# Misinformation about "differential" action on curves



## Greg Elmassian (Jan 3, 2008)

Reading another thread, there was a link to a "scientist" site about how the tapers in the wheel treads provide the differential action so one wheel can traver further around a curve.

Idiots. The pictures showed two large plastic bottles taped back to back. Taking a "wheel tread" as wide as the track gauge should have been a tipoff that this is not how REAL railroad wheels work.










The taper we have in our wheels, even though extreme on the more toylike wheels does not give "enough" differential action.

Let's start with prototypes. The differential action is provided at the FILLET between the tread and the flange. This provides enough difference in diameter to handle the required "extra travel".

(if you still believe it is the tapered tread, then you are wrong and you need to research on google, and do not go to some stupid "Mr. Wizard" site)

In our scale, good wheels will have a reasonable fillet, but often this is not enough, and the wheels may slide a bit or ride up on the flange itself.

Highly tapered wheels have been tried, or ones with very exaggerated fillets, so bad that the fillet radius was that of a common pencil (remember those weird AMS wheels?)

They did not work, and resulted in cars wandering side to side down straight track. 

A mild taper to the tread to keep centered on straight track, and a good fillet between the tread and flange itself works. 

Notice that poor wheel contours and tight curves will make a lot of friction between the wheel flanges and the rail, often producing squeaks.

Greg


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## Garratt (Sep 15, 2012)

This reminded me of a video I once saw which is related. 
Not saying you're incorrect Greg. They don't mention the filet either but you can clearly see it.






Andrew


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## toddalin (Jan 4, 2008)

Show the math to demonstrate your point.

How much larger must the wheel be at the fillet from side to side for various track diameters such that the "differential" action can't work?


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## Totalwrecker (Feb 26, 2009)

Boy a little mis-information goes a long way.

Try to remember about 5 years ago when we watched a vid that showed the flanges never touched the rail. Tight curvature is the exception not the rule.
Now with our toy like curves the fillet is very important in that it provides the Fudge Factor needed in our toys to appear real.

John


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## Totalwrecker (Feb 26, 2009)

http://boingboing.net/2013/04/10/why-do-trains-stay-on-the-trac.html


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## Dwight Ennis (Jan 2, 2008)

Totalwrecker said:


> http://boingboing.net/2013/04/10/why-do-trains-stay-on-the-trac.html


Great find!! Hard to argue with Richard Feynmann no matter how "smart" we think we are!!

LOL!!


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## Garratt (Sep 15, 2012)

I crunched some numbers just for the exercise. There are finer aspects to the equation due to the rail and wheel's width and profile but I kept it fairly simple assuming all riding at the rail's center. The fillet actually rides closer to the rail's inner edge but the difference is minimal.

For a 600mm radius track circle measuring at the track and rail centers I found that using a standard Bachmann 32.5mm diameter wheel, the difference between the wheel radius would have to be approximately 1.35mm.
I then tried it for 1200mm radius track and it was 0.66mm.
I'm not sure if I can trust my maths though. Can anyone else verify?

Our model wheels typically have more width and tread taper which also have looser gauge tolerances than the prototypes so although some model wheels do have an effective increase in riding diameter from the fillet, others have very little effective fillet. 

Andrew


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## Garratt (Sep 15, 2012)

Dwight, he makes the same conclusion for prototypes and also doesn't mention the fillet.
Here is some very detailed info on the subject. Hold on to your scholar's hat, it's very intense.

http://www.wiki.iricen.gov.in/doku/doku.php?id=rail_wheel_interaction










Andrew


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## Dwight Ennis (Jan 2, 2008)

I am willing to accept the word of one of the world's most recognized physicists... indeed the inventor of "Feynmann Diagrams" describing particle interactions via energy/photon exchanges. From my "common sense" point of view, the fillet most likely guides the wheels during the smooth transition from taper to flange, thereby providing a smoothing of the 'differential effect.'. I don't have the mathematical background to back this up, other than some common sense and a basic 'common sense' perception of why tapered wheels and fillets would prove effective to accomplish same. I will leave such to the self-proclaimed experts. With all due respect. But the proof is in the pudding, and real-world analysis and performance on the prototype have proven the effectiveness of this combination beyond any picking apart by the (imho) amateurs on this forum. Again, with all due respect.


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## Greg Elmassian (Jan 3, 2008)

Are you saying we can take the flanges off our wheels Dwight?

Notice I was talking about the differential action, i.e. having enough diameter to go around the curve without skidding.

Feyman is talking about why the wheels follow the curve.

I hope you see the distinction... our issue is we cannot use prototype wheel contours to get enough differential action on our tight curves, especially 4 foot diameter ones.

The centering between the rails is right of course, but we don't have wheel treads 1 inch wide to match the first video.

Greg


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## Dwight Ennis (Jan 2, 2008)

> Are you saying we can take the flanges off our wheels Dwight?


Of course not. What I'm saying is that the fillet, along with the taper, allows the wheel to change its functional diameter depending upon where the wheel is contacting the rail at any given moment, and allowing a wheel and its mate on the same axle to effectively have different diameters. On a curve, the outside wheel rides nearer to the fillet than the inside wheel, effectively increasing its diameter and allowing it to cover more distance with each rotation. The inner wheel does just the opposite, riding further away from the fillet, effectively decreasing its diameter and allowing it to cover less distance.

BTW, I suspect the fillet also has structural reasons for its existence. One never has sharp corners on a casting to avoid cracks from developing in the metal.


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## Totalwrecker (Feb 26, 2009)

To add to the equation.... Weight; tons vs. Ounces.
With our light weights, lateral forces have more say. Toy flanges allow us to approximate reality, not duplicate it.
John


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## toddalin (Jan 4, 2008)

Seems to me:

I run minimum 1200mm radius curves.

1200 mm = 47.24"

Rail is 1.75" wide, so,

inner rail is 46.37" and outter rail is 48.12"

Circle diameter = 2 x pi x r

inner circle = 291" 

outter circle = 302"

302/291 = 3.78% difference in _circumference_ of wheel to make the curve without dragging a wheel.

When you look at the over sized fillets on most wheels, this doesn't seem like much difference.


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## Greg Elmassian (Jan 3, 2008)

The fillet allows you to increase the diameter of the wheel by a significant amount, so for tight turns, you still get the differential action. The smooth transition (or even merely the existance) of the fillet is the key.

Take some time and look at various train wheels, there are many that have NO fillet at all, just a big flange.

Remember the "revolution" that the RP-25 contour created in HO?

Everyone was sure the flange was there to keep trains on the tracks and many trains had deep flanges (and no fillets).

The RP-25 came out with a profile closer to the prototype, a defined tread taper, a defined fillet and a much smaller flange.

Many "experts" SWORE it would not work... the rest is history.

Greg


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## armorsmith (Jun 1, 2008)

Here is a bit of simple math for ya Greg. If a wheel is 36 inches in diameter on the inner side of the tread, and a 3 degree taper is put on the wheel, with a 5 inch wide tread the outer tread is approximately 1/2 diameter smaller than the inside diameter. And the outside circumference is approximately 1 1/2 inches smaller in dircumference than the inside.

When a rail car goes around a curve, the centrifugal force tends to move the car to the outer side of the curve, thus the wheel on the inside of the curve (inner rail) is on the outside of the tread rolling on the smaller diameter of the wheel. The outer wheel is on the inner side of the tread rolling on the larger diameter.

