Paddleducks

Other Marine Models => Live steam => Topic started by: Bierjunge on February 14, 2008, 06:54:21 AM

Title: Scaling factors
Post by: Bierjunge on February 14, 2008, 06:54:21 AM

In http://www.paddleducks.co.uk/smf/index.php?topic=3260.msg14305 , Derek had written:

Quote from: derekwarner_decoy

To this point, would you consider posting a listing of 'scaling attributes' for vessel modeling? as I am sure many [including myself] are sometimes confused.....like
 
scale speed = the ? [function of the real vessel speed x the ?? function of  scale]
scale displacement =   the ? [function of the real vessel displacement x the ?? function of  scale]
scale revolutions = the ? [function of the real vessel wheel RPM  x the ?? function of  scale]
plus any other scale conversion values you think appropriate to our craft

I am not Ivor, but I had made some own thoughts on this topic of scaling factors, which might hopefully be intersting for others as well:

In the following, I am referring to the model scale as "length scale".
A model in 1:100 scale is 1 m long, if the original boat is 100 m long.
Then we get for all sorts of physical properties:

rotational speed	scale to the power of -0,5
acceleration	scale to the power of 0
velocity	scale to the power of 0,5
length; pressure	scale to the power of 1
area, surface	scale to the power of 2
volume, mass, force	scale to the power of 3
performance	scale to the power of 3,5
torque	scale to the power of 4
momentum of inertia	scale to the power of 5

A few examples:

The displacement is scaled by the cube of the length scale: A battleship of 10.000 metric tons displacement as 1:100-model weighs 10 kg.

The velocity is a bit tricky:
Model railroaders, for example, scale the velocity by the length scale, to achieve the same optic impression (same wheel speeds etc.).But this leads to some conflicts with the time scale. But anyway, it would be far too slow for our model boats:
Instead of 30 km/h of the original, the 1:100 model would travel only 0,3 km/h (yawn), and the wave pattern would be too flat.

To achieve a scale wave pattern, the model speed is scaled according to Froude by the square root of the length scale: Our 1:100 example boat now travels 3 km/h.
By the way, the so called hull speed (maximum speed achievable without planing) is calculated as 4,5 km/h times square root of hull length. This also proves that speed has something to do with square root of length scale.

Velocity leads directly to rotational speed (of scale propellers or paddlewheels), if we assume scale slip and thread of the propeller or wheel.
These turn by the square root of the length scale faster than the prototype: If the propeller of our prototype battleship turns at 100 rpm, then the prop of the 1:100 model should turn (at least) 1.000 rpm.
By the way, the same factor applies to the pitch, yaw and roll motions of the scale
ship.

Dependent on the speed is the ram pressure, which acts on the front of the hull, on the propeller blade or the wheel bucket:
Because the velocity acts square in the ram pressure, the pressure itself is scaled by the length scale.
That's cool, because then the water columns being piled up by the bow or the wheel bucket has scale height. But that's no wonder, because the main motivation of introducing Froude speed was to achieve scale waves.

Ram pressure and area lead to the resistance force: Scale to the power of 3, which perfectly matches the weight force as well.
But also the centrifugal force acting on propeller blade tips or buckets is scaled this way, if scale rotational speed (see above) is kept.
In this case, the tendency of wheels to water clog their houses should be similar to the prototype. Amazing, how well everything fits together!

Weight and length, or even ram pressure, bucket surface and wheel diameter lead to the torque. This is scaled by length to the power of 4.
But only in few cases the torque of the prototype engine will be known, unless you calculate it from power and speed, or cylinder dimensions and steam pressure.

And finally, from resistance force and velocity, or from rotational speed and torque, you get the engine performance: length by the power of 3,5 (which already I.K. Brunel had found...)!
This means: A battleship of 10.000 kW would need as 1:100 scale model only one single tiny watt for scale speed!
Other example: A 1:32 torpedo boat of originally 1.000 kW needs around 5,4 W shaft power.
But this assumes the same efficiency of the drive train, so you practically should keep some power reserves (not only for the case of dog or swan attacks...)

