does wheel taper really handle curves?

[gregc]

maybe i have too much free time ... the forums are kinda slow

A common explanation for how solid axles wheels handle the different between outer/inner rail circumferences on curves is that the wheels are tapered (figure at left).   The wheel radius near the flange is larger on the outer rail than away from the flange on the inner wheel.

Some modeling sites indicate a taper of ~3 degree (fig below left).   It appear comparable to wheel profiles illustrated from a Canadian NTSB site (fig below right)

   

But when you do the math, a prototype wheel of width 5.5 in and having a taper of 3 deg would require a curve radius of 7300 ft (0.8 deg curve) for the wheel taper to match the difference between inner/outer rail circumference.  (a taper of ~10deg, a difference of ~1 in on a 33 in wheel, is required for a curve radius of ~2100 ft).

So while the common explantion isn't totally wrong, it doesn't apply to curves of less than a mile radius which include subways, industrial areas, yards and turnouts.

The following figure from the U.S. NTSB illustrates that there is actually a significant amount of wear.   How much of this is from just rolling on relatively straight tracks vs curves where slippage must occur?

 

 

[jrbernier]

Greg,

 You are correct.  But the prototype usually has very wide curves.  On the subdivision that I worked many years ago, most of the curves  were under .5 degrees of curvature.  There were two speed zones that limited passenger trains to 75 mph, and one curve(25 mph) leading to a draw bridge.  On that 25 mph curve, you could really hear the 'chatter' squeal as the wheel sets were pulled around that curve.  The tread taper is a balance of tracking on curves and centering the rail car on tangent track.

Jim

[7j43k]

gregc

 

 

But when you do the math, a prototype wheel of width 5.5 in and having a taper of 3 deg would require a curve radius of 7300 ft (0.8 deg curve)...

 

 

 

 

 

When I do the math, I get a curve radius of 848 feet (7 degree curve).  

 

The UP's mainline curve through Sunol, CA is about 1300 feet.  So the mentioned taper-concept is easily applicable there.  BNSF requires a minimum radius for industrial tracks of 600'.  That may well still be within the taper-concept limits, but we're talking very slow speeds and stresses in this case, so even if the flange is scraping the rail, it's not much of a problem.

 

Now, my calculations could be wrong.

 

So, please check my math:

 

From the chart on page 8 of this source:

 

http://www.apta.com/resources/standards/Documents/APTA-PR-M-S-017-06.pdf

 

I find a reasonable number for the difference of wheel radius due to wheel offset to be .1".

Also note that for a .1" offset on a 3 degree wheel tread taper, one needs a horizontal movement of 2"--well within the distance available on a 5 1/2" wide wheel.

So, for a typical 36" wheel, we add .1" and .1" to get a diameter of 36.2" for the larger diameter.  Or you have the option of subtracting--your choice.

Multiplying each by pi, we get circumferences of 113.1" and 113.73".  And the difference is .63".

Now, if we imagine these two circumferences unrolled and laid out flat 4' 8 1/2" apart, we can extend lines through the two pairs of end points that will meet at the center point of a curve.  That would be the curve of the track that the wheels happen to be sitting on.  If we start moving from the wheels 4' 8 1/2" at a time towards that center point, we can also subtract .63" each time and stay on both lines.  We can count the number of times it takes to subtract .63" from 113.1" (180), and multiply that number by the track gage to get the curve radius:

 

180  x  4' 8 1/2"  =  848'

 

 

Ed

 

 

 

 

[gregc]

Ed, thanks for checking my math.   I believe you are correct.  I made the blunder of basing my calculations on track gauge in inches instead of feet.   Thanks.

I assume a radius of ~800' is a happy medium between mainline and terminal/industrial trackage

 

 

   

[7j43k]

Greg,

 

Yeah, I was worried about that foot/inches thing for my calcs, too.  Slippery little devils.

 

 

Ed

[tomikawaTT]

Wherever it's physically possible the prototype prefers curves which can be handled without the wheel flanges actually contacting the railheads.  However, sometimes reality intrudes on that dream world.  That's when the flanges start to scream and flange greasers get installed.  It's also where speed limits drop off to really slow.

And now you know why prototype railroads try to reduce grades through sharp curves.

