Steam & Excursion > Question: "braking ratio"

What is "breaking ratio"? What does it physically mean? Obviously it is the relationship of two things expressed in numbers. What are those things?

lwilton Wrote:
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> What is "breaking ratio"? What does it physically
> mean? Obviously it is the relationship of two
> things expressed in numbers. What are those
> things?

Braking ratio.

braking ratio = power of a full brake application of a car (or locomotive) divided by the weight of the car on the rails. It's usually written as a percentage and, being a ratio, has no units.

EtoinShrdlu Wrote:
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> braking ratio = power of a full brake application
> of a car (or locomotive) divided by the weight of
> the car on the rails. It's usually written as a
> percentage and, being a ratio, has no units.

It is also commonly calculated and referred to as the average tons per operative brake.

>It is also commonly calculated and referred to as the average tons per operative brake.

Nope, because "tons per operative brake" are units, and a ratio, by definition has no units. It's total car braking force divided by the total weight of the car on the rails, period. IOW, if you have a car which which weighs 100 tons and it's braking system produces a total braking force of 60 tons, then the car has a braking ratio of 60%.

All "tons per operative brake" tells you is that the average weight of the cars in your train is so many tons per car. It will give you an idea on how well or poorly you air brakes will function to control your train, but it gives no specifics about braking power itself.

You can calculate the braking ratio for this 100 ton car metrically, and it will come out just the same: 60%.

EtoinShrdlu Wrote:
------------------------------------------------------->
> Nope, because "tons per operative brake" are
> units, and a ratio, by definition has no units.
> It's total car braking force divided by the total
> weight of the car on the rails, period.

Unless, of course, the car has an empty/load device on it ... which then alters the amount of braking force depending upon the weight of the car. Why do we have such devices? To keep the braking ratio of the equipment relatively consistent regardless of weight, and avoid sliding wheels. There are other factors you also have to consider, such as weather (wet or dry), temperature, and so forth. That is why the braking ratio might be nice to know in theory, but isn't typically used in operation of the train.



Edited 2 time(s). Last edit at 01/29/14 22:10 by bioyans.

EtoinShrdlu Wrote:
-------------------------------------------------------
> braking ratio = power of a full brake application
> of a car (or locomotive) divided by the weight of
> the car on the rails. It's usually written as a
> percentage and, being a ratio, has no units.

Thank you. I think you mean "force" rather than "power" in that statement, but it is reasonably clear.

Still, one more question: braking force, where? At the rails? At the brake cylinder? Someplace else? I would assume, to be useful, "braking force" should really mean something like "total retarding force at the rail interface". If the force is measured anywhere else you have to start asking questions about leverage ratios and rigging efficiencies.

>Still, one more question: braking force, where? At the rails? At the brake cylinder? Someplace else?

Wheel tread/railhead.

>I would assume, to be useful, "braking force" should really mean something like "total retarding force at the rail interface".

The older engineering books don't use the word "interface", but this is the case (assuming all wheels are used for braking). Braking force applied to a wheel (or disc attached to its axle) can't exceed a certain percentage of the frictional force between it an the rail or the wheel will start sliding along the railhead, which is dynamic friction and a lot less than static friction.

>If the force is measured anywhere else you have to start asking questions about leverage ratios and rigging eficiencies

Leverage ratios, brake cylinder size, and the air pressures involved are a balancing act between piston travel, air consumption, and lever angularity. Combined, they provide the total braking force the car can produce. From what I've studied, you start with the desired braking ratio and then design the brake system on the car (air system, foundation rigging, and the truck levers) accordingly.