Enough theory for now...
Regards, Moritz

Title: Re: Scaling factors
Post by: derekwarner_decoy on February 14, 2008, 04:27:53 PM

Hi PD's & thanks Moritz for your comments...I will print them out & try to digest & :ranting understand them

Ivor has come back off line & advises he will pen a few notes, however similar to your commments...sometimes water & scale can seem to defy the laws of physics

regards

Title: Re: Scaling factors
Post by: Bierjunge on February 14, 2008, 10:25:01 PM

Quote from: derekwarner_decoy on February 14, 2008, 04:27:53 PM

Hi PD's & thanks Moritz for your comments...I will print them out & try to digest & :ranting understand them

It is difficult to explain such a complex topic in just a few lines. If you have any specific questions, just feel free to ask! Then I will try to explain it a little better.

Moritz

Title: Re: Scaling factors
Post by: sandy_ACS on February 15, 2008, 09:13:00 AM

 ;D ;D

Hi PD's,

Well,  :squareone after a bit of a problem logging in (my fault :-[ :-[ )... forgot my own log in info, here is something to think about.



Scale paddle speeds?

Whilst I am in total agreement with Moritz regarding the scaling factors he has put forward, one, in particular, requires some further input/study…. Namely rotational speed.

I have no issue with the case of standard propellers (screws), since the results from many hundreds of models clearly show that the typical figures he suggests/calculates are true, however, I am not entirely convinced in the case of paddle wheels.

If we consider that, for the majority of cases, we would consider the rotational speed for model paddle wheels to be between 80 – 150rpm (typical average speeds as stated in many posts on the subject) to be the norm.
If, however, we apply Moritz’s factor to the same typical models, you get a very different, and confusing, range of speeds.

Take a model of PS Waverley at 1/48th scale… gives a model of some 59.75”.

PS Waverley’s engines turn at 57.8 rpm for a given speed of 18.37Knots.

To make life simple, lets say 60 rpm.

Now at 1/48 scale the speed of the paddle wheels would need to be 6.928 (square root of 48) x this, which gives a model paddle wheel speed of 415.68 rpm.
Which is Considerably higher than the highest typical maximum (80 – 150) by a factor of 2.77.

Lets take another case: - i.e. 1/24th scale.
Assuming a similar full size rotation speed this would result in 60 x 4.8989 (square root of 24) = 293.934 RPM, which is almost twice the typical maximum used for models.

 If we now consider the other implications of this: - Engine speed.

Typically we would be thinking of installing a gearbox/pulley system with a ratio of between 2:1 and 3:1 which for a 1/48 scale model would require the engines to be going at: -

For 2:1    = 831.36rpm or
For 2.5:1 = 1039.2rpm or
For 3:1    = 1246rpm.

For a 1/24 scale model engine speed required would be: -

For 2:1    = 587.868rpm or
For 2.5:1 = 734.835rpm or
For 3:1    = 881.802rpm.

For our Derek, with PS DECOY @ 1/24 scale and 5.5:1 ratio geared chain drive the engine speed would need to be a staggering 1616.637rpm. :ranting :shoot :sobbing
 

So what! You ask?

Well, on the surface there does not appear to be a problem, just gear your electric motor accordingly……no problem,   but what about steam engines?

The problem here is twofold: -

1.   Steam engines are designed for best output at relatively low rpm.
2.   Steam consumption becomes a major factor at higher speeds.

The typical model steam engine is best suited to speeds of around 300 – 600 rpm (fully loaded) typically.
So for our 1/48 scale model this would imply either direct drive, or a very low gear ratio.

For our 1/24 scale model we could use up to say 2:1(max) gearing.