Will it keep the wheels from 'slipping' on every curve? I don't know for sure, but I DO understand the principal it is founded on. And I am sure that many decades of railroad experience have proven this theory to be accurate for the greater extent. I am also certain that with todays modern high speed computers, and iterative program could be run to prove every conceivable scenario.


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## Garratt (Sep 15, 2012)

I've noticed some wheels have a very small 'radius' fillet and others are larger that gradually rises well within the tread area as in the last illustration I posted and the test wheels in the high speed train video. What Greg is claiming seems very plausible. 

From what I have learned about prototype wheels:
- The wheel tread taper or 'conicity' keeps the wheelset centered and able to go around curves. Typically 1 in 20. 
- Tapered treads create an oscillation called 'sinusoidal motion'. Hunting from side to side.
- High speed train wheelset tapers are typically 1 to 40 to reduce the oscillation (200 km/h 2 km radius, 350 km/h 7 km radius).
- The wheel fillet needs to be a greater radius than the radius on the edge of the rail.

Large Scale wheels have treads that are 1 to 6 ~ 1 to 10 or thereabouts and some do tend to have fillets that gradually rise from the tread area. 
Some wheels have a very small radius which is smaller than the radius on the edge of the rail making the fillet dysfunctional as a differential effect. 
For instance a Bachmann metal wheel I tested (24.5mm) with LGB brass rail left a thin line of Blu-Tac over the fillet when rolled over with pressure. I estimate the rail edge has a 1mm radius approximately. Other wheels are similar. 
I noticed the Bachmann wheel has a flatter taper than the Accucraft and Brawa ones I looked at.
So it seems some of our wheel and rail combinations are not correct as far as the fillet goes compared to prototype practice but I'm sure there is more to it. 
Make of this study as you wish. It sure beats watching TV. 

Below is a German supplied tool for shaping wheels. The fillet radius is only 0.4mm
The specs are below:

For lathe tool holder with hole Ø 8,0 mm
Total profile width 7.0 mm 
Flange height D 2,4mm / tread 3°
Flange width T 1.8mm
Fillet radius 0.40mm










Andrew


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## East Broad Top (Dec 29, 2007)

Per G1MRA and NMRA standards, the tread taper should be 3 degrees (a whisker over 1 in 20). How close the manufacturers come to this varies greatly, and often varies within a single manufacturer as they use different wheel profiles for different products (and sometimes different wheel profiles for different wheels on the same locomotive!)

*G1MRA* standards call for a fillet of .020" between the flange and tread. NMRA standards do not specify a dimension for a fillet for any of their scales. The footnotes in the Large Scale wheel standards _recommend_ a fillet of between .020" and .030", but the standards themselves do not mandate one. 

The wheel profile itself is covered by *RP25* (wheel profile "recommended practice"). While the chart does not cover large scale wheel sizes, the fillet works out to about 1/7 of the total width of the wheel for the wheel widths listed on the chart. For large scale, that works out to .035" plus or minus. (Large scale wheel widths vary from .236" to .271".) RP25 stipulates that the targets in that chart should fall within the acceptable range of the NMRA's "standard" wheel standards (*S-4.2*). When you extrapolate the large scale dimensions based on percentages, the flange width and depth requirements for large scale wheels are actually smaller (and more "prototypical") than what they would be if you just scaled up RP-25 to large scale. As a result, the fillet would be less than what it would be by just expanding RP-25 to large scale, which would put it between .020" and .030". 

The tool Andrew shows above would meet NMRA standards for profile for their "Hi-Rail" standards (*S-4.3*). The fillet is only .015", which is less than what NMRA and G1MRA would have you use. The flanges are too deep and wide to meet the NMRA's "Standard" standards or G1MRA standards. 

Later,

K


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## Greg Elmassian (Jan 3, 2008)

Bob, I invite you to complete the "simple math" and figure out the diameter of the wheel on the outside rail of a R1 (4' diameter) curve using a 33" scale wheel, and assuming the 3 degree taper. (realize too that the rail will not be at the outside edge of the wheel tread)

I think you will find that the increase in the diameter of the wheel 1/2 a railhead width from the flange will not be enough to make up the extra travel of the wheel.

Everyone keeps quoting the prototype, and our wheels and most importantly our curves are CERTAINLY not prototype. Our curves are much sharper and need more "differential action" from our wheelsets.

So Bob, when you kind of "throw the glove down" with a statement like "simple math" you need to complete the "story", which is what diameter IS required on the outside wheel to accommodate the longer travel.

We can do this together and get some real answers, or we can continue to do dismissive posts that basically are saying "hey, it's obvious to me, and what is your problem?"

So, ready to find out the REAL answer? I'm curious myself. ( I have a strong belief but interested to see the hard numbers)

Regards, Greg


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## Totalwrecker (Feb 26, 2009)

Understanding that my models are on the toy side of high fidelity scale models, I do not expect our wheels to behave anywhere near prototype.
I was of the impression that an oversize fillet was better than too small. Within esthetic consideration. Don't want it to look funky!
John


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## Greg Elmassian (Jan 3, 2008)

I think you are right from an operational viewpoint John, but it would be fun to actually work this out and see.

Greg


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## Garratt (Sep 15, 2012)

Very interesting EBT, thanks for that.

There seems to be two discussions/arguments going on here which are worlds apart: 
- Does the fillet also play a role along with the wheel conicity (tread taper) to create a differential effect on prototype railways?
- How can model train wheels be made to work better for our needs? (our needs can vary greatly too).

It does seem our fillets are under sized considering some of the rail we use. 
This would effectively create a situation of the flange/fillet sweeping against the rail side/corner (curved profiles get ambiguous).
Does the differential effect and correct fillet really matter on models?
I suspect it could be a source of annoying squeaks and flange wear on small radius track.

Andrew


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## toddalin (Jan 4, 2008)

Greg Elmassian said:


> I think you are right from an operational viewpoint John, but it would be fun to actually work this out and see.
> 
> Greg


I asked you to show the math to demonstrate your point way back in the third post. So what's been stopping you??? 

Oh right..., you don't see these.


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## East Broad Top (Dec 29, 2007)

On a 4' diameter (2' radius) curve, the outside rail will be 104% longer than the inside rail. (45mm gauge). If my math is correct, that means the outside wheel must be 104% the diameter of the inside wheel to go that distance with the same amount of rotation. 

A 33" wheel in 1:29 will have a nominal diameter of 1.138". The best differential you're going to get with a 3-degree tread taper will be + or - .004" from nominal. Clearly you're not going to get to 104% with just the tread taper. So you would have to add a fillet. The problem is, you need to increase the diameter to 1.184" to get to 104%, a difference of 0.46". A practical-sized fillet isn't going to get you there. 

I ran the numbers the other night, and it came out to the tightest radius you can run relying solely on the conical taper of the wheel tread alone is about 11', presuming a 3-degree taper. With a typical fillet, you may be able to get that down to around 6 or 7' radius, depending on the radius of the fillet and how much of it you can effectively ride on. 

Later,

K


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## Skeeterweazel (Feb 11, 2014)

For a 4' diameter circle of track i get a inside/outside track differential of 7.6%. And wouldn't the difference in the circumference of the wheels, not the diameter, need to be that differential?
Marty


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## toddalin (Jan 4, 2008)

Skeeterweazel said:


> For a 4' diameter circle of track i get a inside/outside track differential of 7.6%. And wouldn't the difference in the circumference of the wheels, not the diameter, need to be that differential?
> Marty


Doesn't matter. The radius, diameter and circumference are all directly related so all change incrementally together.

