Design of Bulbous Bows  球形船首的设计

Nearly 90 years ago, R. E. Froude interpreted the lower resistance of a torpedo boat, after fitting of a torpedo tube, as the wave reduction effect of the thickening of the bow due to the torpedo tube. D. W. Taylor was the first who recognized the bulbous bow as an elementary device to reduce the wavemaking resistance. In 1907 he fitted the battleship Delaware with a bulbous bow to increase the speed at constant power. In spite of great activities in the experimental field to explore its potential, 70 years had to pass before the bulb finally asserted itself as an elementary device in practical shipbuilding. A suitably rated and shaped bulb affects nearly all of the properties of a ship. Especially for fast ships, the use of a bulb allows a departure from hitherto accepted design principles for the benefit of a better underwater form. The higher building costs are the only disadvantage.
近 90 年前，R. E. Froude 解释了鱼雷艇在安装鱼雷发射管后较低的阻力，认为这是由于鱼雷发射管导致船头增厚的波浪减小效应。D. W. Taylor 是第一个认识到球形船头作为减少造波阻力的基本装置的人。1907 年，他为战列舰德拉瓦州安装了球形船头，以在恒定功率下提高速度。尽管在实验领域进行了大量活动以探索其潜力，但在实际造船中，球形船头的应用直到 70 年后才得以确立。合适的形状和尺寸的球形船头几乎影响船舶的所有特性。特别是对于快速船舶，使用球形船头允许偏离以往接受的设计原则，以获得更好的水下形状。更高的建造成本是唯一的缺点。
The protruding bulb form affects hydrodynamically a variation of the velocity field in the vicinity of the bow, that is, in the region of the rising ship waves. Primarily the bulb attenuates the bow wave system, which usually is accompanied by a reduction of wave resistance. By smoothing the flow around the forebody, there is good reason to believe that the bulb tends to reduce the viscous resistance too. Therefore, the beneficial action of a protruding bulb depends on the size, the position, and the form of the bulb body. See Fig. 1.
突出的球泡形状在船头附近，即上升船波的区域，影响了速度场的变化。主要是球泡减弱了船头波系统，通常伴随着波阻力的减少。通过平滑前体周围的流动，有充分理由相信球泡也倾向于减少粘性阻力。因此，突出的球泡的有益作用取决于球泡体的大小、位置和形状。见图 1。
The linearized theory of wave resistance has provided the main contribution to the understanding of the bulb action (Wigley [3], Weinblum [4|, Inui [5,6]). But it is of no great use for the project engineer. In the preliminary stage of his project, he needs fundamental information on which to base concrete decisions. Later, in the realization stage, the quantitative as well as qualitative guidelines are important, because the hydrodynamic phenomena are not describable by few geometric form parameters alone. For this reason, in this paper, the mode
波阻力的线性化理论为理解船首球的作用提供了主要贡献（Wigley [3]，Weinblum [4]，Inui [5,6]）。但对项目工程师来说，这并没有太大用处。在项目的初步阶段，他需要基本信息以便做出具体决策。后来，在实现阶段，定量和定性指导都很重要，因为水动力现象不能仅通过少量几何形状参数来描述。因此，在本文中，模式

Fig. 1 Bow wave pattern of a model without (upper picture) and with bulbous bow (lower picture)
图 1 无（上图）和有球鼻（下图）模型的波浪模式
of action of a bulb and the influence of bulb parameters on resistance or power reduction, respectively, are described in a qualitative manner; guidelines for bulb design are also introduced. The design charts presented here are the result of a research project; that is, of an analysis of routine test results, of the Hamburg and the Berlin Model Basins supplemented by results of additional tests to fill the gaps. The charts are new and therefore still in need of improvement and completion.
灯泡的作用及其参数对电阻或功率降低的影响以定性方式描述；同时也介绍了灯泡设计的指导原则。这里呈现的设计图表是一个研究项目的结果；即对汉堡和柏林模型水池的常规测试结果的分析，并通过额外测试的结果来填补空白。这些图表是新的，因此仍需改进和完善。

