Calculating Tractive Effort for steam locomotives

[Wile E. Coyote]

I used following formula to calculate max. momentary power:

A=pV

P=A/t=pV/t

with t=1s (work in the one unit of time, like SI-definition) I obtained some results which are in some boundaries of real results (for example, for H&S 33 I obtained 1500 KW, comparing to real 1620), but you must use them with big reserve.

Michael, I know there were used experimental dynamometric equipment (specially equipped train and laboratory rolls). AFAIK German rail company had such equipment. Could you tell more about that?

[michael blunck]

P=A/t=pV/t

Do you mean "power" = dW /dt? (W = "work")

And what values are you using there? p = "pressure"? V = ?

Just to keep you informed that I´ve begun working (again) on this particular problem, but be assured it´s a big mess.

I still don´t get my feet on the grounds in developing a good formula for steam locomotive power, which - in addition - is in good correspondence with values found for "steam locomotive power" in technical manuals or in railway books, or elsewhere on the internet.

Moreover, I have a serious feeling that "power" for steamers is in no way correctly calculated in TTDPatch (nor in OTTD), unlike power for diesels and electrics.

More to follow, hopefully.

regards
Michael

[Wile E. Coyote]

P=A/t=pV/t

Do you mean "power" = dW /dt? (W = "work")

And what values are you using there? p = "pressure"? V = ?

Yes, power is dW/dt (t-time) (I used SI-marks for measured units above)
And work is calculated by p * dV, where p is pressure, and V is volume.

Alternative method could be P = F * v (P-power, F could probably be tractive effort, and v is max. speed), which is also shown in Wikipedia as power at rail, but it's obviously different from maximal power.

I know it's not precise formula, mainly because by SI-definition "work is obtained by myltiplying pressure by change of volume" (and here obviously V is not equal to dV), and many other factors are involved in power, (main factor is quality of coal IMO). I'm just trying to estimate power using raw physics laws.

[michael blunck]

power is dW/dt (t-time) (I used SI-marks for measured units above)
And because work is p*dV, p is pressure, and V is volume of cylinders.

Alternative method could be P = F * v (P-power, F could probably be tractive effort, because it's motion force, and v is max. speed).

Although the physical derivation of "power" would be easy: P = F * v -> F * s / t, resp. P = W / t, calculating the correct value for a steam engine is far from trivial.

Firstly, F isn´t constant. In the case of "tractive effort", F would be largest for v = 0, dropping for increasing speed. Same goes for "pressure". Pressure on piston isn´t constant either (hence usually a pV-diagram is used to determine W), and in fact, you´re not using "V" (cylinder volume) but rather A (piston area, a constant value) * S (piston stroke), S being indeed part of a different calculation, namely "piston speed", for which only a mean value can be calculated as well.

I.e., one way to calculate power for a steamer would be "the physical way":

P = F * s / t -> F * v -> p * A * v

i.e.

P = n * pm * A * vm

with

n = number of cylinders
pm = mean pressure on piston
A = piston area
vm = mean piston speed

The other way I´d like to call the "thermodynamic / heuristic" way of calculation, and can be found in ancient steam locomotive building literature. Here, calculation would be based on factors like "heating surface", "grate area", etc, to calculate the quantity of steam the boiler of a locomotive would be able to generate, and then to establish a relationship between this value and the locomotive´s mechanical properties (driving wheel size, piston size, ..).

I.e., something like

P/H = <factor> (<type> - n/<factor>) * sqrt(n)

with

H = heating surface
n = revolutions of driving wheels per minute
<factor> and <type> being some coefficients describing properties of the locomotive in question


Nevertheless, "power" of a steam locomotive depends on "speed", and I´m unsure to which speed the values for power given in the literature are related to. Max speed? Normal travelling speed? Something else?

And then, if we´ll have a good formula, we still don´t know how all those values for steam locomotive power found elsewhere had been calculated in the first place. Hence no possibility of comparison.


