Talking Thermodynamics

[MJM460]

Hi Derek, thanks for the update, I will await with interest the outcome of further developments.  That pipe insulation looks really great

Hi Willy, more great experimental work.  Back to that in a moment.  Looks like the safety valve is a little erratic.  I wonder if it is a rough spot on the stem or something.  Though I don't have enough records to really know how repeatable the lift pressure can be expected to achieve.  Over speed trips on turbines were a bit like that.  Quite a range was allowed under the test codes, but we had to rerun the test until we had three non trending results.  Sometimes that took a while.  Don't know if the safety valve codes are similar. 

That is another interesting book.  Most books of previous generations had complex graphs like that, as there were only hand calculations, perhaps with the aid of a slide rule, so equations were not much help.  Now with the calculating power of a spreadsheet, the graphs are unnecessary, and an equation, even if it is quite complex, is much more convenient, and calculations easier to check or update for different scenarios.  However it is worth remembering the work of these authors, who did their work developing and using these graphs with limited accurate data.  These days we do indeed stand on the shoulders of giants as someone once said.

Hi again Derek, I am not a great fan of using percentages in relation to temperature and pressure.  Using a percentage implies not only that there is a linear relationship, but also that the linear relationship passes through zero.  For temperature, of course, zero means absolute zero, not zero centigrade.  Similarly, for pressure, absolute pressures needs to be used, not gauge pressure.  A simple test is to extend your example back to very low values.  For example is that temperature comment still valid between say 1 and 5 degrees, the same four degree difference.  On the other hand, when you are talking temperature difference, four degrees difference will usually mean twice as much as two degrees difference, for example in a heat transfer equation, whether you use C, F, R or K to measure the difference.

Now I think that Willy's boiler experiment warrants more examination before we get back to that engine output, so let's give it a try.  First, the answer to the issue of accuracy of temperature measurement is much simpler than I first thought.  If we look at the temperature difference for one minute, we take two readings each at best +/- 1 degree, and subtract them, so possibly at least two degrees error, a large portion of the 15 degree difference being measured.  However, if we ignore the first two minutes where things were clearly not linear, and the last readings where it is likely the safety valve was possibly leaking a little, we have a five minute period with a temperature rise of 82 degrees, but still only that two degrees error.  Much less significant in 82.  So we get around 16.4 degrees per minute average over that period.  This is probably a good basis for checking heat accumulation calculations and heat input.  But also shows your temperature meter is pretty good, so you can rely on it.

Now let's look at those results.  First, the latest run achieved 121 deg from 18 in 7 minutes, while the previous one achieved 120 deg from 17 also in seven minutes, the same temperature rise in the same time.  It looks like the water spilt was perhaps not so important after all, unless you spilt exactly the same amount again.  Then 587g from your 600 ml measure is very good accuracy.  Similarly there is no doubt about your insulation now, and surprisingly little difference between the last two results, unless the ends were insulated for both.  As you can see , once you insulate the boiler, it takes a lot extra to make a huge difference.

Now that cooling experiment, I am delighted that you included that.  I know what you mean about the water works, it catches up with many of us if we live long enough, but might as well get the extra benefit of the cooling readings.  This experiment is particularly interesting as it does not involve steam generation losses, and does not involve the heater with any associated errors.  The process is called Newton's Law cooling.  If you google it, and you will find a maths site from ubc in Canada, near the top.  Don't be put off by the word advanced in the title.  But it leads us through the calculations for a bowl of soup which are easy to use just by substituting your figures.  Basically it means the temperature variation with time is an exponential function, and yes, that is the correct description for this example.  The temperature change in each minute is dependent on the temperature difference.  So it reduces as the boiler cools.  It really assumes the ambient temperature is constant, so I assumed the temperature was 18 all night.  Perhaps not too bad if your house has some insulation, possibly some heating if it is cold, and perhaps a mild night.  But the result is useful even if the air cools a bit more overnight, it means the heat loss will initially be a bit more bit not important.  I can set out the calculations if you like, but for the moment, I calculated a temperature loss of 27 Joule/s at the start when the boiler was still close to 138 degrees.  Obviously much less at the end when the boiler was only 43 C.  Now these figures can be used as a very good estimate of the heat loss from the same boiler temperature during the heating phase.  Not only that, but they agree very well with the heat loss calculations I did earlier, when I wanted to check what those unaccounted for differences might be caused by.  Now the heat stored in the water plus copper is about 733 J/s, so the heat loss by two different methods is about 3%.  However at the start of the experiment, when the temperature is still low, the loss by both methods is much less.  Proportional to the temperature difference remember?  With the boiler at 43 degrees instead of 135, the temperature difference is only 25 instead of 117, so the heat loss would be around 5 Joules/s, so quite negligible.