a, -Type a, -类型

b, 0 - Type b, 0 - 类型
Fig. 2 Bulb types 图 2 灯泡类型

c, - Type c, - 类型

For an adequate presentation of the hydrodynamic properties of bulbs, it is necessary to systematize the different existing bulb forms by means of geometric parameters. Obviously a definitive description of a bulb shape, just as for a ship form, with a finite number of geometric parameters, is impossible. But a rough classification is possible using only few parameters.
为了充分展示灯泡的水动力学特性，有必要通过几何参数对不同的灯泡形状进行系统化。显然，像船体形状一样，用有限数量的几何参数对灯泡形状进行明确描述是不可能的。但可以仅使用少量参数进行粗略分类。
With the shape of the cross section of the bulbous bow at the forward perpendicular as the main criterion, one can differentiate three main bulb types (Fig. 2) |8|:
以前垂线 处的球形船头横截面 的形状为主要标准，可以区分三种主要的船头类型（图 2）|8|：
(a) -Type: Fig. 2(a) shows the drop-shaped sectional area of the delta-type with the center of area in the lower-half part. This shape indicates a concentration of the bulb volume near the base. The Taylor bulb and the pear-shaped bulbs belong to this type.
(a) -类型：图 2(a)显示了三角洲型的滴状截面积 ，其面积中心位于下半部分。这个形状表明灯泡体积在基部附近集中。泰勒灯泡和梨形灯泡属于这一类型。
(b) O-Type: This type (Fig. 2b), with an oval sectional area and a center of area in the middle, has a central volumetric concentration. All the circular, elliptical, and lens-shaped bulbs as well as the cylindrical bulbs belong to this type.
(b) O 型：这种类型（图 2b）具有椭圆形截面 ，其面积中心位于中间，具有中心体积浓度。所有圆形、椭圆形和透镜形的灯泡以及圆柱形灯泡都属于这一类型。
(c) -Type: The nabla-type also has a drop-shaped sectional area (Fig. 2c), but its center of area is situated in the upper-half part, indicating a volume concentration near the free surface. Because of its favorable seakeeping properties, this type is the most common bulb.
(c) -类型：nabla 型也具有一个滴状的截面积 （图 2c），但其面积中心位于上半部分，表明在自由表面附近存在体积集中。由于其良好的航行性能，这种类型是最常见的球形。

With respect to the lateral contour of the bulbous bow, two typical classes are distinguishable:
关于球形船头的侧面轮廓，可以区分出两种典型类型：
(a) The stem outline remains unchanged as with the Taylor bulb. These bulbous bows do not have favorable properties and are no longer built today.
（a）干茎轮廓与泰勒灯泡保持不变。这些球形船头没有良好的特性，今天不再建造。
(b) The stem outline is changed by the protruding bulb as with all modern bulbous bows.
（b）茎轮廓因突出的灯泡而改变，就像所有现代球形船首一样。

In addition to these classification criteria, quantitative bulb parameters are necessary for delineation of the bulb form. The author is of the opinion that six parameters are sufficient for all practical purposes. Figure 3 shows the three linear and three nonlinear geometric bulb quantities that are reduced to the bulb parameters, that is, normalized by the main dimensions of the ship, as described in the following.
除了这些分类标准，定量的灯泡参数对于灯泡形状的划分是必要的。作者认为六个参数对于所有实际目的来说是足够的。图 3 展示了三种线性和三种非线性几何灯泡量，这些量被简化为灯泡参数，即通过船舶的主要尺寸进行归一化，如下所述。

The three linear bulb parameters are
三个线性灯泡参数是

The variation of the linear bulb parameters is easily possible during the project phase. The breadth is not necessarily the maximum breadth of the bulb body that, for hydrodynamic reasons, can also be located before the FP. The depth pa- area of ram bow in longitudinal plane,
在项目阶段，线性灯泡参数的变化是很容易实现的。宽度 不一定是灯泡主体的最大宽度，出于流体动力学的原因，它也可以位于 FP 之前。纵向平面中的深度 pa- 区域的撞击船首，
cross-sectional area at forward perpendicular (FP),
在前垂直面 (FP) 的横截面积，
midship section area,
中部截面面积，
maximum breadth of bulb area
灯泡区域的最大宽度
beam, midship, m  横梁，中船，米
block, midship-section, prismatic, and waterline coefficients, respectively
块，中部截面，棱柱形和水线系数，分别
prismatic coefficient, entrance
棱镜系数，入口
frictional or residual resistance coefficient, respectively
摩擦或残余阻力系数，分别
residual power displacement coefficient
残余功率位移系数
residual power reduction coefficient
残余功率降低系数
lateral parameter  侧向参数
cross-section parameter
截面参数
breadth parameter  宽度参数
length parameter  长度参数
volumetric parameter
体积参数
depth parameter  深度参数
diameter of propeller, or wake field, respectively. m
螺旋桨直径或尾流场，单位：米。
Froude number  弗劳德数
total height of
总高度为
length of entrance, or between perpendiculars, respectively,
入口的长度，或在垂直线之间，分别是
protruding length of bulb, m
突出灯泡的长度，米
delivered, frictional, or residual power, respectively, PS effective frictional or effective residual power, respectively, PS
交付的摩擦功率或剩余功率，分别为 PS 有效摩擦功率或有效剩余功率，分别为 PS
residual power reduction factor
残余功率降低系数
frictional, total, or viscous resistance, respectively, kp
摩擦、总和或粘性阻力，分别为 kp
viscous residual, wave-breaking, or wavemaking resistance, respectively, kp
粘性残余、破浪或造浪阻力，分别为 kp
bulb effect on wave-breaking or wavemaking resistance, respectively, kp
灯泡对破浪或造浪阻力的影响，分别为 kp
secondary bulb effect, bulb effect on viscous resistance, kp
次级灯泡效应，灯泡效应对粘性阻力的影响，kp
Reynolds number  雷诺数
ship surface or total bulb surface, respectively,
船体表面或总球泡表面，分别是
draft at or midship, respectively, m
草稿在 或中船，分别为 m
ship speed, knots  船速，节
total bulb volume,
总灯泡体积，
volume of protruding bulb part,
突出球部的体积，
displacement volume,
排量,
height of the foremost bulb point over baseline, m
前端灯泡点相对于基线的高度，米
thrust deduction or wake fraction, respectively
推力扣除或尾流分数，分别
propulsive efficiency
推进效率
viscosity of water,
水的粘度，
density of water,
水的密度，
acceleration due to gravity,
重力加速度，

