# How does the angle of the bow of a boat affects its coefficient of drag? PLEASE HELP

Discussion in 'Hydrodynamics and Aerodynamics' started by Catatau, Nov 11, 2012.

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Catatau

Firstly well done on a jolly interesting and impressive school project.

What you need to decide is whether you are investigating the angle of entrance on the total resistance, or simply establish a relationship of the angle of entrance with speed.

There are simplified graphs of half angle of entrance (it is always quoted as half angle, not full angle) versus speed. What you would then do, is over lay examples of boats onto the graph you produce to establish a trend.

For example, boats that have a low Length to Beam (L/B ) ratio but wish to travel fast, the angle of entrance will be high. Even though the boat is intended for higher speed, being very short for its length means that the angle will also be high. So this is a fixed parameter as such.

Whereas boats with a high L/B ratio which are also fast, their angle of entrance shall be lower. Simply because there is more length to reduce the angle at the bow.

So, if you plotted say, tugs or container ships or fast ferries or yachts onto the graph, noting their angle of entrance and their speed and of course their L/B ratio….you will establish or discover a relatively simple trend.

So this is one way of presenting the results. In empirical form showing that the speed and L/B ratio boats have “common” values.

Why this is true, leads into the total resistance, or drag, drag aspect. That is probably a step too far. But you can simplify this by doing the following.

Calculate the wetted surface area (WSA) of each model. This is simple from your shapes shown. As the shape is a rectangle with a triangle. From this, you can calculate the frictional resistance. This is a little complicated but can should be ok for you. It is done it 2 stages:-

1) 1/2x1000xWSAxspeed^2

The 1000 is density of fresh water, as I assume you are doing this in fresh water not salt/sea water. The speed must be in m/s.

2) Calculate what is called the Reynolds number (Rn) and then work out the friction based upon this Rn.

The Rn is speedxlength /viscosity.

The viscosity is dependent upon the salinity and temperature of the water. You can get this from simple tables such as here:

The length is the length of the model, and speed as before, in m/s

Once you have that you can calculate the friction coefficient by this formula:

Cf = 0.075/(logRn – 2 )^2

You then calculate the Rn for each speed and the Cf.

Then multiply #1 and #2 together to obtain the total frictional resistance. In tank testing we add what is also called a correlation allowance, but it is is not necessary for this purpose.

So then wave making drag, or resistance, is simply the total drag (weight being used) less the frictional drag you have just calculated.

So what do you do with this wave making drag value??

Work out what is called the length-displacement ratio (L/D). This is to non-dimensionalise the results. This is simply the length/displacment^1/3

For example a length of 10m, with a displacement of 100 tonne is 10/100^1/3 = 2.15

Then calculate the Froude number (Fn), already noted above, for each run.

Then you can plot the wave making resistance, or drag, versus the Fn, for each shape.

The shape of each shall have different L/D ratio.

You can then also do the same for different ratios, such as angle of entrance, which is your original question.

Hope this makes sense?

I would also recommend having 5 points per hull, rather than 3. So do 2 more test runs at lower speeds, i.e. around 0.2 and 0.4 Fn.

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### rxcompositeSenior Member

I read this thread twice and still could not figure it out. Are we talking of a bow angle as viewed from the profile, or vertical deviation or are we talking of bow angle as seen from the top view or waterline plan?

A search on the net showed that there is no clear definition of what a bow angle is. Googling the net even BD forum showed two results, one is vertical, one horizontal view. Other site showed that discussions on the bow angle refers to the entrance angle, others refer to to optimum rake from the vertical.

NA book refers only to half entrance angle and the length of entrance. There is a mixture of terms in other articles such as defining the bow as plumb bow, axe bow, raked bow, reverse bow. bulbous bow, and even swim bow. I beleive this refers to viewing the bow from the profile view and the sharpness of the bow refers to entrance angle as seen from the waterline view.

Is there really a difference in the use of the terminology, i.e. the "bow angle"?

3. ### tunnelsPrevious Member

yeah they sit on the toilet to !! and talk a differant language to us common low landers .
All this is really really interesting and i get exactly what you are sayng . a plumb bow must increase the water line length of a boat of a given size !! right?? so if the bow is 120 degrees and racked back the water line length is less so the boat sits further in the water due to lack of bouyancy up front . Its all to much to think about i will stick to glass thats easy !
it either works or it dosent !!

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### DCockeySenior Member

Look at the illustration Catatau included in the first post. He is varying the top view angle which is sometimes called the entrance angle. While that illustration is not to scale the dimensions show that he kept the beam and draft constant, and altered the length to keep the displacement constant.

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### rxcompositeSenior Member

That is the whole point Tunnels. If the bow is raked from the vertical, then a lot of things changes like the Cp distribution, LCB, ect. But again if you look at the waterline (top view) it could be anyting from a barge with a 180 degree entrance angle to a very fine ship with a 4 degree half entance angle.

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### rxcompositeSenior Member

Yes I saw that but my question is is the term applicable only to entrance angle? Changing the rake (as seen from vertical) changes also a lot of things. I had the temptation to assume he is running it to vertical but it is only my assumption.

