Calculating displacement for scale model ship

[Peter Binns]

Firstly, hands up, I am a marine modeler, not a real boat owner. However, whilst combing the web for information on how to calculate displacement I came across a very old post from Guillermo who said,

"You need to know waterline length, waterline beam, and body draught amidships (just body, not total draught under the keel). Then you need the "Block coefficient" which may vary a lot depending on hull forms. But for a rough estimative on a sail boat it should be not far away from 0.4
So if you multiply Lwl*Bwl*Hd*0.4 you get (roughly) the underwater volume of the hull. Now multiplying this by the weight density of water (If salt then it's around 1.025 tonnes/m3 or 64 lbs/ft3 depending on units chosen) you get the displacement weight in tonnes (if you chose measurements in metres) or pounds (if you did it in feet).
As said, this is a rough figure just to get a first idea. Being accurate takes quite a bit of more time and knowledge."

Because I am planning a new project - a 1:18 scale live steam-powered working model of a 1906 passenger steamer that worked on the River Fal in Cornwall, UK, for which I only have a poor copy of the original 'general arrangements' deck and profile drawings - I need to estimate the likely displacement of my model in order to select the size and specification of steam plant to power the vessel adequately. I have used the formula set out by Guillermo, but I am unsure as to what value of 'block co-efficient' I should use. As a yardstick he quotes 0.4 as typical for a sail boat, but the hull shape of my model is broad and fairly flat-bottomed, although as typical for the era, it has a vertical and fairly sharp bow line. I therefore adjusted the 'block co-efficient' to 0.7, thinking that the hull shape was a lot nearer to a floating cube than a sail boat!

I'd be grateful for any comments from big-boy boaters on this, or a better way to calculate displacement weight. I'm attaching the drawings I have (difficult to see at small size) and contemporary photo of the vessel in question.
Hope someone can help.

Many thanks.

 

[TANSL]

You have to consider for your model exactly the same block coefficient of the big ship since that number is dimensionless. But, given the diversity of elements to take into account and the different specific weights of the elements of your model and those of the "parent" boat, you will probably have to add fixed ballast to the model so that the full load draft of it is equivalent to the full load draft of the original.

 

[bajansailor]

Welcome to the Forum Peter.
Do you have any other information available regarding this 1906 passenger steamer?
For example, what her names were in the past, and her overall dimensions, and what her designed operating speed was?
Knowing a length and a speed, then you can calculate a Froude Number.


It might be worthwhile asking at the Maritime Museum in Falmouth, or the National Maritime Museum at Greenwich, to see if they might have any plans for her in their archives?
Do you know which yard built her?
I would agree that starting off with a block coefficient of approx 0.7 should put you in the right ball park.

 

[Peter Binns]

You have to consider for your model exactly the same block coefficient of the big ship since that number is dimensionless. But, given the diversity of elements to take into account and the different specific weights of the elements of your model and those of the "parent" boat, you will probably have to add fixed ballast to the model so that the full load draft of it is equivalent to the full load draft of the original.

Thanks for your reply. The supplier of my steam plant (boilers, engines, fittings etc) gave me weight displacement limits for various steam plant kits (eg up to 20kgs etc) and suggested I calculate the displacement of the model based on where the waterline is marked on the plans and using Guillermo's formula. Although in 'miniature', I thought using the model's dimensions and the block coefficient would give me a true displacement value. After all, water is water, whatever the quantity! But I take your point that the weight of the propulsion unit, electronics, the materials used to construct the boat and everything else inside may still not be sufficient for the craft to float in the water at the waterline level, requiring additional ballast. I have done this on most of my previous models.
If the model was made and all weighted up so that it floated in water at the waterline I could easily calculate the displacement simply by taking before and after water level measurements in my test tank and calculating the difference in volume of water displaced, and hence its weight. But for planning purposes I need a number before I start!

 

[Peter Binns]

Welcome to the Forum Peter.
Do you have any other information available regarding this 1906 passenger steamer?
For example, what her names were in the past, and her overall dimensions, and what her designed operating speed was?
Knowing a length and a speed, then you can calculate a Froude Number.


It might be worthwhile asking at the Maritime Museum in Falmouth, or the National Maritime Museum at Greenwich, to see if they might have any plans for her in their archives?
Do you know which yard built her?
I would agree that starting off with a block coefficient of approx 0.7 should put you in the right ball park.

Thank you for your welcome.

The vessel in question was an 81' twin screw steel passenger steamer built in 1906/7 at Cox & Co in Falmouth and named Princess Victoria. She saw service on the River Fal between Truro and Falmouth until WW2 when she was requisitioned by the Admiralty and never returned to Cornwall. No data on speed I'm afraid but fairly slow I should think. You'll have to educate me as to what a Froude number is!

