the basis of site conditions, but in
the other two cases we are going to usually recommend or we are going to provide that
interchange at that particular crossing.
Now expressways, then expressways means if we have to look at the conditions with respect
to expressway and the mobility on the expressways, then we are probably going to talk about or
provide. So what you found is that the things are coming in the sense that if I put it in
this form as a matrix, then all of the things are getting repeated and that is how we can
create it. But if you look at the rural highways where we have different categorizations as
like intercity expressways or national highways or street highways or the district roads,
so here also the same condition is observed where what you found is that when you are
talking about ODR or MDR with an expressway, then it is usually being talked or recommended
based on the site conditions and when we say site conditions, we are looking at the amount
of traffic which is going to be there and which needs to be separated out so as to ensure
the mobility on the expressway and the same way if we try to see, then we can again create
a line here and when we create this line, then this matrix is going to be repeated.
In that sense, if we look at the expressway, we have to provide the connectivities with
rest of the things, then this is going to be provided and of course, when expressway
crosses an expressway, then it becomes a highly recommended situation.
But when we are trying to provide different type of interchanges which we have looked
at, we have talked about 3 arm interchanges, 4 arm interchanges or service or a system
interchanges, there different categories were discussed and if you took at those categories,
then here in this slide we are talking about the amount of space which is required and
you can see that the minimum space is required in the case of diamond where it is 28000 square
meters.
But if you are going to a rotary which is having 2 levels or 1 level system, then it
is going to be enormous.
It is 1,80,000 square meters area which is to be acquired beforehand and in the case
of full cloverleaf also, it is not a small amount.
It is quite a big one as 73,000 square meters are required.
Now, let us talk about the geometric features.
Now when we talk about geometric features, then the very first thing which needs to be
looked at is the design speed and this design speed is to be talked under different scenarios
like when we are talking about the highways, then we have already talked about it.
We have discussed in the very starting of this course and it is considered like 80 kilometers
per hour or 100 kilometers per hour.
But if it is an urban expressways, then 80 kilometers per hour is the value.
If you are talking about the ramps on the multilane highways, then it should not be
less than 40 kilometers per hour and wherever the 2 connectivities are there on which that
speed difference is going to be observed, say you are moving on a highway and now you
are exiting the highway, so you have to reduce the speed and then get out of the system.
So in those cases, the speed differential becomes an important thing and this speed
differential at any point of a time when it is being considered, it should not be more
than 10 kilometers per hour.
So it is a sequential manner.
So you are coming from 100 to 90, 80, 70 and so on.
So that is how it keeps going on.
Now when you are talking about interchanges, when you are at different levels and we have
discussed there are loops, there are semi-direct connectivities, direct connectivities, diagonal
connectivities, all those type of things are there and therefore, an essential element
is the ramp.
Now when we are providing these ramps, then what are the things needs to be taken care
of is what we are going to talk now.
The very first thing is that it should have 2 lanes as far as possible instead of having
a single lane system, because tomorrow you cannot reconstruct if the traffic increases
and the requirement is there, then it will become very difficult to have one more lane.
So from the very starting we talk about a 2 lane system.
Entry and exit ramps which are going to be there, they shall have acceleration and de-acceleration
lanes respectively.
So this is an additional feature, because this allows and this helps in negotiating
in a form of a speed differential with the values of increments or decrements of 10 kilometers
per hour.
Length is decided based on the speed differential between the project speed and the speed which
is being permitted on the ramp.
So if we are talking about 40 kilometers per hour as a speed on a ramp and we are coming
at a speed of 80 or 100 kilometers per hour, so this difference has to be taken care of
and when you are accelerating and de-accelerating, so whatever the acceptable or the comfortable
acceleration or de-acceleration rates are there, on the basis of that we can get those
lengths.
So there are certain values which are already been given and few of the things we have looked
previously also.