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Rene,

I believe what you are referring to is this:

You must read between the lines as such.

He is a high school student thus not familiar with the correct terminology and second he is from Brazil, additionally, like you English is probably not his native language. Hence, I assume, you are reading his terminology too literally. After studying for some time and recognising there are correct definitions that NAs use, he would indeed use the terminology that is used to define such things, that being the "angle of entrance" of the waterlines at the bow, or FP, in plan view.

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### rxcompositeSenior Member

Thanks AH. It was not his definition but the whole definition of what was in the net.

Maybe it is just me, as my latest education forces me to think in more than one dimension. Attached why.

I also found the Le/Lr i definition I was inquiring before. It was right here in the forum in ITTC definition or dictionary.

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### JoakimSenior Member

Really impressive hight school project! How old are you?

You say in some points "under water". What do you mean by that? Submerged or just that the whole length of the boat touched water?

Since you are using rather high speeds (Fn 0.8-1.6) my first assumption would be that bow angle has no effect on drag, because bow is typically not touching water for that kind of hull shape at those speeds. But that depends on many things like weight, weight distribution and moment from pulling string.

For that reason it is very important how you pull the model. The point where you attach your line has affects the trim (the angle between water and keel line).

Since bow is not typically touching water at planing speeds (Fn ~1 and above), it would be better to lower the speeds using much smaller weights. But certainly you have already done more than enough for a high school project.

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### rxcompositeSenior Member

It reminded me of the way of thinking of W. Froude, a man well beyond his age, about Froude's experiment on frictional resistance and bow wave making in the late 1800.

Could be another Froude in the making given the right spark.

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### philSweetSenior Member

I'll jump on the bandwagon and say good job.

Stick it out and draw your conclusions from your experiment. Let the book learning stick to your experience where it wants to, but don't force it.

If you have kept the wetted area constant, I'm guessing the weight varies among test hulls. You could try to run them with trim weights so they would all weigh the same, letting draft vary a bit.

You could also try to run one of them with different trim weights such that it's speed was the same as a different hull for the different tow weights. This would be time consuming since you need to guess at the weights, but you could get close.

These three series combined would let you isolate the bow angle affect from some other things that may be going on. As you have already figured out, it is very difficult to just change one thing in a boat. But you can change things in pairs and try to keep everything else as constant as possible.

As described above, weight, speed, and bow angle are variables with area about constant. Weight and speed because of the experiment's design. This isn't a complaint about the experiment's design. If it wasn't weight and speed, it would be something else. That's just the way it works.

There is also reason to be concerned about friction in your pulling setup. Can you think of a way to quantify how much force is lost to friction? Maybe you could double the number of pulleys an rerun a couple tows. You could then back the difference out twice. You would need to do this for each tow-weight if it was important. But it may not be.

Of course you may not have time to do any of these things, but thinking about what else is changing and learning where errors can creep in are part of the game. Fluid experiments are messy.

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### parklandSenior Member

I am not the smartest cookie in the jar.
Just had to get that out of the way haha.

Now, I noticed in you're drawings, that you are adjusting the length of the boat, to compensate for the bow design.
Would this not change the boats hull speed?

I think the bow angle might be giving you data in you're results, but the hull speed might be affecting your results too, as the bodies lengths are different.

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### CatatauJunior Member

Ad Hoc, first of all thank you for your time and input. Yes what I want to do is investigate the angle of entrance with total resistance. With your post I just realized that Cf values vary with speed and are not fixed for an object, that is one thing that I didnt know and was confusing me.
So I did what you said with the two steps. I calculated reynolds number and a Cf values for my first boat at each one of the three speeds, I then multiplied the Cf value by the density*WSA*velocity^2 to get the total frictional resistance. I then calculated the wave making drag by using, total drag (weight) = frictional drag + wave making drag (that is what you meant isnt it?). However, I believe that my results are kind of strange. I only did this for my first boat so far (120 degrees bow angle) and I got -0.007, 0.428 and 0.788 for the 96.6g, 196.7g and 296.2g masses respectively, does this seems somewhat plausible even though I got a negative value for my first weight?

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### CatatauJunior Member

Thank you for your suggestions. I will not have time to test the friction of the pulley but it is certainly something that I am going to mention in my evaluation.

About the weight because the surface area is the same and therefore the volume is the same, the weight for each model should be the same as well. The models are not perfectly made but they are pretty good, I weighted each one of them an all are within the range 1300g-1350g. What is different in my models is the angle of entrance and the length, because I made it shorter or longer to keep surface area, volume and weight the same. I am attaching a to scale drawing of my models so it is easier to visualize.

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### CatatauJunior Member

When I said under water a literally mean that the whole boat was submerged, like a submarine. For the boats with the smaller angle being pulled by the biggest weight, however, sometimes the bow did emerge out of the water. When I did the experiment I didnt think about this, but now I see that this has probably affected my results for the last two boats (40 and 60 degrees) a lot. This is ok, though, because even though the results will probably not match with the others it is something I will talk about and explain in my evaluation.

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