Now if you were talking about area..., that's different.


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## East Broad Top (Dec 29, 2007)

Circumference = Diameter x pi, so it's a linear relationship. 

Here's my equations: A 48" diameter circle of track, measured at track centerline. At 45mm gauge, the outside rail is a whisker under 49", and the inside rail is a whisker over 47". 

47 x pi = 147.7"
49 x pi = 153.9"

153.9 / 147.7 = 1.04 (104%)

A 33" wheel in 1:29 (1.138") has a circumference of 3.575". It would make 41.3 revolutions to travel around the 147.7" of inside rail of the circle. So, for a wheel to travel 153.9" in 41.3 revolutions, the wheel would have to have a circumference of 3.726", thus a diameter of 1.186". 

Later,

K


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## toddalin (Jan 4, 2008)

East Broad Top said:


> The best differential you're going to get with a 3-degree tread taper will be + or - .004" from nominal. Clearly you're not going to get to 104% with just the tread taper. So you would have to add a fillet. The problem is, you need to increase the diameter to 1.184" to get to 104%, a difference of 0.46". A practical-sized fillet isn't going to get you there.
> 
> I ran the numbers the other night, and it came out to the tightest radius you can run relying solely on the conical taper of the wheel tread alone is about 11', presuming a 3-degree taper. With a typical fillet, you may be able to get that down to around 6 or 7' radius, depending on the radius of the fillet and how much of it you can effectively ride on.
> 
> ...




Are you missing the bigger picture here?

As one wheel gets "3 degrees bigger" the other simultaneously gets "3 degrees smaller" yielding an effective taper of 6 degrees across the axle.


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## Garratt (Sep 15, 2012)

Skeeterweazel said:


> For a 4' diameter circle of track i get a inside/outside track differential of 7.6%. And wouldn't the difference in the circumference of the wheels, not the diameter, need to be that differential?
> Marty


Yep, that's what I get too and I've done it on paper and a second time in an entirely different way.
Yes it is the circumference. 

A few other issues too, the wheels don't run on the gauge and a 3% taper is half way between prototype and high speed trains. All the model wheels I look at are no where near 3%.

I have something in the pipeline for all to play with soon.... 

Andrew


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## East Broad Top (Dec 29, 2007)

The tread has a 3-degree taper, with the 3 degrees measured from square (parallel to the axle). That gives a total conical taper to the wheel tread of 6 degrees because it's a wheel. All the math is done with right triangles. A prototypical railroad wheel has an effective tread width of about 3". (That excludes the fillet, flange, and the chamfer along the front edge of the wheel.) A 3-degree right triangle with a height of 3" results in a base of 0.15". That's the maximum difference in the radius of the wheel. The diameter would be twice that, so 0.30" maximum difference in the diameter of the wheel. That's regardless of the diameter of the wheel itself. The biggest difference you can get on a set of wheels (exclusive of the flange) is when one wheel is riding on the very outside edge of the wheel, and the opposite wheel is riding right at the point where the tread meets the flange. On properly-gauged track, that can't happen because the wheels are gauged such that the very outside edge of the wheel never gets near the inside of the railhead, but in theory, that's the maximum difference in diameter. 

Later,

K


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## East Broad Top (Dec 29, 2007)

Andrew, a 1 in 20 taper is 2.8 degrees. A 1 in 40 taper (high speed trains) is 1.4 degrees. These are right triangles, so the base is 1, the height is either 20 or 40. 

*Triangle Calculator*

A 3-degree taper is steeper than prototypical, but close enough given the small sizes we're working in.

Can you post the equation you're using to get a 7% difference between inside and outside rails? Compare to my equations above for how I came up with my values.

Later,

K


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## Garratt (Sep 15, 2012)

EBT, I can see your error now.
The outside rail is nearly an inch larger in diameter on both sides of the circle. Same goes for the inside one which is nearly an inch less on both sides.

Assuming a gauge difference of 1.77 (45mm). Gauge 1 @ 1.75 is slightly different.

46.23 x pi = 145.23"
49.77 x pi = 156.35"

156.35 / 145.23 = 1.076

Andrew


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## Garratt (Sep 15, 2012)

Ah, it's a degree. I kept thinking of it as a percentage like a slope. Silly me, I must be going blind! 

Here's a screenshot of what I've been fiddling with this afternoon here.
I need to re-check the fillet part with fresh eyes tomorrow and will paste the code up here for all to play with. The calculator, paper and pencil way was driving me nuts. Those interested can save it as a htm file and use it in their browser for prototype, models, metric, inches whatever...










Andrew


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## East Broad Top (Dec 29, 2007)

Andrew, your radii are wrong. The gauge is 1.77, but that has to be _halved_ to get the inside and outside diameters from centerline of the track. You're using an inside rail diameter of 46.23" and outside diameter of 49.77", which results in a gauge of 3.5" 

Later,

K


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## Greg Elmassian (Jan 3, 2008)

Also, why are you using 5% tread conicity instead of 3%?

Also, what assumptions are you making as to where the rail contacts the treads?

Some people were calculating from the minimum diameter of the wheel to the max diameter, which is wrong, that would say that on a curve, pushing the wheelset to the outside, the inside wheel would be almost off the rail.

You need to state this, I suspect the difference in diameters would be between 1/2 railhead width from the flange to possibly that the inner wheel would be flush with the inner edge of the rail head.

To be clear, it is not accurate to compare the max dimension of the wheel near the flange to the min diameter of the wheel at it's extreme edge.

The 2 measuring points is most likely 1/2 of the tread width, not a full tread width.

That would mean the "extra diameter" gained is half of what your calculator shows.

Please identify the two "points" on the tread you are calculating for the diameters.

Greg


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## East Broad Top (Dec 29, 2007)

Greg Elmassian said:


> Some people were calculating from the minimum diameter of the wheel to the max diameter, which is wrong, that would say that on a curve, pushing the wheelset to the outside, the inside wheel would be almost off the rail.


Absolutely right, but it's difficult to pinpoint exactly where rail meets the tread in both model and prototype. On the prototype, they broaden the gauge on some curves. (If I recall earlier research, the gauge can be widened 1" or 1.5" on tight curves, but I forget what the criteria are.) The inside edge of the railhead wouldn't be right on the outside edge of the wheel, but it could be fairly close to it in those circumstances. Model track gauge isn't exactly as "fixed" as one might hope, either. I figured for simplicity's sake, it was easiest for the calculations just to take the mathematical limits. 

Later,

K


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## SD90WLMT (Feb 16, 2010)

If someone actually used a measuring tool to read the 45mm across a wheel set ya might see what I saw!
There is only around 1/32" of clearance. Laterally..across the tread..placed against limiting flanges...
So..reality shows us a very small change in taper difference from a straight section to curved track..

Ya guys are working too hard here...tho in fun..must be raining at home for some of you to be so consumed in an approach you won't go out n change on your layout or cars...

Have Fun...


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## Garratt (Sep 15, 2012)

'Also, why are you using 5% tread conicity instead of 3%?'
Greg, I'm using a slope rather than a degree like prototypes are typically specified 1 in 20 ~ 1 in 40 etc. Probably simpler to convey it like that. The *3 Degrees* quoted for models is 1 in 19.11 or 5.23% slope.