So here, if you see that the two types of interchanges which we have discussed previously
a system or the service interchanges, for those again the three categories of ramps
have been talked and when we are looking at this range of the speed on expressway which
can be 80, 100 and 120.
So you have two categories like 80, 100 and 120.
For those the ramp design speeds have been specified and again if we look at in the categorized
form what we found as in the system interchanges the speeds are higher as compared to the service
interchanges.
The another thing is the highest value which we are looking at is the lowest of the speed
range on the expressway.
So the same way if you can look on the other side then we have 80 as a value which is again
the lowest of the speed range of expressway.
So these are the values which can be considered.
So these are the different type of speeds which are there and as we discussed it should
not be less than 40 kilometers per hour.
So it is also being talked here.
Now here in this slide the further information has been incorporated and this information
is in terms of not only ramp design speed but these two features which are radius of
the curvature and safe stopping sight distance in meters.
Now these are being given for say the design values on the major highways which can be
80 or 100 kilometers per hour and for those 80 and 100 kilometers per hour what can be
the minimum or desirable values of these three components are being given but these we have
already discussed.
So let us see that what are the radius of curvature or SSD which are being talked here.
So they talks about 60 or 45 meters in terms of a minimum but desirably 90 or 60 meters
as a radius or SSD respectively at a speed of say the ramp speed when we are talking
is 50.
So for 50 SSD is 60 otherwise also and the same thing is being done here for ramp design
speed of 65 then SSD comes out to be 90 and then for radius of curvature is being defined
as 155 but ramps if they are there then in this case the values are now being given here
as 45 meters of SSD and 60 meters of the radius of curvature.
So when you are designing this and when the loop is taking a curve in this form then another
thing which may happen is that you have to look at the super elevation and the maximum
value of the super elevation as we again discussed previously when we talked about the alignment
is 7% here.
Now when we are looking at this sort of a ramp and the ramp structure is going continuously
in change with respect to its elevation then the side distance is one thing which we are
trying to look at and for that side distance as you can see here then the driver side here
has been kept as 1.1 meters but if you talk about the object then the object height is
being kept as 0.
So for this whatever is this line of sight is there that is being observed and that is
being tried to be ensured and when we are trying to ensure this then this is going to
result in some value x meters.
Now this x meters when we are looking here and when we are trying to look at the profile
these two be adjusted in such a manner that the distance which is going to be travelled
here is the distance being travelled in 10 seconds time.
So that is the minimum value which needs to be ensured.
So this is how we are going to try to find out that from where to what point we are going
to do it but at the same time this is a point which you are talking here.
This is actually in plan can be defined as the nose of the island.
So from that nose of the island we are again taking a distance x meters and at that x meters
if our vehicle is there then this is how this is going to be ensured.
So these are the ways in which we are going to start and then another thing which is going
to be there is because you have a design in this form and there can be a nose of the island.
So when we are looking at this so another thing is that the start of the taper is there
and from that start of the taper also we should have the distance which is visibility distance
should be available and that visibility distance is what is being thought as x for 10 second
movement.
The same thing has been shown here in the form of a plan.
So we have a island here.
So this is island and this is the nose of this island.
From this nose we are going x meters.
So we have come to this point and this is the point of tapering.
So from there also we are going to another point.
So this is again x meters of course being travelled in 10 seconds time and that is how
we are going to create a overall system of the movement or the changeover which is going
to be there.
Now here what you can see is there is a deacceleration lane being shown.
So when you are looking at deacceleration lane again there is a nose point at this one.
From this nose point we are going x meters.
So we get another point and if we talk about this point from where the taper has started
then again we are going back to x.
So this is the amount of sight distance, the very clear sight distance, clear of all of
the obstructions needs to be ensured.
So this is what we are going to do it here.
But when we are looking at this auxiliary lanes then the time which we are considering
so as to calculate x is 7 seconds instead of 10 seconds.
Now here again what you can see is that this is an exit nose.
So this is the point and this one is the island and here we have the chevron markings.
So these chevron markings culminate at this point and then it extends as a straight line.
We have discussed about it when we talked about the pavement markings.
Now what we are doing is from the nose we are again taking x meters.
So you have come to x meters at this point and then there is another point which we are
talking here is that we have a location.
At this particular location we observed that we are going to have the tapering.
So at this particular area the tapering is required on the basis of the deacceleration
lane length to be provided under this condition.
Now what it is saying is that if there are constrained side distances then how we can
readjust the things is that from this particular point we are going back again x meters.
So we come to this and from here then we are looking at the side distance which is available.
So we are coming to this point and from there now the taper has been provided.
So this additional auxiliary lane length is going to be there which may be required and
again the distances is being calculated on the basis of 7 seconds time.
Now the next thing which is happening is because this ramp is going say from an elevated system
to a ground level where there is a at grade intersection with another road can be there.
So the gradient also needs to be looked at.
So there are different values which are being talked.
So tangent grades which are talked here when we are looking at when you are coming towards
the ground side then this is a preferably flat limited to 4% but not exceeding 6%.
But when you are on ramps then they are desirably 6% not more than 7% and on high speed facilities
or flyovers or excess control facilities then these are 2.5% to 3.5%.
Now when you are coming from the top and you are reaching a bottom so the system is going
to be in this form.
So you have a summit curve and a valley curve.
So that is what is being talked there is a valley curve at the lower end and summit curve
at the upper end.
So that needs to be designed.
So what is going to be the length of this curve is also to be taken care of.
Then another thing is that the medians if they are provided or the shoulders if they
are provided what should be the width of those.
The medians they should have a minimum width of 1.2 meters as well as shoulders if we are
talking then they should be provided as 2 meters wide but out of this 2 meters wide
then 1 meter can be a paved situation.
Then the number of lanes we have already said that at minimum 2 lanes we should try to provide
but then there may be a requirement of increasing the number of lanes and that depends on that
what is the total amount of traffic volume which is going to move on these particular
ramps and at the same time what is the capacity of 1 lane on a ramp.
So based on that this total numbers are going to be identified.
Now here we are just looking at a condition where what super elevation value is there
what should be the radius and they have been defined for different values of the speeds.
So the values which you can see here they are being talked to as low as 2% of the super
elevation that means here in this case like it is as good as Camber but when you are going
above then this is 4 or 6%.
So 4% is the usually value which we have adopted for urban areas and then we try to
go to even 6 or 7%.
So desirably it is 6% but maximum if required we can go to 7% and accordingly even not only
from this particular graph we can also calculate these values directly by using the formula
which we have discussed previously.
Then if we are required to provide this acceleration and deacceleration lanes because there is
a changeover in the speed from highway to ramp or ramp to highway then these acceleration
lane or deacceleration lane may have a length of 250 meters as desirable and 180 meters
as a minimum for acceleration lane and 120 meters or 90 meters respectively for deacceleration
lane.
Then another point which may come is that what can be the lateral clearances which needs
to be ensured.
So if there is a road which is going at the top and then there is an underpass like this
so the road is also going in this form.
So we need to see that what should be this value as a lateral clearance as well as a
vertical clearance.
Now when we talk about the lateral clearance so whatever is the carriageway which is being
provided here along with the shoulder on the sides is what we are going to talk about.
So the roadway with the normal shoulder is what we should try to ensure and then overpass
in the case of overpass means this particular road which is going here.
So what should be the lateral clearance which should be there with respect to the carriageway
is what we are talking here.
So we may have a curved section and if that curved section is there then it can be 225
mm wide and there should be the open parapet walls being provided on the side so that no
vehicle gets out of the system and falls down.
But you are looking at this vertical clearance then this vertical clearance is usually governed
by the type of vehicle which is going to use this underpass.
