# Dragon Boat Drag Calculations

Discussion in 'Hydrodynamics and Aerodynamics' started by alexz, Mar 22, 2011.

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### alexzJunior Member

Hi guys,

I'm doing my final year dissertation on the biomechanics of Dragon Boat racing. One of the topics I have to discuss is the fluid mechanics.

I want to express skin friction drag as a function of the skin friction coefficient, wetted surface area and hull velocity as shown here this is where I'm confused

I have seen equations for rowing eight
Code:
`fr=R=0.0041SV^1.83, OR fr=R=kSV^2 which gives resistance in pounds`
I am using the following formula from ITTC to get the skin friction coefficient
Code:
`cf=0.075/(logRn-2)^2`
and calculating the wetted surface area using dimensions from the blueprints.

However in doing so I will have numerous skin friction coefficients, one for every value of Reynolds number as the velocity goes from 0 - steady race velocity, this would result in numerous formulas.

I wanted to ask if you guys think that the value for "k" in the formula for a rowing eight is the skin friction coefficient at race speed? Since then I can use the above formula and obtain a single value rather than numerous.

Also since a dragon boat is a bulky thing, is there a chart/formula which can help in determining the wave and form drag it experiences, I have been trying to use the froude number to aid in this matter but it is getting me nowhere. Or can I assume skin friction to say contribute 60% of drag and divide the skin friction drag by .6 ?

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### BYDEJunior Member

I think you can consider just the steady race velocity, or just take a time average, it seems like a reasonable simplification.
Looking at the link, ''k'' is just a coefficient function of velocity:
k = 0.0041*V^-0.17
I think the author uses it just because he doesn't like the exponent ^1.83 and wants to use ^2...

Form drag can be assumed ~ 0 imo for such a narrow hull, isn't the dragon boat also symmetric about the midship?
What's the Froude number? I guess also the wave drag is pretty small as they are slow canoes. Anyway it's easy to calculate.

In general, since you are a student of biomechanics I think it could be nice to use a rather 'unusual' method:
assuming that you know the power developed by a human body to paddle the boat forward (but if you don't know it should be easier to find references), then you can divide the power by the speed (mean speed, or can be time dependent) and obtain the total resistance. The form drag is zero, you subtract the wave drag, and eventually you get the friction drag.

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### alexzJunior Member

I understand why he uses ^2, I was referring to the 0.0041 being k in the first equation and wondering if thats the skin friction coefficient.

I was going to consider the steady race velocity to calculate my value, but I think I have a better method. Since Rn=VL/mu, I can integrate VL/mu over the velocity range (from 0 to steady state) and get a value for Rn, I am then going to use this Rn value in the skin friction formula by ITTC and get my coefficient. However still confused why V is raised to a power, is it some other formula or perhaps an empirical value derived from data.

That's the thing, My tutor says because the boat is long and bulky, form drag and wave drag cant be neglected.

EDIT: I understan why there is wave and form drag now. There are two types of racing dragon boats, crew of 22 and crew of 12. The crew of 22 is long and slender whilst the crew of 12 is a brick.

The boat design I am working with holds a crew of 22, is 12.4 meters long, 11 meters sits in water, 1 meter wide, 2000kg fully loaded, 9.712 m^2 waterline area and the following cross section

Froude number is a ratio of velocity to wave velocity, basically an extension of the speed length ratio. It helps in determining the critical velocity, which when the boat cannot overcome the waves and the velocity is limited to fluid velocity.

You mentioned being able to calculate wave drag, can you point me to some resources that explain how?

That sounds nice. I think Ill have the conventional way of calculating drag, and Ill compare it with the method you've just described. Thanks

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### Leo LazauskasSenior Member

"Michlet" works quite well for long thin hulls. See:

The program calculates the wave resistance and skin-friction. You can also include form factors.

Have fun!
Leo

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### BYDEJunior Member

yep, Leo's tool would be ideal.

you posted only the last page, so I can't be 100% sure, but I guess it's just a coefficient, not the Cf. As you say, it's probably to fit some data and create an empirical formula.

In my opinion your method is fine, but it's an overkill as you have greater simplifications already in other areas (such as the ITTC57 formula) which eventually will determine the error. Moreover the boat will not have a steady velocity all the time after the initial acceleration, there will be continous accelerations over all the course which I guess are difficult to predict.

i'm a naval architect, i heard about the Froude number...
I didn't mean to ask an explanation of it, sorry maybe I wasn't clear, I wanted to know the value. So now you gave me length already, give me also an average speed.

A long hull (or actually slender) will make less wave drag. It can also be bulky, but the speed matters. Wave drag is related to the froude number, which is related to speed. In fact at low speed the wave drag is very small, that's why I asked the Fn. And again, a greater length will give a smaller Fn so lower drag.

The form drag is due to the pressure field that doesn't recover at the stern (the wake basically) so it starts to matter when the hull is beamy and with a large transom. Your boat has a L/B = 11, absolutely a thin hull.I don't know if it has a transom though.
The waterline can be more interesting for this than the cross section.

Anyway just use Leo's code so you have a sure answer.

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### Leo LazauskasSenior Member

It's not too hard, especially for a biomech department.