I used the term *track width* instead of *gauge*. It gets ambiguous where the wheels actually tread upon the rail. It depends on rail profiles etc. The user is advised to add a little more to the gauge for track width rather than myself making assumptions buried in the tool code.
I figure adding about half the width of the rail head to the gauge would be fairly close as the calculations are for cornering.

Also I only calculate the extra circumference by the tread conicity (taper) of how much is achieved with the input of *Wheel Side Play*. 

Kevin, when comparing the two different diameters of the rails in a circle the difference is twice the gauge (ignoring rail width) but I'll check it once more.

I'll fiddle with it, adding some notes etc. checking things again and post it up so others can perfect it and send it on a moon mission if they wish. These things will never be perfect unless there is a whole lot more specifications made. 

Andrew


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## Totalwrecker (Feb 26, 2009)

OH yeah?

















I'm working on the Narrows ... the drop from Vail to Marsh Station, the route that goes down a wash.
John


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## Totalwrecker (Feb 26, 2009)

Stoopid program turned 'em both sideway!


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## Chris Scott (Jan 2, 2008)

Totalwrecker said:


> Stoopid program turned 'em both sideway!


I thought that was a integral to your comment.


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## armorsmith (Jun 1, 2008)

@ Greg - As I stated in my post, a program could be developed to calculate any possible combination your heart could possibly desire. I have no intention of being that person....not worth my effort.

@Kevin - Circle centerline diameter of 48". To obtain the inside rail diameter you are correct in that you would deduct _1/2 the gauge[_, however you would do that from *both sides of the diameter* resulting in deducting the full gauge from the diameter to obtain the inside diameter. Same applies to the outer rail


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## rdamurphy (Jan 3, 2008)

I think it's a bit overwrought to describe something as "misinformation" when the point was simply to illustrate, with an example, of how something works, without explaining it to an nth degree of detail.

Sort of like using the Bernoulli effect to explain lift on an airplane's wing surface, when, in fact, that's only part of the explanation of how it works. Obviously, well, I would hope anyway, railroad wheels and axles aren't shaped like the ones in the example I posted, but it does illustrate how they work, and why there's a certain amount of squeal because of the solid axles involved.

Sort of like using the 45 degree banking of race car tracks as an example of how superelevation reduces curvature (increase the banking to 90 degrees, and curvature is reduced to zero) rather than posting complicated mathematical formulas that demonstrate the exact same thing but take a great deal of time and effort to understand.

Sometimes the best way to help someone is simple explanations, rather than way overcomplicated technical jargon that simply confuses people.

Robert


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## East Broad Top (Dec 29, 2007)

Duh! I was thinking diameter, but using radius in my math.  Shades of my experience in calculus coming back to haunt me. One little detail, and everything goes awry.

107% it is (says I, sheepishly.) 

Later,

K


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## Greg Elmassian (Jan 3, 2008)

Robert, the misinformation stems from another thread, where the "dixie cup demo" was presented in relation on what keeps the trains on the tracks.

Mr Feynman, Dwight, and I all agree the dixie cup demo correctly shows what keeps wheelsets centered on the track.

As I have stated a number of times in this thread, I want to get to the bottom of what it takes to have "true differential" action on our non-prototype curves.

I believe it cannot be done with just the 3 degree taper of the wheels alone, and I have stated you need to ride up on part of the fillet to get enough increase in diameter to get the differential action.

We are moving towards getting the answer, we are not there yet, still some errors in the calculations, but if everyone keeps going, we will finally get some good answers.

I believe the differential action (i.e. not have one of the wheels slipping) for our non-prototype curvatures will required use of the fillet, i.e. it cannot be accomplished by the tread taper alone.

Let's see if we can continue the excellent contributions and get to a result.

Greg


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## SD90WLMT (Feb 16, 2010)

Bearings...

...that is..till they get dirty...


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## East Broad Top (Dec 29, 2007)

Okay, I'm going to toss my earlier math out the window, because I can't confirm I was thinking straight. So, let's take a typical large scale wheel made to G1MRA/NMRA specs. Wheel width of 0.271", with a .070" wide flange and .030" fillet. That eats up 0.100". That gives you a tread width of 0.171". With a 3-degree taper to the tread, that gives you a difference in _radius _from fillet to edge of .009" {sin(3) x 0.171}. The resulting difference in _diameter _of the wheel, then, is 0.018". 

As has been noted earlier, the track gauge and wheel gauge likely would prevent the situation where one wheel on one rail is riding on the thickest part (next to the flange) and the opposite wheel is riding on the narrowest part (at the end of the wheel). In truth, if you take the dimensions of the wheel, you end up with a wheel with a gauge of 1.760", riding on track gauged to 1.772", which leaves you all of 0.012" lateral play with the wheels riding on the tread (exclusive of the fillet). What that means is that there's virtually no difference in tread diameter {sin(3) x .012" = 0.0006"} As a result, the taper of the tread would likely not allow for any amount of differential action with regard to going around a curve. The wheel would need a fillet for any kind of differential action to allow the wheel to go around a curve without slipping.

Just for mental exercise, however, let's see how tight of a curve the taper of the tread could theoretically allow given the maximum difference in diameter. 

Let's take a 33" wheel in 1:29, so 1.138" nominal diameter. Let's say that nominal point is midway through the tread, so the minimum diameter is 1.129" and the maximum diameter is 1.147". The maximum diameter is measured where the tread meets the fillet, which is also the gauge point (1.760"). Add to that the width of one tread (0.171"), and we have a distance of 1.931". (Yeah, it exceeds the gauge of the track. This is a theoretical exercise just based on the wheels.) Now, let's work in radii so we can work with right triangles to keep the math neat. 

Largest radius = 0.574"
Smallest radius = 0.565"
Difference = .009"










So, we have a right triangle with a height of 1.931" and a base of .009". That gives us an angle (x) of 0.267 degrees. We extrapolate that to a right triangle with a base of the widest radius (0.574") and an opposite angle of 0.267 degrees, and we get a triangle with a height of 123.174", and a hypotenuse of 123.176" (10' 3"). That is the minimum radius which could be turned by differential action of this wheelset. But--as noted--the track would have to be woefully out of gauge to get to this maximum difference.

Later,

K


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## Garratt (Sep 15, 2012)

Kevin, I have gone about it entirely different than you have but my calculator is getting results somewhere near yours. 
I'm sure there are differences in some of the details especially the wheel side play. I just checked what is laying around here.
Here is a screen shot of similar setup and as you can see there is only 0.002" of fillet for the result of 135" radius. The zero point is 156" radius.










Andrew


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## Chris Scott (Jan 2, 2008)

Are there some variables missing that supersede just talk about the tread, 
- The truck wheel/axle separation
- Radius of the curve
- Angle of attack
In the graphic the wheel flange and fillet, of all 4 wheels, are on the rail, both inner and outer rail. The taper seems to have no role. 

Don't one or more of the 3 above factors have to be addressed before, at a minimum, at the same time as the wheel taper to arrive at the proper taper?










Additionally, doesn't the specific railroad car type, minimum radius of the line traveled by that car, super-elevation dimensions for those curves, speed, weight, (probably a number other factors I can't think of) come into play as the railroad manages the operating economics of their business. Doesn't the railroad design the track, rail line curves, etc., with all that in mind as well when they spec their rail car wheels. That seemed to be the underlying message of the high speed rail video.