Now in the normal circumstances if you are talking about an urban area so there may be
a possibility of the high buses or say if you talk about a double decker bus then the
height is going to be quite high as compared to a normal bus.
So looking at all those environments then the minimum height which needs to be ensured
is 5.5 meters and in the case of rural highways there can be different type of underpasses.
It can be for pedestrians, for cattle, for the LCVs or for all type of vehicles depending
on that then these values are going to be different.
Then spacing of interchanges in the case of urban areas that should not be less than 1.6
kilometers but if you are on a rural highways or undeveloped areas then it should not be
less than 4.8 kilometers.
One another feature is that as we talk about interchanges we again and again say that there
are limited access to it.
There are limited access in a sense of entries and exits.
So entry to the system and exit from the system.
So when we are looking at this then the various things which are usually considered here as
that what is the functional classification of a road.
Obviously when we say arterials or when we say expressways then this access control is
going to be quite high or what are the characteristics of the traffic, how much traffic is there,
what is the amount, what is the composition and what are the cutting traffic which are
there on the crossing roads.
So we have to take care of that.
Along with that we have to see that how much is the traffic which gets in and gets out
of the system.
So what are their proportions.
Then current and the future land uses they are also going to make a difference in terms
of the traffic which is going to be either attracted or generated at that location.
Environmental factors or aesthetics of the design, highway design and operation and economic
concentration.
So there are so many attributes or so many variables which needs to be taken care of
when we are trying to discuss about these.
Now what are the typical challenges which needs to be taken care of when you are providing
these interchanges.
The very first thing is the sight distance needs to be ensured.
So wherever the exit is there we have already looked at it that the sight distance has to
be taken care of from the nose of the island and when we are talking from the nose of the
island then we have also said that there is going to be a chevron in this form and then
a straight line which can be 30 to 60 meters long.
So when we are looking at this then one thing is that these are we are talking about the
gore nose to the paved gore.
So this is a gore nose area but when you are looking at a condition where here the
system is going to be in this form.
So this is another area which is a paved gore because the funnel is getting created here.
So that is what this total distance should be unobstructed and this is again we have
discussed in terms of x values and other.
Then exit speed change because when you are coming out of a system in this form and then
going so this exit speed change which is there from say 100 kilometers per hour to 50 kilometers
per hour.
So what is this?
So we have to use the deacceleration lane here.
So we have to take care of that.
The merges which are going to be there, the merges means we are talking about the movement
here and then this is the system.
So the vehicle is coming from here, it goes along then takes and this deviate and comes
into the main traffic.
So here when we are providing these acceleration lanes so what happens is the rear end crashes
they can be reduced a lot.
Then right side entrance and exits they should be avoided because they are going to be opposite
to what the driver is otherwise assuming.
So if we are coming in this area so it should not happen that we are trying to provide a
direct connectivity in this form.
If it has to be ensured then it probably can be done by way of coming out of below this
particular highway and then going in this direction.
So now there is no confusion as well as the 2 vehicles which are moving in the same direction
they are aligned and therefore there is not going to be any hazardous situation which
may appear here.
Then fixed object hazards, so fixed object hazards may come because there are requirement
of illumination, there are requirement of providing the road signs or if there is a
metering on the ramps then the signals are going to be there or there is the rails which
are provided on the sides of the carriage way at the extremities of that.
So whatever such things are there they should not create any obstruction as such they have
to take care of that.
Wrong way entrances, now wrong way entrances happens because there is a flaw in the design.
When that flaw is there then what will happen is that the vehicle which is not expected
to come from a particular direction is now coming and creating a confusing state for
the other drivers or the vehicles.
So that needs to be taken care of and this also happens when say you are coming in a
system in this form and then at the same time we are going out of it.
So if the highway is being provided, so there is a traffic goes here and there is a traffic
comes here.
So what is that area which is being provided between these type of connectivities and which
happens more in the case of say the cloverleaf arrangements and so.