See, for example, the report I attached to this post:
http://www.boatdesign.net/forums/boat-design/designing-fast-rowboat-14250-55.html#post416511

For very thin, slender hulls, use the added mass concept as a first approximation of unsteady effects.
Leo.

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### alexzJunior Member

I'll have a look, thanks for the link

Your'e right, the accelerations are difficult to predict, and thus are assumed to be uniform. However having done the math with some arbitrary values the errors obtained are negligible so it is safe to assume that acceleration from the stroke is uniform at steady state.

Wow, I'm excited to be having a discussion with a naval architect. I'm sorry to having provided an explanation, that is the meaning I drew out of your comment. Anyway during a race the average race speed is 3-4m/s, so that would give Fn to be 0.36 if using normal length or 0.39 if using waterline length.

I understand that the the longer and narrower the boat the less wave and form drag there is. However as my tutor explained, there are two types od dragon boat; a long slender one with a crew of 22 and a short bulky one with a crew of 12. I thought I was analysing the drag for the long one alone, however I need to calculate it for the smaller one as well. This clears a lot of my confusion up.

This is what the small one looks like
Here are some more pictures of the waterline levels (long one)

This one is only half of the boat, its symmetric anyway. It shows the waterline
This is a front and back view of the waterline
This is what it looks like in action

Anyway, I will have a look at michlet. I do not understand the table of offset and some other values in there, also I cant seem to get drag to show up by pressing 'R', hopefully the manual helps.

I'll have a read of this as well man, looks like a good report.

8. ### Submarine TomPrevious Member

Regarding wave form. The wake produced by a dragon boat compared to a rowing shell is many times larger so shouldn't be negated IMO.

-Tom

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### BYDEJunior Member

i'm touched now... hehe

0.39? those guys with the weird paddle push really a lot then, I thought the dragon boats were much slower. At this Fn then the wave resistance isn't neglectable imo, it should be around 20%-30% of the total (just my rough guess).

anyway, looking at the picture that you posted i notice also that the crew is paddling all along the hull, doing a lot of mess on the wave profile. If you run Leo's code, I guess (I didn't try it myself, but it should be) one of the output is the wave pattern, and at that speed you should notice a clearly defined wave along the hull. That is the theoretical 'ideal' condition, but in this case it looks quite far from the real case according to the picture of the yellow boat.
So what's the influence of all the paddles?
well, I don't envy you in figuring out this task...

when I asked about the waterline I meant the planform (top view)... but ok, i'm fine with the side view too.
the yellow boat in the photo has an horrible blunt bow/stern which makes a lot of form drag. But maybe they're overloaded (I count more than 30 people, while you said 22) or with a bow trim.
however your hull looks more streamlined. Again, to see the planform would be better, as now I'm just trying to imagine the waterlines in my mind according to the other 2 views, so I may say something wrong.

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### Leo LazauskasSenior Member

Michlet will not give you the hull wave profile - it only calculates far-field waves.
For near-field effects (hull wave profile, squat etc) you need to use Flotilla or some other code.

Leo.

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### BYDEJunior Member

Ok, sorry. I remembered that I saw the pictures of some wave patterns but I didn't remember which code was it. You release too many programs!

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### BYDEJunior Member

I just saw the youtube video (it's a blocked website in china and I hadn't my vpn on before): seriously there's a world championship for dragon boats??
I thought it was just a chinese tradition...
They go really fast

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### Leo LazauskasSenior Member

I could release another dozen tomorrow if I didn't hate writing manuals so much!

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### alexzJunior Member

Yea sorry about that picture of the small boat, that's just a traditional boat and not the one they use for racing, i.e the one I am analyzing.
Here is a plan view of the racing model I am analysing.

Your right, the crew is facing the direction of motion and paddling. This creates interference towards the middle and end of the boat, as the first few people are catching into dead water and the back into fast moving, therefore there is a need to carefully evaluate where to position the strongest, heaviest, quickest, etc crew for optimal performance.

Also any sudden movements of the crew's center of gravity (cog) to cause a slight acceleration in speed need to be minimized, as doing so will increase drag and slow the boat down if their cog surges forward. This is unlike what happens in rowing, where surging forward causes a speed increase as they have their backs to the direction of motion.

Do you mind providing a link to the code, near field wave effect simulation sounds interesting.

Also I had a look at michlet, however I can't seem to get drag by pressing R as stated in the manual?

There is a body that governs them as well, the International Dragon Boat Foundation

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### Leo LazauskasSenior Member

I have never heard that happening. Did you press Shift-R, i.e. R, and not lowercase r?

There are some interesting arrangements that arise in rowing.
The non-zero nett moment of the "standard" rig shown at the top of the attached figure causes the boat to wiggle as it progresses down the course. The other four rigs are "zero-moment" arrangements.
These arrangments assume all rowers are identical and exert identical forces on the oars. (Some minor adjustments are required when rowers exert different forces.)

I'm not sure if a similar analysis could be used to good effect with dragon boats.
Is it in the rules that paddlers must be placed in the same way as the "standard" rig, or are other arrangements allowed?

There is a demo of Flotilla 2.07 at:
http://www.boatdesign.net/forums/design-software/flotilla-demo-2-07-a-32276.html

Good luck!
Leo.

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