Fig. 3 Linear and nonlinear bulb quantities
图 3 线性和非线性灯泡数量
rameter is a valuation factor of the beach slope of the bulb top (thick line in Fig. 3).
参数是灯泡顶部海滩坡度的估值因素（图 3 中的粗线）。
The three nonlinear bulb parameters are
三个非线性灯泡参数是

The volume is the nominal bulb volume. The total or effective bulb volume is the sum of and the fairing volume , which results from the fairing of the bulb into the ship hull.
体积 是名义灯泡体积。总或有效灯泡体积 是 和整流罩体积 的总和，整流罩体积是由灯泡整流到船体中产生的。

Finally, a distinction is possible between an additive and an implicit bulb. An additive bulb increases the displacement volume of the ship by the effective bulb volume . The sectional area curve of the original hull remains unchanged. On the other hand, the effective volume of an implicit bulb is part of the displacement volume of the main hull that is shifted from unfavorable regions and concentrated in the vicinity of the forward perpendicular. By this process, the sectional area curve of the original ship is changed.
最后，可以区分加法型船首和隐式船首。加法型船首通过有效船首体积 增加船舶的排水体积 。原始船体的断面面积曲线保持不变。另一方面，隐式船首的有效体积 是主船体的排水体积 的一部分，这部分体积从不利区域转移并集中在前垂线附近。通过这个过程，原始船舶的断面面积曲线发生了变化。

Before discussing the influence of the bulbous bow on the ship's resistance and required power, respectively, we should mention other important hydrodynamic qualities which play a role in the decision whether a bulb should be used or not. The change of resistance influences the thrust loading of the propeller and, consequently, other propulsive characteristics of the ship; for example, the quasi-propulsive coefficient, the wake, and the thrust deduction fraction [9-11|. Figure 4 shows this indirect influence of a bulbous bow on thrust deduction and wake fraction. Both are increased by an additive as well as by an implicit bulb, if the bulb ship has a lower total resistance than the bulbless form. But there is also a direct influence of the bulbous bow on the wake distribution in the propeller plane In Fig. 5 the radial distributions of axial wake components of ships with and without a bulb are compared. Within the propeller disk area the axial wakes of all bulb ships are higher
在讨论球鼻船首对船舶阻力和所需功率的影响之前，我们应该提到其他在决定是否使用球鼻的重要水动力特性。阻力的变化影响螺旋桨的推力负荷，从而影响船舶的其他推进特性；例如，准推进系数、尾流和推力扣除系数。图 4 显示了球鼻对推力扣除和尾流系数的间接影响。如果球鼻船的总阻力低于无球鼻形式，则两者都会因附加和隐含的球鼻而增加。但球鼻对螺旋桨平面尾流分布也有直接影响。图 5 比较了有球鼻和无球鼻船舶的轴向尾流分量的径向分布。在螺旋桨盘区域内，所有球鼻船的轴向尾流都更高。

Fig. 4 Influence of a bulbous bow on thrust deduction and wake fraction (- . . - with, - - without bulb)
图 4 球形船首对推力扣除和尾流分数的影响（- . . - 有球形船首，- - 无球形船首）

Fig. 5 Influence of a bulbous bow on the radial distribution of circumferencial average nominal axial wake component (- . . . . . with, -— without bulb)
图 5 球形船首对周向平均名义轴向尾流分量的径向分布的影响（- . . . . . 有球形船首，-— 无球形船首）
than the wakes of the bulbless ones. The reason for this is the change of flow around forebody and bilge, which is observable in the model case up to the propeller disk \12,13]. But in the correlation of model test and full-scale results, scale effects play a very important role [10] and it is not certain if this bulb effect is also found at the ship.
比无泡沫船体的尾流要好。这是因为在船首和舱底周围的流动变化，这在模型案例中可以观察到，直到螺旋桨盘\12,13]。但是在模型试验与全尺度结果的相关性中，尺度效应起着非常重要的作用[10]，并且尚不确定这种泡沫效应是否也存在于船上。