Thanks. So to pick a specific example, if we have a particular hopper car that weighs 68K pounds empty, and 140 tons loaded, and has a braking ratio of 23% empty and 11% loaded, then it seems to me that:

Empty retarding force = 68000 * .23 = 15640 pounds
Loaded retarding force = 140 * 2000 * .11 = 30800 pounds

So in this case, it would seem to me that the loaded car has twice the retarding force of the empty car.
Whether that is a good or bad thing when trying to balance a heavy car with no brakes is an interesting question.
Let's try an experiment:

10 hoppers, empty = 680K pounds, retarding force 156K pounds
10 hoppers, loaded = 2.8M pounds, retarding force 308K pounds
1 dead engine, 600K pounds

engine + 10 empty hoppers = 1.28M pounds, retarding force = 156K, braking ratio = 156400 / 1280000 = 12.2%
engine + 10 loaded hoppers = 3.4M pounds, retarding force = 308K, braking ratio = 308000 / 3400000 = 9%

So, assuming the math above is right, it seems that 10 empty hoppers would actually be slightly better at stopping the dead engine than the 10 loaded hoppers, but is is pretty close to a wash. Of course, with the empty hoppers and a 23% braking ratio on the empty cars, there is a moderate chance under bad conditions of locking the brakes and sliding the wheels, reducing the braking ratio to near zero. That is unlikely to happen with the loaded hoppers.

The interesting question would be, is there an optimal weight per hopper and number of hoppers to get the maximum possible (and reliable) braking ratio?

lwilton Wrote:
-------------------------------------------------------
>
> So, assuming the math above is right, it seems
> that 10 empty hoppers would actually be slightly
> better at stopping the dead engine than the 10
> loaded hoppers, but is is pretty close to a wash.
> Of course, with the empty hoppers and a 23%
> braking ratio on the empty cars, there is a
> moderate chance under bad conditions of locking
> the brakes and sliding the wheels, reducing the
> braking ratio to near zero. That is unlikely to
> happen with the loaded hoppers.

Again, all nice in theory for people who want to throw around numbers. But, with over 2 decades plus of actually RUNNING trains, I can tell you that two trains of identical equipment ... one loaded and one empty ... the empty train will stop quicker and with less braking effort.

The part that you are missing, is that IN THEORY the loaded car might generate more braking force, the momentum from the extra weight that is motion REQUIRES more force to stop. This is why a loaded car, given the same trainline reduction, takes longer to stop than an empty car.

To also say that sliding wheels won't slow a train is also wrong. While the "brake ratio" might be near zero theoretically, the friction of the dragging wheel DOES offer enough resistance to stop the equipment. You will end up damaging the wheels (by flat spotting them), but it still provides retardation force to the train. Now, snow and ice between the shoe and wheel? Now you're going for a joyride, if you don't take precautions during those winter weather conditions ...



Edited 1 time(s). Last edit at 01/30/14 12:47 by bioyans.

lwilton Wrote:
-------------------------------------------------------
> Thanks. So to pick a specific example, if we have
> a particular hopper car that weighs 68K pounds
> empty, and 140 tons loaded, and has a braking
> ratio of 23% empty and 11% loaded, then it seems
> to me that:
>
> Empty retarding force = 68000 * .23 = 15640
> pounds
> Loaded retarding force = 140 * 2000 * .11 = 30800
> pounds
>
> So in this case, it would seem to me that the
> loaded car has twice the retarding force of the
> empty car.
> Whether that is a good or bad thing when trying to
> balance a heavy car with no brakes is an
> interesting question.
> Let's try an experiment:
>
> 10 hoppers, empty = 680K pounds, retarding force
> 156K pounds
> 10 hoppers, loaded = 2.8M pounds, retarding force
> 308K pounds
> 1 dead engine, 600K pounds
>
> engine + 10 empty hoppers = 1.28M pounds,
> retarding force = 156K, braking ratio = 156400 /
> 1280000 = 12.2%
> engine + 10 loaded hoppers = 3.4M pounds,
> retarding force = 308K, braking ratio = 308000 /
> 3400000 = 9%
>
> So, assuming the math above is right, it seems
> that 10 empty hoppers would actually be slightly
> better at stopping the dead engine than the 10
> loaded hoppers, but is is pretty close to a wash.


First, not all cars are required to have empty-load devices. Only if a class of cars cannot meet the minimum and maximum NBR set by AAR Standard S-401 for new and rebuilt cars (assuming a nominal brake cylinder pressure of 65lb in a 90lb system equipped with COBRA brakes). Even if a car has an empty-load device, the range can vary, so selecting say 0.23 as a NBR for a whole set of empty cars is theoretical.

