BR Standard class 6 No. 72010 'Hengist' and Clan Discussion Thread

Absolutely. Power is defined as Force (tractive effort) x Velocity, but in circular motion it's Torque x Angular Velocity (basically rpm), so it's all related.

When we say Tractive Effort, most people assume Nominal Tractive Effort as quoted in their ABCs. In real terms, we should be talking about actual T.E. as delivered to the rails at specified speeds. With a steam engine, the actual T.E. is highest when stationary and falls exponentially as speed rises. That rate of decline varies with many parameters, wheel diameter being one of them.

 

I would have thought that maximum power output would be required when accelerating from a slow speed, or when maintaining forward motion on a bank.
Unless the railhead is dry and conditions perfect, would maximum power be achievable from rest without a slip?

The reason for my first sentence was a memorable trip on the NYMR a few years ago behind the T2... After departing Grosmont on a damp day, I listened to the beat from the first window all the way to Moorgates, and it was very slightly slipping, continuously, all the way from Grosmont to Goathland. It wasn't a wheelslip, but a steady pull right at the limit of traction. This, I think, was possibly maximum power being laid down onto the rails. The load was 7 Mk1s, and from the sounds being made, I would be surprised if the regulator wasn't wide open.

Richard.

 

It's quite common for regulators to be wide open with 7 on whilst ascending Goathland bank with the likes of the Standards, Black 5's and the S15 but not with the Q6. I usually drive it with the second valve part open and the reverser set at '3'. It doesn't have the cut off marked in percentage, just 1-5. How that relates to actual cut-off, I don't know but I'd guess about 45-50%

 

Whilst theoretically, a steam engine is a constant torque machine (unlike a diesel electric, which is constant horsepower), as LMS2968 says, the reality is that torque falls off with speed for several reasons. Without increasing adhesive weight, the higher tractive effort (torque) available is of little use when starting. The big advantage of a higher boiler pressure is that the torque-speed curve will be higher so the souped up Clan will produce a given torque at a higher speed with the operational advantage that brings.

 

Remember reading an account of a (probably overloaded) Clan struggling with keeping a train on time on some bank or other in Scotland, the steam was there and the adhesion was there but simply not enough grunt to beat the gradient and speed fell off ... will try and dig it out.

 

The theoretical stall load for any given loco on any given gradient is calculable. But not by me right now.

 

If said account pops out of the ether, any chance you've something on the performance of the Clans on their regular stamping ground of the Stranraer line (where crews had the opportunity to acclimatise to them)?

 

Will do over the weekend....
Wouldnt expect you to be able to do that in your head Sheff , even on paper there is only a predicted rather than an actual curve available for Clans

 

I see that the team are working on the front end at present. (https://www.theclanproject.org/Clan_News.php)

Both 'Plates for preventing down draught' are being worked on as well as the front apron and buffer beam.

The extension plates have been welded to the main plates for the 'deflectors'. There is a photo somewhere showing how the extension plates could be removed on shed to enable maintenance to the cylinders, is it anticipated that it would be easier to remove the 'plates' intact if such work is required in future?

 

Nice!

Looking at the revised CAD model, maybe you should try it with German (Witte) pattern deflectors...

 

Naah, that's not heresy ...... this is heresy => I was half wondering if any of the design tweaks would render deflectors unnecessary.

 

If I remember the report on the exhaust its not quite optimal but even so likely to be a little softer than the originals...

 

Wait until April the 1st for that one to be announced

 

Is that along with the red/black colour scheme...?

 

I have had occasion to spend a bit of time seeking to understand the tractive effort formula promulgated in the Ian Allan ABCs. The "Ian Allan" formula is the same as the formula used by the AAR although the latter used different constants for different loco types (the "85% of boiler pressure" used in the UK is a constant of 0.85 or 85%). To save readers looking up the formula it is (for a two cylinder loco): TE = (D squared x S x P x K) / W, where D = the cylinder diameter, S the stroke, P the boiler pressure, K is a constant and W is the wheel diameter. Depending on how you quote K the constant, you might have to also divide by 100. The concept seems reasonable - it is the force (pressure x area of the piston) acting on the crankpin which is geared down by the relationship of the crankpin's eccentricity to the wheel's radius (and to avoid using half the stroke and the wheel's radius, it compares the stroke to the wheel's diameter) which will always be less than 1. For a given piston stroke, the increased leverage arising from a smaller wheel diameter is apparent. Now an obvious issue is using D squared as a proxy for the area of the piston. Mathematically, a circle of diameter D has an area of approx. 0.78 x the area of a square of side D so to the extent that the formula seeks fundamental accuracy, it seems to overstate the value.