Apart from that, I suspect the calculation for steam locomotives in TTDPatch is generally wrong. Because a steam locomotive, in contrast to a diesel or an electric locomotive, is a "constant force engine" (i.e., as long as you affect the same steam (mean) pressure against the piston faces, the same force is produced regardless of the locomotive´s speed), whereas diesel and electric engines are "constant power engines". That difference should be clearly noticeable on grades, e.g.

regards
Michael

[krtaylor]

Actually, that's a good point: this discussion isn't just an arcane detail, it actually would make a noticeable difference on grades. However, if I'm interpreting it correctly, it would make steam locomotives worse on grades. This, I think, is a bad idea, because unlike in a real railroad, we don't have control over the steepness of grades - they are what they are, which is really steep. Making steam locomotives respond to them realistically (even if this could be done) would excessively handicap steam, and make the beginning of the game a great deal more difficult.

[michael blunck]

[...] if I'm interpreting it correctly, it would make steam locomotives worse on grades. This, I think, is a bad idea, because unlike in a real railroad, we don't have control over the steepness of grades - they are what they are, which is really steep. Making steam locomotives respond to them realistically (even if this could be done) would excessively handicap steam, and make the beginning of the game a great deal more difficult.

Well, first of all, I´ve always been arguing for the introduction of more "realism" into this game, simply because it will add (and it proved that in the past) more variety. Especially "realistic acceleration" is one of TTDPatch´s great features, which not only allowed to have many engines which hadn´t been possible to include otherwise, but opened a whole new approach to track building and train composition.

Granted, by calculating steam locomotives more "realistically" they would be weaker on grades as now, when hauling too heavy loads.

OTOH, there would be means to cope with this drawback, which are both "realistic" and would enhance gameplay even further:

- you may (have to) use lighter trains in mountainous regions,
- you may (have to) use additional engines in these trains (bankers, helpers),
- you may (have to) build your lines with more regard to topography. I.e., you may avoid having two (or more) consecutive slope tiles,
- you may (have to) use more specialized locomotives, and thus powerful but slow "mountain locomotives" would gain more interest than now.

Speaking for myself, I´d like to introduce an interesting powerful locomotive like the Bavarian Gt 2x4/4 Mallet, which would make sense only for such a specific "niche". And o/c, new "limitations" like this could spur further interest in a more "automatic" handling of bankers/helpers, as already suggested a couple of times before.

Nevertheless, I don´t think that a modification of steam locomotive kinematics will happen in the very near future. It´s just that I noticed that wrong behaviour when re-thinking the whole problem of calculating steam locomotive power.

regards
Michael

[krtaylor]

- you may (have to) build your lines with more regard to topography. I.e., you may avoid having two (or more) consecutive slope tiles,

I've got no problem with that solution at all. However, my point is that if steam loco power is handled realistically, this won't be a workable solution.

In real life, you have the option of making the grade exactly as gentle as you want, based simply on how much banking and excavating you are willing to pay for. You can make the grade suit the power of your locomotives and the loads you expect them to haul.

In TTD, however, you can't. Grade steepness is not a continuum as in real life, but specifically metered step changes. It is not possible to have a grade that is less steep than one tile. So, if you have a loco that in real life could perfectly well handle a fairly moderate grade, but cannot handle the preset steepness of a one-tile grade, then you have created a situation where that loco, though "realistic" in performance, will be unrealistic in usability because of the grade limitations of TTD.

And that's what I want to avoid, for the reasons you give: we want the game to be as realistic as feasible. We recognize that there are certain compromises that have to be made because of the limitations of TTD, such as for distances and times - the distance and time are greatly foreshortened to make the game playable. The same is necessarily true for the grades.

But if you want to improve the realistic handling of grades that are 2 or more steps, that's fine - because even in TTD, you can avoid 2-step grades with a little engineering.

[athanasios]

I think it doesn't worth the effort, unless we get more smooth slopes, something I believe will never happen in Patch and maybe after many many years in OpenTTD.

regards
athanasios

[Snail]

Let's get back on topic...

I have another question, how to calculate the TE of an Engerth locomotive? I would like to add a 042 of this type to the French set...

[ostlandr]

Actually, what real railroads did (well some of them- the smart ones) was to change the variable for driver diameter. Figure a 300 RPM "sweet spot" in the HP/TE band for a steam locomotive. (Max HP is at max RPM.) Smart mechanical officers spec'd the drivers for the speed the loco would normally operate at, to stay in the "sweet spot". So a switching, logging or mining locomotive that never operated above 30 MPH would have very small drivers, to keep the driver RPM in that sweet spot (and also increase max TE.) A freight locomotive operating regularly at 50 MPH would have larger drivers, sacrificing some TE for higher speed.
500 RPM might be the "redline" above which the locomotive would be damaged, so for a passenger loco, you would spec a passenger loco for huge drivers to the max speed you need while staying under the 500 RPM redline. The locomotive would only produce it's max horsepower at max driver RPM, but this was okay for a passenger locomotive where aerodynamic drag and friction become factors.

