Nominal Tractive Effort
Posted: Sat Dec 11, 2021 5:37 am
Modern locomotives have their true tractive effort measured in purely scientific terms and directly relate to their actual performance, but in the earlier days of steam when most things were done by ”rule of thumb”, a group of the then current locomotive engineers (known by various titles) frequently met to share many of their ideas one of which was about comparing the power outputs of of locomotives.
At a meeting of one of the many organizations, (others may have more details) in the early years of the 20th century a group of eminent locomotive engineers came up with a formula for this purpose. Although some had access to actual performance details via their newly established dynamometer cars and loco mounted indicators it was decided that a formula for calculating nominal potential performance could be useful using known specifications such as boiler pressure, cylinder size, number of cylinders and the driving wheel diameters.
The initial formula they agreed on was as follows based on 85% of boiler pressure (although some subsequently used 80 or 100% so take this into account when reading specifications)
.85 BP x bore squared x stroke (square pistons and rectangular cylinders?) multiplied by number of cylinders all divided by the wheel size.(BP was in lbs/sq inch and the others were in inches.)
When this was compared to actual data from the dynamometer car they must have found it to be about double the measured figure and it was decided to divide it by 2.
To give an example an 1899 NER class R 440 calculated by this method would show the nominal tractive effort as 31,134 pounds (lbs), but current dynamometer figures indicated a maximum pull of about 7 (then used, long) tons, i.e. 7x2240=15680 lbs, so it was probably decided to divide this calculated figure by 2 making a more realistic 15,567lbs.
The formula adopted -
.85 BP (in lbs per sq. inch) x bore x bore x stroke (all in inches) x number of cylinders.
Divided by the driving wheel diameter (also in inches)
Divided by 2.
i.e. .85 x BP x B x B x S x n All divided by 2
Divided by wheel diameter
I like to simplify this to what I call “the .425 formula” as follows-
.425 x BP x B x B x S x n
Divided by wheel diameter in inches.
Remember this figure is “nominal” only and actual performances were influenced by other factors such as restrictions in steam passages, limitations and state of boilers, advent of superheating, positive valve events, grate restrictions and other factors limiting or maintaining the accessibility of each locomotive to that estimated power .
Also good luck in calculating compounds !
PS- I have forgotten my formula for “adhesive factor” -can anyone refresh my memory?
Regards, Jon.
At a meeting of one of the many organizations, (others may have more details) in the early years of the 20th century a group of eminent locomotive engineers came up with a formula for this purpose. Although some had access to actual performance details via their newly established dynamometer cars and loco mounted indicators it was decided that a formula for calculating nominal potential performance could be useful using known specifications such as boiler pressure, cylinder size, number of cylinders and the driving wheel diameters.
The initial formula they agreed on was as follows based on 85% of boiler pressure (although some subsequently used 80 or 100% so take this into account when reading specifications)
.85 BP x bore squared x stroke (square pistons and rectangular cylinders?) multiplied by number of cylinders all divided by the wheel size.(BP was in lbs/sq inch and the others were in inches.)
When this was compared to actual data from the dynamometer car they must have found it to be about double the measured figure and it was decided to divide it by 2.
To give an example an 1899 NER class R 440 calculated by this method would show the nominal tractive effort as 31,134 pounds (lbs), but current dynamometer figures indicated a maximum pull of about 7 (then used, long) tons, i.e. 7x2240=15680 lbs, so it was probably decided to divide this calculated figure by 2 making a more realistic 15,567lbs.
The formula adopted -
.85 BP (in lbs per sq. inch) x bore x bore x stroke (all in inches) x number of cylinders.
Divided by the driving wheel diameter (also in inches)
Divided by 2.
i.e. .85 x BP x B x B x S x n All divided by 2
Divided by wheel diameter
I like to simplify this to what I call “the .425 formula” as follows-
.425 x BP x B x B x S x n
Divided by wheel diameter in inches.
Remember this figure is “nominal” only and actual performances were influenced by other factors such as restrictions in steam passages, limitations and state of boilers, advent of superheating, positive valve events, grate restrictions and other factors limiting or maintaining the accessibility of each locomotive to that estimated power .
Also good luck in calculating compounds !
PS- I have forgotten my formula for “adhesive factor” -can anyone refresh my memory?
Regards, Jon.