Even assuming the particular model steam engine could run at speed of up to 1000- 1200 rpm (fully loaded) without placing un-necessary strain on the moving parts, providing the beast with steam (at full pressure) whilst doing so for more than a few minutes, would be a big problem.
This would require a pretty hefty boiler installation.

In our Derek’s case, with his engine going at 1616 odd rpm (fully loaded) he would need to install 2 or 3 more boilers. But I very much doubt that his engine could achieve such speeds, especially at 35-45psi).
Not that I am suggesting his engine is not suitable, just not designed for such high speed use, as indead non of mine are.

 Clearly there is something else at work here, which the scaling factors (as stated) do not take in to account, since the typical RPM figures of 80 – 150rpm paddlewheel speed are at odds with the above.

What this is; is un-clear, at this point in time.

So..... do we need a steam engine which can run at 1600 rpm or more?, if so, then we will certainly have steam generation issues; or one that can produce sufficient torque at say 300 to 400 rpm for direct drive?... which would tend to favour large bores and long strokes, but again these will impact on boiler size..... or should the paddlewheels be going much slower than Moritz's scaling suggests?

I am unable to come up with a suitable answer to this  :-\ :-\... can any of you ? ;) ;)
 
All very interesting and worthy of more study. :gathering

Ok that will do for this post.

Keep happy.

Best regards.

Sandy.  ;D :beer :breakcomp

Title: Re: Scaling factors
Post by: Bierjunge on February 15, 2008, 02:15:29 PM

Hello Sandy,

Quote from: sandy_ACS on February 15, 2008, 09:13:00 AM

If we consider that, for the majority of cases, we would consider the rotational speed for model paddle wheels to be between 80 – 150rpm (typical average speeds as stated in many posts on the subject) to be the norm.
If, however, we apply Moritz’s factor to the same typical models, you get a very different, and confusing, range of speeds.

Take a model of PS Waverley at 1/48th scale… gives a model of some 59.75”.

PS Waverley’s engines turn at 57.8 rpm for a given speed of 18.37Knots.

To make life simple, lets say 60 rpm.

Now at 1/48 scale the speed of the paddle wheels would need to be 6.928 (square root of 48) x this, which gives a model paddle wheel speed of 415.68 rpm.

You've calculated absolutely correct. But remember that all this is under the assumption that we're aiming for Froude speed. If not, things look different of course.

Anyway, the Waverley seems to have relatively small (and thus high speed) wheels compared to older paddlers. I have no idea what her wheel diameter is, but from your numbers, assuming a typical wheel slip of some 20%, a would guess that the wheel diameter should be around 3,8 meters (please excuse my metric brain). Close enough, I hope?

If we assume that the 1/48 scale model has the same wheel slip (which has basically something to with the ratio of the fluid resistance of the buckets versus the hull), the model wheel MUST roate your 415 rpm in order to reach Froude scale speed of 2,7 knots or 1,37 m/s (instead of the 18,4 kn or 9,45 m/s of the prototype) at 20% wheel slip. Sorry about this!

If the model wheels turn only 150 rpm, the model would attain (again assuming 20% slip) only 0,5 m/s, which is only 36% of Froude speed (but anyhow 250% of "model railway speed"). The drawback of this is the considerably underscale wave pattern (the waves would have only 13% of scale height, because the speed gous in quadratic); the advantage is the much smaller needed power of only 5% (sic!) of the power (resistance times speed) needed for Froude speed...

But don't worry too much abaout power: I've read the Waverley has 2100 hp (being 1565 kW). With an exponent of 3,5 for the power, the 1/48 model would need 2,0 W for Froude scale speed, which should be achievable by a model boiler. That's for the 415 rpm boat, nota bene.
The "slow 150 rpm variant" would need only 5%, being 0,1 W, mechanical power...

Quote

1.   Steam engines are designed for best output at relatively low rpm.
2.   Steam consumption becomes a major factor at higher speeds.

The typical model steam engine is best suited to speeds of around 300 – 600 rpm (fully loaded) typically.
So for our 1/48 scale model this would imply either direct drive, or a very low gear ratio.