Anyway, to my point, it doesn't make much sense to use a steam locomotive with a top speed of 75 mph on a string of ore hoppers whose bearings will overheat above 50. Maybe if I can figure out NFO coding and "borrow" DanMack's regearing wizardry, I can start with something like a grf to make the original TTD steam engines regearable, using the forumulas on this thread to recalculate the TE for different driver sizes. Not going to change horsepower, as that was dependent on the other variables. Anyway, I hope the result is steam locos that can be geared for higher TE (giving better acceleration) at the expense of top speed. Conversely, this would mean that the fastest steam locos would have terrible acceleration and climbing (pretty accurate.) So, for heavy passenger trains that stop a lot (local service) you may want to lose that 110 mph top speed. OTOH, for a "limited" passenger train that doesn't stop often (if at all) go for all the speed- if the trip is long enough, the slower acceleration will be made up by the higher top speed.

[...] if I'm interpreting it correctly, it would make steam locomotives worse on grades. This, I think, is a bad idea, because unlike in a real railroad, we don't have control over the steepness of grades - they are what they are, which is really steep. Making steam locomotives respond to them realistically (even if this could be done) would excessively handicap steam, and make the beginning of the game a great deal more difficult.

Well, first of all, I´ve always been arguing for the introduction of more "realism" into this game, simply because it will add (and it proved that in the past) more variety. Especially "realistic acceleration" is one of TTDPatch´s great features, which not only allowed to have many engines which hadn´t been possible to include otherwise, but opened a whole new approach to track building and train composition.

Granted, by calculating steam locomotives more "realistically" they would be weaker on grades as now, when hauling too heavy loads.

OTOH, there would be means to cope with this drawback, which are both "realistic" and would enhance gameplay even further:

- you may (have to) use lighter trains in mountainous regions,
- you may (have to) use additional engines in these trains (bankers, helpers),
- you may (have to) build your lines with more regard to topography. I.e., you may avoid having two (or more) consecutive slope tiles,
- you may (have to) use more specialized locomotives, and thus powerful but slow "mountain locomotives" would gain more interest than now.

Speaking for myself, I´d like to introduce an interesting powerful locomotive like the Bavarian Gt 2x4/4 Mallet, which would make sense only for such a specific "niche". And o/c, new "limitations" like this could spur further interest in a more "automatic" handling of bankers/helpers, as already suggested a couple of times before.

Nevertheless, I don´t think that a modification of steam locomotive kinematics will happen in the very near future. It´s just that I noticed that wrong behaviour when re-thinking the whole problem of calculating steam locomotive power.

regards
Michael

[DaleStan]

Maybe if I can figure out NFO coding and "borrow" DanMack's regearing wizardry,

I'm pretty sure that's Pikka's wizardry. Anyway, it uses CB36 in conjunction with CB19 and var F2.

[michael blunck]

Well, I don´t see much use in "re-gearing" steam locomotives, because "re-gearing" in this case would mean a change in driving wheel sizes, something which would be quite uncommon.

In fact, as ostlandr pointed out again, driving wheel diameter is a decisive criterion in steam locomotive design, determining basic properties of a locomotive like tractive effort, speed and fuel consumption, and even more basics like locomotive dimensioning, wheel base length, etc.

I.e., a fast passenger steamer would be designed as a relatively light engine with a smaller number of driving axles with a large wheel size (> 2 m), and OTOH, a heavy freight steamer would be configured having a large number of driving axles with a small driving wheel diameter.

how to calculate the TE of an Engerth locomotive? I would like to add a 042 of this type to the French set...

I don´t see any special problems with an Engerth type? IMO, you´d only need to add part of the tender weight to the locomotive driving axle load, but it shouldn´t affect the drive itself, like e.g., it does for a "real" articulated engine like a Mallet.

regards
Michael

[Snail]

how to calculate the TE of an Engerth locomotive? I would like to add a 042 of this type to the French set...

