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Literature Review of Planing Craft Design - Rough Water Performance

Having considered various components of planing craft theory, it is apparent that so far the designer has only had to be concerned with flat water situations and performance prediction in flat water. The presence of waves has considerable importance on the design of planing craft and complicates the design problem somewhat. The hull form is dependant on the expected wave encounter spectra, or perhaps the worst wave spectra envisaged, since the new problem must include a measure of seakeeping ability, so that hull accelerations and response amplitudes can be determined.

It is well known that for planing craft the flat-water/rough-water problem is essentially one of a compromise between speed and seakeeping. The Delft Ship Hydromechanics Laboratory in the Netherlands has conducted tests on high speed planing craft to determine their seakeeping ability [Keuning 1986]. It is noted that results of these tests show that a very important parameter in the seakeeping behaviour of the planing craft is the deadrise angle [Van den Bosch 1970]. Results of such tests are presented in terms of vertical accelerations as a function of forward speed against wave length. From this it may be concluded that the vertical accelerations may be reduced by as much as 75 per cent in certain conditions by the increase in deadrise angle from 12 degrees to 25 degrees. Additionally, extreme accelerations are much less likely to occur with large deadrise angles, for example, during harmonic accelerations. Due to the adverse influence that deadrise has on resistance, the Delft Ship Hydromechanics Laboratory extended the original Clement series [Clement and Blount 1963], with a similar series of models with 25 degrees deadrise [Keuning and Gerritsma 1985]. 

To be able to improve the seakeeping behaviour of planing craft, Delft Ship Hydromechanics Laboratory  have sought methods to calculate the motions of these craft in waves. Firstly, calculations have been made using a linear strip theory model [Keuning and Gerritsma 1985], the results of which are in good agreement with experimental results. Secondly, use was made of a computer program developed by Zarnick [1979]. This program is based on a non-linear set of equations solved in the time domain. Again, results show good agreement between experimental results and calculated results.

It is known from calculations and from measurements that vertical accelerations are the limiting factor in the operability of planing craft at sea. These accelerations vary considerably along the length of the ship. The maximum is at the bow, the minimum is at about 30 percent of the length from the transom. A carefully chosen working space (bridge usually), may reduce vertical accelerations by as much as 50 per cent [Keuning 1986].

In the USA, Savitsky and Brown [1976] have been conducting their own hydrodynamic studies on several planing hull phenomena and have presented the results of several studies, in conjunction with work done by Fridsma [1971]. This firstly summarises the earlier work performed by Savitsky [1964], then moves on to consider effects of trim tabs, effect of warp, re-entrant vee hulls and preplaning resistance (all flat water design problems), which have been discussed earlier. The final set of experiments which Savitsky and Brown [1976] have detailed are on the behaviour of planing craft in a seaway.

The results of the study are embodied in a series of design charts for predicting the added resistance in waves (power requirements), impact loads on hull structure at the bow and centre of gravity, and the craft heave and pitch motion amplitudes. It is recognised that, both in smooth and rough water, in determining the performance of different hulls, it is necessary to evaluate them at the same running trim, as well as the same load and speed. 

The results showed that the increased deadrise has a beneficial effect on rough water performance, for example, increasing the deadrise from 20 to 30 degrees reduced the added resistance by 20 per cent. Secondly, motions are also attenuated by  higher deadrise angles at high speed. It is on the impact accelerations that deadrise has the most important effect, increasing deadrise from 10 to 30 degrees halves the impact accelerations. Decreasing the trim has a beneficial effect on  loads and motions; reducing running trim from 6 to 4 degrees results in a 33 per cent reduction of impact accelerations, although there is a substantial resistance increase. Increasing the load decreases the impact accelerations, the motion amplitudes at high speeds, and generally reduces the added resistance. Increasing the length to beam ratio raises the acceleration levels at all speeds and amplifies the motions at high speeds. At low speeds, increasing the length/beam ratio increased the added resistance, and at high speeds it reduced the added resistance.

The data was reworked into equations for predicting the added resistance in waves and the impact acceleration at the centre of gravity and at the bow. These equations facilitate performance prediction and are comparable in accuracy with the charts from which they originated. Since the equations are based on empirical data it is necessary to respect the range of applicability and not extrapolate beyond this range (which is somewhat limited). These equations are suitable for computational use and are given in conjunction with Table 2.1:

Table 2.1: Range of applicability of empirical equations. 

(After [Savitsky and Brown 1976])

2.4.1 Added Resistance at V_k/L=2:

                                        [2.07]

Note:    No effect of deadrise.

            Precision 20% .

2.4.2 Added Resistance at V_k/ L=4:

                                                         [2.08]

Note:    No effect of length-beam ratio.

            Precision 20% .

2.4.3 Added Resistance at V_k/ L=6:

                                [2.09]

Note:    No effect of trim.

            Precision 10% .

2.4.4 Average Impact Acceleration at CG, g units:

                                   [2.10]

Note:    Precision 0.2g.

2.4.5 Average Impact Acceleration at Bow, g units:

                                                                     [2.11]

Note:    Precision 20% .

Whilst Savitsky and Brown [1976] presented their results in conjunction with the work done by Fridsma [1969], Fridsma's own work was in fact divided into two volumes; a systematic study of rough water performance of planing boats in regular waves and a systematic study of the rough water performance of planing boats in irregular waves [Fridsma 1971]. The main conclusion of his earlier work was that added resistance, motion response and accelerations are generally non-linear functions of the wave height. Linear behaviour occurs at the extremes of wave height, i.e. contouring of waves (following the wave profile) at low speeds and platforming (jumping from wave crest to wave crest) at very high speeds. Furthermore, it was seen that the wavelength of the maximum resistance was constantly shorter than the wavelength of the maximum response motions. The results of the model tests were collapsed into a simpler form by using a wavelength coefficient:

Wavelength Coefficient:                                                                    [2.12]

The 1971 report has been summarised by the work done with Savitsky and Brown [1976], with design charts and preliminary equations for designers use. The equations developed by Fridsma [1971] are given, with a list of the limits of applicability in Table 2.2:

Table 2.2: Limits of applicability of the added resistance charts.