Although unfavorable effects are possible, bulbous bows in general do not influence the course stability or the maneuverability [14]. No significant changes of the overshoot angle or the period in zigzag tests could be established. The bulb is an ideal place for the arrangement of bow thrusters and acoustic sounding gears.
尽管可能存在不利影响，但一般来说，球形船首不会影响航向稳定性或机动性[14]。在锯齿形测试中，未能确定超调角或周期的显著变化。球形船首是布置船首推进器和声学探测设备的理想位置。

The seakeeping qualities of a ship are a special problem, and a very broad field, which will be discussed here only briefly.
船舶的抗波性能是一个特殊的问题，也是一个非常广泛的领域，这里将仅简要讨论。

Fig. 6 图 6
Damping coefficient of partially immersed bulbous cylinders as function of wave number
部分浸没的球形圆柱体的阻尼系数 作为波数 的函数

Except for the relative foreship motion against the water surface, the bulbous bow has no unfavorable influence on either the remaining motions or on the maximum bending moment in the midship section [15, 16]. In spite of the higher relative motion of a bulb ship, the danger of slamming of a well-shaped bulb is no higher than with the bulbless ship [17). In detail, the bulb mitigates the pitching motion of the ship by its higher damping. It should be mentioned here that the damping coefficient of bulb cylinders in a two-dimensional case vanishes for a certain wave number |18| as shown in Fig. 6. Since nonbulbous cylinders do not show this quality, the damping effect of a bulbous bow, for example, of O-type, can vanish for definite wave numbers, and the bulb ship moves like a bulbless one.
除了相对于水面相对前进运动外，球形船首对其余运动或中船段的最大弯矩没有不利影响[15, 16]。尽管球形船的相对运动较大，但形状良好的球形船的撞击危险并不比无球形船高[17]。具体来说，球形船首通过其更高的阻尼减轻了船的俯仰运动。这里需要提到的是，在二维情况下，球形圆柱的阻尼系数在某个波数下消失|18|，如图 6 所示。由于无球形圆柱不具备这种特性，因此例如 O 型的球形船首的阻尼效应可能在特定波数下消失，球形船的运动就像无球形船一样。

In regular waves, model tests show that the critical Froude number from which the bulb ship begins to be superior increases with increasing ratio . As a function of at constant Froude number, the resistance of a bulb ship increases more rapidly than that of the bulbless form. Therefore, most of the smooth-water advantages of bulb ships vanish above about . In irregular waves, nearly all bulbous ships have disadvantages above Beaufort 8 . Since in the North Atlantic the probability of the occurrence of wind intensity more than Beaufort 8 is only about 10 percent, and up to the bulbous ship is the best ship [20] regardless of seakeeping aspects, the bulb design consequently may be carried out in view of the smooth-water performances only.
在规则波浪中，模型试验表明，灯泡船开始优越的临界弗劳德数 随着比率 的增加而增加。在恒定弗劳德数下，灯泡船的阻力作为 的函数比无灯泡形式的阻力增加得更快。因此，灯泡船在大约 以上的平水优势几乎消失。在不规则波浪中，几乎所有的灯泡船在博福特 8 以上都有劣势。由于在北大西洋，风力强度超过博福特 8 的概率仅约为 10%，而在 之前，灯泡船在不考虑航行性能的情况下是最佳船只[20]，因此灯泡设计可以仅考虑平水性能。

In navigation in ice, the bulbous bow has proved to be advantageous. Its form enables a tipping of ice floes coming from the front in such a way that they glide along the hull of the foreship with their wet-side friction coefficient, which is small. Due to this effect, the speed loss of a ship with a bulbous bow is smaller than that of a bulbless one.
在冰上航行时，球形船头被证明是有利的。它的形状使得来自前方的冰块能够倾斜，从而以较小的湿侧摩擦系数沿着前船的船体滑动。由于这一效应，球形船头的船只速度损失小于没有球形船头的船只。

If from the beginning a bulbous bow is included in the shaping of the underwater hull form, then for fast ships especially it is possible to leave the traditional recommendations on the fullness of the forebody and the unavoidable abaft position of the center of buoyancy. Without disadvantages, the bow bulb allows a fuller foreship form and therefore better trim and stability properties. Using an implicit bulb, a more slender aft-body is possible at constant total block coefficient with improved propulsive performance. Without increase of the resistance, a greater angle of entrance for the waterlines can be used as compared with the accepted practice so far [22].
如果从一开始就将球形船首纳入水下船体形状的设计中，那么对于快速船只来说，尤其可以不再遵循传统的前体丰满度建议和不可避免的浮力中心位置在船尾的要求。船首球泡没有缺点，允许更丰满的前船体形状，从而改善了船的吃水和稳定性特性。使用隐式球泡，可以在保持总块系数不变的情况下实现更纤细的船尾，并提高推进性能。与迄今为止的公认做法相比，可以在不增加阻力的情况下使用更大的水线入水角度。