I tend to agree that for a "typical 2 cyl model engine" of' let's say, somtehing between 1/2" and 2 cm bore and stroke, and the small wheels of a 1/48 Waverley (some 8 cm???), only a low gearing of not much more than 2:1 should be needed.

Quote

Clearly there is something else at work here, which the scaling factors (as stated) do not take in to account, since the typical RPM figures of 80 – 150rpm paddlewheel speed are at odds with the above.

What this is; is un-clear, at this point in time.

If we stick to your Waverley example, could you please provide the wheel dimensions (diameter, width and and height of buckets)? I have written a simple Excel calculator, which gives me the estimated wheels speed, shaft power and steam consumption depending on cylinder dimensions, steam pressure and gear ratio. Then we could try to justify the scaling factors.

But again: As soon as you're not heading for Froude (or so called "scale speed"), things might look different.

Best regards, Moritz

Title: Re: Scaling factors
Post by: derekwarner_decoy on February 15, 2008, 05:12:46 PM

Hi PD's....& welcome back Sandy :beer...I do freely admit I was stumped with my calculations & assumptions of scaling paddle shaft speed for PS Decoy....so applied the recommendation from ANTON as below for his 2CC horizontal Quartz paddle wheel engine

His WEB site quotes a recommendation of 'a reduction of 6:1 to 8:1' ....so considering that my JMC3H has 50% more displacement than the Quartz I considered I could lower the reduction ratio & maintain the preferred odd to even pinion tooth ratio for chain life & adopted the smallest 9 tooth :48 tooth = 5.5:1 ratio

Finding manufacturers that publish model steam engine speeds is difficult  :shhh :ranting...however SAITO do publish  engine speeds & these seem to indicate approx the 3000 RPM [unloaded] ....so considering  :squareone a 40% reduction for loading this bought me to consider approx 200 RPM paddle shaft speed max for Decoy which had a safety factor of 30% for emergency.....

Interesting subject :terrific :nahnah



Quote from ANTON.....'This engine, in its horizontal version, and is particularly suited to the propulsion of vessels wheel (side or rear). L'installation du moteur se fera avec une réduction d'un rapport de 6 à 8 (courroie cratée ou pignon). The engine installation will be done with a reduction of a report from 6 to 8 (or cratée belt sprocket)'  

Ce moteur sera utilisé dans des bateaux de 5à 10kgrs, avec des roues de Ø100 à 150 mm. This engine will be used in boats 5à 10kgrs with wheels Ø100 150 mm.

Title: Re: Scaling factors
Post by: Bierjunge on February 16, 2008, 01:30:41 AM

Quote from: derekwarner_decoy on February 15, 2008, 05:12:46 PM

Finding manufacturers that publish model steam engine speeds is difficult  :shhh :ranting...

How could they do this? The engine speed is HIGHLY dependent on the steam pressure, on the output resistance (size of prop or wheel) and an optional output gearing. So engine speed just HAPPENS, depending on what the custumer does to the engine...
All the manufacturer could to is either
- publish a no-load speed (of questionable use for the customer)
- or a typical load speed under normal conditions (e.g. "with a 90 mm prop at 3 Bar")
- or a maximum speed above which mechanical damage to the engine could occur.

If you give full pressure to an engine with no load on the output shaft however, it will flare to silly speeds of several thousand rpm.
Graham for example gives a no load speed of 4000 rpm at 30 psi for their TVR1A engine ("for the youngsters just to see how fast it will go"), but recommends to do this only for a couple of minutes...