All things considered isn't this discussion about the wheel taper putting the wheel before the car (so to speak)?


Super-Elevation Reminiscing ;
This reminds of the discussion of the benefits of super-elevation for our model railroading. The final word on that was a definitive article in the G1MRA NL&J analyzing it in great detail. The conclusion was SE have no real benefit in our scale. In fact SE would cause undo wear on the outer wheels and rail. Isn't the conclusion, we can ignore super-elevation in model railroading scales.


Prototypical Curves;
Someone mentioned that our layout curves are non-prototypical in scale, or something along those lines. Anyway, If the smallest radius on the D&RGW Narrow Gauge is 24 degrees is ~240 ft. In 1:20.3, 11.85 ft.(1). My layout min. radius is 14 ft. Isn't that meet (exceed the minimum) to scale prototypical radius and facilitate an accurate analysis of wheel taper to rail? 

And therefore, doesn't this, the other stuff above and more seem to lead to the same conclusion as for super-elevation; we can ignore wheel taper, as long as there is some taper, in our model railroading scales?



Squeaky Wheels;
As for Squeaky Wheels on sharp non-prototypical curves, this would all seem to lead to the conclusion that wheel squeaking is inevitable with that combination. Aren't there just two solutions; 1. Live with it; or 2. ball bearing wheels (not bearings in the journal.) 


Like Dwight said, in his infinite wisdom (and he is very wise), all just seems like common sense to me. But then I'm still working on angle parking.



1. http://www.urbaneagle.com/data/deg-curve.txt
Degrees of Curvature to Scale Radii for calculating prototypical curves on model railroad layouts. N to #1 scales; Rick Blanchard, Urban Eagle.


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## Semper Vaporo (Jan 2, 2008)

All this theory is all well and good, and I am enjoying the discussion immensely. I have done all these calculation myself many years ago when I questioned the value of taper and filet on 1:1 (real) stuff. 

Just to toss the wrench of the south-paw primate into the mix... 

Take a look at the allowable wear limit of a real-world wheel. This is an OLD diagram and may not be valid anymore, but please note two points...

The filet at the condemning limit.
The slope of the taper at the condemning limit.










(From the 1922 Car Builders Cyclopedia.)

Just to express my impression of the two points... there is no filet and the slope is inverted. 

That means the more the wheel wears, the less any of this discussion is pertinent. 

To tie this to our marvelous toys... Do plastic wheels wear faster than metal ones?


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## Garratt (Sep 15, 2012)

Chris, that is more about the dynamics in motion and the sinusoidal motion effect of the trucks to 'hunt' as they roll up the track and the finer points of the flange profile. What you refer to is an inherent aspect of when the pivoting is not over the actual axle. I think the flange slope helps this. 
Designing the best wheel profile is another matter. We are just working out the basics of creating the differential effect on curves, the limitations and perhaps possible improvements. 

The 240 ft radius limit you quoted for D&RGW works out to need a 0.089" extra fillet height to provide the required differential effect going by my calculator. Not sure if that's correct but seems plausible to me. I'm no physicist though.

Super elevation would still need a differential effect but it does help in the weight distribution. 
Some more stuff on the subject: http://www.wiki.iricen.gov.in/doku/doku.php?id=rail_wheel_interaction

Semper, the tires on my car sometimes get pretty bad too but I always start with good ones. 

Andrew


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## Chris Scott (Jan 2, 2008)

Andrew;
*
The Gauge One Model Railway Association*

*G1MRA Standards, Documents & Guidance*
http://www.g1mra.com/resources-links/standard-guidance/

G1MRA Standards Sheet 1 – Track & Wheels
G1MRA Standards Sheet 2 – General Dimensions
ScaleOne32 Standards
Suggested Track spacing for non-British stock


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## Greg Elmassian (Jan 3, 2008)

So Kevin and Chris, you have come to the same conclusion, the wheel taper alone cannot provide enough differential action alone.

That differential action has to be provided by the fillet, or one wheel skids.

Thank you for going the distance to do the math, and it's personally nice to see my suspicions confirmed.

This all came about from a thread on squeaking wheels on tight curves.

Thanks guys!

Greg


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## East Broad Top (Dec 29, 2007)

Greg, I'm not convinced even with a fillet there would be enough there to keep the wheels from slipping on most of our common curves. I think it helps, but if you have a fillet of .030" radius on the wheel, less than half of that can effectively be used to increase the diameter of the wheel, as there's a point where it gets too steep and the weight of the car prohibits it from riding any higher on the fillet. I think it'd be safe to say that even with a .030" fillet, any curve less than 8' radius (16' diameter) will cause the wheels to slip to some extent as they go around. 

I wonder what it would take to make an operating flange oiler in this scale...

Later,

K


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## Garratt (Sep 15, 2012)

Kevin, what was the actual track radius you got from your calculations using the G1MRA specs of 0.012" lateral play?
I also have suspicions the necessary extra fillet height would be difficult to implement on our little wheels without causing problems. 

Andrew


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## Semper Vaporo (Jan 2, 2008)

East Broad Top said:


> {snip}
> 
> I wonder what it would take to make an operating flange oiler in this scale...
> 
> ...


Get a Live Steamer... they come with a built-in flange (and everything else) oiler.


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## Greg Elmassian (Jan 3, 2008)

Kevin, I think if you do the math, you will find the prototype will work with the fillet on normal prototype curves, but some sidings will be an issue.

I agree with you, that we probably still have some slippage on our curves.

I think I also stated as such when I started the thread, but it's what I have always suspected, our curves are just so much sharper than prototype.

Oh, as you see on prototype wheel contours, the fillet does indeed "blend" into the flange much better than the typical model train wheel.

Thanks, Greg


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## East Broad Top (Dec 29, 2007)

I'm sure it works with the fillet on the prototype. When you take a differential of 0.15" on the radius of the wheel due to flange taper (maximum value for a 3-degree taper over a 3" effective tread), you end up with a track curvature of 11 degrees for a 33" freight car wheel. (Same calculations as above.) Typical mainline curves in standard gauge are in the 5 - 8 degree range. A flillet on a prototype wheel has a radius of 1/2" or so. Even if the tread were flat due to wear, the fillet would easily compensate for the difference in diameter needed to negotiate curves typical of standard gauge railways.

Going the other way, a 6-degree curve has a radius of 955' (11,460"). Solving for the necessary difference in diameter between wheels to go around that curve without slipping, you end up with a difference in radius from one wheel to the other of only 0.08"! Most definitely, if the tread alone cannot handle that (or if it's worn flat), the fillet most certainly can. 

For narrow gauge folks, using the same calculations for radius differential, but 36" gauge and 26" wheels, we end up with an effective curve of 22 degrees. That's pretty much in line with typical curves on the narrow gauge lines. (The tightest on the EBT was 17 degrees.) 

If nothing else, this demonstrates why narrow gauge curves could be tighter than standard gauge. The same wheel profile, combined with a narrower gauge and smaller wheel cuts the required radius in half. 

To put that in perspective, though, an 11-degree curve in 1:29 equates to an 18' radius (36' diameter) curve. A 22-degree curve in 1:20.3 equates to a 13' radius (26' diameter) curve. Maybe at Dr. Rivet's place, but "not in my back yard." 

