Physics of the Westinghouse Brake System

[k4kfh]

Discussion on the physics and math behind the brakes should take place here. Please feel free to comment; there is no wrong way to jump in and talk!

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Findings So Far

To keep things organized, discoveries and necessary information for the development of the brake system will be kept in this post.

Useful Papers

• NMRA Paper on Railway Brake Components (Freight and Passenger)
• Al Krug's "Freight Train Air Brakes of North America" - A copy hosted on third-party server since Mr. Krug's site is down

Brake Shoes

Typical Brake Pads have a coefficient of friction of 0.4 and the following dimensions:

• Length: 12"-16" (some very small locomotives may have 8" length pads)
• Width: 3 and 3/8"
• Thickness: 2"

Train Brake Line

The air signal propagates along the train line at ~920fps under ideal circumstances. To account for the imperfections of typical equipment, we will assume 900fps is the standard rate for a change in air pressure to travel along the brake line.

[k4kfh]

http://stoptech.com/docs/media-center-documents/the-physics-of-braking-systems will probably be useful in brake physics math. It explains how to take the linear force on the brake pads and convert it to a torque working to stop the rotation of the axle.

[k4kfh]

One example of brake pad area can be found here:

Product Sale Page
Product Data Sheet - Contains Area in cm^2

The brake pads being sold here, according to the data sheet, are available in 175cm^2 and 200cm^2 sizes.

[k4kfh]

Upon further searching, it seems that US railway brakes are more like the ones sold here. Another example can be found at New York Air Brake:

• NYAB Freight Car Brake Shoes
• NYAB Locomotive Brake Shoes

The message I'm getting from this is that the standard width is 3 3/8", the standard thickness is 2", and the length varies between 12" and 16" depending on the company and the applicaiton.

I have updated the standard sizes listed above to reflect these new numbers.

[k4kfh]

I found reservoir sizing info thanks to New York Air Brake.

Additionally, I found an excellent paper from the NMRA explaining several parts of the freight car brake system: http://www.nmra.org/sites/default/files/d9o.pdf

If NYAB's reservoir above (the auxiliary side) is treated as the standard size "main brake reservoir" on a freight car, using Al Krug's 2.5 ratio of brake reservoir to cylinder, the brake cylinder is 1000 cu. in., or 4 gallons.

[k4kfh]

According to Bruce Kingsley, older cast-iron brake shoes lose 10% of their braking power per minute due to heat losses.

[k4kfh]

This could be a useful forum thread: http://www.trainorders.com/discussion/read.php?1,2129770

On the old BN and most likely the new BNSF, the independent brake pressure with steel brake shoes was 45 psi. The composite brake shoes was 72 psi.

[k4kfh]

At least for the time being, most of the brake development is taking place in the psi-simple branch. Following Bruce Kingsley's advice, I am not using Boyle's law and/or actual pneumatic math in the simulation. There's no sense in constantly performing calculations that return virtually identical results, and using Boyle's law creates a need for many more functions and variables to keep track of the additional numbers. So I have opted to simple add and subtract PSI from variables, representing pipes, at a certain rate.