Of course I actually needed to know if you did any significant steam production and hence reduced the water content of the boiler.  I assumed you stopped after the safety valve lifted, but if you ran the engine, the cooling experiment needs to know the mass of remaining water as there is less remaining stored heat to loose by cooling.  However, that only reduces the calculated heat lost by cooling so does not change the conclusion that the heat loss, once you added insulation, is insignificant.  At this stage, there is more than enough data.  I am very much of the opinion that the only way to really shorten your boiler heat up time would be to add extra heating elements, perhaps a longer boiler with two each end.  Or fill it with hot water from the jug.  I think the only thing you have not done is to generate some steam and determine how much water your boiler evaporates in a given time.  After all, this is the purpose of the boiler, and should give us a good idea of the size of engine it could drive.

That is enough for today, perhaps back to engines tomorrow.

Thanks for following along.

MJM460

[steam guy willy]

Hi MJM and Derek, yes the safety valve is about 8 years old so will need looking at....Thanks MJM for all the additional info however more questions.....First when the boiler is heated with an element that is linear ? the heat rise is linear !  However when it is cooled with a linear ambient temp the graph is as you say exponential ???? also i took more readings which showed my comment about the cooling was wrong !!This measuring was possibly quite an eyeopener for the early  experiementors and i wonder who came up first with the term exponential or was there a Mr/Herr/Mrs  Exponential that was about in the past ......Also when i got up about 12 i noticed the temp of the probe in the boiler was 19 C that i thought was a bit high,,,so i removed it and the temp shown went down to 16 C......I then replaced it and it returned to 19 c ?? i then removed it and it eventually went down to 13 C .!! here are some photos that show this  !!   So any ideas about this ??? Thanks for your time spent with all these queries and it is that question/answer graph coming into its own again !! More photos in the next post ....

[steam guy willy]

Hi...More photos and graphs........Also does an exponential graph ever reach infinity or zero ? When you have a room at ambient temp i think that everything in the room is the same temp, if you touch a bit of steel it feels cold because you fingers feel it as cold ,but if you touch say amber it feels less cold because you fin get takes more/less temp from it  ok...so does a temp probe act in the same way ? and does this explain/confound why the temp rises /falls when the probe is placed next to the copper.(cold) and placed on the  plastic covered wooden bench 9Not so cold, feeling) is this still thermodynamics or quantum mechanics that we are getting into !!??

[MJM460]

Hi Willy, I probably should have included the equation for that Newtonian cooling we were discussing yesterday, so here it is.

T(t) = T(a) + (T(0) - T(a)) x e^(-k x t)

As usual I should use subscripts, but on the iPad, it's too hard.  Read it like this :-

The temperature at time t, T(t) equals the ambient temperature, T(a) plus the difference between the initial temperature, T(0), and T(a), or (T(0)-T(a)), raised to the power of (that ^ symbol), minus k  x t.