Later,

K


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## East Broad Top (Dec 29, 2007)

Garratt said:


> Kevin, what was the actual track radius you got from your calculations using the G1MRA specs of 0.012" lateral play?


In terms of just using the tread with that little lateral play, there's virtually no difference in radius (something like 0.0006"), so essentially it's flat. The radius the wheel could negotiate without slipping would be dictated by the radius of the fillet and how much of that fillet the car would be able to use. That's determined by the weight of the car, as the wheel has to lift exponentially more of the weight of the car as it moves along the radius of the fillet. If you take 1/3 of the fillet radius (0.030") as being usable, that gives you an extra .010" onto the radius of the wheel. The gauge would be 1.772" (presuming the track is in gauge). That results in a workable track radius of 8' 6" (17' diameter). 

Later,

K


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## East Broad Top (Dec 29, 2007)

Semper Vaporo said:


> Get a Live Steamer... they come with a built-in flange (and everything else) oiler.


Ha! Ain't that the truth!

On a serious note, the curves at the Colorado RR Museum are 25 degrees. (They had been 28, but recent track work eased them a bit.) Both #346 and #491 have flange oilers on their drivers. I can't tell if they were on the locos in regular service or not, though they definitely look like they were added later in life. 

Later,

K


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## Totalwrecker (Feb 26, 2009)

Getting to the bottom....
Which rail profile are you using?
Some of the diagrams picture a square railhead, looking at a fresh section of Aristo SS, shows it has beveled edges which may negate the fillet!

Oh my! lol

John


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## Garratt (Sep 15, 2012)

Kevin, 

Very interesting. That's exactly what I get when I punch in 102" (8.5) ft radius. That's assuming the inside wheel is in the center of a 0.12" (3mm) rail and the outside wheel is running on the rail edge. Same wheel diameter of 1.138" and 3 degree wheel tread taper.

With 2 more inches in radius it then changes to 0.009" fillet and at 94" it becomes 0.011".

Andrew


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## Garratt (Sep 15, 2012)

John, 

From what I can gather the G1MRA specs for the wheel fillet is 0.5mm radius and the rail's edge is 0.4mm radius so if the rail and wheels used are true to specs, there will be an opportunity for the rail radius to fit inside the wheel fillet radius to create some extra side play of 0.031" (0.8mm) difference. 

Andrew


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## Ted Doskaris (Oct 7, 2008)

*Factory Metal Wheel Comparison*

As to the pragmatic, shown below are selected trucks with respect to their flange, fillet and tread differences.










Note how the relatively new Kadee wheel has developed a wear ring in the fillet area when riding up on the track of the typically under gauged rail spacing of an Aristo No. 6 turnout.

-Ted


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## HMeinhold (Jan 2, 2008)

Bill Allen pointed me to this thread. Here my 2 cents:
1. Are you guys sure that with our conditions centrifugal forces win out over drag? I think in most cases the cars will be drawn to the inside rail instead of being pushed to the outside by centrifugal forces. If this is the case, the discussion is moote.
On my garden layout whenever I pull a long train and the cars derail, they tip to the inside of the curve.
2. I am currently building cars for my Guinness tram. The curves on this system (1' 10") were pretty severe, probably even if scaled sharper than on our layouts. One wheel was loose on the axle to ease friction due to the difference in rail length. This also means, there was no sinusoidal oscillation of the cars even on straight track. The system was in operation for almost 100 years.
3. The Guinness wheels also had fillets. In my understanding the most important task of fillets is to prevent the wheels from climbing up, not to increase circumference.
4. If you want an ideal system, look at Hunts:
http://americanindustrialmining.com/c.w.-hunt-locomotives-and-industrial-railways
Thy used outside flanges and in curves the outer wheels rode on the treads. As the rail system was a kit, the radius was standardized to perfectly cancel the difference between inside/outside rail.
Regards


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## SD90WLMT (Feb 16, 2010)

Henner... describe what your layout curves are actually..
Describe a long train to your thinking and running.

Thanks.... there are far too many apples .. oranges..and other fruits in here to make reasonable comparisons to other toy train issues..let alone real world practice..where trains don't tip over in curves...

Thank You..


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## Greg Elmassian (Jan 3, 2008)

1. Actually "centrifugal force" refers to a force outwards, centripetal force is the force inwards.

Having a degree in physics, I can tell you easily that the velocities involved are not high enough for either of these "forces" to overcome the mechanics of weight, wheel taper, etc.

Now, the drag on the cars will have an effect, and it's up to the weight of the cars to keep the train from moving to the inside of the curve. We have all seen "stringlining" of cars to prove what you have seen, but it's not the centripetal force.

on your 2, yes of course, everything you say makes sense, allowing the wheels to be independent takes care of the required "differential action", whether the 2 wheels are independent or not does not impact the self centering action explained by Robert Feyman, i.e. the tapers of the wheels provide the self centering.

3. actually if you think of it, the fillets would HELP climbing up in terms of making a smooth transition. Unfortunately your understanding of their function is not correct and does not agree with all the refrences and physics presented.

4. cute, curved track had an exaggerated foot that allowed the flange to ride on it, so you have a bigger diameter wheel and thus the needed differential action.

Regards, Greg


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## HMeinhold (Jan 2, 2008)

SD90WLMT said:


> Henner... describe what your layout curves are actually..
> Describe a long train to your thinking and running.
> 
> Thanks.... there are far too many apples .. oranges..and other fruits in here to make reasonable comparisons to other toy train issues..let alone real world practice..where trains don't tip over in curves...
> ...


The curves on my logging line are 8' diameter and the tipping occasionally occurred with 4 pairs of empty disconnects and a caboose at the rear. This also seemed to happen in real life, as can be read on page 84 of "Railroads in the woods": The big 4 truck shay "had a tendency to pull everything off the tracks on sharp curves". When I see long model freight trains at e.g. Sacramento with the loco almost chasing the last car, I cannot imagine that centrifugal force keeps all the flanges at the outside of the rail. This might be different for a short fast passenger train.
We could actually test this with marking dye applied to the wheels and running through one curve.
Regards


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## Greg Elmassian (Jan 3, 2008)

Henner, if you don't want to take my word with my physics background, please look up the definitions of the words you are using.

You can also calculate the centripetal acceleration and you will see the force is virtually nothing, the velocity is too low.

Again centrifugal and centripetal forces are so low as to not affect the situation.

Greg


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## Garratt (Sep 15, 2012)

East Broad Top said:


> .......
> In truth, if you take the dimensions of the wheel, you end up with a wheel with a gauge of 1.760", riding on track gauged to 1.772", which leaves you all of 0.012" lateral play with the wheels riding on the tread (exclusive of the fillet). What that means is that there's virtually no difference in tread diameter {sin(3) x .012" = 0.0006"} As a result, the taper of the tread would likely not allow for any amount of differential action with regard to going around a curve. The wheel would need a fillet for any kind of differential action to allow the wheel to go around a curve without slipping.
> .......


Kevin, I can see why you could not calculate much of a radius because the lateral play is more like 0.078" not 0.012". The rail's edge radius of of 0.4mm will sit mostly if not entirely in the flange fillet radius of 0.5mm. That's 2mm lateral play all up. Most wheelsets I have from manufacturers have that and some more. Also their tread tapers seem steeper than 3 degrees to me. 

