OK. I asked a similar question several years ago, but after more research I still don’t have a satisfying answer. So this time around, please bear with me as I give very specific details. Maybe that will help get the answer I need:
The short of it is that I’m trying to figure out how long an air compressor on a locomotive would take to bring the pressure in the brake system of a train from 14.7 psia (atmosphere) to 90 psia.
Suppose the train consists of 100 cars. Each car is 50 feet long. The main brake pipe has an internal diameter of 1 inch. Let’s call the piping on each car 60 feet long to account for secondary pipes, the additional length of hose to couple one car to the next, etc… Using the formula:
V = pi * r^2 * L
we can determine the volume of the pipe on a single car is 47.123 cu. in., or 0.027 cu. ft. (47.123 / 1728).
It is a pretty consistent fact in the railroad industry that each car also has a "service" and "emergency" air reservoir with a combined volume of 6000 cu. in, or 3.47 cu. ft. This give us a total volume per freight car of 3.499 cu. ft. Multiply that by 100 cars and the locomotive compressor needs to pressurize basically 350 cu. ft.
Now here’s where I have a problem: I have a locomotive manual sitting in front of me that says the on-board air compressor "capacity" is 254 cu. ft. / minute. My assumption (probably wrong) up to this point has been that the "capacity" is the pressurized output. But theoretically that would mean the entire 100-car train could be pressurized in about 1.37 minutes (350/254).
If the "capacity" is actually an intake figure, would there be a way to calculate the rate of outflow? Perhaps 254 cuft / [90psi / 14.7psi atmosphere] = 41.48 cuft / min outflow?
If the above is legit, that still only gets me half way to where I need to be. 350 cuft / 41.48 = 8.43 minutes. But all my research both via articles and talking to actual railroad engineers suggests it can take better than 15 minutes to pressurize the system.
Additional consideration is that a train almost never has just 1 locomotive. That 100-car train may have 3, each with an air compressor contributing to the system. Divide that 8.43 minutes by 3 contributing compressors and I’m back down under 3 minutes — WAY short of that 15-minute mark.
Can anyone shed some light on what I’m missing in my thought process? Thanks in advance.
Response to Ecko:
I know the train charge time isn’t properly provided. In part that’s because there is no single answer. There are too many factors — temperature, humidity, length of train, leakage in the connections between each car, etc… I’m just trying to get a ballpark formula. When my first-hand sources agree that 15 minutes is a reasonable time and the best I can come up with is 8 minutes, something has to be off in my assumptions.
The links you provided look very promising. Looks like I have a lot of reading to do 