I have an ongoing enquiry with the National Maritime Museum in Falmouth but because of the pandemic they haven't come up with anything yet. I have also tried the Cornwall Records Office and A&P Shipbuilders Falmouth which acquired the company Silley Cox and the yard they still occupy, which was formerly Cox & Co before WW1. The tatty plans came from Alan Kittridge, the author of the book 'Passenger Steamers of the River Fal' that inspired me to make this model, but his source passed away in 2014 so there's nothing else, such as the all-important 'lines' I need for accurate hull shape and construction. I haven't tried NMM Greenwich yet but that's my next port of call, pardon the pun.

I am relieved, however, that my guess of 0.7 for the block coefficient wasn't too far off the mark!

 

[TANSL]

Guillermo's formula is exact. If you know the Cb of the base boat, multiply each of the values of the length in the waterline, beam in the waterline and the draft value of the scale by the scale of the model, those new dimensions, multiplied by the Cb, which does not change , they will give you the displacement that your model should have.
I don't know if you can't do that or you just don't know the block coefficient. In this case, if you have the body lines of the model, I can help you to obtain the straight fairings of the boat and, therefore, to know the displacement at different drafts.

 

[DCockey]

How accurate does your estimate need to be?

If you know the displacement of the full size boat then the displacement of the scale model will be

Scale model displacement = (Scale ratio)^3 * Full size displacement

For a 1:18 ratio model the ratio of displacement will be (1/18)^3 = 1/5832 = 0.0001715

Be aware that registery "tonnage" is different than displacement.

If the model was made and all weighted up so that it floated in water at the waterline I could easily calculate the displacement simply by taking before and after water level measurements in my test tank and calculating the difference in volume of water displaced, and hence its weight.

Or you could simply weigh the model after it is ballasted to float on the waterline.

 

[Mr Efficiency]

I might be missing something here, but without an accurate lines drawing of the vessel, you can't work out too much at all, with any accuracy.

 

[TANSL]

For a 1:18 ratio model the ratio of displacement will be (1/18)^3 = 1/5832 = 0.0001715

I do not know if the problem is knowing that displacement, but knowing how to achieve it, how much weight to add or remove. But I am not very clear about what is to be solved either.
I agree with Mr Efficiency that probably nothing useful can be done without a body lines plan.

 

[Ad Hoc]

The problem is that the data for the vessel is thus:

Queen of the Fal (1)
(1893-1906 - Built: 1893)
Built: 1893 - 62 gross tons - 81.6 ft long

Therefore, without knowing how the GT was calculated in 1906 and how it applies to the actual full load displacement, it is not possible to perform a simple geosim calculation.

 

[rxcomposite]

The formula is correct but it will be useless if you are building a model. You can try drawing the lines plans from the old drawings and try to calculate using the formula given.

However, the materials and equipment you use will determine how heavy the boat is going to be which will not be in agreement with your "designed displacement". You may want to go the long way, that is calculate how much each materials and parts that is going to your "designed boat" and see if it floats within the "designed waterline".

I am a model builder myself. Small model that is, not scaled working version.

 

[gonzo]

Models need to float on the same lines as the original to look good. The displacement will be the submerged volume times the density of water. Stability will be another different issue.

 

[rxcomposite]

As a yardstick he quotes 0.4 as typical for a sail boat, but the hull shape of my model is broad and fairly flat-bottomed, although as typical for the era, it has a vertical and fairly sharp bow line. I therefore adjusted the 'block co-efficient' to 0.7, thinking that the hull shape was a lot nearer to a floating cube than a sail boat!

You are within the ballpark. Looks like a bilged hull round stern with skeg. 0.7 to o.76 will do.

 

[Tiny Turnip]

The problem is that the data for the vessel is thus:

Queen of the Fal (1)
(1893-1906 - Built: 1893)
Built: 1893 - 62 gross tons - 81.6 ft long

Therefore, without knowing how the GT was calculated in 1906 and how it applies to the actual full load displacement, it is not possible to perform a simple geosim calculation.

I found this piece on historic methods of calculating tonnage.

How tonnage is applied to ships - Maritime Archaeology Trust https://maritimearchaeologytrust.org/tonnage-applied-ships/

It would look likely from the dates that the George Moorsom method was used at the time of construction. From the article,

'The gross-registered tonnage was the enclosed under deck volume of the ship (ft3) and the net-registered tonnage was derived by deducting non-cargo carrying volumes from the gross figure, thus reflecting earning capacity. The permitted deductions included Master and crew accommodation, safety and storage spaces, water ballast tanks, and an allowance for propelling machinery. As the resultant figures were large, both were divided by 100 to arrive at more manageable values, thus one registered ton was the equivalent of 100 ft3 (2.83m3), and the values were used for ships’ Certificates of Registry.'

The example given in the article, and this piece, very helpful to layfolk like me, include above deck structures in the volume calculation.

A Guide to Understanding Ship Weight and Tonnage Measurements – The Maritime Site https://www.themaritimesite.com/a-guide-to-understanding-ship-weight-and-tonnage-measurements/

However, as has been pointed out, getting an accurate idea of the hull volume is going to be tough without lines.

 

[Tiny Turnip]

Another photo. I imagine you have this, Peter:

https://i.ebayimg.com/images/g/Xp8AAOSwXf1aXnIX/s-l400.jpg