So what is the spacing between the entrances and exits and these spacings between the entrance
and exits needs to be looked at with respect to the weaving portion and what should be
the length of the weaving portion.
So we will be talking about this also or the staggering of the ramp terminals and controlling
the access to the ramp is another way that we can control the things to make it more
safer.
Excessive speed on the minor roadway, so that may happen and if they are exiting or entering
the main highway with the high speed then they may not be able to be controlled in this
area and this may be fatal to the vehicle or it may become fatal to the other road users
too.
So this needs to be designed by way of a good design in terms of a ramp design or a merge
design and that is where the length of acceleration lane, deacceleration lane, the side distances
which needs to be ensured on that with respect to the nose of the islands and all this is
what we have discussed has to be taken care of.
Now let us talk about the ramp terminals.
Now ramp terminals are what?
These are the portions which are adjacent to the through travelled way which includes
speed change lane, tapers and islands.
So we are having a condition that the vehicles are coming out of the system.
They are may be negotiating in this form or they are negotiating directly outwards say
in terms of diagonal ramp.
So that particular element which we are talking is now we are looking at.
As far as possible they should be designed as a free flow type and there is not going
to be a reverse flow on these because all of the traffic is moving in the same direction.
Now these can be of 2 types.
One is an entrance terminal, another one is an exit terminal.
Now when we talk about the entrance terminal it means the traffic is coming from a minor
road and it is coming on a major highway and therefore this ramp traffic is getting
merged on a high speed road.
But exit terminal means now here we are talking about a condition where the vehicle is going
out from a highway on which it was moving at a higher speed and now coming on the ramp
where the speeds are going to be lower.
So this is the 2 things.
So in one case there is going to be a merging action.
In another case there is going to be a diverging action and we have talked about and we have
looked at the design of the acceleration lane and deceleration lane which are basically
related with these situations.
Now when we are looking at these connectivities where the merging and diverging are happening
and all.
So they should be at flat angles as far as possible and this will ensure the smooth flow.
Then based on the type acceleration lane and deceleration needs to be provided.
So whatever are the conditions we have already said that if we are talking here then this
is acceleration or deceleration lanes are going to be there.
The speed change lanes shall be visible to the approaching traffic moving on the horizontal
curve or the vertical curve.
When we exclusively talk about the entrance terminal then they shall have sufficient length
so that the vehicles can take a turn on the ramp and when they are taking a turn then
whatever in the tables we have seen about the speed, the design speed which can be there
on a ramp is what we are trying to ensure simultaneously and then they can increase
the speed to that of the operation speed on the highway because they are coming with a
speed say of a 50 kilometers per hour but on a highway the speed is either 80 or 100
kilometers per hour.
So it is progressively increasing.
There shall be sufficient maneuverable space so that the entering driver has a view of
the traffic in adjacent lane and can move laterally to the main lane of the highway
as soon as the opening appears.
So this is what it says that it should have this sufficient distance which is going to
be there in this form.
So the traffic which is moving here and there is a traffic which has come in this form and
then gets into the situation like this.
So this is what we are talking that sufficient space needs to be ensured.
No curve shall be provided within the length of the acceleration lane.
Then these can be of 2 types, the direct and the parallel type.
The one we have discussed here this is a parallel type one and another thing can be that you
are coming from here and then getting into the system in this form.
So the traffic is going in this way and the traffic comes and then tries to merge in this.
So this is a direct case which can be there.
Now this direct taper provides a direct entry at flat angles and it is preferred usually
by the drivers though if they go into parallel situation that they have more space to have
a better visibility of the traffic which is moving in an adjacent lane and it requires
more space if there is a turning curve at that location.
When we talk about the parallel type then it creates an additional lane as we have already
looked at.
So this is going to be a sort of an additional lane in this case because this is what we
are having and it provides an opportunity to both the drivers in the adjacent lanes
to visualize each other to judge what are the speeds of each other and accordingly do
those maneuvers and it is satisfactory and safer in that.