It works out to be just over 21 feet radius obtained just by the tread taper in my calculator. That's to G1MRA specs. 

Andrew


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## East Broad Top (Dec 29, 2007)

Andrew, here's where I'm getting my numbers. You've got a back-to-back of 1.560" (NMRA minimum). Flange width of 0.070" (x2), and fillets of 0.030" (x2). That gives a distance from fillet edge to fillet edge of 1.760". (That's not the gauge of the wheelseet, as the gauge does not include the fillet.) With a track gauge of 1.772", that leaves you 0.012" of tread (exclusive of the fillet) for the calculations of what the taper of the tread alone is able to do with respect to curves. A slight radius on the railhead may broaden the effective gauge of the track ever so slightly, but I don't think it would be sufficient to make any significant difference.

Later,

K


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## pfdx (Jan 2, 2008)

I don't want to interject into the main stream of discussion but I would like to add some prototype information.

There are many different profiles of tapered treads, flanges and the fillet between. I have seen at least 4 described in the Baldwin Standard Practice, including industrial narrow gauge, gauges above 36", switching service and mainline service. Today there are unique profiles for transit and light rail applications, 2 AAR profiles, narrow and wide flange for freight applications, there is a passenger profile for Amtrak wheels and now there are high speed passenger profiles in use and under development. I can't tell you where diesel locomotives fit into the scheme but from experience the profile in use is different from a multi wear passenger profiles.

There are a lot of factors that go into the profile. Speed and curvature are the major factors. In short the, need for one excludes the other. In 1:1 railroading a wheel with a good profile on good will track smoothly without contacting the face of the flange. However once something get too far out of spec, all bets are off.

There is a lot of research on going into the wheel rail interface at the FAST loop in Pueblo. I'm not sure whether the argument between two or one point contact will ever be answered, but millions of $$$ are being thrown at it annually.

So to bring this back to the topic, I think it fair to say that there should be two sets of wheel standards for the traditional R1 crowd and one for the wider radius factions. But they still won't track the way they should because you would then have to figure out how to tram your trucks within 0.001" (we shoot for 1/16" on the real ones) alignment of the couplers and center-plates on the bodies to the same 0.001" because it all has an effect on the tracking of the wheels.


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## HMeinhold (Jan 2, 2008)

Greg Elmassian said:


> 1. Actually "centrifugal force" refers to a force outwards, centripetal force is the force inwards.
> 
> Having a degree in physics, I can tell you easily that the velocities involved are not high enough for either of these "forces" to overcome the mechanics of weight, wheel taper, etc.
> 
> ...


Dear me, my reply gets lengthy...
#1 I have a PhD in physics.
#2 Your fillet theory about the increased diameter works only, if the cars are pushed outwards by centrifugal force. If the wheels stay close to the inside rail, the taper/fillet makes things even worse, as the larger diameter is now inside.
#3 I did not say "stringlining" is caused by centrifugal force. My point is, that the wheels tend to rub on the inside of the curve, making the effect of taper/fillet worse, as I stated above.
#4 Self steering goes away, once the wheels are independent, as each wheel is "happy" with its diameter. This has been shown numerous times in the real world and is a big problem for cars without a continuous axle. Taper/gravity is not sufficient to steer the wheel back.
#5 A wheel climbs up, when the flange touches the rail at a critical angle. The fillet helps to avoid this. This is also one of the reasons, wheel profiles are closely monitored.
#6 Many slower running railroad vehicles like trolleys have a cylindrical wheel profile, as there are no long stretches of straight track, where self-steering would be advantageous. But the wheels still have fillets to prevent derailments.
Regards


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## Garratt (Sep 15, 2012)

Kevin, I know how you are getting that figure but that would only be the case if the rail had a square edge.
The curve on the edge of each rail gives the extra play I'm talking about before riding up the fillet.

Andrew


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## East Broad Top (Dec 29, 2007)

That depends on the cross-section of the rail. My code 250 stuff is not "right angle" square, but there's not a whole lotta "round" to it, either. Nor does the LGB stuff I have here offer much rounding on the corners. Maybe 0.010"? I've got some AMS code 332 which is nicely rounded, but that's about it. You'll have more variation in the gauge just from how the rail is held in the ties than you would from any rounding on the railhead. 

Later,

K


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## Garratt (Sep 15, 2012)

Keven, yeah I understand the edges of rail differ, some having less radius on the edge than others. A picture below shows some profiles.
I figure to work out sideplay you either measure it on your own given scenario or calculate from G1MRA specs. 

Effectively, by ignoring the rounded rail edge of 0.016" (G1MRA specs 0.4mm) you lose 0.032" (0.8mm) in calculated side play.
Some of your figures are rounded versions of G1RMA ones then you multiply them. 
The G1MRA metric numbers have lost precision a little too when doing this type of equation. The numbers can bite sometimes. 

The track below give a sideplay of about 2mm or more. a little less for the code 250 and perhaps near only 1mm for the code 200. 
Now combine the various different wheels in the image posted by Ted and things go all over the place.

The wheel lateral sideplay is a critical factor in determining the widest possible track radius for the differential effect to work because the equation extrapolates the final result by such a small degree of tread taper, typically 3 degrees and sometimes more. 

EDIT: I later discovered the Peco Code 200 rail is actually made to a gauge of 44.5mm. 



















Andrew


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## Greg Elmassian (Jan 3, 2008)

Henner you have a PhD in Physics and you use the term "centrifugal force"?

I am very surprised, as there is NO force with that name, every physicist, even students knows that it is an "imaginary" force which seems apparent to people, but it is the result of velocity and centripetal acceleration/force (which does exist)

This is one of the myths explained and dismissed in high school physics way back when I went to school. 

So, I'll let you have your opinions, and I'll keep mine. No reason fighting over something clearly ingrained in each of us.

I don't argue about the fillet working when the wheels are forced to the outside of the curve, I believe this thread is getting muddled by mixing in what happens in our models as compared to the prototype.

I started this thread about MODELS and what may explain squeaking, because we cannot accomplish the needed differential action to keep one or the other wheel on a solid axle from slipping, and thus squeaking.

Luckily 2 other people have worked out the math and proven that the wheel taper alone cannot provide this.

Another helpful person has shown that few wheels even have a fillet that could help.

What I had set out to be illuminated has been accomplished, and I thank the people who looked at it dispassionately to get to the truth. 

Greg


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## Totalwrecker (Feb 26, 2009)

Uh oh, I meant to be 'Stimulating of thought'. Is this a Monty Python Discussion?






I do see where drag (accentuated in a model with; simulated bearings, weight and speed) can lead to the pull necessary for a string-line effect. I would expect that Henner's light weight disconnects would exacerbate the inward pull. There fore I cannot discount his observation.

Without measuring, it looks like the taper on my section of Aristo SS would negate any fillet on their wheels and USA.
The fillet runs so high on the AML that it looks engineered for that rail. Although it should be noted the wheel gauge set bears on the discussion as well. Too narrow and you could be off the fillet. 


Since I tend to pull it out of the box and run, vs checking all specs. I wonder who has spec'd their equipment against the numbers?

Of course if the course has been run, never mind.
John


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## Greg Elmassian (Jan 3, 2008)

I surely don't want to go off in this direction, but things get a lot more complex when you consider the interaction of the truck, and the angles of the wheels presented to the rails, and then add on truck mounted couplers and the forces they transmit to the trucks, and also equalization or lack thereof, and basically all **** breaks loose ha ha!