Even if a munfacturer gives a typical load speed (e.g. 1000 rpm), this can vary highly depending on the operational conditions:
- Take the double steam pressure (e.g. 3 Bar instead of 1,5 Bar), and you will get 141% of the engine speed (1414 rpm) and 283% of the power consumption.
- Make the gearing to the wheel shaft twice as short (e.g. 8:1 instead of 4:1), and you will get 283% of the engine speed (2828 rpm), again 141% of the wheel shaft speed and again 283% of the power consumption.
- Halve the area of the wheel buckets, and you will get again 141% of the engine- and wheel speed and 141% of the power consumption.
- But if you combine all these three measures, you will get 566% of the engine speed (5655 rpm, which might damage the engine...) and 1131% (!) of the power (which the boiler presumably won't deliver)

You get similar effects for a propeller drives vessel depending highly on the diameter and, even more important, pitch of the propeller.

Maybe we should ask Eddy to transfer this thread into the Live Steam section?

Title: Re: Scaling factors
Post by: derekwarner_decoy on February 16, 2008, 07:56:46 AM

Hi PD's..........Moritz suggests.......maybe we should ask Eddy to transfer this thread into the Live Steam section? .....this is a good idea Eddy..... :whistle

More interesting by the day...however...I am not racing out to purchase a 19 or 21 tooth pinion just yet

1) Australian paddlers travel/ed at approx 3 knots in the rivers system...not like the Scottish paddlers of 15> 18+ knots in their trials in the ocean
2) ANTON is aware that I have a JMC3H & I have questioned his recommended 6:1 to 8:1 Quartz speed reduction....... but with little response  :sobbing :shhh
3) I have a photograph of the straight cut spur gear reduction on PS Marion & this must be in the order of 50:1

Even electric driven paddlers seem to hold a certain mystique over prop vessels...you know  :terrific wheels thrashing around but going nowhere fast...it is not a SKI boat......so to combine this with a visual of a real steam engine is my plan :crash :towel  :whistle

Title: Re: Scaling factors
Post by: derekwarner_decoy on February 16, 2008, 10:13:35 AM

Hi PD's..... ???..to attempt another view or opinion...the following is self explanatory to my engine builder Jean Marc Cloup...let's wait & see if I get a response..... :porkies or will it be :shhh
...


----- 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 recommendation sur le rapport de réduction de vitesse de moteur de vapeur à l'axe de palette il serait le plus apprécié sincères amitiés Derek
--------------------------------------------------------------------------------

Greetings Jean Marc...from Derek Warner in Australia

My colleagues in our world wide model paddle vessel group are currently discussing steam engine speed reduction ratio to the paddle shaft

I have still not finished my model, but enclose a .jpg of my JMC3h engine installation

If you would be so kind to offer your comment or recommendation on the steam engine speed reduction ratio to the paddle shaft it would be most appreciated

kind regards
Derek

Title: Re: Scaling factors
Post by: derekwarner_decoy on February 16, 2008, 10:56:56 AM

Hi PD's & I understand as Moritz says......how could they do this? The engine speed is HIGHLY dependent on the steam pressure, on the output resistance (size of prop or wheel) and an optional output gearing

But we teach symplistically that steam & electricity are parallel energy sources......one is contained in a pipe, one is contained in a wire...they both have the potential to expend energy & provide work [output]

They also both have a deadly common factor ...like don't  :ranting touch or you will get burnt....

So if the manufacturers of electric motors can talk about no load RPM for voltage & resultant current draw & delta T........model steam engine producers have a similar ability

I also recognise the economies of scale or size here with the multi national MABUCHI company producing 50 million minature electric motors PA to Sandy producing a slightly smaller quantity of model steam engines & so cannot fund the $17.5M for the effiency calculations for each engine design  :hehe :nono :terrific :shhh

Title: Re: Scaling factors
Post by: Bierjunge on February 16, 2008, 01:27:35 PM

Quote from: derekwarner_decoy on February 16, 2008, 10:13:35 AM

My colleagues in our world wide model paddle vessel group are currently discussing steam engine speed reduction ratio to the paddle shaft

If you would be so kind to offer your comment or recommendation on the steam engine speed reduction ratio to the paddle shaft it would be most appreciated

Derek, if you tell us
- the number of cylinders, bore and stroke of your engine,
- the boiler's typical operation pressure,
- the diameter of your paddlewheels,
- the size (width and height) of the buckets/floats
- the average number of buckets being simultaneously immersed at one wheel,
- and maybe the scale and length of your model and the speed of the prototype,
I could offer to maxe some rough approximative calculations on which gearing ratios and speeds might be feasible. Not to make own experiments redundant, but it could give some hints narrowing your solution space.