The most important effect of a bulbous bow is its influence on the different resistance components and consequently on the required power. Although the design charts represent the power reduction due to a bulb, for a better understanding the hydrodynamic phenomenon shall be discussed by means of the influence of the bulb on the resistance. For this purpose, the following subdivision of the total resistance is used
球形船首最重要的效果是它对不同阻力成分的影响，从而影响所需的功率。尽管设计图表显示了由于球形船首而导致的功率减少，但为了更好地理解，应该通过球形船首对阻力的影响来讨论水动力现象。为此，使用以下总阻力的细分。

where 哪里
viscous resistance  粘性阻力
frictional resistance
摩擦阻力
viscous residual resistance
粘性残余电阻
wavemaking resistance
波浪阻力
wave-breaking resistance
抗波破坏能力
The latter two components are related to wavemaking. Their contributions to the total resistance are very different for ships with different block coefficients and speeds. Here, an explanation is to be found for the fact that the resistance reduction due to a bulb for full, slow ships can exceed the wave resistance alone, which at is a negligible part of the total resistance.
后两个组成部分与造波有关。它们对总阻力的贡献在不同的船舶块系数和速度下差异很大。在这里，可以解释为什么对于满载、低速船舶，因球鼻而导致的阻力减少可以超过单独的波浪阻力，而在 时，波浪阻力在总阻力中占的比例微不足道。

The additional bulb surface always increases the frictional resistance , which is the main part of the viscous component . Up to now, it is not quite clear whether the bulb affects the viscous residual resistance due to the variation of the velocity field in the near bow range . But in the reanalysis of test data based on Froude's method, presented here, this open point is of no account.
额外的灯泡表面总是增加摩擦阻力 ，这是粘性成分的主要部分 。到目前为止，灯泡是否影响由于近船首范围内速度场的变化而产生的粘性残余阻力 尚不清楚。但在这里基于弗劳德方法重新分析的测试数据中，这一开放点并不重要。

There is no doubt concerning the influence of the bulbous bow on wavemaking resistance . The linearized theory of wave resistance has rendered the most important contribution to the clarification of this problem . According to this theory, the bulb problem is a pure interference problem of the free wave systems of the ship and the bulb. Depending on phase difference and amplitudes, a total mutual cancellation of both interfering wave systems may occur. The position of the bulb body causes the phase difference, while its volume is related to the amplitude. The wave resistance is evaluated by analysis of the free wave patterns measured in model experiments .
毫无疑问，球形船首对波浪阻力的影响 。线性化的波浪阻力理论对澄清这个问题做出了最重要的贡献 。根据这一理论，球形问题是船舶和球体自由波系统的纯干涉问题。根据相位差和振幅，两个干涉波系统可能会完全相互抵消。球体的位置造成相位差，而其体积与振幅相关。波浪阻力通过分析在模型实验中测得的自由波模式来评估 。

The wave-breaking resistance depends directly on the rising and development of free as well as local waves in the vicinity of forebody and is a question of typical spray phenomenon. Understanding of the breaking phenomenon of ship waves is important for the bulb design for full ships. includes all parts of the energy loss by the breaking of too-steep bow waves. The main part of this energy can be detected by wake measurements . The local wave system contributes the main part to this resistance component. This wave system consists mainly of the two back waves of bow and stern which are generated by deflection of the momentum. The deflection rate of the flow is a degree of the steepness of these back waves, of which only the bow wave is of a practical importance in bulb design.
波浪破坏阻力 直接依赖于船首附近自由波和局部波的上升和发展，是典型喷雾现象的问题。理解船舶波浪的破坏现象对全船的船首设计至关重要。 包括由于过陡船首波浪破坏而导致的所有能量损失部分。这部分能量的主要部分可以通过尾流测量 来检测。局部波浪系统对这一阻力分量贡献了主要部分。该波浪系统主要由船首和船尾的两个背波组成，这些背波是由动量偏转产生的。流动的偏转率是这些背波陡峭程度的一个指标，其中只有船首波在船首设计中具有实际重要性。

The wave-breaking resistance can be diminished only insofar as it is possible to prevent the breaking of bow waves. According to the reason of its creation, this is only possible by changing the deflection of momentum or the bow near the velocity field, respectively. In principle this may be achieved not only by a bulbous bow, but by suitable hydrofoils as well [29]. A theoretical treatment of the linearized problem has recently begun .
波浪破坏阻力只能在防止船首波破坏的情况下减小。根据其产生的原因，这只有通过改变动量的偏转或船首附近的速度场来实现。原则上，这不仅可以通过球形船首实现，还可以通过合适的水翼实现【29】。对线性化问题的理论处理最近开始了 。

The effect of the bulb on the different resistance components
灯泡对不同电阻元件的影响
can be discerned by taking the differences of the corresponding resistance components of the ship without (index ) and with bulb (index ):
可以通过取船只在没有（索引 ）和有灯泡（索引 ）情况下相应电阻组件的差异来辨别