However, superficially, the calculation is of the TE produced by one cylinder, presumably on the basis that when the big end is perpendicular to the force through the connecting rod. the leverage of that crank is at its maximum while the other crank is on (or near) the piston centre line so is exerting little or no force. I think this situation is a simplification of the average force as if you plot out the values of the sine of the angle that the crank has to the horizontal and add the result of each crank together for each position, then the situation where one crank is perpendicular is the one which has the least combined leverage. I hasten to add that one can say that at a point in the stroke, the steam inlet will be cut off and, at a later point before the stroke is completed, the valve will open to exhaust, so to calculate the actual force at all points throughout a stroke is complicated. Presumably this is intended to be overcome, at least in part, by taking mean effective pressure (mep) as the pressure (i.e. K as a % of max boiler pressure). Potentially however, using one cylinder could be a factor tending to understate the result.

However, even at maximum cut off, 85% seems generous as a proxy for mep (mep is the area enclosed by the outline produced by an indicator diagram compared with the cylinder area (2 dimensional as indicator diagrams are 2 dimensional)). It will be seen that there is no component for speed in this calculation, but the reduction of TE with speed is caused by two factors: 1. as a matter of practice, the cut-off is shortened as the loco moves faster, which will reduce mep, and 2. the amount of steam admitted through a port is a function of both the area the port is open to steam (which area reduces with earlier cut-off) and the time for which it is open (which is affected by the speed of the valve - in Caprotti gear I believe the cut-off is adjusted purely by the time which the valve is open, the poppet valves always open fully) and a shorter time will also reduce mep.

Those familiar with indicator diagrams will know how the plot reduces from a rather plump area to a rather banana-like shape, although the power output is not in proportion to this. If you look at the indicator diagrams for the V2 in the relevant BR Performance and Efficiency Test, the diagrams are rather unequal for inside and outside cylinders (as you might expect with Gresley gear) but nevertheless, the loco produced 1740 ihp on rather anorexic indicator diagrams at 72mph at 22% cut-off. These reports also show tractive effort but the values are not given until around 20mph, the value then being nearly 26,000lb compared with the quoted TE of 33,750. The V2s were three cylinders of course and the result of the TE formula above is multiplied by 1.5 to give the notional figure. However, it does suggest that it may have been of similar order to the theoretical value at lower speeds, despite the apparent shortcomings of the formula.

 

That's a highly complex analysis of what is a simple formula which has been used by both the railways and industry almost since the inception of the steam engine (and not simply Ian Allan) to establish the average force at the point of application, which in the case of a locomotive is at the wheel rail interface or a mill engine at the driving ropes. It is very easily derived. If we have a cylinder of diameter d, the force acting on the piston is:

(Π x d x d)÷4. (a)
​

The average force acting on that piston is this area x the mean effective pressure (mep) and the force applied is mep x (a):

mep x (Π x d x d) ÷ 4. (b)
​

For one wheel revolution, each piston moves back and forth through one stroke (L) so the total distance moved is

2 x L. (c)
​

Therefore for the work done (force x distance) is (b) x (c) :

(mep x (Π x d x d) ÷ 4) x 2 x L. (d)
​

and for a two cylinder engine becomes:

2 x (mep x (Π x d x d) ÷ 4) x 2 x L which simplifies to mep x Π x d x d x L (e)
​

In one wheel revolution, the rim of the wheel of diameter D will travel :

Π x D . (e)
​

Therefore the average force at the wheel is (e) ÷ (f), which is:

mep x Π x d x d x L ÷ (Π x D) which simplifies to:

mep x d x d x L ÷ D
​

The unknown in this is the value of mep. The usual thing is to take this as being 85% of the maximum boiler pressure. This is a best guess based on a theoretical p-v curve of the cylinder at 75% cut off but there are many variables that can affect it. Thus, for a boiler pressure P we end up with a tractive effort equation of

0.85 x P x d x d x L ÷ D

With a three cylinder loco, this requires multiplying by 1.5 and with a four cylinder loco, 2.

Hunslet Engine Co. always took mep as being 75% of boiler pressure. I think the Midland did the same, as well. Not sure about other builders/railways. The small effect of the piston rod (and any tail rod) is always ignored

​

 

Thanks Steve, that is very helpful.

 

North British also used 75%.

 

New Zealand seems to have used 80%, judging by the figures in my copy of “The NZR steam locomotive”, except for occasional locos quoted at 75%!

Tom

 

I am still puzzling over why the varying angle of the crank does not come into this. When the piston is at front or back dead centre, the entire force on that piston is stretching or compressing the frames, without contributing any work to the wheel rim, and a component of the force will be doing this throughout the cycle apart from when the crank is perpendicular. Any thoughts?