Dimension alignment in a station in curve

[yabi]

I have a question regarding constructing subway platforms in curved line.

As we know, in a curve, wagons get out of linear alignment and become closer in inner radius and separate from each other in outer radius. I want to know the relation between dimension of car, dimension of structure connecting wagons to each other and dimension of the curve in plan view.

The question arises because of a debate between me and my colleague. In our project, there is a station in the curve. My colleague say that, with dimension of spaces in the project, there will be the possibility that cars have impact to each other, therefore we have to shift the station location to a straight place.

He can't show any concrete reason or calculation and we have to prove by numbers to our boss.

Please guide me where can I find data in this regard.

Your help is highly appreciated.

 

[DickL]

In real life subway stations are placed on curves. Generally, one tries to avoid putting stations on curves because the gap between the door threshold and the platform edge varies with where the doors are placed along the length of the car.

Subway cars, and rail cars in general, have a minimum curve radius that they can negotiate. Stations would not be place on minimum radius curves. The minimum radius is determined by the amount of bogie pivot available (linkages, suspension movement, nearby equipment can limit the angle the bogie can pivot), and the car end clearance between adjacent cars. While freight cars tend to have square ends on the cars, subway cars generally have a curved end to provide more interior space for passengers, and still allow the car to negotiate the minimum curve. Assuming the bogie pivot angle doesn't limit the curve radius, the primary parameters determining the minimum curve are the total length of the car, the length between bogie centers, the space between cars, and the shape of the car ends. Its fairly simple, straightforward geometry to work out the minimum curve radius.

Once you've decided on a curve for the station platform area, you do need to look at the minimum and maximum space between the sides of the car and the platform (you generally need to look at cars being on both the inside and outside of a curve). As a car moves through a curve the mid-ordinate of the car moves inside on the curve, while the car ends overhang to the outside of the curve. Positive clearance must be maintained, including allowances for suspension motions, track misalignment and wear. Also the gap between the doors needs to be kept within fairly tight limits to avoid people getting their feet caught in the gap (Mind the Gap). In the US the maximum gap is generally limited to 3 inches (75 mm) and the minimum gap (with most of the movement allowances considered) would be kept to more than 1/2 inch (12 mm).

I am aware of 1 subway station on a curve (its an old station) that has been retrofitted with 'gap fillers' that move out when a train stops to reduce the amount of gap. This approach is far from typical and was done for a variety of reasons.

If the curve through a station has super-elevation (or rail cant), this complicates the station-car interface as the car will be tilted laterally. If the curve is not super-elevated, then the speed through the curve will be limited to a lower speed.

Economics is part of the equation. A lot of construction money can sometimes be saved by locating a station on a curve. For a given maximum train length longer cars are more economical, but require greater curve radii. Additionally there are safety, security, and operational considerations to having stations located on curves. The final decision, either way, involves a lot of trade-offs.

 

[Studiot]

Another reason for preferring straight platforms.

Trains are stationary at platforms.
Stationary trains require the greatest tractive effort to get moving and if the carriages are not in a staight line the pull of each on the next is off line to the next and so diminished by the cosine of the deflection angle.
Moving trains can more easuly negotiate curves on account of inertia.

go well

 

[yabi]

Dear DickL and Studiot

Thanks for your replies. The points you mentioned are informative for me.

I need some formulas governing this issue. Do you know any standard or guidebook to have such formulas?

 

[DickL]

Regarding Studiot's comment, it does apply with locomotive hauled trains. Most subways have every or every other car powered and because of the distributed traction power & tractive effort this effect doesn't come into play for subways. The curves are generally not tight enough to cause this problem, nor are subway trains long enough to span a significant curve arc.

The geometry for the clearance and curving overhangs is really quite straight forward, once you have the the vehicle's dimensions. I've always just worked out the calc's from basic geometry rather than searching for references, it was faster. Data you do need (or at least intelligent guesses) are the vehicle's dimensions (length over coupler pulling faces, length over end sill of vehicle, width at floor, distance between bogies, location of doors and their width), bogie and suspension motions (primarily lateral motions and wear limits) curve radius, track alignment standards (lateral alignment tolerance, maintenance/wear allowance for track, gauge tolerance), and the station platform to track tolerances (this is often forgotten by the architects/engineers that design stations during early part of a system design). There should be a vehicle dynamic outline drawing or clearance drawing that would provide much of the information.