Chuck (Modeling Central Japan in September, 1964 - with speed limited flange-screamers)

[locoi1sa]

  Greg.

 Lines that handle faster and more tonnage would super elevate the curves too. The amount of super elevation would also add to the diameter taper. I looked through my copy of the CE78 dated 1906 on construction and maintenance of track and stucture but did not find anything about degrees of curvature and super elevation adjustment. There must be a standard somewhere. The PRR had a standard for everything.

   Try posting this on the trains magazine general discusion forum. Maybe Mudchicken will reply. He knows everything about trackwork.

            Pete

[locoi1sa]

Greg.

I found this online. Most of the book has to do with turnouts but there are some degrees of curvature and engineering formulas.

http://babel.hathitrust.org/cgi/pt?id=mdp.39015021053460;page=root;view=image;size=100;seq=1

       Pete

[yankee flyer]

Hey Guys

I must have missed something here. It looks to me, that if you are pulling a train around a curve the inside wheels move toward the inside rail head making them larger diamenter and the outside wheel sets move away from the railhead making the outside wheel set smaller. Thus, working the opposite of correcting for a solid axle. 
I can see where the wheel taper could lend it self to keeping the train centered on the track on a straight line.
I have been lurking on the forum but haven't done any train stuff for over six months.
Been busy taking Chemo, and a cold basement didn't make it too inviting.

Have fun 

Lee

[7j43k]

yankee flyer

Hey Guys

I must have missed something here. It looks to me, that if you are pulling a train around a curve the inside wheels move toward the inside rail head making them larger diamenter and the outside wheel sets move away from the railhead making the outside wheel set smaller. Thus, working the opposite of correcting for a solid axle. 
I can see where the wheel taper could lend it self to keeping the train centered on the track on a straight line.
 

 

Lee,

Here's a brief discussion of the matter:

 

http://www.youtube.com/watch?v=y7h4OtFDnYE&feature=youtu.be

Note, particularly, his mention at the end of how the wheels correct for a bump.  Even on a straight track, the wheels tend to steer themselves into a "centered" mode.  They do that also on a curved track, except that the proper "centering" will have the appropriate offset, such that the differential effect will work.

Your comment about how you can see where the wheel taper could keep the wheels centered on a straight track assumes, I think, that the wheels kind of fall to the center because of gravity and the taper.  This isn't what's happening, as Mr. Feynman notes.

It's natural to think (I tend to) that the differential effect doesn't happen until the wheels have turned once.  Or maybe twice.  Or "a whole bunch".  But it happens pretty much instantly and all the time.  The only time I think it would be defeated (other than an overly sharp curve) is if you could change from straight to a curve the way you do when you connect two pieces of Lionel O gage track--right away.  Then it would take some unspecifed distance until it was corrected.  But real rail won't bend that quickly.  So you don't.

 

Going back to your second sentence, I think you're talking about the predecessor of stringlining (where the train is pulled off towards the inside of a curve).  To overcome the natural differential effect and jam the flange up against the inside rail takes a lot of force.  The train is normally just affected by rolling friction, but you now have sliding friction (towards the inside rail) caused by the locomotive trying to go around a corner (sort of); and that's pretty huge.  Imagine trying to pull a train with all the wheels locked--sorta like that.  It happens, I s'pose.  It especially happens on MODEL railroads; but, among other things, we use curves that are an awful lot like that corner I mentioned.  I used to stringline trains on my old Lionel layout with O gage curves until I picked up some O-72 (wide radius) track.  Problem solved.

 

 

Ed

[cacole]

I have several videos of Norfolk Southern, Union Pacific, and other trains going slowly around curves, and there is a lot of banging-type noise that sounds like one or more wheels slipping because of the difference in rotation, even on locomotives.

 

[BRAKIE]

cacole

I have several videos of Norfolk Southern, Union Pacific, and other trains going slowly around curves, and there is a lot of banging-type noise that sounds like one or more wheels slipping because of the difference in rotation, even on locomotives.

 

 

Exactly..As any trainman can tell you curves including elevated curves- have speed restrictions as does switches..You just don't fly around curves or bust wide open through switches like the majority does when they run their trains.

Flange squeal at slow speeds around curves will tell you why curves have those speed restrictions.