Now this might need a bit more explanation.  That k is a time constant (not thermal conductivity) and t is the elapsed time in the units you choose, seconds, minutes, hours or whatever is convenient.  The units are not important, but will affect the value of k in your calculation, as it has units which must be based on the same time units.  Also, raising a number to a negative power gives the reciprocal of raising it to a positive power.  The symbol, e, is a well known standard mathematical constant, and is the base for natural logarithms, but that is another subject.  Your calculator has it, as does any spreadsheet program.

So, using any two coincident time and temperature readings from your cooling readings, you can determine k with a little simple algebra.  I used minutes and calculated k = 0.00496, using the times for 138 degrees and 43 degrees.  I spent a bit of time looking at the value of k in terms of the insulation conductivity, the convection coefficient, density, surface area and so on, but decided it was more complex than it was worth.  Unfortunately k is not totally a constant but to see how much it varies you would need a few more readings in the first 100 degrees of cooling to compare with the value I obtained and also to calculate more values from the last bit of cooling, a great job for a spreadsheet.  The formula is a mathematical equation which closely enough follows the same curve as the actual cooling, and does indeed predict infinite time for the boiler to reach ambient temperature.

However, in practice two things happen that mean the temperature is reached sooner.  First, even the equation soon predicts that the temperature difference is no longer large enough to be detectable.  You can calculate how long to get to 19 degrees, the smallest temperature you can measure with your instrument above the ambient of 18.  Second, and equally important is that particularly when you are talking about cooling times of several hours, the ambient temperature is likely to change, thus moving the cheese so to speak.  However the time constant, k is useful in indicating how quickly the cooling is likely to occur, the very low value in this case is caused by the insulation and means a long time to cool.  A high value would be found with no insulation and indicate a shorter time to reach equilibrium temperature.

When your steel and amber are in a room long enough to reach room temperature, as you say, they will all be at the same temperature as the room and almost everything else it the room, however your finger is not.  Your blood supply is trying to keep the finger up to about 37, though it often does not quite make it in cold weather as we all know.  So when you touch anything at 20 degrees, there is heat flow to the object controlled by the contact resistance of your finger, and the conductivity of the object.  Your nerves are close to the skin, again every day experience, so your finger can feel itself being cooled by the steel which of course conducts very well.  When you touch the amber, your finger is not cooled so much as the amber does not conduct so well.  The situation is controlled by the steady state heat flow from your finger which is receiving heat from your blood, to the object you touch.

The thermocouple is quite different as there is no heat source.  Heat only flows from the hot object it is placed against until the thermocouple reaches the temperature of the object it is touching.  So that time constant does determine the time it takes the thermocouple to reach the temperature of the object, when the zeroth law of thermodynamics says there is no further heat flow. 

There is a new one for you.  It really is called that.  While it was only clearly put into words after the first and second laws, logically it is necessary to have this one before you can properly deduce the others.  And it cannot be deduced from other laws.  Definitely still thermodynamics.  If you put some insulation outside the thermocouple so there is minimal loss to the outside air, and use it to hold the junction, or the sheath in the case of your instrument, in close contact with the object you want to measure, you will get both better accuracy and a quicker response to temperature changes.  Oh, and wrap the wires (or the part of the sheath, in contact with the air with some insulating material to minimise heat flow along the wires.  This dependence on conduction to make the temperatures equal is the reason temperature measurement always has a slower response than pressure.

It looks like consideration of engines will have to wait for another day,

Thanks for looking in,

MJM460

[steam guy willy]

MJM, thanks for this explanation and the thermometer is now reading the same both in and out of the boiler !! However i was surprised that it took 15-17 hours to reach equilibrium !! is this a record ? So let us continue with engines now.!!.....

[steam guy willy]

MJM, thanks for this explanation and the thermometer is now reading the same both in and out of the boiler !! However i was surprised that it took 15-17 hours to reach equilibrium !! is this a record ? So let us continue with engines now.!!.....
[/quote

Hi the next time i have 15-18 hours spare i may do the same experiment again and record the first 5 hours , and the remaining 5 hours to complete the graph !! So...with locomotives that stopped running at 11 Pm and then brought back into service the next morning to start running again say about 5 hours ,the boilers must still have been quite warm. And is there any data for this available ?

[Maryak]

Every steamship I have served in has hand easing gear for the safety valves. If the ship is sinking then releasing boiler pressure lessens the chance of an explosion when the flooding water reaches the boiler(s). i.e. it's part of the abandon ship routine.

Regards Bob

[crueby]

Every steamship I have served in has hand easing gear for the safety valves. If the ship is sinking then releasing boiler pressure lessens the chance of an explosion when the flooding water reaches the boiler(s). i.e. it's part of the abandon ship routine.

Regards Bob

Reminds me of an old ad I saw for the Sabino when it was being run privately before the museum acquired it. It had a line that: your ticket would be refunded if the ship sank!

[MJM460]

Hi Willy, I would be the last to suggest that anybody should sit looking at the boiler cooling for 15 hours.  Like watching the kettle boil, only not as exciting, especially with a metal kettle.   Time would be better spent smelling the roses, contemplating the mysteries of the universe, or having a snooze even.  No real imperative to repeat the experiment, which has already yielded sufficiently accurate excellent data, though if two or three readings happened between switch off before dinner time and bed time, the experiment would be complete, repeatability demonstrated and the data more than good enough for the purpose.  But you have already admirably and quite accurately demonstrated that the heat loss during heat up, even at the high temperature end, is only around 25 J/s compared with around 700 J/s stored in the water and copper, and is a fairly convincing demonstration that there is not much heat lost from the insulated boiler.   I am sure we can conclude that energy missing in the heat balance is just not being provided by the heating elements.

Now the more important next step is to remove that temporary insulation, and work out what you want to do as the permanent job, something more in keeping with the beautiful work you do on the engines.  Then, some convenient occasion, a few readings as the boiler cools by around 50 to 80 degrees would demonstrate the effectiveness of the final effort.  From your photos, I would suggest some thinking about how to reduce the heat loss from the ends, where there seems to have been no insulation at the start of this work.  And I would even leave thicker insulation on the shell to your next boiler, rather than disturb that nice brown cladding.  You have done a great job of some real science there, and enabled us all to learn from your work.  And I feel that you have also made this thread better for your participation and insightful questions.

Your boiler is very well insulated, the only aid to cooling is the steam pipe coming out, like a small cooling fin, a fired boiler has a cooling air flow due to stack draft unless the airflow is deliberately closed off, perhaps for a quicker startup the next day.  Also I don't know how much of the locomotive boiler outline is actually insulated.

Hi Maryak, I hope that was not the only time they were used.  In any case they would need regular testing.  You would not want to find it rusted up when the big day came.  More seriously, especially on steel boilers, the thermal stresses due to the sudden asymmetrical cooling might actually crack those early steels before tougher steels and impact testing were as widespread as today.  In which case, better to have minimum pressure.  So the procedure makes sense.

Hi Chris, did they also offer to dry your clothing?

Ok, so back to engines.

It is worth giving some thought to what that work calculated from the experimentally observed supply and exhaust steam actually means.  The steam tables are considered an accurate model of real steam behaviour down to the level of accuracy implied by the four significant figures tabulated.  You will appreciate by now that has taken some very precise experimental work by dedicated researchers.  Also, the first and second laws of thermodynamics, and that zeroth law, are well established fundamental laws of physics that allow us to calculate those useful extra properties of enthalpy and entropy.  The point is that that calculated work from the observed temperatures and pressures is real, within the limits of accuracy of the instruments used.  I have done the calculations to the limits of the tables, as it makes them easier to check, but have no illusions about the accuracy of my simple test setup.  So without putting too fine a point on the meaning of the last significant figures, let's accept that it is a reliable measure of some quantity of real work done, by real steam in a real engine, and look a bit closer at what it means.

Before there is any of the work available at the shaft, the steam has to overcome the pressure on the exhaust side of the piston, which is pushing the opposite direction.  Also it has to overcome piston friction against the cylinder wall and friction in the rod seal.  Then the  cross head guides, the two conrod end bearings, eccentric strap friction, another pin, valve rod packing and the friction of the valve on the valve face.  So many more unknowns, and when I list them, I am amazed that in a small engine running on such low pressures, even with no extra shaft load, that there is enough work from the steam to run at all.

I know that some have doubts about that exhaust pressure.  But I am coming at this from first principles, applying the relevant laws of thermodynamics.  The pressures are absolute pressures, as this is the relevant pressure when the work done is calculated using the fundamental formula for work.  Work = Force times distance.  In the cylinder, Force on the piston = pressure times area.  So work by the steam is pressure times area times distance, the distance being the length of stroke.  That work is done by the steam.  You then have to start again to calculate the work done by the exhaust steam on the other side of the piston.  And due to the force directions, the net work on the piston requires subtracting the exhaust side pressure from the power side pressure. 

Of course, if you have a single acting engine of any kind, or if you have atmospheric exhaust pressure, you can take a mathematical short cut and use gauge pressure on the power side, then ignore the exhaust side.  It is the same as assuming exactly atmospheric pressure for the exhaust, but you risk missing any effect of the time it takes for the exhaust side of the piston to reduce to atmospheric pressure after the preceding power stroke.  You also potentially hide the understanding of what is going on.  This is probably acceptable for a single acting engine, but as we have seen, this can lead to significant oversights in a steam engine for the exhaust stroke of the cycle, though it is still a suitable calculation for a double acting engine when calculating power through indicator diagrams, as the exhaust pressure is then properly accounted for.

All the sources of friction I have mentioned, and there are sure to be some I have missed, meaning that we still don't know the shaft power output of the engine.  We still have to do an engine test to find what power is available at the shaft.  However the theoretical analysis does give us a real figure for the maximum power output that can be obtained from a real engine under any observed  steam conditions.  If you go on to calculate the overall thermal efficiency, is a discouragingly small figure, but when you know just how much of the steam energy must be carried away in the exhaust steam, it is not surprising.  I hope you can see that there is some justification, when talking about an engine, to talk about adiabatic efficiency.  An engine test which actually measures torque and rpm is still not going to give a very high figure, but it will be a lot more encouraging to compare it with an adiabatic process than the overall thermal figure.

Well, can we make any estimate of all those mechanical losses?  I suppose that we could devise a complex range of experiments and tests to quantify some of those losses.  But not many of us, including me, will be sufficiently motivated.  However, I think there is one thing we can do. 

When we run the engine unloaded, all the work done by the steam is used in overcoming all the friction.  If it runs at constant speed, then there is no excess power at the shaft under those conditions of steam and exhaust pressure and temperature.  It there was any excess, Newton's laws say that the engine will accelerate.   So by measuring the engine rpm, we can say the friction at that time is equal to the work done, and we can make an assumption that that is representative of the friction resistance at that speed.

Next time, let's look at that a bit further, to see of there is anything else we can infer from that suggestion.

Thanks for looking in,

MJM460

[steam guy willy]

Reminds me of an old ad I saw for the Sabino when it was being run privately before the museum acquired it. It had a line that: your ticket would be refunded if the ship sank!

Hi Chris , yes, but was there some small print that said   "only the distance not travelled on the ship will be refunded " !!!

[steam guy willy]

Hi MJM, Thanks for your latest observations .I have now removed the clumsy insulation and may do another cooling graph showing the initial cooling figures without it. Are there reverse steam tables available showing the cooling cycles ? Also are there available port sizes available for different sorts of engines, Condensing /Compound/ triple expansion,  etc etc ? Also would needle roller bearings help with efficiency that are available in comparable sizes with sintered bronze bushes ? .....I have just given my temp gauge to an 11 year old boy to stick into anything and everything he can find, except his younger sister ,of course !! the new generation of thermodynamic engineers is on the way ?!!!...........also.. what temp does copper /steel/ brass have to be to not feel cold to the touch ??..

[MJM460]

Hi Willy, the cooling graph with only the original insulation will be most instructive to compare with the values obtained for your temporary insulation.  Looking forward to the result, if you can get that temperature instrument back.  Ah well, a second one is always useful!  Good idea to give it to him.  The boss' grandson came in to work for secondary school work experience, and I was surprised to find that he not only had never had technical Lego or Meccano, but he also didn't have a voltmeter.  It was a bit cheeky of me, but I called in the boss and told him I had solved his Christmas gift problem, the boy needs a voltmeter, after all the boss was also the chief instrument engineer, and some technical Lego.  Unfortunately, Meccano is not as readily available these days.  But how will STEM education progress if kids don't have voltmeters and other real technical toys.  Unfortunately the same answers from all the kids coming in for a week to see if they would like to choose an engineering career!

Don't need reverse steam tables.  Steam tables list steam properties at various pressures and temperatures.  The characteristic of a property is that it just depends on the measurable states at the time of measurement, and does not depend on how the substance got to that condition.  Like  your height above sea level.  It does not matter whether you came up hill or down to get to your location, nor whether you came from East or West.  When you stand at that little surveyors mark in the pavement near your home, you are always at the same height above sea level.  So if you have steam at 100 kPa and 103 degrees C, you don't have to know how it came to be that way, you just look in the tables to find that it is superheated, the specific volume, internal energy enthalpy and even entropy.  It does not matter if it is engine exhaust, or if it got there by being heated.  In fact the tables are even more reliable than your height above sea level, as even an earthquake, continental shift or climate change cannot change the values.

Port sizes for engines are just about velocity as we have already discussed, and the shape of the transition between different flow areas.  The flow area, gives the velocity from the steam flow and volume which you need to estimate or predict on some way for each port.  Smooth transitions reduce energy losses.  Of course the shape of the cross section will need to be made suitable for the valve shape and movement, but overall you are aiming for that compromise between pressure losses and excessive volumetric clearance.  In most cases, you make the passage as large as other considerations allow.

For any material not to feel cool, it has to be the same temperature as your skin so there is no heat flow.  Obviously your skin temperature is not quite at blood temperature so there will always be some heat flow until objects are at 37 degrees.  But as the objects get close to this, the object will obviously feel warm your skin, so will feel warm until there is equilibrium from the object through to your blood vessels.  I am not quite sure just exactly what point this would be.  And I guess there is a small heat flow that will not produce a temperature difference you can feel, so there is probably a small range where it feels neither warm nor cool.  Time to put a temperature controlled heating element in a block of steel and set that boy to work as your laboratory assistant.

Needle roller bearings, right on topic with that one, I think I have answered it below, let me know if more information is needed.

So far, we have seen that we can show real work being obtained from a real engine, and that in a simple unloaded test run, all that work is used in overcoming friction.  No problem for an exhibition, it is easy to apply a bit more pressure if necessary to make the engine go the speed we would like, and many previous threads show that we all appreciate that running on lower pressure is a good thing, and a compliment to the quality of our work.

Is it possible to use this unloaded test run data as an estimate for the engine friction load for other load conditions?  At the limits of my comfort zone here, entering a new area of application for all that has gone before together with a few other basic principles.  So let's have a look at a few questions that might help us.

Does this friction vary with speed or steam conditions?  Generally, friction load is roughly proportional to the load causing the friction.  So for example the force pushing the the valve against the port face varies with pressure.  This means the valve friction load varies with steam pressure.  The size of the valve has to be sufficient to cover the ports as necessary for proper operation, but any excess area obviously increases the force and therefore the friction at the port face.  Various valve designs have been tried to balance this load and some are almost certainly applicable in model sizes, especially for larger models.

What about all those bearings?  Willy has mentioned needle roller bearings.  Ball or roller bearings both replace sliding friction friction with rolling friction.  We all know that reduces friction, that is why  the wheel was such a great invention.  I think we can take a lead from Professor Senft's work on his LTD Stirling engines, that ball bearings make a worthwhile reduction to the friction when you literally only have candle power (or less) to run your engine.  But these bearings also bring complications.  Heavier loads require lubrication, and that brings a need for dust seals, seals add friction, so a little care is required with the details if we are to benefit.  But almost certainly worthwhile for a model engine as opposed to a model of a historical prototype.  Ball bearings involve a close approximation to a point contact, and this limits the load capacity, as the deformation at the contact point introduces fatigue which limits the life of the bearings, and this becomes significant at higher loads.  Rollers have closer to a line contact, so are able to support much higher load for a given life before the surface fails and the bearing becomes noisy and friction increases.  But with due attention to the details, ball or roller almost certainly offer an area for friction reduction, which of course leaves more of the work done by the steam to be available for shaft work.  Have a look at Beson and Rayman's trials with flash steam for an example.

I don't know much about sintered bronze bearings, but I assume the big advantage is more consistent lubrication by oil seeping through the pores of the sintered structure.  And good lubrication certainly reduces friction. Oh course poor lubrication would do the opposite, neither dry running, or in-appropriate lubrication by say a heavy grease would help one of those LTD engines run well.

Next time I will look at the cross head loads, another interesting area.

Thanks for looking in,

MJM460

[steam guy willy]

Hi MJM  thanks for all this ,but i do feel a bit like that annoying kid at the front desk in the class that stops the other kids learning by rote and keeping the teacher on his toes/knees instead of keeping to the allotted time in the curriculum  !! would a bit of lubricated steam leakage help lessen friction ? or is this a further case of diminishing returns !!so only one question for today/night....Thanks

Willy....

[MJM460]

Hi Willy, please don't let up on the questions, I have never been one for rote learning.  All those hours we all spent reciting times tables were a real waste, but when you think about it, the teachers had very little in the way of resources, calculators were only a very dim gleam in someone's eye, and no one dreamed that our primary school kids would be walking around with more calculating power in their hands than the Apollo team had to send Neil Armstrong to the moon.  And without those things, there was very little in the way of other tools for the job.  Not much point starting on a slide rule even until you get a bit past the adding and multiplication tables.  Fortunately they can now skip the rote learning, use a calculator, and start learning how to use it and how to use and check their spreadsheets.  At least I hope that is what they are doing.  If not, surely they soon will be.

So it is no use me rabbiting on about some esoteric issue, if no one has understood the first point.  And many others will have the same questions you re asking.  So keep them coming.  It keeps my feet on the ground.  If I can explain a few basic principals to those who are interested, I will have made a good contribution in return for some of what I have learned from all the others generous enough to post their efforts in such an instructive manner.  I don't have a syllabus or timetable to meet.

The displacement lubricators we put in the steam lines just put that little smear of oil into the cylinder that helps reduce friction against the cylinder walls, the valve and port face and the rod packing, similarly the oil we put on the bearings and slides, and it is all very necessary.  Running on air, I know industrial tools have an oiler in line, but I don't know how well they work when running an engine on air at much lower flow rates and pressures.  My full size reciprocating compressors actually inject oil through the cylinder wall to lubricate the rings.  A short post tonight, extended family duties suddenly call.  Expect to be back tomorrow.

MJM460

[MJM460]

Continuing on looking at the various friction loads on our engines. 

I should have mentioned when talking about those bearings, that the friction torque is a function of pressure on the piston, though using ball or roller bearings reduces this significantly from what would be expected from a plain circular bush.  I specifically say circular bush, as that is what we normally use when we drill or ream a hole for a bearing.  With a little oil, the pin can tend to ride on the oil film to reduce the torque more than you might expect from metal on metal friction considerations alone.  Some industrial bearings achieve even more load carrying capacity by using a non circular bush, a lamellar bearing I think it is called, a bit lemon shaped.  Oil builds a wedge between the shaft and the bush and the shaft rides like a hydro planing tyre on the oil film.  Tilting pad bearings have even higher load capacity, as the bush is divided into three or five pads each mounted so it can tilt slightly to the optimum angle for the oil film load carrying capacity.  Of course these bearings have a copious supply of oil supplied at pressure to ensure adequate lubrication.  Very heavy shafts even have high pressure jacking oil to lift the shaft off the bearing for startup.  And a very recent development in turbo machinery is the active magnetic bearing, where the shaft is suspended magnetically so there is no friction even from a thin oil film.  A bit like those desk top pen stands where the pen is suspended magnetically. Sophisticated electronics actively measure the shaft position throughout each revolution and vary the magnetic field continually to keep the shaft on centre.  I doubt that this technology will be available for modellers in the near future, though with the speed of development in electronics, who knows.  Not really in keeping with a traditional steam engine though.

Cross head loads are due to the sideways component of the conrod load when the con rod is at any angle other than in line with the piston rod.  Like the bearing and valve face loads, it is proportional to the force, which in turn is proportional to the operating pressure.  Not a steady load, it varies from zero to a positive and negative maximum each revolution as the conrod and crank angles change.

As we think about all these different friction sources, they are pretty much all proportional to the steam pressure in the valve chest or on the difference in pressure between the upper and lower piston faces.

The power absorbed by that friction for linear motion is force times velocity.  For rotary motion, it is torque times rotational speed.  For rotational speed, the appropriate units are radians per second, which means that we have to multiply our normal units of rpm by 2 times Pi, and then divide by 60.  So power = 2 x Pi x N x T/60.

We had better look at the velocity component of those friction forces.  Do the forces and torques vary with speed?  The normal friction model taught is that the magnitude of the friction force (in the direction resisting motion) is a constant times the normal force.  The constant is called the friction factor, and there are tables of typical values in many books.  However a more sophisticated model includes a stick-slip component when motion first starts.  Then the model talks of static friction which has to be overcome before movement starts, followed by dynamic friction which is a little lower while the motion occurs.  For the intermittent motion occurring in a reciprocating engine, obviously both come into play each stroke.  But I believe that the dynamic component does not vary greatly with speed.

Based on that very simple analysis, I suggest that we can assume that the friction force and torque are constant with speed, but increase in proportion to the absolute steam pressure.  The power, of course is directly proportional to speed, so power is proportional to pressure and speed.  If this assumption is reasonable, we can possibly use the simple unloaded engine test with the steam temperature measurement to make an estimate of the friction load, and when combined with a simple test of steam consumption, perhaps make some estimate of the power potentially available at higher pressure.  I don't know if it is of any practical value, as we don't usually have any better idea of the power required by the load, whether it be a generator or propellor, or a miniature sawmill.  But it's an interesting thought.  It does allow us to make some estimate of the division between engine friction load and the driven load, which may be of some interest.

Definitely at the boundaries of my comfort zone with regard to the application of this basic friction model to our model world, so time to harness our collective knowledge and understanding, to see if we can take this any further. 

Obviously a load test with torque and speed measurement gives the only definitive answer to our engine power output, however a careful analysis of what we know can help us understand the most productive aspects to work on to improve the power output of our engine, especially one just about good enough, but a bit borderline.  We may be able to improve an otherwise satisfactory model instead of having to start again.

My intention is to do a few more tests on my engines to confirm the reliability of the data, and I have made a start on gathering materials to make a simple engine brake for torque measurement.  But until I have something to report, I will move on.  If anyone else tries some tests, please tell us about your results.

Well it has taken quite a while to get to this point, but there at last.  Obviously a great point for more questions, then I will see where I can apply some thermodynamics to boilers and fuels.

Thanks for following along,

MJM460