(After [Fridsma 1971]).

The following is the formula for correcting the added resistance from model tests for C =0.6 and l/b=5, for applicability to other craft within the ranges given above:

                                    [2.13]

The value of the above coefficient 'E' can be calculated from Table 2.3:

Table 2.3: Value of coefficient for equation 2.13. 

(After [Fridsma 1971]).

2.4.6 Motion Corrections:

Similarly, the following is the formula for the motion corrections:

                                                [2.14]

            For trim:                                                                            [2.15]

            For Deadrise:                                [2.16]

2.4.7 Average Centre of Gravity Accelerations:

An approximate formula was deduced for the average accelerations at the centre of gravity (CG):

                                                                                         [2.17]

The related charts are accurate within the ranges given above, and the designer should be careful not to make gross extrapolations beyond those limits.

A paper by Hoggard and Jones [1981] summarises the work done by authors such as Fridsma, Savitsky and Brown, on the subject of pitch, heave and accelerations of planing craft operating in a seaway. The object of this paper is to provide the designer with a usable procedure specifically developed for hard chine planing craft and it provides a useful summary of the calculations required for seakeeping analyses.

Blount and Fox [1976] offer an alternative analysis of Fridsma's work, providing tabulated data for the range of applicability of several calculations developed by Fridsma, for the added resistance of a planing craft in waves. These equations are also given in a table, however, this analysis is not as comprehensive as that of Hoggard and Jones [1981], who include example calculations for heave motions and accelerations.

Further research that has been undertaken at the David Taylor Naval Ship Research and Development Centre, Maryland, USA, on the subject of the prediction of motions of high speed planing boats in waves and includes a theoretical study [Martin 1976]. A theoretical model was derived for predicting the linearised response characteristics of constant deadrise high speed planing boats in head and following waves (the computer program was developed by Hubble [1980] and is fully documented). It is shown that comparisons of the theoretical predictions of the pitch and heave response-amplitude operators and phase angles with existing experimental data show reasonably good agreement for a wide variety of conditions of interest.

Martin [1976] shows that non-linear effects are of more severe consequence at higher speeds, principally because of the reduction of the damping ratio of the boat with increasing speed, and the consequential increase in motions in the vicinity of the resonant encounter frequency. It is concluded that the linear theory can provide a simple and fast means of determining the effect of various parameters such as trim, deadrise, loading and speed, on the damping, natural frequency and linearised response in waves.

This mathematical model is developed from the equations for the pitch and heave degrees of freedom, although the equation for the surge degree of freedom is derived as well. Surge is not included in the calculations since Fridsma [1969], [1971], found from visual observation and examination of the time-history record of model boat motions, that little surging motion took place, particularly at higher speeds.

Hubble [1980] documented the development of her computer program for performance prediction of a planing craft operating in a seaway. This provided a procedure for the prediction of powering requirements and vertical accelerations at the preliminary design stage. Envelopes of operating speed against wave height were developed, based on the following:

• Maximum speed in a seaway due to engine limitations (powering) and propellers

• Human endurance limits due to vertical accelerations.

The habitability limits are given as follows:

                                           [2.18]

                                     [2.19]

Any position between the bow and the CG can be interpolated for by linear interpolation.

For her predictions based on human endurance limits, the average 1/10 highest vertical accelerations were taken as 1.0 g for 4-8 hours endurance, and 1.5 g for 1-2 hours endurance.

Another mathematical model that has been developed is a non-linear model for the prediction of vertical motions and wave loads of high speed craft in head seas. This model was developed in Taiwan [Chiu and Fujino 1989] and compares the non-linear motions and wave loads of planing craft and round bilge craft at high speed, in waves. Unfortunately, this paper is less useful in its conclusions, in terms of what a designer needs to know, but does comment on the occurrence of  huge sagging moments acting when travelling in a head sea. The mathematical model is based on 'strip method synthesis' (strip theory), with the use of non-linear equations of ship motions in the heave, pitch and surge degrees of freedom.

It has been seen that there are several ways to improve the behaviour of a planing boat in a seaway, for example, by increasing the deadrise at the cost of some power, or by reducing the running trim. Reducing the running trim has the additional advantage of reducing the likelihood of porpoising (but increases the risk of broaching). Thus, as mentioned earlier, the use of trim tabs is the most obvious solution to this problem. Wang [1983] undertook a study of motions of high speed planing boats with controllable trim tabs in regular waves. The theoretical analysis was made in an attempt to evaluate the function of a controllable trim tab as a kind of heave and pitch reducing device. As with previous studies of this kind, the equations of motion are based on modified strip theory.

The theoretical study and model tests have shown that the contribution of controllable trim tabs improves the overall performance of a planing boat. Controllable trim tabs could be designed to make a planing boat run at or near optimum attitude in various environments, which result in minimum resistance and avoids porpoising. Most importantly, it is shown that the vertical motions and the acceleration of the boat in waves may be reduced. The agreement between calculated results and experimental results demonstrated that the theoretical method proposed in the report seems to be reasonable for the prediction of the response characteristics of planing boats with controllable trim tabs in waves. The model tests also demonstrated that introducing a pitch velocity feedback to the trim tab in an automatic control system is very effective.

Next Chapter; Planing catamarans...

There is plenty more of this review, to be published at a later date. Contact JB if you have any particular questions.

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