Start with the ideal case, no tolerances, etc. considered and work out the geometry so you understand the relationships. Then start adding in the various allowances (generally you can group the vehicle allowances together to create a near worse case for the vehicle motions, and the same for the track allowances). Add them in as logic dictates. Remember, you will probably need to consider both the inside and outside of the curve separately (typically there will be a station on each side of the line and the curves are often parallel rather than concentric). In figuring out the worse case, remember the bogies can (and will) move in opposite directions to cause a greater angle of the car to the track center line.

In combining the various allowances/tolerances, use your head to put together only logical combinations of parameters, some are mutually exclusive. When you dig into all the details (typically only for final design) there are many parameters to be accounted, having all of them at worse case is not terribly realistic, so I have several times applied a statical approach to combining everything. If you go with the statical treatment, I suggest you run that approach by the powers to be.

 

[Bob S]

On a curve, the outside wheel wants to turn faster than the inside wheel. If the axle is solid, then one wheel will need to slip (exceed static friction limit). This is part of the friction requiring more tractive power to start.

 

[yabi]

Regarding Studiot's comment, it does apply with locomotive hauled trains. Most subways have every or every other car powered and because of the distributed traction power & tractive effort this effect doesn't come into play for subways. The curves are generally not tight enough to cause this problem, nor are subway trains long enough to span a significant curve arc.

The geometry for the clearance and curving overhangs is really quite straight forward, once you have the the vehicle's dimensions. I've always just worked out the calc's from basic geometry rather than searching for references, it was faster. Data you do need (or at least intelligent guesses) are the vehicle's dimensions (length over coupler pulling faces, length over end sill of vehicle, width at floor, distance between bogies, location of doors and their width), bogie and suspension motions (primarily lateral motions and wear limits) curve radius, track alignment standards (lateral alignment tolerance, maintenance/wear allowance for track, gauge tolerance), and the station platform to track tolerances (this is often forgotten by the architects/engineers that design stations during early part of a system design). There should be a vehicle dynamic outline drawing or clearance drawing that would provide much of the information.

Start with the ideal case, no tolerances, etc. considered and work out the geometry so you understand the relationships. Then start adding in the various allowances (generally you can group the vehicle allowances together to create a near worse case for the vehicle motions, and the same for the track allowances). Add them in as logic dictates. Remember, you will probably need to consider both the inside and outside of the curve separately (typically there will be a station on each side of the line and the curves are often parallel rather than concentric). In figuring out the worse case, remember the bogies can (and will) move in opposite directions to cause a greater angle of the car to the track center line.

In combining the various allowances/tolerances, use your head to put together only logical combinations of parameters, some are mutually exclusive. When you dig into all the details (typically only for final design) there are many parameters to be accounted, having all of them at worse case is not terribly realistic, so I have several times applied a statical approach to combining everything. If you go with the statical treatment, I suggest you run that approach by the powers to be.

Dear Dickl
Thank you very much for your detailed information. I should add that this is the first time I am going to do such calculation. I don't have any previous experience. I would highly appreciate if you could kindly guide me to a site/book to get the basic formulas.I have one more general question. I have seen some computer animation representing three dimensional design which you can see your object from different angle, rotate it and even walk through it. Is there any special program for animation of subways or trains in Rails. I think using this method and changing parameters will be quite easy to understand.

Thanks
Rasoul

 

[yabi]

On a curve, the outside wheel wants to turn faster than the inside wheel. If the axle is solid, then one wheel will need to slip (exceed static friction limit). This is part of the friction requiring more tractive power to start.

Thanks for your contribution. I think the point you mentioned is about the mechanics or let say dynamics of the system. This is out of my business.

Basically I am asking about the geometry of the system and its limitations.
Off course what you mentioned is quite important and should be noticed by mechanical engineers.