When we look at the exit terminal then the length of exit terminal again has to be long
enough to allow the vehicles to reduce the speed from a highway speed to a ramp speed
and then if they are taking a curve then they should be able to negotiate those turning
curves too.
So the radiuses are already being taught with respect to the design speeds on ramps and
here also we can have both the type of designs one can be the direct taper another can be
the parallel taper and the nose separating the through lane from the turning lane shall
be offset from the edge of the through lane by 2 meters.
So that is what we are saying here is that this is a nose which is provided and there
is a through lane here and there is another lane in which the traffic is going in this
direction.
Now this is going to be offset by 2 meters backwards the reason being if by any chance
any vehicle has gone in this deacceleration lane and wants to come back then that should
get an opportunity to do that.
The core area which is formed by the edges of the through lane and the turning lane immediately
after the point of divergence shall be kept clear of all obstructions.
So that they allow recovery to the vehicle which is getting out of control.
So this point we have already taken care of when we discussed about the deacceleration
lane and the sight distance is being ensured in that.
So here what you can see is that this is a case where the traffic is coming from this
direction and it is accelerating here.
So this is parallel type for accelerating condition the through traffic is coming from
this side.
So what you found is that this is a parallel type of a system where this distance remains
constant up to a certain length and then it becomes taper.
So there are different widths which are going to be there which is being talked here.
So what it says the location marked at A this is creating a funnel condition wherein
the width has been reduced from W2 to W1 here and this W1 is the width which is going to
be the width of a lane at this point which is 3.5 meters wide.
Then if you are talking about the taper design that one difference which is coming is in
terms of these element that means what you found is that the nose which is getting into
the area that is increasing in length.
So your point B is increasing in that direction.
So here you are trying to exit but basically at this point it is happening.
So that is where our W1 is going to be at this location and the taper which is used
is 1 in 25 to 1 in 30 say whereas this is a deacceleration situation.
from here is deviating to this direction and then finally is going out of a system.
So when it is going out of a system at this point again because this is a parallel type
so therefore this is 3.5 meters.
So this W1 changes to W2 it is now increasing in that form and it is allowing the traffic
to get out of the system and there is an additional thing which we are trying to look at is that
in this case whatever traffic which is coming in this direction on this direction they may
hit the nose.
So the nose has to be protected one thing.
Second thing is that when we are looking at this tapered system what you can see here
in this sketch it has been tapered downwards and the reason is that if any vehicle hits
here then it will go back into the lane.
So it is not going out of control it allows the vehicle to recover and get into the lane.
So this is a location C which is being marked and that should be tapered at 1 in 10.
So whatever this tapering is being done this is 1 in 10 and this is for length of 20 meters.
Finally these are the acceleration lengths which are there desirable and minimum we have
talked about and they are also going to be affected by gradient.
We have discussed about 1-0.03, 0.06, 0.08g or plus 0.08g and all those if you remember.
So here these are the minimum acceleration lengths which are being given for expressway
design speeds and the speed which is going to be there on entry curve and that is how
we found that the maximum value which is going to be there is like say here 490 meters when
the speed on the expressway is 120 kilometers per hour and the speed at the entry curve
is 40.
So that is a big change therefore more length is required and parallel type taper rate it
shall be 8 is to 1 for speeds up to 50 kilometers per hour and 15 is to 1 for speeds of 80 kilometers
per hour and so.
Similarly in the case of the acceleration length, deacceleration length also we talked
about desirable and minimum and the same way the values have been given here.
But what you can see is that these values are much lower than the values which are otherwise
there in the case of acceleration length and here also the taper values remains the same
as 8 is to 1 or 15 is to 1 depending on the speed which is there.
So with this we close our interaction in this particular lecture now.
We will be continuing these in the next lecture.
Till then thank you and bye.