I'm again thankful for the people who went to the trouble to work the numbers.

Greg


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## HMeinhold (Jan 2, 2008)

Greg,
I use the word "centrifugal force" deliberately, as most people are familiar with it. But anyways, there is another thought: Many cars nowadays are equipped with ball bearings in each wheel (not on the axle), which makes them independent. In this case taper/no taper does not matter. During one of our next steam-ups I will test, if the cars tend to go to the outside of the curve ("centrifugal force") or to the inside (due to drag). If there is enough time, we will do this test on the first/last car and/or slow freights/logging trains and fast passenger trains.
Regards


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## Greg Elmassian (Jan 3, 2008)

Henner, you must be rich, very few cars have wheelsets that have both wheels independent of the axle!

Those can cost a lot of money. Maybe you are talking live steam people who tend to have a lot less rolling stock, in fact a favorite "consist" for a loco, and where drag is a very important issue to running. 

Us poor people can only wish for the $$ to have these. I do have them on cabooses, since I also use them for power pickup.

Indeed a wonderful solution if you ignore cost. The inexpensive ones also rust easily.

But on the positive side, it will be very interesting to see what you find out, and also can you keep track of the weight of the cars (roughly only) because I believe this is also a factor, both in prototype and our models. I think there should also be some variation based on speed, and of course curvature.

Regards, Greg


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## du-bousquetaire (Feb 14, 2011)

It is really funy these issues in Forums. I find that we have to reinvent the wheel every so and so. It just goes to show how old I am now... Like Greg said this issue was outlined and explained very clearly in a Model Railroader article back in November 1967 Basic Model Railroading Wheels, when the RP25 contour sort of became standard (except on Rivarossi stuff made to NEM standards). It is the fillet that is important not the flange height. Gauge one was a minority scale back then, but then it is twice the size of S scale which *was* on the charts! So R1 which is the fillet radius is 0.41mm or 0.014 in, inches just multiply by two that gives 0.82mm filet radius and 0.028 inch radius for gauge one.
For those who would be interested Europe stayed back on this for years because the NEM standards had been jeopardised by the manufacturers lobbying (Marklin, Fleishman Rivarossi etc.). But today every manufacturer seems to be making RP25 contours the norm in Europe! So somebody at the NMRA must have gotten it right back then. 
I have been using RP25 wheel contours ever since as much as is possible, and have no problems at all. As I have often said, real railroad equipment is designed to operate on around 350' foot radius curves, found in engine terminals, wyes and interchange tracks. so just keep to that and you will be OK for standard gauge. Everything will run, and run fine and look good too. Thanks good ol' John Armstrong, Frank Elison Lynn Westcott... These guys made the hobby we have today, they sure new what they were talking about. And I am talking with experience about sixty years of it...


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## Greg Elmassian (Jan 3, 2008)

Just to underline part of a very good post: I model 1:29 scale, 350' radius is 12' radius, 24' diameter in my scale.

And 350' radius in prototype is where they go really slow, not mainline curves.

Interesting to hear, no matter what continent, the battle between the manufacturers and the customers is really no different.

Greg


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## Garratt (Sep 15, 2012)

Interesting point and I tend to agree with it in general terms to the final radius as a workable 'approximate'.
The G!MRA fillet is defined as 0.02" fillet. A larger one will give less radius with all other specs considered excluding any effect the wheel fillet may have on the differential effect.

What I don't agree with is Kevin's claim of only a 0.012" of effective side play on the outcome of wheel tread taper differential effect. I also disagree that the rail edge radius has little effect on the side play. I figure the effective differential side play is 2 or 3 times that and near double it again because of the rail edge radius. That's a lot more than claimed which grossly effects the minimum radius from the effective wheel tread taper. That's why he couldn't get a satisfactory result without tweaking the outside wheel's radius.

Another thing is when studying the other larger live steam model gauges going by IBLS specs, there is no side play (discounting the +- tolerances and possible gauge widening) so I question, where does any differential effect come from unless it is from gauge widening, the rail edge radius and possible wheel fillet differential effect? 

Andrew


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## SD90WLMT (Feb 16, 2010)

A full scale prototype curve of just over 3° is about 1740 ft in real life
A full scale curve in around 4° is about 1300 ft..or so..

These equate to 60 ft & 45 ft radus in our 1/29 ranges...for everyday normal freight or AmTrak speeds...in real life..

How fast can you run at this level of curvature to truly input any real change in gravity in play to have effect on our light weight plastic cars...? All winds aside!!


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## Garratt (Sep 15, 2012)

How fast can you go?

I'm not touching the physics. There may be an unpredictable little dog and a ball involved too. 






Andrew


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## machiningfool (Nov 15, 2008)

If you guys are really worried about wheels cheating around a curve, why not split the axle and not worry about it?, Bob.


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## Ted Doskaris (Oct 7, 2008)

Bob,
Good idea; can you put it to practice and show us how to do it without using individual ball bearing wheels that are available?
-Ted


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## Semper Vaporo (Jan 2, 2008)

The 'Theory" of coned wheels/taper treads is well established as a good thing in "REAL WORLD/FULL SIZED/1:1" railroading... they have been like that for a goodly long time and many experiments have been done to determine the "best" practice... But that doesn't necessarily translate to "best" practice for the Modeler of RR's. Our track is not maintained in gauge tolerance as well as the 1:1 would be, and our curves are often much shaper than the 1:1 would have to contend with.

There are wheel-sets available that have the wheels separate from the axle (one or both) so that they free-wheel in relation to each other... do bit of shopping and you will find them, and I am sure they are fine wheels. Some people say they work fine or that they cured a problem on their miniature RR.

But there are those of us that are into following the real world railroading practice and are seeking the best compromise of real world practice and what works best in the miniature world with our particular problems (sharp curves, poor gauge tolerance, etc.).


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## Greg Elmassian (Jan 3, 2008)

I agree, "dual ball bearing", i.e. both wheels indepedent of the axle are very expensive, often as much as the rolling stock itself.

For most people, too expensive.

These, NOT the most expensive come out to $83 PER car.


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## Gary Armitstead (Jan 2, 2008)

A couple of weeks ago at the Los Angeles Live Steamers 60th Anniversary Meet, there were quite a few large scale ride-on manufacturers that were discussing this issue. It all revolved around the taper of the tire and the fillet radius between the tire and the flange. At the end of the day, they all agreed that why re-invent what the full-sized railroads have used with success. Made good conversation for a while though .










Note the size of the flange on these wheels. They are 5-1/2 inches in diameter at the tire where the tire meets the flange. There is a .100 radius at the tire to flange intersecting point. These wheels are pressed unto the axle and gear driven. NO differential here. Just like the prototype and no sign of wear caused by the inevitable slippage from one wheel to the other. BTW, we use steel rail.........not aluminum.


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## Nick Jr (Jan 2, 2008)

I don't know if this has anything to do with this discussion. Yesterday on the History Channel there was a documentary titled LOCOMOTIVES. It showed BNSF and Chessy, said the flanges of the locomotives are lubricated with a graphite substance. Later in the program it showed a rectangular shoot about 1ft long that a solid stick was slid inside it and it was pointed directly at the wheel flange. the narrator said "helps the locomotive on curves" Google research said it is to reduce wear on curves. thank you.


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