BR
Yabi

 

[DickL]

When I first did this type analysis, it was in the medieval ages, that is the only computers were main frames or micro-computers built and used by hobbyist. I used paper, pencil and a scientific calculator. It took about 1/2 a day to work out the basics and get initial results. Later on, as the world evolved, I used spreadsheet programs (SuperCalc was the first one I used, one of the early spreadsheet programs that you've probably haven't heard of). I've stayed with spreadsheet programs for this type of analysis, partly because I've never become comfortable using 3D CAD or solid modeling programs. Either 3D CAD or solid modeling programs should work, particularly if you need 3D graphics or animation. To my knowledge there are no rail or subway specific programs; I have seen several such animations and 3D models of station areas, track / train/ and adjacent construction that was done with off the shelf CAD and modeling programs. My personal opinion is that unless the problem under study is complex, they are not worth the time and cost of applying them, just because they can show pretty pictures. The problem is only 2D, hence I've never felt the need to do other than spreadsheets, of course your results may vary.

I've made a simple 2D drawing that shows the primary geometry. Hopefully I'll be successful in uploading it. This drawing is not to scale, the curve radius is much tighter, compared to the vehicle length than would be actual. Once you've got the basic geometry worked out, the various allowances become adds (or subtracts) from the offsets. In practice you can figure all the offsets as being parallel to the car's longitudinal center line. The several dimensions I've indicated are: Lcb/2 = 1/2 car body length, Lbogies/2 = 1/2 the distance between bogy centers, Offset mid = radial offset from the track center line at the mid car, Offset door = radial offset at center of a doorway from the track center perpendicular to the car body center line, W = car body width.

You probably have some specific designs and dimensions to work with, but some typical values I've encountered are vehicle lengths of 16 to 22 m, bogies spaced at approximately 60% of the vehicle length, curve radii on operating lines (not in yards and storage areas) greater than 200 m.

There are railroad standards and engineering analysis available, and these are often used, as appropriate for subways. However, most subway systems have many unique aspects that prevent wholesale use of the railroad standards. Each subway system is usually unique from others, which has kept the industry from standardizing much of the engineering into codes or handbooks. That is not to say that subway engineering isn't soundly based on recognized practice, but there is a strong element of picking and choosing the practice to be used at that site.

With regard to the comments raised about how rail vehicles negotiate curves, there is a common misconception that the flanges on the wheels steer the bogies and car around a curve. They don't, except in extreme situations. Most rail vehicles have wheels that are tapered (smaller diameter to the outside, larger diameter to the inside, toward the flange). As an axle set enters a curve the rail contact point moves laterally across the wheel, toward the flange on the outside of the curve (larger wheel diameter), away from the flange (smaller wheel diameter) on the inside of the curve. This difference in wheel diameters causes the axle set and bogie to steer into the curve. This coupled with a small amount of compliance in the axle's mounting results in a only a small increase in drag due to the curving. It also greatly aids axle and bogie stability, below the critical speed.

I hope this helps you. You are probably getting the idea that I am not going to give you a cook book, and that is correct as I don't have one to give.

 

[yabi]

When I first did this type analysis, it was in the medieval ages, that is the only computers were main frames or micro-computers built and used by hobbyist. I used paper, pencil and a scientific calculator. It took about 1/2 a day to work out the basics and get initial results. Later on, as the world evolved, I used spreadsheet programs (SuperCalc was the first one I used, one of the early spreadsheet programs that you've probably haven't heard of). I've stayed with spreadsheet programs for this type of analysis, partly because I've never become comfortable using 3D CAD or solid modeling programs. Either 3D CAD or solid modeling programs should work, particularly if you need 3D graphics or animation. To my knowledge there are no rail or subway specific programs; I have seen several such animations and 3D models of station areas, track / train/ and adjacent construction that was done with off the shelf CAD and modeling programs. My personal opinion is that unless the problem under study is complex, they are not worth the time and cost of applying them, just because they can show pretty pictures. The problem is only 2D, hence I've never felt the need to do other than spreadsheets, of course your results may vary.

