Sailing Mechanics Modeling Part 1 - Resistance (Lessons Learned so far)

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This is the second post in a series of blogs which is basically me stumbling through ideas and seeing how they hold up to coding implementation with reasonable results that I have in mind. I'm interested in sailing speeds as this was a major characteristic that dictated if a chase ended in an action. Example, when the Royal Navy started using copper bottoms (major advantage) before others, they basically became masters of the sea, able to initiate or deny the enemy an engagement.

From my studies so far, the sailing speeds that a captain used may have not been the best achievable speed due to decisions of bearing for intercept or to deny the chaser his best point of sail. I'm not going into that aspect, as I am only interested at this stage in what the "steady" speed is at the current conditions. I say "steady" because the wind is rarely constant and the wave shapes and frequency were also changing. Another big aspect of speed was the skill of the crew. A good helmsmen could see the wind before it arrived (approaching texture upon the surface of the ocean) and compensate early for a gust which kept the ship tracking on its desired bearing. Once again this is only to determine what the theoretical speed would be if all inputs were "frozen" for a bit.

[Design Criteria]
I know what historically the ships' averaged which are recording in shipping logs so if my model mirrors that then I know that I am in the ballpark.

[Design Approach]
The steady state sailing speed is obtained when all of the forces acting on the ship along the axis of interest are summed up and equals zero. Limiting this discussion to the forward/rear axis of a ship, this is when the forces that are driving the ship forward are diametrically opposed by the resistances. So breaking down the equation we have [Driving Forces] = [Resistive Forces] at steady hull speed.

My initial approach was to take on one side of the the equation using theoretical and empirical models and then backfit the other sides' parameters to align with a known speed. Once this works then the same model can work for a range of conditions.

From my college studies of fluid mechanics I foolishly assumed that the drag resistance associated with the incompressible nature of water was an easy and straight forward process to model. What I found after browsing the web and several white papers was quite the opposite.

[Hull Resistance Forces]
The resistance of the hull can be summarized as: (excluding air resistance here)
Total Resistance (TR) = Frictional Resistance (FR) + Wave Resistance (WR)

The FR term is straight forward and mirrors what I initially thought about the parameters involved with the resistances associated with a hull. It can be determined via making a small scale model and then measuring the resistance in a pool and scaling up the results to apply to the full sized ship. It does contain a lot of resistance subcomponents as shown. (Below I interchange the meaning of coefficient and resistance but this doesn't change the approach):

Frictional Resistance (FR) = [Flat Bottom Plank] + [Form Resistance 3D] + [Rudder] + [Fouling] + [High Seas]

The [Flat Bottom Plank] resistance uses hull length and speed as inputs for a family of shapes. Think skin effect here as water exerts a shear along a surface in turbulent flow region.

The [Form Resistance 3D] takes into account the eddies and vortex flows around a 3D hull shape. Ship designers use a Form Factor (k) multiplied by the skin effect to model this:

[Form Resistance 3D] = [Flat Bottom Plank] *[k]

k - can be calculated using hull length, keel depth, beam, block coef., volume displaced. This will be one of terms I will back calculate at a given speed to align my model with historical results.

The remaining terms are minor and will be fine tuned to reflect degraded conditions such as a fouled hull, lack of copper plating or old copper. Rudder input resistance is associated with any turns of the helm off of amidships that are required to sail on the bearing (bad trim, compensation for sail damage). High Seas will be the resistances encountered with waves hitting the bow (heavier ship is less impacted), so a bigger ship will perform better here)

[Resistance - Wave Effect]
Ok, the terms above seem pretty straight forward. This isn't the case with Wave Effect (WE). I'm not going to attempt to define it here as you can read about it all over the web but in short, as the hull moves through water, waves are generated underneath the hull. The number of waves, wave length, etc is contributed to the many characteristics of the hull. One major contributor is the length of the hull along the water/air interface. The length of the hull determines what the ships "Hull Speed" is. This is the speed at which the wave length equals the length of the boat (i.e. the bow resting on a wave peak and the stern resting on a wave peak with the rest of the boat laying along the trough). To sail any faster requires sailing "uphill" over the bow wave and this rapidly ramps up the resistance. For British rated ships, the associated speeds will not approach this "Hull Speed", but, the effect is still present in the resistance term (one source states around 1/3 of the total resistance for a sailing ship, grain of salt taken here). Example, for a frigate that is 142ft long (not sure what the waterline length is), but at 142ft the hull speed comes out to roughly 16knots (they sailed way under that).

The issues associated with modeling wave effect is that.. well you can't calculate it as no theoretical or empirical model is very good at it. (according to sources). You have to build a model and drag it in a tank, then subtract out the frictional forces, and what is left is the wave effect. Lucky for the ship designers, the wave effect of a model will be the same for the full sized ship as long as the model shares the same shape and is tested at a relative speed to the full size that produces the same wave conditions (this speed is known). What that means for a software modeler of an 18th century sailing ship is that I have to take a swag at this term. Therefore I am placing this parameter into the "back-fit" the number to match historical performance bucket.

So knowing what I now know (I Arrr smarter now ), I am reversing my initial (now foolish) approach of first calculating the hull resistance through empirical models. Now, I will empirically model the forces of the sails at a known speed and then backfit the resistances.

(A little spoiler, I've already looked into the sails and this is the correct approach for my project.)

My next blog entry will show a sample of the sails modeling.

Until next time...

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Updated 12-30-2017 at 09:58 by Aaron