Consequently it is possible to define three different bulb effects. In any case, a positive bulb effect means a resistance reduction, and vice versa. The two latter terms in equation (8) account for the primary bulb effect, which for bulb design are the most important. The difference of the wave resistances
因此，可以定义三种不同的灯泡效应。在任何情况下，正灯泡效应 意味着电阻降低，反之亦然。方程（8）中的后两个项考虑了主要的灯泡效应，这对于灯泡设计是最重要的。波阻抗的差异

is the interference effect, which is the sum of the interference resistance and the wave resistance of the bulb body alone. Its contribution to the total bulb effect can be estimated by an analysis of the interfering free wave patterns [26|. According to Froude's law, it can be scaled directly to the full-scale ship. Only for slender fast ships does it give the main proportion to the total bulb effect, where the amount depends essentially on the bulb volume and the sign on the longitudinal position of the bulb center.
干扰效应是干扰阻力 和灯泡本体的波阻力 之和。通过对干扰自由波模式的分析，可以估计其对总灯泡效应的贡献[26|。根据弗劳德定律，它可以直接缩放到全尺度船只。只有对于细长的快速船只，它才对总灯泡效应贡献主要比例，其数量主要取决于灯泡体积和灯泡中心的纵向位置符号。

The difference between the wave-breaking resistances
波浪破坏抗力的差异

is the breaking effect, which is the main contribution to the total bulb effect for full, slow ships. Its contribution is: the bigger the bulb, the better the deflection of the flow in the vicinity of the bow region. This means for the bulb form an optimal distributed bulb volume in the longitudinal direction to minimize gradients of the hull surface in the region of rising bow waves. Using geosim model tests, Taniguchi [12] and Baba [23] have shown that the wave-breaking resistance, and consequently the breaking effect, is Froude number dependent.
破浪效应是全速慢船总灯泡效应的主要贡献。其贡献是：灯泡越大，船头附近的水流偏转效果越好。这意味着灯泡形状在纵向上应形成最佳分布的灯泡体积，以最小化船体表面在上升波浪区域的梯度。通过地模拟模型测试，谷口[12]和巴巴[23]表明，破浪阻力，因此破浪效应，依赖于弗劳德数。

The difference between the viscous resistance parts
粘性阻力部分之间的差异

is the secondary bulb effect, which is of minor importance for the total bulb effect. Due to the larger surface of bulb ships, the frictional resistance term of equation (11) is always negative and diminishes the bulb action. For reasons mentioned before, the contribution of the difference of viscous residual resistance is not taken into account.
次级灯泡效应，对总灯泡效应的重要性较小。由于灯泡船的表面积较大，方程（11）中的摩擦阻力项始终为负，并减小了灯泡作用。由于之前提到的原因，粘性残余阻力差异的贡献未被考虑。

Finally, the question has to be answered whether equivalent variations of the ship may result in the same improvements as an addition of a bulb, for example, an increase of block coefficient corresponding to the bulb volume, or an elongation of the ship length corresponding to the bulb length . It has been shown by model experiments [14] and by linear theory [22] that the effect of a bulb cannot be achieved by form variations (9).
最后，必须回答的问题是，船舶的等效变化是否会产生与添加灯泡相同的改进，例如，增加与灯泡体积相对应的块系数 ，或增加与灯泡长度相对应的船舶长度 。模型实验[14]和线性理论[22]已经表明，灯泡的效果无法通过形状变化来实现（9）。

At constant Froude number , the bulb effect is a function of all six bulb parameters:
在恒定的弗劳德数 下，灯泡效应是所有六个灯泡参数的函数：

This multidimensional relationship complicates the understanding of the dependencies on single parameters, the knowledge of which is very helpful for bulb design. Unfortunately, a quantitative description of these dependencies is possible in only a few cases, because systematic model experiments are too expensive and some parameters cannot be varied independently. On the basis of linearized wave resistance theory, however, a qualitative picture can be developed, supported by special model experiments, for example, the wave cuts , which not only prove the tendency of the dependence.
这种多维关系使得对单一参数依赖性的理解变得复杂，而这些知识对灯泡设计非常有帮助。不幸的是，只有在少数情况下才能对这些依赖关系进行定量描述，因为系统的模型实验成本太高，并且某些参数无法独立变化。然而，基于线性化波阻力理论，可以发展出一个定性的图景，并通过特殊的模型实验来支持，例如波切 ，这些实验不仅证明了依赖关系的趋势。

Fig. 7 Dependence of interference and primary bulb effect on the length parameter . Comparison of theory and experiment with an elementary ship of the form [31]
图 7 干涉和主灯泡效应对长度参数 的依赖性。与形式为 的基本船舶的理论与实验比较[31]

Because of the doubts connected with the secondary bulb effect, the following consideration is confined to both parts of the primary effect only-to the interference and breaking effects, respectively. The relationship between the two and the magnitude of their contributions to the total bulb effect are not discussed at this stage.
由于与次级灯泡效应相关的疑虑，以下考虑仅限于主要效应的两个部分——干扰效应和破坏效应。此阶段不讨论两者之间的关系及其对总灯泡效应的贡献大小。