Title: Re: Scaling factors
Post by: derekwarner_decoy on February 16, 2008, 02:43:56 PM

Hi PD's & thankyou Moritz......this is interesting....my answers below in RED

Derek, if you tell us
- the number of cylinders, bore and stroke of your engine, -  two cylinders 10 mm bore x 10 stroke..double acting
- the boiler's typical operation pressure, - WP will be set 1.5 Bar typical
- the diameter of your paddlewheels, - 140 mm diameter
- the size (width and height) of the buckets/floats -width = 50 mm wide x 12 mm high
- the average number of buckets being simultaneously immersed at one wheel, - 3 flat floats equally spaced @ 36 degrees
- and maybe the scale and length of your model and the speed of the prototype, - scale of PS Decoy = 1:24, post to post = 1150mm- speed as built was I believe 11 knots....but in the OZ rivers say 3 to 5 knots max...so the latter 3>5 knots is the max desired scale speed

I could offer to maxe some rough approximative calculations on which gearing ratios and speeds might be feasible. Not to make own experiments redundant, but it could give some hints narrowing your solution space.

Moritz....I have drawn the plans for Decoy from two 50 x50 mm postage stamp photographs...& the engine & boiler selection were simply by choice...& not from original specification...but again I thank you  :beer...as this is an interesting exercise....regards

Title: Re: Scaling factors
Post by: Bierjunge on February 16, 2008, 03:45:52 PM

Quote from: derekwarner_decoy on February 16, 2008, 02:43:56 PM

Hi PD's & thankyou Moritz......this is interesting....my answers below in RED

That was fast! OK, let's go!

What I'm doing:
First, I'm estimating the torque the engine can deliver. With your data, I get piston downforce of 11,8 N. If we assume 50% cylinder filling (cutoff) and 50% mechanical efficiency (half of the piston force being lost by friction), I get 1,9 Ncm as average crankshaft torque.

Now to the paddlewheel: The idea is that the (geared) engine torque is balanced by the wheel's drag torque, caused by the dynamic fluid pressure acting on the floats.
As simplest (and worst) case, I am assuming a standing boat (like being tied to a pole) to calculate the speed of the wheels churning in still water (100% slip). Even worse and simpler, I'm calculating as if the floats (cw=1) didn't help each other by causing a flow; each acts in still water.
The idea behind this worst case: In reality, if the boat is moving, the resistance on the wheels is much less, so either the wheels could turn faster (and the boat could run faster) than the circumferential wheel speed in the "pole-pulling" experiment, or less steam would be needed.

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

Nota bene, the "prototype speed" in the table is not the precise vessel's speed, but just the wheel's circumferential speed after applying Froude scaling and converting into knots. And the steam consumption is just a very rough estimate, treating steam as ideal gas (which it isn't).

But anyhow:
So gearing ratios 3:1 and 4:1 seem too weak and too slow.
Ratio 6:1 should deliver healthy and reasonable speeds of wheel and engine without consuming too much steam. By the way, the Decoy's website states a max. wheel speed of 24 rpm, which corresponds to 118 rpm of your model wheels after Froude scaling.
Gearing of 8:1 could still be OK, but 10:1 seems too short, because the engine speed gets very high, and the steam comsumption increases drastically without major speed increase.

So if I were you, I would design the boat for a ratio of roughly 6 (or maybe somewhere between 6 and 8 ), but keep the option to change gear sizes later just in case that the practical experience proves something different.

