# resistance scaling

Discussion in 'Hydrodynamics and Aerodynamics' started by previah, Jan 19, 2012.

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### previahJunior Member

Hi,

If I know the resistance curve (R vs speed) for one particular draft, is there a way to estimate the resistance for other draft? It does not need to be spot on estimation (maybe the likes of admiralty formula estimation).

Best regards,
-Arman-

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### gonzoSenior Member

Do you mean if you increase the displacement of the vessel? The answer for that is no. The shape of the hull changes as it submerges deeper. You need to recalculate.

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### Leo LazauskasSenior Member

If:
1. the hull does not have too much flare near the free surface,
and
2. you know the beam and the shape of the waterplane
and
3. you know the wetted area,
then you can get a reasonable estimate for small changes in draft.

You can estimate the viscous drag using a friction line in the standard way
using the length and the wetted surface area.

You can estimate the increase or decrease in surface area from the
longitudinal girth multiplied by the change in draft, and hence you can
estimate the change in skin-friction.

Wave resistance can be assumed to vary with beam squared.
So, multiply the original wave (or residuary) resistance by (B1/B0)^2,
where B1 is the new beam.

It's rough, but should give reasonable results quickly for small changes in draft.

Good luck!
Leo.

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### DCockeySenior Member

If the vessel has vertical sides at the waterline, then which is the better approximation for small changes in displacement and draft:
1) Wave resistance does not change with small displacement changes
- or ? -
2) Wave resistance scales with displacement

The suggestion above implies the answer is 1).

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### gonzoSenior Member

The skin friction will not increase in direct proportion to displacement increase. Other parameters won't scale in direct proportion either. For example, prismatic coefficient.

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### DCockeySenior Member

What about wave resistance, aka residuary resistance. Obviously it doesn't scale exactly with displacement, but is scaling with displacement a reasonable first order approximation?

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Assuming the resistance curve is total resistance, then yes it is very easy.

It is simply pro-rata one displacement to the other as a ratio.

Resistance at new displacement = (displ new/displ old) x resist at old displ.

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### Leo LazauskasSenior Member

There are a few traps in all of these methods.
IMO, it would be imprudent to apply them to hulls with large bulbous bows and/or large
transom sterns, and possibly planing hulls.

Last edited: Jan 19, 2012
9. Joined: Oct 2008
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Indeed.

For example, a 10m boat, going from say 10 tonne to 20 tonne, is somewhat different from a 100m boat going from 500 tonne to 550 tonne.

But, in understanding the generality, it works well, when used with common sense.

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### gonzoSenior Member

You need not just common sense but experience to be able to interpret the results.

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### Leo LazauskasSenior Member

Interesting question, David.

It is probably "between" 1) and 2) because wave effects tend to decrease exponentially with depth.

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### DCockeySenior Member

That would be my guess also. What would be a good characteristic length for the decay, length corresponding to Froude number of 0.4?

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### philSweetSenior Member

Perhaps the biggest problem in attempting to do this is regarding changes in trim. If the weight goes in anywhere other than the center of flotation, you mess up everything. If you started out at anywhere other than ideal trim you are also pretty much screwed. You can add weight to an out-of-trim canoe and significantly reduce resistance. In a sailboat, adding weight would effect leeway, heel, transom immersion, rudder angle and the dynamic response of the boat to the seas. Roll and pitch damping affect resistance in the real world, so changes in linear and rotational inertia are important considerations.
There are rather drastic constrains to even trying to do this.

However, if you can explain in gory detail where you're starting from and where you're ending up, maybe the forum can agree to ignore many of the above objections.

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### Leo LazauskasSenior Member

I don't have time to do it, but it is possible to use Michlet to get a reasonable answer quickly.

For example, set up a long thin parabolic strut (say L=10m, B=1m) with a draft of 1m.
Use the sinkage option to float the "hull" at 0.5m and calculate the resistance.
Then float it at 0.6m and calculate.
Then 0.7m, etc.

Plot wave resistance/Displacement weight as a function of Froude number.

You can then try with a more realistic hull. I suggest a parabolic strut because:
1. input and results are easy to understand,
2. Michlet calculates the spectral functions exactly for parabolic struts and Wigley hulls,
3. Many post-processing calculations can be done by hand or in a spreadsheet.

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### gonzoSenior Member

The resistance on a strut or keel is in part from the tip vortex. The would be the same regardless of displacement-draft.

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