> Of course, with the empty hoppers and a 23%
> braking ratio on the empty cars, there is a
> moderate chance under bad conditions of locking
> the brakes and sliding the wheels, reducing the
> braking ratio to near zero. That is unlikely to
> happen with the loaded hoppers.

The NBR doesn't change if the wheel is sliding or slipping. The commonly accepted formula for NBR is

0.79d*e*N*B*L / w

where

d = diameter square of the brake cylinder (in inches)
e = brake rigging efficiency.
N = number of brake cylinders
B = brake cylinder pressure
L = lever ratio
w = weight.

Since none of these change while a wheel is slipping or sliding, NBR doesn't change. What changes is the adhesion force of the wheel on the rail, often expressed as w*u, where u is the coefficient of friction. When w*u > braking force, the wheel will roll. A slipping or sliding wheel still offers retarding forces, it's just that it offers less and more importantly, damages wheel and rail, which can be very costly.

In the days before wide spread diesels and dynamic brakes, the Santa Fe spotted empty reefers at Summit for the express purpose of aiding trains in braking if tonnage exceed reasonable braking capabilities. Of course these cars did not have empty-load devices, so the best braking car would be from an empty car.

This discussion centers on the hopper cars used to aid in braking for 4014 movement. I cannot say why the UP chose the cars they did nor the number, but it's possible they were the only ones available, even if they were loaded. Even though from one engineer's view point dynamic brake was sufficient to control the train, they were probably added as a precaution in the event that the dynamic brakes failed.

BCHellman Wrote:
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> This discussion centers on the hopper cars used to
> aid in braking for 4014 movement. I cannot say why...

What bothers me about a lot of things today, and this whole "discussion" of the hoppers in particular is, that everyone seems to be expressing the attitude of "Don't think. Don't ever *think*. Someone else in the past thought once, and they doubtless did it better than you ever could, so there is no point in worrying your sorry stupid head trying to understand things your betters figured out and forgot a century ago."

That's fine for 50 years or so. Then all those people that knew how to think a century ago are dead, and all that we have left is a bunch of unquestionable government regulations and wife's tales telling people how to do things. Nobody knows WHY they say the things they do, and nobody cares why, because nobody dares think about it, because thinking is bad for modern Americans. After a while the technology we import from China changes (because they don't have our regulations and wife's tales, so can still think) and the old rules stop working quite as well. But all the people that made the unquestionable regulations are dead, and the knowledge is dead, and nobody understands it anyway, because thinking is bad for Americans, so is outlawed to protect them. So people start dying in droves by following a law they don't understand, until The Government saves the day by outlawing Chinese technology and going back to push carts and drags.

lwilton Wrote:
-------------------------------------------------------
> BCHellman Wrote:
> --------------------------------------------------
> -----
> > This discussion centers on the hopper cars used
> to
> > aid in braking for 4014 movement. I cannot say
> why...
>
> What bothers me about a lot of things today, and
> this whole "discussion" of the hoppers in
> particular is, that everyone seems to be
> expressing the attitude of "Don't think. Don't
> ever *think*. Someone else in the past thought
> once, and they doubtless did it better than you
> ever could, so there is no point in worrying your
> sorry stupid head trying to understand things your
> betters figured out and forgot a century ago."
>
> That's fine for 50 years or so. Then all those
> people that knew how to think a century ago are
> dead, and all that we have left is a bunch of
> unquestionable government regulations and wife's
> tales telling people how to do things. Nobody
> knows WHY they say the things they do, and nobody
> cares why, because nobody dares think about it,
> because thinking is bad for modern Americans.
> After a while the technology we import from China
> changes (because they don't have our regulations
> and wife's tales, so can still think) and the old
> rules stop working quite as well. But all the
> people that made the unquestionable regulations
> are dead, and the knowledge is dead, and nobody
> understands it anyway, because thinking is bad for
> Americans, so is outlawed to protect them. So
> people start dying in droves by following a law
> they don't understand, until The Government saves
> the day by outlawing Chinese technology and going
> back to push carts and drags.


