Beebe Power Calculation

I have written much about calculating the required power for any given boat and received a lot of help and advice on the subject.
For smaller boats I think I prefer the system in Voyaging under Power. My copy is the 4th edition. The graphs provided in the book are limited to 95 ton displacement and SL = 1.65. Could anyone provide me with the maths behind the Graphs. So that I could calculate power for SL of about 2 and several thousand tons. I know other formula can provide these answers but I would like to compare Beebe results to say Wyman's formula. This is a purely maths question and yes I have little else to do in my life.
Mik the stick.

 

Ok no one can help,but I found a formula for required horsepower which seems to me to be quite accurate, Like the Gerr formula and others it has a coefficient which if you get it wrong makes nonsense of your results so I worked on this coefficient b which equals 0.3546 for the Queen Mary. As I have posted before the Diesel Duck makes 8.17kts on about 30hp in calm conditions. Yet the specified engine is 80hp. CONDITIONS MUST BE CALM INDEED.
According to Beebe's book the DD makes 9kts on 80hp. The Qween Mary has a L/B ratio 3.77 times larger than the DD which makes its coefficient b =0.985. When the formula is applied to the DD the result is 72.7hp is needed to make 9kts. This is I think the best formula I have found on the subject and don't feel the need to find anything better. It is not a difficult formula and can be split into two parts Frictional resistance and Residual resistance.
If anyone is interested in this formula I will post it.
Mik the stick.

 

What you can do is to plot the graph in Excel using arbitrary values to closely approximate the example graph. Once you have the values and the graph, run the trendline option of Excel and choose an appropriate type of graph (linear, exponential, polynomial, ect). The formula will give you one to six unknown values (in case of the 6th level poly curve). Use the "What If" scenarios function of the Excel to get a good grasp of the unknown. That is, what value will affecr what portion of the curve.

This method can be very accurate but for your purpose it might be naught. There are many resistance and powering prediction formulae and each one is suited for a particular hull, further broken down into a set of parameters that will work. You need to choose the correct formula in order to gain some accuracy in your prediction.

 

I'm not that good with spreadsheets I will have to ask my daughter's help with that. The formula is frictional resistance is fnSV^1.825 + the Residual resistance b x (D^.666/L) xV^4. I think Beebe may have used this formula to create his graphs. Why?, because people who shy away from maths, and they are probabley in the majority can learn to use graphs. The calculation is also faster.
mik the stick

 

Some shy away from learning naval architecture obviously.

 

What is the definition of the terms used?

fnSV?
D= displacement? in tonnes or long tons?
V= speed in knots?

 

One problem with theoretical graphs is real engine output ( HP produced per Gal ) can vary on identical engines by 5% - 20% or more.

The Beede graphs are great for mental ************ comparing boat A with boat B , but you will need your own on board testing to find dry tank range.

 

D is long Tons V is knots.
I think the vast majority of sailors are not Naval Architects or maths experts I think Beebe may have been trying to produce something useful for the average sailor who has a reasonable grasp of maths. These days I find young people to be very very good at maths or quite poor.
mik the stick
Learning Naval Architecture is very hard for me as I'm teaching myself and I don't thing I'm great at maths.

 

I can recognize fnSV^1.825. It is a friction formula modified by RE Froude from his father W Froude but I don't recognize the Beebe residual resistance formula. Not in my reference books.

Are you sure it is the correct one? I tried to program it in Excel and compare it with Gerr A, Gerr B(method), and Wyman's. The only way it will come close is if I change the Rr formula exponent to ^3, not ^4 as you have posted.

 

I,m in london at the moment, my youngest daughter nearly died in childbirth. mother and new grandson are now doing fine, back to business.

Trust me use^4 it is correct.this formula came from Sponberge. His Pdf links to a document which has Kieths speed formula as he originally wrote it.

Unfortunately formulas are only as good as what you put in, rubbish in gets rubbish out. b is not clearly defined. I got some reliable states and did some number crunching. The most reliable was the Abdiel class minelayer Manxman.
Manxman S = 18414 Fn = 0.00952 Disp =3450tons SHP =72000 this gave b as 0.282. To get b for other ships I divide 0.282 by the L/B ratio and multiply by 10.23, ratio for Manxman. I then tested the formula on other ships.

Bangor class 2000shp =16.5kts, results 2000shp =16.23kts 2146shp =16.5kts
Dullisk Cove 2500shp =12kts, results 2500shp =12.32kts 2293shp =12kts

 

For rxcomposite

Please accept my apologies I WAS NOT CLEAR. b is not beam it is a coefficient based on L/B ratio. 0.5 for merchant types up to less than 0,35 for Liners.

I found reliable info on Manxman L/B =10.23 plugged the numbers in the formula and b turned out to be 0.282 multiply this by 10.23 and divide by 36.66/12.75 to get b=1.002 for the short fat Diesel Duck which calculates to 69.63bhp with 7% mechanical loss.

The boat in your spreadsheet (which I like very much thank you) has one mistake in it. 432EHP with 55%eff prop is 432/0.55 = 785shp not 432 x 1.55 = 670shp I calculate b= 0.346 for your boat. Plugging the numbers in your spreadsheet she requires 441shp a bit less than wynans formula.

However perhaps there is a more suitable formula for S Froudes formula (for warships) gives 404 for the DD against your formula is about 360.

 

No need for apologies Mik. I just made the spreadsheet because you said you are not too good in it and need to ask your daughter. Just plug in the numbers, do as you want with the spreadsheet and make the corrections.

The boat ratios are theoretical but within the range. I just wanted to compare how Beebe is with other known and published formula that I have.

 

For rxcomposite

Thanks again for the spreadsheet, I normally struggle away with a calculator because I take much longer to construct a spreadsheet to do what I want than it takes to get results on a calculator.
The only formula I know are Wyman, Gerr A, Gerr B, and Kieth,s Formulas.
If there are others I don't know about I would appreciate it if you would share them with me.
I have attached a pdf with wymans improved formula on it just in case you don't know about it. It is supposed to give more accurate results perhaps as you have said it depends on the boat.
mik the stick

 

The results for the Nordhaven 46 in Beebes book(third edition) are

5kts =12.6bhp
6kts = 25.6bhp
7kts = 46bhp
8kts = 91bhp
9kts = 144bhp

I realised you perhaps did not have this book. beebes graph starts at SL =0.7. hope that is what you want.
mik the stick

 

If you can forward me the article on Beebe, I will include this in my list. I see it has varying coefficients. No problem for me, I can program that in Excel but I must be careful. Errors creep in and sometimes the source has a typo error (that includes Principles of Naval Architecture and Introduction to Naval Architecture).

I looked at Dave Gerr's revision of Wyman's formula. Again varying coefficient. Must be the third version. I came to notice it when it was published in PB magazine years ago then another contributor corrected the coefficient saying that it tracks the trendline more accurately. That is what I am saying. The Excel function can do that efforlessly.

I have a collection of powering formulae. Some are so complex it need a 5th order parabolic function to track the varying coefficients. The complexity is further complicated as most of this formulae will work only on a range of ship coefficient/ratios and type of ships. That is why software are so expensive. I think we paid USD 6,000.00 for the last one we bought.

If you want to know more about simple formula, the late MikeD of this forum has posted a Froude + Taylors wavemaking method. I think in the latter part of his post, he attached a spreadsheet.

I am attaching a list of resistance and powering method. The Wetted Surface Area (WSA) I have posted before.