I've made a simple 2D drawing that shows the primary geometry. Hopefully I'll be successful in uploading it. This drawing is not to scale, the curve radius is much tighter, compared to the vehicle length than would be actual. Once you've got the basic geometry worked out, the various allowances become adds (or subtracts) from the offsets. In practice you can figure all the offsets as being parallel to the car's longitudinal center line. The several dimensions I've indicated are: Lcb/2 = 1/2 car body length, Lbogies/2 = 1/2 the distance between bogy centers, Offset mid = radial offset from the track center line at the mid car, Offset door = radial offset at center of a doorway from the track center perpendicular to the car body center line, W = car body width.

You probably have some specific designs and dimensions to work with, but some typical values I've encountered are vehicle lengths of 16 to 22 m, bogies spaced at approximately 60% of the vehicle length, curve radii on operating lines (not in yards and storage areas) greater than 200 m.

There are railroad standards and engineering analysis available, and these are often used, as appropriate for subways. However, most subway systems have many unique aspects that prevent wholesale use of the railroad standards. Each subway system is usually unique from others, which has kept the industry from standardizing much of the engineering into codes or handbooks. That is not to say that subway engineering isn't soundly based on recognized practice, but there is a strong element of picking and choosing the practice to be used at that site.

With regard to the comments raised about how rail vehicles negotiate curves, there is a common misconception that the flanges on the wheels steer the bogies and car around a curve. They don't, except in extreme situations. Most rail vehicles have wheels that are tapered (smaller diameter to the outside, larger diameter to the inside, toward the flange). As an axle set enters a curve the rail contact point moves laterally across the wheel, toward the flange on the outside of the curve (larger wheel diameter), away from the flange (smaller wheel diameter) on the inside of the curve. This difference in wheel diameters causes the axle set and bogie to steer into the curve. This coupled with a small amount of compliance in the axle's mounting results in a only a small increase in drag due to the curving. It also greatly aids axle and bogie stability, below the critical speed.

I hope this helps you. You are probably getting the idea that I am not going to give you a cook book, and that is correct as I don't have one to give.

Dear DickL

Thank you very much for your valuable knowledge. Through reading your posts, I understand that I am talking to a veteran, so I admire your comments and notes.

I have got the concept and I will try to figure it out and write the cookbook by myself.

BTW your attachment had a scaling problem. It is to small to be read. Zooming also didn't work I think due to low resolution issue. Would it be possible to re-upload with a proper scaling?

Thanks in advance for all your time and knowledge.

BR
Yabi

 

[Studiot]

With regard to the comments raised about how rail vehicles negotiate curves, there is a common misconception that the flanges on the wheels steer the bogies and car around a curve. They don't, except in extreme situations. Most rail vehicles have wheels that are tapered (smaller diameter to the outside, larger diameter to the inside, toward the flange). As an axle set enters a curve the rail contact point moves laterally across the wheel, toward the flange on the outside of the curve (larger wheel diameter), away from the flange (smaller wheel diameter) on the inside of the curve. This difference in wheel diameters causes the axle set and bogie to steer into the curve. This coupled with a small amount of compliance in the axle's mounting results in a only a small increase in drag due to the curving. It also greatly aids axle and bogie stability, below the critical speed.

To back this up:
Both the rail and wheel hub profiles are quite complicated.
If you look at a line of rails in frequent use, notice that only the top surface of the rails are polished through contact. The sides remain dull.

I suggest you look out some older surveying textbooks to obtain the geometry of circular curves, reverse curves, transition curves and so on.
Even much of the basic geometry of circles is omitted these days in (UK) school curricula, unfortunately.

Try: Engineering Surveying by Frank Shepherd.

go well

 

[yabi]

I am aware of 1 subway station on a curve (its an old station) that has been retrofitted with 'gap fillers' that move out when a train stops to reduce the amount of gap. This approach is far from typical and was done for a variety of reasons.

1 By an old station, I conclude that, in modern stations, they avoid putting stations in curve. Is this conclusion correct?

2 Is it possible to name this station and if you have any photo to upload it.

3 Why using gap filler is fr from typical?