I don´t see any special problems with an Engerth type? IMO, you´d only need to add part of the tender weight to the locomotive driving axle load, but it shouldn´t affect the drive itself, like e.g., it does for a "real" articulated engine like a Mallet.

Well, I can understand what you say if we use the formula for the TE starting from adhesive weight. The latter would increase, and so would the TE. If we adopt the one starting from the locomotive specs (TE = D² * S * const * p / d), though, the additional effort of the tender driving wheels is ignored. But this contrasts with one of the very reasons of building locos of the Engerth type (higher TE).
Moreover, in this case we would have two sets of driving wheels (those of the loco and those of the tender), with possibly different diameter. What should "d" be in the formula? I guess the average of all of the driving wheels' diameters, weighted by each axle weight?...

[michael blunck]

I don´t see any special problems with an Engerth type? [...]

Well, I can understand what you say if we use the formula for the TE starting from adhesive weight. The latter would increase, and so would the TE. If we adopt the one starting from the locomotive specs (TE = D² * S * const * p / d), though, the additional effort of the tender driving wheels is ignored. But this contrasts with one of the very reasons of building locos of the Engerth type (higher TE).

Well, no. As already written in my posts above, weight on the driving axles allows TE to be exerted. And BTW, that´s why it´s called "adhesive weight". And o/c, it´s an important part of the calculation: first we´re calculating the amount of TE which could be produced by having cylinders with certain dimensions charged with a certain pressure and transformed by a certain gear ratio (driving wheel diameter) and in a second step, we´ll have to calculate which fraction of that amount of TE could be transfered to the rails by taking into account adhesive weight and friction.

And exactly in this way, the weight of an Engerth-type tender adds to the adhesive weight and hence to TE of the locomotive.

Moreover, in this case we would have two sets of driving wheels (those of the loco and those of the tender), with possibly different diameter. What should "d" be in the formula? I guess the average of all of the driving wheels' diameters, weighted by each axle weight?...

AFAIK, that´s a misconception. Although, Engerth´s original design indeed included an indirect drive from the main driving wheels to the tender wheels, this arrangement turned out being too complex to maintain and was dropped at an early stage (already during those Semmering trials?).

And even the remaining design wasn´t successful at all. Both French Nord and Est, as well as German (Bavaria, Saxony) and Austrian Railway companies (Südbahn) rebuilt them into ordinary tenders very soon. But neither French nor German railways ever used Engerth-type locomotives with powered tenders (AFAIK).

regards
Michael

[Snail]

Well, no. As already written in my posts above, weight on the driving axles allows TE to be exerted. And BTW, that´s why it´s called "adhesive weight". And o/c, it´s an important part of the calculation: first we´re calculating the amount of TE which could be produced by having cylinders with certain dimensions charged with a certain pressure and transformed by a certain gear ratio (driving wheel diameter) and in a second step, we´ll have to calculate which fraction of that amount of TE could be transfered to the rails by taking into account adhesive weight and friction.
And exactly in this way, the weight of an Engerth-type tender adds to the adhesive weight and hence to TE of the locomotive.

Right... I forgot the fact that we need to calculate both numbers, and take the minimum between the two.

AFAIK, that´s a misconception. Although, Engerth´s original design indeed included an indirect drive from the main driving wheels to the tender wheels, this arrangement turned out being too complex to maintain and was dropped at an early stage (already during those Semmering trials?).
And even the remaining design wasn´t successful at all. Both French Nord and Est, as well as German (Bavaria, Saxony) and Austrian Railway companies (Südbahn) rebuilt them into ordinary tenders very soon. But neither French nor German railways ever used Engerth-type locomotives with powered tenders (AFAIK).

Well, yes, I also read the same. That's why my plans were to add it, maybe with a higher TE if it resulted from the calculation, but with a higher maintenance cost to counterbalance it and to add some realism. It's true that they weren't successful, but this shouldn't be a reason not to give them a try in TTD; if we only include highly successful vehicles, we'd lose some realism and we'd fall into survivorship bias.

About the TE calculation, I read the way you got the TE for that Serbian Mallet engine. So, if I'm not wrong, TE there has to be calculated the same way as for a compound engine, right?

[DanMacK]

The equatiion I've been using is HP=SpeedXTE/375. That gives a reasonable idea of HP.