According to linearized theory, the interference effect depends on the volumetric parameter in a quadratic manner [32]. is a measure of the amplitude of the wave pattern. The breaking effect shows a similar dependence. With increasing bulb volume, both effects increase up to a maximum with a subsequent decrease. The optimal bulb volumes corresponding to the maximum values of the different bulb effects do not, in general, coincide. For the interference effect, the optimal volume can be estimated for a given ship-bulb combination by the wave cut method [26]. In a similar way, the interference effect depends on the breadth and cross-section parameter.
根据线性化理论，干扰效应以二次方式依赖于体积参数 [32]。 是波形幅度的度量。破坏效应显示出类似的依赖性。随着灯泡体积的增加，这两种效应都增加到最大值，然后随之减少。不同灯泡效应的最大值对应的最佳灯泡体积通常不重合。对于干扰效应，可以通过波切法[26]估算给定船舶-灯泡组合的最佳体积。以类似的方式，干扰效应依赖于宽度和横截面参数。

For a constant bulb volume and depth, the length parameter has a great influence on the interference effect. As it is a measure for the phase relation of the free wave systems of ship and bulb, typical maxima and minima appear as a direct consequence of the interfering waves. As shown in Fig. 7, this tendency is confirmed by model experiments [31]. The influence of the length parameter on the breaking effect can be caught intuitively by its mode of action. With increasing , this effect increases at first and after a maximum decreases monotonically to zero, due to the fact that the deflection of momentum in the vicinity of the bow is hardly altered by a very long cylindrical bulb. Because the lateral parameter is strongly related to the length parameter, its influence on the bulb effect is similar.
对于恒定的灯泡体积和深度，长度参数 对干扰效应有很大影响。由于它是船舶和灯泡自由波系统相位关系的度量，典型的极大值和极小值是干扰波的直接结果。如图 7 所示，这一趋势得到了模型实验的验证[31]。长度参数对破坏效应的影响可以通过其作用方式直观地理解。随着 的增加，这一效应最初增加，达到最大值后单调减少至零，因为在船头附近的动量偏转几乎不受非常长的圆柱形灯泡的影响。由于横向参数与长度参数密切相关，因此它对灯泡效应的影响也类似。

The dependence of the interference effect on the depth parameter is described simply by linear theory because the term of a spherical bulb coincides with the center of the sphere. If such a bulb of constant volume and longitudinal position is moved from infinite depth up to the water surface, the interferential effect increases at first monotonically from zero to a maximum, decreases subsequently, and finally becomes negative due to an increase of the resistance of the emerging bulb body. The breaking effect behaves similarly, but it can become positive again, if , as with the -type. In this case the behavior of a ship-bulb combination is similar to a longer main hull increased in length by .
干扰效应对深度参数 的依赖可以通过线性理论简单描述，因为球形灯泡的 项与球体的中心重合。如果这样的恒定体积和纵向位置的灯泡从无限深度移动到水面，干扰效应最初单调地从零增加到最大值，随后减少，最后由于浮出水面的灯泡体的阻力增加而变为负值。破坏效应表现得类似，但如果 ，如 型，它可以再次变为正值。在这种情况下，船舶-灯泡组合的行为类似于通过 增加长度的更长主船体。

Fig. 8 Optimal bulb volume of a ship-bulb combination as a function of Froude number . The prismatic coefficient of the elementary ship form is the parameter of the curves
图 8 船舶-灯泡组合的最佳灯泡体积 与弗劳德数 的关系。基本船型 的棱柱系数 是曲线的参数。
[31]

Flg. 9 Optimal bulb volume of a ship-bulb combination with as a function of Froude number . Depth position is the parameter of the curves [31]
图 9 船舶-灯泡组合的最佳灯泡体积 与 作为弗劳德数 的函数。深度位置 是曲线的参数[31]

