# Resistance scaling

Discussion in 'Sailboats' started by willfox, Nov 6, 2009.

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### willfoxJunior Member

Do you use the same procedure for scaling Side force as well as drag force. I.e break it down into frictional, use 1+k to get viscous and take this away from measured to get wave. Then scale this up?

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### JoakimSenior Member

No. I think the most common way is to define the side force as perpendicular to motion (not to keel). There is no (important) viscous part in this force and also not a wave part although wave pattern has some effect on the side force.

The side force is porpotional to area (~L^2) and V^2 as it is pressure/form based. Depending on what you are looking for you can calculate the effective drag that can be used to define the added resistance due to side force. You can also define the side force vs. leeway. Look at the VPP papers by e.g. Oossanen: http://www.oossanen.nl/download/petervanoossanen_-_predicting_the_speed_of_sailing_yachts.pdf

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### willfoxJunior Member

Thanks Joakim, So im thinking in the same way as you scale up residuary. Thanks for the help

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### daiquiriEngineering and Design

One thing you have to take care about when scaling lift and drag force is the transition from laminar to turbulent flow.

If you consider flow field far from the water surface, then the flows around the scale model and around the full-size boat will be similar if their Reynolds number (Re) is the same. In other words, if you could impose the same Re between the model and the full-size ship, you would obtain the same lift coefficient CL in both cases and no further corrections, either for lift or for drag coefficient, would be necessary.
That happens because having the same Reynolds number assures you that the point of transition from laminar to turbulent flow will happen in the same point at both the model surface and the surface of the full-scale ship, and the turbulent wake will also be physically similar between the two.

But Reynolds number similarity is in conflict with the necessity to have the Froude number similarity in order to obtain the correct wave system at the air-water interface. Since the study of wave system around the hull is the essence of towing-tank testing, Reynolds number similarity is always sacrificed to Froud number similarity - hence the necessity to correct the friction drag estimates with ITTC or other formulae.

As you can't have the same Reynolds number, the only thing you can do to avoid gross errors in determination of lift and drag coefficients is to promote a forced transition from laminar to turbulent flow with the use of turbulators of varios kind. Establishing their correct size and position is not a trivial problem and requires a separate study.

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### ancient kayakeraka Terry Haines

For a modern sailing hull with high aspect ratio keel I suspect the behavior of the hull and keel can be treated separatedly, within reason. That assumes the keel has negligible effect on the flow around the majority of the hull's surface and the effect of the hull is mainly limited to preventing a vortex off the upper end of the keel.

The leeway required to obtain the neccessary lift with a keel with an efficient profile is due to its angle of attack (alpha) which should be so small that the flow around a rounded bilge hull would not be much effected, IMHO.

If these are reasonable assumptions then the scaling calculations are much easier to solve. However they would not apply to a hull with hard chines or a boat with a long keel.

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### willfoxJunior Member

Thanks guys, I have tank tested a bulb keel and im currently comparing these to a standard keel. I have taken the reynolds number for each appendage separately ie. for model, Re for keel = (mean chord x V (m/s))/Kinematic viscosity, Re for rudder is the same equation, Re for hull uses 0.9.lwl instead of mean chord. As it is a bulb keel, what should i use for the Re of the bulb? 0.9 x its length? or chord length? a bit confused.
Thanks daiquiri, I have use studs in the experiment to simulate turbulent flow.

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### daiquiriEngineering and Design

If you are testing the appendages separately from the hull, it is not really important whether you will use length of the bulb, the chord of the keel or the diameter of the bulb...
You want to obtain the same Re number between the scale model and the full-size ship. So, by equating the respective Re numbers, you will obtain a relationship of this kind:
V1/V2 = L2/L1 = D2/D1 = 1/a,
Where V1 and V2 are flow velocities of scale model and of full-sized ship, respectively, L1 and L2 is the reference length of the two and "a" is the scale factor.
Therefore, V1/V2 = 1/a regardless of what reference dimension you are considering, because all the linear dimensions are scaled by the same scale factor.

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