Huh? What's this got to do with NBR?

lwilton Wrote:
-------------------------------------------------------
>
> What bothers me about a lot of things today, and
> this whole "discussion" of the hoppers in
> particular is, that everyone seems to be
> expressing the attitude of "Don't think. Don't
> ever *think*. Someone else in the past thought
> once, and they doubtless did it better than you
> ever could, so there is no point in worrying your
> sorry stupid head trying to understand things your
> betters figured out and forgot a century ago."

I don't believe anyone is trying to say this. There is a difference between knowing figures that are better off left to those who design or repair freight equipment, and that those numbers don't always transfer over to the operational end of the equation. If the numbers discussed were truly important in the operational end, then every engineer out there would be given a calculation of their train's brake ratio, rather than a tonnage profile that expresses the numbers in a fashion that is of far more practical use.

If anybody has "Trains Magazine" issues for Dec. 1975 and Jan. 1976, dig them out. There is a two issue article by David G. Blaine, called "The Westinghouse Air Brake Story" that offers one of the best reads about air brakes I have seen. I went into Engine service in Jan. of '79, and this article did more for my understanding of air brakes than the big green Santa Fe AB&TH book. It must have been popular, because Kalmbach published and sold the entire article in a booklet form a few years later. I highly recommend it if you can find a copy. Yes, it explains braking ratio.



Edited 1 time(s). Last edit at 01/30/14 15:52 by ddg.

>So in this case, it would seem to me that the loaded car has twice the retarding force of the empty car.

It doesn't because the brake system is designed up for a specific braking force when the car's empty. When loaded, the braking force stays the same, which means the braking ratio becomes more unfavorable, and the car is more difficult to stop.

This is a reason for the empty-load brake, which dates back as far as K triple valves of 100 years ago. With this, there was a second brake cylinder and a second reservoir which assisted the primary one when cut-in to give additional braking force (IOW, it increase the braking ratio). Some E-L brake systems use different means to do this. Their was either a manual change-over valve or air-operated load sensing apparatus to cut the secondary braking power in or out.

>Huh? What's this got to do with NBR?

My only comment is that it's quite amazing what those old timers figured out without today's fancy instrumentation. Other than this, I agree with you.

>I don't believe anyone is trying to say this. There is a difference between knowing figures that are better off left to those who design or repair freight equipment, and that those numbers don't always transfer over to the operational end of the equation. If the numbers discussed were truly important in the operational end, then every engineer out there would be given a calculation of their train's brake ratio, rather than a tonnage profile that expresses the numbers in a fashion that is of far more practical use.

Yes. People need to think in terms of "tons/operative brake" as a measure of how well your train's brakes are going to control your train (and your max speed on any given downhill grade) without resorting to all the arcana of braking ratios, adhesion, and so on. Doing so would be an exercise in futility, not to mention confusion (look what's going on here). Not only this, the locomotive engineer would actually have to have a mechanical engineering degree of sorts in order to figure out what TOB does so very simply.

Braking ratio is how many hours you work before you get a brake right?

I thought it was how many knuckles you "brake" compared to how many in the train. ;)

In the article I mentioned above, it has a little about braking ratio in the early days of modern air brakes. "Braking ratio, usually expressed as a percentage, is the force pressing the brake shoes against the wheels compared to the weight of the car. For easy comparison, braking ratio normally is stated at 50 PSI brake cyl. pressure". Goes on to say "empty car braking ratio of 100% is getting close to the ordinary wheel-on-rail adhesion. Based on much practical experience, and on testing by Westinghouse and others, the Master Car Builder's Assn. recommended a 70% braking ratio in freight service. Many roads braked their empty frt. cars at closer to 60%." (My old green Santa Fe AB&TH handling book from the 70's gave the ratios as 75% for empties, and no less than 18% for loads) What they are saying is, an empty car with a 70% braking ratio is being braked at about 70% of the force necessary to slide the wheels (around 100%) when that car is empty. When you fully load that same car, the ratio goes to about 18%, meaning the braking compared to the weight of the car is now only about 18% enough to slide the wheels on the heavier car. The flat spots you hear when the train rolls by are not caused by normal or emergency braking when empty, they are caused by dragging empties around with an overly tightened hand brake.