Speed is, as ostlandr said, a vatriable factor. Basically the speed used is the one where the locomotive is at its most efficient and HP and TE are in sync before the TE starts to go down as speeds rise.

I normally use hte following: 20MPH for switch engines, 25MPH for freight engines and 35MPH for passenger engines.

Passenger engines usually have a highre HP and speed but lower TE than a freight engine.


Once again, it's all variable, and adjustments may have to be made for gameplay.

[michael blunck]

[Engerth-type steamers]

[...] my plans were to add it, maybe with a higher TE if it resulted from the calculation, but with a higher maintenance cost to counterbalance it and to add some realism. It's true that they weren't successful, but this shouldn't be a reason not to give them a try in TTD; if we only include highly successful vehicles, we'd lose some realism and we'd fall into survivorship bias.

Well, as a set designer you may include any vehicle you like from whatever reason, or even by no reason at all.

In any way, it would be easy to set the stats for such a locomotive, especially if you have values for adhesive weight.

About the TE calculation, I read the way you got the TE for that Serbian Mallet engine. So, if I'm not wrong, TE there has to be calculated the same way as for a compound engine, right?

Because most Mallets are compound engines, they´re calculated as compounds. In the rare event where this isn´t the case, you may simply calculate them as plain steam locomotives.

regards
Michael

[ostlandr]

It was uncommon to change the driver diameter after a locomotive was built, but not unheard of. The NYC "999" world record locomotive had it's tall drivers replaced with shorter ones when it was downgraded to freight service, and that's what it wears today in the Museum of Techonolgy in Chicago, IL. Rather, what I'm talking about is ordering a locomotive with a certain driver diameter. What makes this possible is that the overall diameter of the wheel changes, but the position of the crank pin doesn't. So it's basically a simple operation (this being a relative term dealing with steam locomotives) with the limiting factor being the position of the boiler above the frame. A passenger locomotive would have the boiler raised to clear its tall drivers. Conversely, a freight locomotive would have a lower boiler, limiting the max driver size. But within a range, it's possible to change driver sizes, and it was possible to order a "standard" locomotive with various driver sizes depending on its intended use.

Well, I don´t see much use in "re-gearing" steam locomotives, because "re-gearing" in this case would mean a change in driving wheel sizes, something which would be quite uncommon.

In fact, as ostlandr pointed out again, driving wheel diameter is a decisive criterion in steam locomotive design, determining basic properties of a locomotive like tractive effort, speed and fuel consumption, and even more basics like locomotive dimensioning, wheel base length, etc.

I.e., a fast passenger steamer would be designed as a relatively light engine with a smaller number of driving axles with a large wheel size (> 2 m), and OTOH, a heavy freight steamer would be configured having a large number of driving axles with a small driving wheel diameter.

how to calculate the TE of an Engerth locomotive? I would like to add a 042 of this type to the French set...

I don´t see any special problems with an Engerth type? IMO, you´d only need to add part of the tender weight to the locomotive driving axle load, but it shouldn´t affect the drive itself, like e.g., it does for a "real" articulated engine like a Mallet.

regards
Michael

[ostlandr]

OK, I'm stumped. How would I go about calculating the TE for a geared steam locomotive? I know that you multiply the torque by the gear ratio, but the old brain is tired. Can I just divide the driver diameter by the gear ratio?

If somebody feels really generous, here is the problem I am trying to solve:

This is a theoretical "future tech" steam locomotive I am working on. It has 6 HP and 6 LP cylinders, in opposing pairs with the cranks set at 120 degree intervals. EDIT: This is an odd configuration- in each pair, the HP cylinders are facing the crank, and the LP are on the outer ends away from the crank.

HP cylinder area is 0.2025 sq meters (x6)

LP cylinder area is 0.09 sq meters (x6)

Stroke is 0.6096 m

Boiler pressure is 20.68427188 bar.

Driver diameter is 1.016 meters- BUT there is a 4:1 gear reduction between the engine and the drivers.

Help!

[DaleStan]

BUT there is a 4:1 gear reduction between the engine and the drivers.

If my recollection of physics is accurate:

Ignore that. Run the calculations without the gear reduction.
Then divide the speed by 4 and multiply the force (TE) by 4. Power remains unchanged.