So much for now. Moritz

Title: Re: Scaling factors
Post by: derekwarner_decoy on February 16, 2008, 05:17:47 PM

Hi PD's...this is amazing.......but my PC broke last year  :breakcomp :sobbing :whistle...however my calculations & guestimations provided a reduction ratio of 5.5:1 via the 9 tooth to 48 tooth chain drive pinion set for my PS Decoy

Then 2 years later Moritz SCRUNCHES the numbers into his mind/brain & PC  :respect....& confirms

but anyhow- so gearing ratios 3:1 and 4:1 seem too weak and too slow....Ratio 6:1 should deliver healthy and reasonable speeds of wheel and engine without consuming too much steam

Thank's again Moritz....your calculations suggest my 5.5:1 is a healthy median between 4:1......&.....6:1.....however I do have one scaling trick plan up my OZ sleeve :shhh

Irrespective of the final test results....the paddle float height can be varied from 12 mm high to +2 = 14...or - 2 = 10 high which provides a +/- 20% varience in blade surface area :goodnews

Title: Re: Scaling factors
Post by: derekwarner_decoy on February 17, 2008, 02:39:28 PM

Hi PD's...just  :thinking & back checking.... Moritz from my original 2005 assumptions & all seems OK...but I do have one question from this....based upon Decoy @ 1:24 scale & being steam driven ie., ... reversable engine...however I would like the paddles & hence engine to stop prior to engaging the ASTERN engine command   :towel :whistle

Rotational mass [RM] =
1) the driven chain sprocket + the shaft + coupling + the chain = 165 gms~~~~
2) paddle set...= 250 gm~~~~
3) engine flywheel + drive sprocket = 50 gm~~~negating crankshaft as effiecency loss]
So RM....10% of the net vessel displacement @ 72 tonnes [which is a good % number for RM]  :clap

We understand that a moving paddle vessel 'without power' will come to rest quickly due to the braking or drag effect of the immersed wheels.....

Title: Re: Scaling factors
Post by: Bierjunge on February 18, 2008, 12:33:02 AM

Quote from: derekwarner_decoy on February 17, 2008, 02:39:28 PM

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). :whistle

- 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.

Title: Re: Scaling factors
Post by: sandy_ACS on February 18, 2008, 03:42:14 AM

 ;D ;D ;)

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 ;) ;) :D :D :great

Keep happy.

best regards.

Sandy :breakcomp :coffee :beer

Title: Re: Scaling factors
Post by: oldie on February 18, 2008, 04:26:39 AM

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

Title: Re: Scaling factors
Post by: Eddy Matthews on February 18, 2008, 04:51:21 AM

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!

Title: Re: Scaling factors
Post by: Bierjunge on February 18, 2008, 05:02:49 AM

Quote from: oldie on February 18, 2008, 04:26:39 AM

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

Title: Re: Scaling factors
Post by: Roderick Smith on February 18, 2008, 08:24:18 AM

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

Title: Re: Scaling factors
Post by: sandy_ACS on February 18, 2008, 10:21:38 AM

Quote from: oldie on February 18, 2008, 04:26:39 AM

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

 ;D ;D ::)

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.

Quote

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. ;) :coffee :beer :goodluck

Best regards.

Sandy.

Title: Re: Scaling factors
Post by: derekwarner_decoy on February 23, 2008, 02:29:56 AM

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.... :darn...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

Title: Re: Scaling factors
Post by: steamboatmodel on February 24, 2008, 04:23:38 AM

Quote from: oldie on February 18, 2008, 04:26:39 AM

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

Title: Re: Scaling factors
Post by: Alan Haisley on February 26, 2008, 01:11:27 PM

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.

Title: Re: Scaling factors
Post by: derekwarner_decoy on February 26, 2008, 04:22:36 PM

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.... :nono

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  

Title: Re: Scaling factors
Post by: derekwarner_decoy on February 27, 2008, 06:28:28 AM

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