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

So I am writing a physics paper for school and the research question I chose is the one above: How does the angle of the bow of a boat affects its coefficient of drag?

I have done my experiment and successfully calculated the coefficient of drag (Cd) for each of my boat shapes. I did my boat shapes in a way that the only thing different from one another would be the angle of the bow, so I kept surface area and volume the same. The boat shapes I did are in the attachment, have a look; they all have 4cm as depth too.

I calculated Cd using the drag equation: Fd=1/2*p*v^2*Cd*A. And I took the reference area to be the total surface area of the boat, because in my experiment the whole boat was under water so it is equal to the total wetted surface.

I got 0.006078, 0.005467, 0.00465, 0.003425 and 0.00318 for my 120, 100, 80, 60 and 40 angle boat shapes respectively. Does this seem plausible? This give a quite neat linear relationship between Cd and angle of bow.

My problem is that now I have to explain why my results are the way they are. I have to write a hipothesis as well. I have researched a lot about fluid dynamics but the more I read the more I get confused. Can someone please help me with the theory please? Thank you

 

I think that drawing the different angles to scale will make it easier to visualize. You can't have different angles and keep the same volume and surface area the same. A boat with the same displacement and different prismatic coefficient will have different surface areas. You will have to take that into consideration in your calculations.

 

Did you assume Cd based on wetted area stays the same as bow shape changes? What is your reasoning?

 

I dont understand what you mean with "did you assume". these are the results I got from my experiment. In my experiment I got values for velocity, density, force of drag and the reference area I calculated from my boat shapes (all of them have the same one around 0.17 m^2). And used these values to calculate Cd for each shape. My problem is that I cant explain my results, the theory behind what is happening

 

My mistake.

 

What speeds were used for the testing? What were the corresponding Froude numbers?

The usual method for dealing with the drag of a boat or ship is to assume it is made up of two components. One is assumed to be a function of wetted area and Reynolds Number and frequently called "viscous resistance". It is usually calculated using a formula such as the ITTC curve.

The other is frequently called "wave-making resistance" or similar and is defined as the total drag less the "skin friction drag". It is assume to be a function of Froude number and independent of Reynolds Number.

 

I actually used weights and a pulley. So boat was connected to a weight using a string that passed through a pulley which had sensor in it that calculated time and velocity. I then took Fd to be the same as the weight of the mass when the boat reached constant velocity (forces are balanced, weight pulling boat = drag). this constant velocity and Fd were then used to calculate Cd. I just want a simple explanation of how drag is created and why it would be different when the angle of the bow changes. Remember I am in high school and everything I know about fluid dynamics is self thought.

 

An impressive project for a high school student.

Unfortunatley there isn't a real simple answer for how drag is created by a boat moving though the water.

Drag changes due to changes in the angle of the bow can be due in part to differences in the wave generated by the bow. But some the differences in drag in your experiments could also be due to the differences in the overall lengths of the models.

Another cause of the differences in your data could be due to different speeds. Did you test each design at several speeds or each at one speed? How much difference was their between the speeds of the different designs?

 

Ok so I am attaching a diagram of my experiment to show exactly how I did it. I used three different masses for each boat (96.6g, 196.7g and 296.2g) and each boat reached different constant speeds with these weights pulling them. So the boat with angle 120 for example reached an average constant velocity of about 1.45m/s with the 96.6 mass pulling it and the boat with the angle 40 reached an average constant velocity of about 1.85m/s with the same mass pulling it. To calculate the Cd for a boat I calculated it individually for each speed and weight pulling it and then averaged the three out (three weights used for each boat, three different constant velocities) to get an average Cd for the boat shape.

 

Froude number is a coefficient which can be used to compare speeds of boats of didferent lengths.
Fn = Velocity / (square root (g * Length))
where g is the gravitational constant (9.8m/s^2) and length is the waterline length. Consistent units need to be used. I assume your models had vertical bows so the waterline length is the same of the overall length.

Averaging the resistance for different weights doesn't help with understanding the differences between the models.

If I did the math correctly the 120 degree model with a length of .358m at a speed of 1.45m/s would have a Froude number of 0.77, and the 40 degree model with a length of .436m at a speed of 1.85m/s would have a Froude number of 0.89. Were the models planing or were they generating large waves?

For each model try plotting the drag/displacement vs the Froude numbers corresponding the the speeds with the three weights. Put a curve through the points for each model and then compare the curves of the different models.

Also what are the wetted surface areas for the models?

 

When a boat moves through the water the bow has to separate the water molecules that then slide down the side of the boat and come back together behind the boat. The molecules resist this action in a number of ways, first they resist being separated in the first place, at the bow, then they resist the movement down the sides of the boat.

So why does a pointy bow move through the water with less drag? Think about the initial point of contact with the water. If this initial point of contact is a flat surface, like a totally flat front of your boat, it is always pushing some water ahead of it before the water splits and goes around...ie lots more force needed to go forward.

Now think about putting a shallow point on that bow. The initial contact with the water becomes a line instead of a plane. Because it's a line instead of a plane the forces generated per unit area at the contact point are multiplied many times over. In theory. the finer the initial contact point the less force needed to separate the water. I say in theory because, as david has said, there are many other factors involved.

With a boat you have width, beam. So when you put that point on the bow you have effectively created 2 inclined planes that are sliding through the water. The steeper the plane is the more energy it takes to move along it. Thats why the smaller that angle is at the point the less force needed to separate the water, ie less drag.

I hope this helps. I congratulate you on taking on this experiment.

 

It is pretty impressive. Congratulations on your project.

 

Here's a couple more ideas for you.

1. As was suggested before, do all your drawings to scale. It will help u visualize what is happening, and will impress your teacher.

2. Whenever you do an experiment it's good to have a base line to compare your results against. In this case a logical base line would be to do the tests with no point at all on the bow.

 

Thank you seadreamer6, Gonzo and David for all your compliments and the help you have given me this far. So first, David, I did what you told me and plotted the graph for Froude Number x Drag for all shapes and I will attach it so you can have a look. It seems to me that for the first three boat shapes (120, 100, 80) the line is being shifted upward however the pattern kind of breaks down with the two last boat shapes. I think this might be due to the fact that the last two shapes were sometimes planning while the others were always totally under water. Also, the wetted surface area is about 0.17 m^2 for all of the shapes.

Seadreamer6, your explanation was very clear an just what I was looking for. Thank you very much for that. I will also take your advice to draw the diagram to scale. What I didn't understand was your second suggestion; what do you mean with no point at all on the bow? Do you mean a shape with just a rectangle without the triangle on the top?

Gonzo, it is always nice to get compliments

 

Yes. Basically like a block of wood with a flat surface for the bow. After thinking about this I'm not sure you need this. Your basic idea is to look at the effect of different bow angles, so knowing the drag for no angle probably wouldn't add much. It would however give you some nifty information on why bows are pointed at all.