Posted 16 December 2018 - 09:41 AM
Here are B&O's steam era guidelines for train handling in the friction bearing timeframe:
If temp was below 0 degree F - add 6 tons trailing weight per CAR
If temp was between 0 - 20 degree F - add 4 tons trailing weight per CAR
If temp was between 20-35 degree F - add 4 tons trailing weight per CAR
Regarding Steam locomotive themselves, I found this
I have added a "fudge factor" to my steam friction calculations. This is something that Joe Realmuto's excellent calculator does not account for.
According to numerous references in my collection of books pertaining to locomotive engineering, construction and operation,when calculating steam locomotive friction (resistance) an additional factor must be added to the standard Davis formula.
The Davis formula for locomotives is as follows, and is the basis for Joe's calculations ( and real world tonnage ratings ):
R=1.3T + 29N + 0.03TV + 0.0024CAV
Where
R=Resistance in lbs
T=locomotive weight in (US 2000lbs) tons
N=Number of axles
V=Velocity in MPH
C=Coefficient of friction ( air resistance )
A=Front area of locomotive in square feet
Now, here is the missing bit, quoting Ralph P. Johnson in "The Steam Locomotive":
"In calculating total resistance for the steam locomotive it is customary to use the same values for journal, flange and air resistance as the electric locomotive, but to add a constant amount for all speeds of 20 lbs per ton of weight on the driving wheels to cover the internal machine friction of the locomotive between the cylinders and the driving axles. The total gives the resistance at the rail."
(I can't cite the exact reference right now, but in a newer book in my collection it states that it is permissible to reduce this factor by 20% for engines with lightweight roller bearing rods ( N&W J Class and the last five A Class 2-6-6-4's 1238-1242 for example) and by 50% for those equipped with poppet valves and Franklin Rotary Cam valve gear (PRR T-1 and Q-2 Duplex locomotives for example ))
So the modified Davis calculation may be expressed as follows:
R=1.3T + 29N + 0.03TV + 0.0024CAV + 20D
Where D=the weight on driving wheels in tons.
Now, how do I translate this into the sim, and what is the effect of all of this stuff?
I want to use Joe's calculator and save myself the aggravation of hand calculating the Friction parameters for each engine so I came up with an idea. if I take the factor 20D, and divide it by 29, I come up with a number of "phantom axles" that when added to the total number of actual axles, will cause the calculator to add the additional resistance. I can bore you with the math, if anyone wants to see, or you can take my word for it.
Level track numbers for Union Pacific Big Boy where T=381 N=12 V=5 C=1 A=120 20D=5400, and the resulting Friction parameters from Joe's calculator:
Without the fudge factor: 907.65 lbs resistance:
MSTS Friction Value:
3750.8N/m/s -0.10 1.3mph 34.957N/m/s 1.631
Rolling Stock Type: Steam Freight Locomotive
Axles:12 Mass: 345.6 tonnes Frontal area: 11.15 m Cd: 1.00
Davis=Fcalc speed: 70 mph
RMS Error(2 mph to 80 mph): 44.6760 N
Maximum Error(5 mph to 80 mph): 92.57 N @ 80 mph
English Davis Equation(V-mph, R-lbs): R = 843.22 + 11.4287 V + 0.288042 V
Metric Davis Equation(V-m/s, R-N): R = 3750.81 + 113.7197 V + 6.411361 V
With the fudge factor (186.21 phantom axles): 6307.65 lbs resistance:
MSTS Friction Value:
27771.0N/m/s -0.10 1.7mph 11.096N/m/s 1.950
Rolling Stock Type: Steam Freight Locomotive
Axles:198 Mass: 345.6 tonnes Frontal area: 11.15 m� Cd: 1.00
Davis=Fcalc speed: 66 mph
RMS Error(2 mph to 80 mph): 247.2583 N
Maximum Error(5 mph to 80 mph): 506.06 N @ 6 mph
English Davis Equation(V-mph, R-lbs): R = 6243.16 + 11.4287 V + 0.288042 V�
Metric Davis Equation(V-m/s, R-N): R = 27770.96 + 113.7197 V + 6.411361 V�
As you can see, the there's a dramatic increase in the Friction parameters for the second calculation. (of course, the NALW Big Boy is in 2 parts in MSTS, so you would calculate each part using 1/2 of the "real world" values. )
The result is that the locomotive now pulls the "real world" rated load up the proper grade at a proper speed ( a walk instead of a trot, 8-10 MPH vs. 15-17 MPH ).
I have created 2 slopes in the sim, 1.14% to represent the Wahsatch grade out of Ogden and 1.55% to represent the "old line" over Sherman Hill, Westbound from Cheyenne.
The real world adjusted tonnage ratings were 4450 for the 1.14% and 3250 for the 1.55%, both with a car factor of 5.
The NALW Big Boy now performs prototypically on both grades with the rated load. It also handles a 3600 ton fruit block up the 1.14% at about 15 MPH as was the case in real life.
These are adjusted tonnage ratings. If anyone needs an explanation as to what are "adjusted tons", "car factors" and how to calculate, ask and ye shall receive. I can also provide some tonnage rating info for certain engines on certain grades, and am in the process of calculating ratings for various engines on various routes in the sim.