Help with Tractive Effort/Tractive Force Calculator

[LMS2968]

1 hour ago, PenrithBeacon said:

There are times when you are infuriatingly condescending. I'm not just on the right lines, everything in my post is simply a rephrasing of the historical records at Kew. You could make the effort yourself.

 

The formula for calculating the tractive effort does include the speed of the engine and when that speed is zero tractive effort is zero. The nominal speed is conventionally considered to be 4mph and that is the figure used in the Ian Allen books.

 

As to the way that BR(S) classified some, but not all their engines, eg 7P 5FA the A (or B) is an index of how well, or not, a locomotive could brake an unfitted train. It has nothing to do with actually moving the train. Some locomotives did have the B allocated eg 2P 2FB for the E4s but by no means all had this form written on cab or bunker.

Thank you for that, so much for trying to assist.

 

I'll grant that zero mph is a speed, but one of the assets of a steam engine, and very much the opposite of an internal combustion engine, is that it produces its maximum torque - and tractive effort - at zero rpm, and of course zero mph. It's power output which is zero at zero rpm.

 

The explanation, assuming you want it: power is defined as torque x angular velocity in circular motion; force (tractive effort) x velocity in linear motion. Anything multiplied by zero comes out at zero, so the maximum T.E. x zero mph gives a power output of zero horse power.

[Compound2632]

4 hours ago, 34theletterbetweenB&D said:

True for saturated operation only, and something of an article of religion among those not fully at home with the benefit of superheating.

 

Ah well, I'm always thinking in terms of 19th century locomotives.

[PenrithBeacon]

2 hours ago, LMS2968 said:

...

 

The explanation, assuming you want it: power is defined as torque x angular velocity in circular motion; force (tractive effort) x velocity in linear motion. Anything multiplied by zero comes out at zero, so the maximum T.E. x zero mph gives a power output of zero horse power.

Having been an engineer for most of my working life I think i'm only too aware of this, and my post should have provided you with the clues that I have that knowledge, assuming you have the nous to work things out. Your last sentence is very much a duplicate of one I posted. 

 

Essentially the power classification system for steam locomotives is a way of conveying the power of a locomotive without expecting those at the front end to have to work it out from scratch every time. Although the manager in charge of a shed would have that knowledge, most were very educated men, those employed on the footplate or the traffic office would probably not have the technical education to be able to do it. Which isn't to say that they wouldn't be able to decide, empirically, whether a locomotive would have been able to carry out the task allotted to it. This, of course, calls into question the need for such a system anyway.

[Nearholmer]

It’s a ready-reckoner, for use bu controllers, shed staff, timetable/diagram compilers etc etc, just like SLUs (standard length unit) for vehicles, or any number of other useful approximations that make running a railway easier/possible.

 

While it may be derived from physics and engineering, a lot more than that went into tweaking it for workability.

[Compound2632]

20 minutes ago, Nearholmer said:

It’s a ready-reckoner, for use bu controllers, shed staff, timetable/diagram compilers etc etc, just like SLUs (standard length unit) for vehicles, or any number of other useful approximations that make running a railway easier/possible.

 

While it may be derived from physics and engineering, a lot more than that went into tweaking it for workability.

 

It's rough and ready because of the approximations in the physics.

 

Now, consider a perfectly spherical shedmaster...

[LMS2968]

34 minutes ago, Compound2632 said:

 

It's rough and ready because of the approximations in the physics.

 

Now, consider a perfectly spherical shedmaster...

The Fat Controller?

[RLBH]

 

On 03/02/2020 at 13:04, PenrithBeacon said:

The formula for calculating the tractive effort does include the speed of the engine and when that speed is zero tractive effort is zero.

 

Given that the parameters of the standard formulaare limited to the number, bore and stroke of pistons, the boiler pressure, and the driving wheel diameter, I'm curious how speed or free gas area might appear. If you have another formulation featuring these, please do share it. Sadly Kew is about 400 miles away, and my employer takes a dim view of disappearing off to London to check such things.

 

Certainly the LMS system adjusted for speed - strictly, for piston speed - by means of an estimated mean effective pressure as a proportion of boiler pressure. There's a copy of the relevant curves - as well as the BR formulae and associated tables - in Ransome-Wallis's Last Steam Locomotives of British Railways.

 

On 03/02/2020 at 17:32, PenrithBeacon said:

This, of course, calls into question the need for such a system anyway.

I've always understood that it was primarily a management figure - Control didn't necessarily need to know precisely what locomotives a shed had on hand, just what trains they could pull. Any locomotive with a power class of 4F ought to be able to handle any freight train with the corresponding rating, and so forth.

[DenysW]

I'm afraid I'm joining this rather late, but here goes anyway. And, for the avoidance of doubt, I don't actually think I'm actually disagreeing with any of the posts. Patronising - you can make up your own minds.

 

I came across this graph on Catskill Archive which adds a rule of thumb on heating area (max 2.5 hp per sq-ft, but - empirically - lower at low speeds) to the starting tractive calcs discussed on this thread. So the family of curves ask you to divide the starting tractive force by the heating area, and then use the curve for that number at your target speed to get a de-rating factor. Sparately, a  cutting-edge 1906 paper from Iowa asserted 2.3 hp/ft-sq had 'recently' been measured by the Pennsylvania Railroad, so even these curves are a bit rubbery and technology dependant. They are also for simple expansion, saturated steam. The suggestion for compounds and superheated steam was to add up to 20% to the available power. A second caveat was that the grate and the fuel supply to it were not limiting. The third one was an adhesion factor of at least 4:1 weight:tractive force.

 

Is this the type of calculation the the Midland used to get its power classifications? It would give differences at 25 mph and 50 mph that are not obvious from the simpler formula that only uses cylinder and driving wheel dimensions plus boiler pressure.

 

O.S. Nock in "British Steam Engines" states that you can calculate the starting tractive effort using the formula Corbs started this thread with, but that so many factors affect the tractive effort at speed that the only true answer is to measure it using a dynamometer car. I do not believe that the Midland (or LMS, or BR) carefully measured every class of locomotive they'd build or inherited, so I suspect some approximation like the graph above.

[Compound2632]

See the discussion around about (before and after) this post, which altogether gives the full method for the LMS calculation: