Scaling factors

[Bierjunge]

however I would like the paddles & hence engine to stop prior to engaging the ASTERN engine command
(...)
My question is...have I balanced the opposing forces adaquately...or is the kinetic energy TOO high?

Derek, I wouldn't worry too much about this:

- First you don't have "3.9 tonne of driven mass attempting to act as the brake...and ~~~3.4 tonne of rotating mass  in kinetic energy attempting to maintain revolving": The entire rotating mass is trying to keep its rotation, and on the other hand, the dynamic water drag forces, drivetrain friction, and, most important, cylinder compression, are braking....

- I you want to calculate it in detail (which I don't think is needed), you can't just take the masses of the revolving parts. You would have to use the moment of interia of the verious parts, which depends on how far from the axis of rotation their mass is distributed. Unit: kg * m², which leads to a scaling factor of length⁵ in our list of scaling factors (there was a little flaw concering this in my original list on top of this thread, which I just corrected).

- If everything behaved similar to the proptotype, then the revolution would stop in 1/(24^0,5) or ca. 1/5 of the original time. Accordingly, we could also interpret the Froude speed as time being scaled: Everything on a 1/24 boat happens 5 times faster than in reality: The boat running it's own length, one revolution of the wheels, a cornering manoeuvre of the boat, something falling from the upper deck, ....
You can therefore expect the wheel rotations to stop as well in 1/5 of the time compared to the prototype. Or even faster, because the friction of model engines and drive trains ins much higher compared to the real thing.

[sandy_ACS]

 

Hi PD's

This is fun is it not?


Firstly, Moritz, I am unable to furnish you with much data on the ‘Waverley’s’ paddle wheels other than they are 18ft (5.48metres) dia.

This, and other info quoted was obtained from the ‘Waverley’ website, but they don’t provide much more detail.



Derek’s PS DECOY calculations.

Now that is interesting Moritz, as we now appear to have got the paddle wheel rotation speeds into the generally accepted area, more or less,… i.e. 91 – 166 RPM.

So it would appear that just using the scale square root factor, as in my original calculations, does not provide a satisfactory wheel speed for a model.
It is very clear that much more account must be taken of wheel dia, linear speed/ circumferential speed etc, in order to arrive at a much more accurate figure for our model.

OK, now that we have some more accurate rotation speed figures to work with I thought it might be a good idea to use these to assess the steam usage, and also see the effect of changing something like, say working pressure, so: -

Lets take a look at the requirements for both 6:1 and 8:1 ratios, since these appear to be the preferred ones.

Since my steam tables are imperial, I will take the liberty of using this for the following calculations, hence 10mm bore and stroke become 0.3937” bore and stroke.
And, therefore, volumes etc will be in ‘cu ins’ rather than ‘cc’.


First we need to find out how much steam is required for each cylinder full of steam.

Cylinder swept volume = Bore area x Stroke

         = pi x 0.3937”2 /4 x 0.3937” = 0.048 cu in.

This is the volume of steam required to fill the cylinder when the piston travels from one end to the other (1/2 revolution)

 Since we have double acting cylinders (same amount of steam is required to drive the piston back again) so we need to multiply this by 2

         = 0.048 x 2 = 0.096 cu in per revolution.

We also have 2 cylinders so again we need to multiply x 2

         = 0.096 x 2 = 0.192 cu in per revolution.


So, assuming 100% steam cut-off (worst case) and probably more useful for small model engines anyway.
If the engine is of the oscillating type (or of the piston valve type using port reversal as a means of reversing the engine) this will be the case anyway, since these would have 100% cut-off (as near as) by design.
Slide valve engines can use early cut-off between (40% and 85% typically) they would certainly be operating at the higher end of the range for a good part of their work, so using 100% is not as big a problem for the calculations.

So how much steam is required?

Ok, this is where the paddle wheel gearing, and hence engine speed plays the major role in the calculations.

taking the figures provided/calculated by Moritz...

If we look at the 6:1 ratio: -
Wheel speed = 129rpm
Engine speed = 773 rpm

So for this case we need to multiply the revolution volume by the required rpm.

In this case this becomes = 0.192 cu in x 773 = 148.416 cu in/minute

         Which is 8904.96 cu in/hr

For the 8:1 ratio: -

Wheel speed = 149 rpm
Engine speed = 1191 rpm

For this case the steam consumption becomes: -
 = 0.192 x 1191 = 228.67 cu in/minute

Which is 13,720.2 cu in/hr

 

So what do these figures mean for the boiler?
How much water do we need to turn into steam? And at what rate?, in order to satisfy the above requirements.

The first criteria is the WORKING PRESSURE, since this has a big effect on the volume of steam available for each cu ins of boiler feed water evaporated.

With a working pressure of 1.5bar = (approx 22psi)…….. (why so low Derek)?

Each cu in of evaporated water can provide 691 cu in steam.

At 3bar pressure (45psi) this figure changes to 437 cu in steam.


We will look at the effect of this difference a bit later on.


To return to our calculations: -

To satisfy the 6:1 case (148.416 cu in steam/min) at a working pressure of 1.5bar (22psi) the boiler will be required to evaporate: -

         148.416/691 cu in water per minute

         = 0.214 cu in water/minute.

         = 12.84 cu in water/hour.

Which is approx equal to 209.959 grams/hour.

For the 8:1 case (228.67 cu in steam/minute) at the same pressure the boiler will be required to evaporate: -
         
         228.67/691 cu in water per minute.

         = 0.330 cu in water/minute.

         = 19.8 cu in water/hour.

Which is approx equal to 323.77 grams/hour.


The rate at which a boiler can evaporate water is directly proportional to the area of heated surface available, and for model boilers it is usual to use the figure of between 1 and 3 cu in per minute per 100square in of heated surface.
 
For a simple pot boiler the lowest figure would be use, whilst for a multi water tube boiler of, e.g. Yarrow type, the higher figure would be more appropriate.

For the purpose of this discussion I will use the figure of 1cu in evaporated per minute per 100sq in Heated Surface. i.e. the worst case.

So: - for the 6:1 case the required heated surface would be: -


Heated surface sq in =100/1 x 0.214  = 21.4 sq in.
 

And for the 8:1 case: -

   Heated surface sq in =100/1 x 0.330  = 33 sq in.   


NOTE WELL These figures represent the minimum heated surface requirements the boiler must have in order to meet the steam requirements at the required pressure if the evaporation rate is 1 cu in per minute per100 sq in heated surface.


Lets take a quick look at the effects of increasing the working pressure.

Lets take 3 bar (45psi) as the new working pressure: -

In the 6:1 case the cu in water/minute evaporation rate required would change to: -

         148.416/437 cu in water per minute

         = 0.339 cu in water/minute.

And the required HEATED SURFACE would increase to: -

         100/1 x 0.339 = 33.9 sq in. 


For the 8:1 case the cu in water/minute evaporation rate required would change to: -

         228.67/437 cu in water per minute

         = 0.523 cu in water/minute.

And the required HEATED SURFACE would increase to: -

         100/1 x 0.339 = 52.3 sq in. 
         
         
Derek’s boiler has a HEATED Surface area of approx 45sq in.

Therefore, given the above figures it would be ok for the 6:1 case but would fall well short requirement of the 8:1 case.
         
OK DEREK , PANIC OVER, you have nothing to worry about, since your boiler has an evaporation factor of approaching 2 cu in water per 100 sq in heated surface.
And anyway, you are running at 1.5 bar (22psi) not 3 bar (45psi), however, the figures do serve to illustrate that any given boiler has a maximum conversion rate and that it is not always obvious, to the un-initiated, why a seemingly small change (like increasing the working pressure) should make such a difference.

WARNING….Never, under any circumstances, change the working pressure (safety valve setting) of your boiler to a setting which is higher than that for which it is designed.
To do so could lead to a boiler failure and possibly a nasty accident.
Similarly, never attempt to use a larger burner in order to get more steam…. This will certainly overload the safety valve, which will not then be able to vent off overpressure steam volume fast enough to stay within the boiler certification requirements.
The burner fitted to your boiler, by the manufacturer, is carefully matched to ensure this requirement is met.

OK: -, to tie this together with Moritz’s figures for the 1.5bar (22psi) case lets adjust for 50% cut-off.

This is a simple matter of halving all the above results: -

Total cylinder Steam required was 0.192 cu in steam/rev.
This now becomes 0.096 cu in/rev.

So for 6:1

@773 rpm total steam volume required becomes 74.208 cu in/minute

Evaporation rate required becomes 74.208/691 = 0.1074 cu in water per minute.

                     = 6.444 cu in water/hour

                     = 105.372 grams/hour
and for the 8:1 case: -

@1191 rpm total steam volume required becomes 114.335 cu in/minute

Evaporation rate required becomes 114.355/691 = 0.1655 cu in water per minute.

                     = 9.93 cu in water/hour

                     = 162.375 grams/hour

These figures relate to dry saturated steam.


I will let you work out the ‘Heated Surface’ requirements; however, this should not prove to difficult.


Ok enough already

Keep happy.

best regards.

Sandy

[oldie]

After all that, I have decided to steer clear of steam and go back to `lectrics.   Oldie

[Eddy Matthews]

I find the whole thing fascinating..... I have to admit that I'm just assuming all the maths is okay as I don't intend checking it!

To be honest I never realised that steam engines were that complicated, with one tiny change affecting the whole setup - I take my hat off to those that have the skill to produce these things, and more so to those that can design them!

[Bierjunge]

After all that, I have decided to steer clear of steam and go back to `lectrics.

Oh dear, I've already had that concern that we might scare away some readers by too extensive calculations discussed coram publico.

Sandy, I appreciate your calculations leading to comparable results, but I abstain from commenting them here. I wut be just too boring for the rest of the readers to discuss all these numbers, I'm afraid.

Nevertheless, I'm attaching my little excel spreadsheet I've written to calculate just this kind of things. There are two pages, one for propeller driven ships and one for paddlers. You can insert the geometric data of engine and wheel or prop, and get results for speed, power and a very rough estimation for steam consumption.
After all, this is meant to make things easier, not to frighten people away...

I would highly appreciate if some of you could compare the results of my excel sheet to existing layouts to see if it fits or not.

Regards, Moritz

[Roderick Smith]

I have found it very interesting, but haven't had the time to digest it yet (and won't for a month).
Similar principles are required for miniature live-steam railway locomotives.

I haven't had the time to digest the material yet.  One problem with scaling is that some factors vary with length cubed; some vary with length squared.  Principles or proportions which work in full size won't work in scale.  This was introduced in high-school physics, explaining why Earth cannot be overun with gigantic spiders from outer space.  A 10-times bug-eyed monster would have a mass 1000 times bigger, but a leg strength only 100 times bigger; it could not support itself to go chasing beautiful earth maidens.  It does take skill to transfer the results measured in wind/water tunnel tests to the full size version when designing aeroplanes/ships.

I have yet to pore through the comments on predicting hull speeds and efficiencies of floats.  I can't see either being an exact science.  This is much the same as air resistance in a railway environment: there are lots of formulas.  There was a vogue for streamlining in the 1930s, but it didn't confer much in the way of practical benefit at level of speed which was common then.  In a boat, it seems that streamlining of the hull confers far more benefit than streamlining the body, so efficiency of thrusting water is far more important than air resistance. 

I had a lengthy discussion with a full size builder regarding the proportions for floats.  He looked at three moored nearby, asked me which was fastest, then noted that it was the one with the least power, but built with his float proportions.  When replica Lady Augusta was on its first voyage, the second day was spent trimming the floats.

There have been discussions on the benefits of feathering floats.  I don't know where the technique was used commonly in full size.  It seems that most modellers feel that either the complexity (or cost) is beyond them, or confers too little benefit to be worth the cost.  AFAIK most large prop-driven aeroplanes have feathering props.  One benefit is that they can be self-propelled backwards on the ground.

Regards,
Roderick B Smith
Rail News Victoria Editor

[sandy_ACS]

After all that, I have decided to steer clear of steam and go back to `lectrics.   Oldie

 

Hi PD's.

Oldie, don't you believe it my friend.....'lectriks' can be just as complicated...... try calculating all the effects of doubling the applied voltage to your lectrik motor.

result would be much the same as increasing the steam pressure in that you could need a bigger battery, and you may also need much heavier wiring and possibly a heat sink, or possibly even a larger motor.

Ok chaps, I agree it is time to put asside the heavy maths/theory stuff, for a while at least, but I am sure some of you will begin to appreciate the complexities involved when SCALE is involved.


Moritz, thanks for the spreadsheet I will play with it some more over the next few weeks.
The main reason for doing the steam calculations was to see how close 2 differing approaches to the steam requirements came to each other. I am sure you will agree that your model is well within acceptable probability.
Neither method will be totally accurate, sincce each installation will have many variable which differ from the next, so a ball park number is the best that can be achieved.

All great fun though, and a little more is learnt every time, which, at the end of the day, is what it is all for.

Roderick.

There have been discussions on the benefits of feathering floats.  I don't know where the technique was used commonly in full size.  It seems that most modellers feel that either the complexity (or cost) is beyond them, or confers too little benefit to be worth the cost.  AFAIK most large prop-driven aeroplanes have feathering props.  One benefit is that they can be self-propelled backwards on the ground.

Quite a few large paddlewheelers use feathering floats, but these are not the same as feathering props.

In their original form, feathering props on aircraft were used in order that, in the event of an engine failure, and hence, stopped engine, the blades of the propellor could be turned to a position directly in line with the airflow so as to reduce the drag.

Later,(during the 2nd world war), some bright spark, worked out that they could get better engine/thrust efficiency if the pitch of the propellor could be changed to suit different conditions... eg. take off, cruising, high speed etc. and the variable pitch propellor became the standard fitting on most types of prop driven aircraft, including single engined light aircraft.
Certainly the UK Lancaster heavy bomber, the American B52 bomber and some of the later fighter aircraft were fitted with them.

The logical next step was to be able to change the pitch of the blades far enough that the thrust was reversed... this was used extensively on VSTOL (very short take off and landing) aircraft, both large and small.

Quite a few smaller, screw driven, marine vessels were fitted with such variable pitch props, since it saved the extra weight necessary for reversing gearboxes etc, but I don't believe they found much favour for larger ships.

Ok chaps, I will leave it at that for now.

Keep happy.

Best regards.

Sandy.

[derekwarner_decoy]

Hi PD's....it is now one week since my communication request to JMC for his comment on speed reduction for his JMC3H engine......= no response....a little dissapointing.... ...but as expected......Derek

----- Original Message -----
From: Derek L Warner Pty Ltd
To: jmc
Sent: Saturday, February 16, 2008 10:02 AM
Subject: JMC3H


Marc de Jean de salutations... de Derek Warner en Australie
Mes collègues dans notre groupe modèle mondial de navire de palette discutent actuellement le rapport de réduction de vitesse de moteur de vapeur à l'axe de palette Je n'ai toujours pas fini mon modèle, mais enferme un jpg de ma installation de moteur de JMC3h Si vous seriez ainsi sorte pour offrir votre commentaire ou recomendation sur le rapport de réduction de vitesse de moteur de vapeur à l'axe de palette il serait le plus apprécié sincères amitiés Derek

[steamboatmodel]

After all that, I have decided to steer clear of steam and go back to `lectrics.   Oldie

The `lectrics guys can be more involved in the math, plus some of them use data loggers  http://www.eagletreesystems.com/ to either record or tramsmite on board conditions, some of them even have GPS units on board.
Regards,
Gerald

[Alan Haisley]

One factor that hasn't been considered here is the appearance of the paddlewheel(s). It seems to me that you need to decide which scale factor is more appealing, the motion of the boat through the water with the produced wakes and waves, or the revolving of the wheel. If I understand what has been written so far, it seems that you can't have both.

The wheel on a paddler is just so obvious that I'd think that having it spin at a non-scale rate would be unacceptable.

[derekwarner_decoy]

Hi PD's & welcome Alan...I quote a posting from our member 'Moritz' a few days back & we see scale wheel speed in RPM is considered.... one would conclude that these scale circumferential paddle speeds will produce both the scale vessel speed and semi scale wake & waves

According to the 40 photographs from 'Clyde River Steamers ...of the Last 50 Years' - M'Queen - printed prior to ISBN in Year 1923...most side wheelers appear to have produced one wake wave aft of the paddle to the stern, so with side wheeler paddles being covered the visual overspeed is of lesser consequence

Naturally I understand a model stern wheeler at any scale having a paddle rotation up to 200 RPM may look a little fast....

Quote from Moritz.....
In the following you get the results for different gearing ratios:
gear ratio 3 4 6 8 10 -
engine speed 273 421 773 1191 1664 rpm
wheel speed 91 105 129 149 166 rpm
circumf. speed 0,67 0,77 0,95 1,09 1,22 m/sec
prototype speed 6,4 7,3 9,0 10,4 11,6 knots
steam mass flow 64 99 182 280 392 grams/hour
output power 0,5 0,8 1,5 2,4 3,3 Watt

[derekwarner_decoy]

Hi PD's...finally received a response from JMC as below......

Translation.....for information, one should not exceed 80 revolutions per minute on the wheels. Unfortunately, I have more information not having never to manufacture paddle boats....... friendship
----- Original Message -----
From: jmc.vapeur
To: Derek L Warner Pty Ltd
Sent: Monday, February 25, 2008 1:02 AM
Subject: Re: JMC3H

bonjour

pour information , il ne faut pas dépasser 80 tours minute sur les roues. Malheureusement, je n'ai pas plus d'information n'ayant jamais fabriquer de bateaux a roue
amitié
JMC