Linear theory permits comment on the influence of some ship main parameters on bulb size. The theoretical results relate to the interference effect only, but have general validity throughout and, in particular, are applicable to the breaking effect. For discussion, the most suitable case is the optimal bulb, which minimizes the wave resistance of a ship-bulb combination. With elementary ships of the form ( [31], it may be shown that an increased prismatic coefficient or block coefficient , respectively, is associated with increasing volume of the optimal spherical bulb. Figure 8 gives an impression of this fact. From this it follows, for ships with long parallel middlebody, that with increasing and decreasing , the optimal bulb volume increases (Yim [22], Fig. 4). The depth of the bulb has a similar influence. As shown in Fig. 9, at constant Froude number and longitudinal position, the optimal bulb volume increases with increasing depth position . Moreover, both figures clearly indicate the enormous influence of ship speed on optimal bulb volume, which increases in an undulating manner with increasing speed. These theoretical results are upper limits for the actual effects. While their absolute values are hardly of practical interest, the tendency of the dependence of bulb volume on speed, block coefficient, length of entrance, and bulb position is useful for the actual design.
线性理论允许对一些船舶主要参数对灯泡大小的影响进行评论。理论结果仅与干扰效应有关，但在整个范围内具有普遍有效性，特别适用于破坏效应。讨论中，最合适的案例是最优灯泡，它最小化船舶-灯泡组合的波阻力。对于形式为（ [31]）的基本船舶，可以证明，增加的棱柱系数 或块系数 分别与最优球形灯泡的体积增加相关。图 8 给出了这一事实的印象。因此，对于具有长平行中体的船舶，随着 的增加和 的减少，最优灯泡体积增加（Yim [22]，图 4）。灯泡的深度也有类似的影响。如图 9 所示，在恒定的弗劳德数 和纵向位置下，最优灯泡体积随着深度位置 的增加而增加。此外，这两幅图清楚地表明了船速对最优灯泡体积的巨大影响，随着速度的增加，最优灯泡体积以波动的方式增加。 这些理论结果是实际效果的上限。虽然它们的绝对值几乎没有实际意义，但灯泡体积对速度、阻力系数、入口长度和灯泡位置的依赖趋势对实际设计是有用的。
Since the wave system is created only by the nonparallel part of the main hull, and in the real fluid the forebody makes the main contribution, the length of the parallel middlebody has hardly any influence on the bulb size and, therefore, the same holds for the length/beam ratio too. For ships with , the wavemaking resistance is only a function of , as shown by the upper limit curves in Fig. 10 (see also Baba [23], Fig. 10). The beam/draft ratio has a great influence on bulb effect, bulb size, and draft parameter (upper limit curves in Fig. 11). Consequently, for dimensioning of a bulbous bow, the main-hull parameters are , and . Unfortunately, in the preliminary design phase, , and often too, is unknown. Therefore, the following design guidelines are mainly based only on block coefficient and beam/draft ratio .
由于波浪系统仅由主船体的非平行部分创建，而在真实流体中，前体贡献最大，平行中体的长度 对船首灯泡的大小几乎没有影响，因此，长度/宽度比 也是如此。对于具有 的船舶，造波阻力仅是 的函数，如图 10 中的上限曲线所示（另见 Baba [23]，图 10）。宽度/吃水比 对灯泡效应、灯泡大小和吃水参数 有很大影响（图 11 中的上限曲线）。因此，在灯泡船首的尺寸设计中，主船体参数是 和 。不幸的是，在初步设计阶段， ，而且通常 也是未知的。因此，以下设计指南主要仅基于块系数 和宽度/吃水比 。

It is well known that the existing design methods, for example, the classical method by Taylor, are not sufficient for power estimation of a bulb ship and for modern bulb design. To fill this gap in the design guidelines, a large number of routine test results of ships without and with bulb, carried out by the two German model basins, have been reanalyzed in a research project. The design guidelines derived, the design charts, and a computer program have been successfully applied on various occasions. From the multitude of diagrams developed in this paper, only one example is depicted. For complete information, reference has to be made to FDS Bericht No. 36/1973|8] and VWS Bericht No. 811/78[38]. It is emphasized that the information content of the design diagrams cannot be better than that of the original data base, especially in the cases with very small data collection.
众所周知，现有的设计方法，例如泰勒的经典方法，无法满足灯泡船的功率估算和现代灯泡设计的需求。为了填补设计指南中的这一空白，德国的两个模型水池对没有灯泡和有灯泡的船只进行了大量常规测试结果的重新分析。所衍生的设计指南、设计图表和计算机程序已在多个场合成功应用。本文开发的众多图表中，仅展示了一个例子。有关完整信息，请参考 FDS Bericht No. 36/1973|8]和 VWS Bericht No. 811/78[38]。强调设计图表的信息内容不能优于原始数据库，特别是在数据收集非常少的情况下。

Since the bulbous bow affects primarily the wavemaking resistance, the design guidelines should correctly be related to the wave or residual resistance. During preparation of the research work, it became evident; however, that most of the usable data were propulsion rather than resistance test results. Since in principle it makes no difference whether the bulb effect is derived from resistance or propulsion tests, a power specific bulb effect, or power reduction factor, respectively, was defined:
由于球形船首主要影响造波阻力，设计指南应正确与波浪或残余阻力相关。在研究工作准备过程中，然而，显而易见的是，大多数可用数据是推进而非阻力测试结果。由于原则上球形效应是源于阻力还是推进测试并没有区别，因此定义了一个功率特定的球形效应或功率减少因子：

In this form the bulb effect is the power difference of the ship without and with bulb related to the power of the bulbless ship. According to this definition, a positive bulb effect corresponds to a power reduction, and vice versa.
在这种形式下，灯泡效应是指有无灯泡 和有灯泡 的船只的功率差异，与无灯泡船只的功率相关。根据这个定义，正的灯泡效应对应于功率减少，反之亦然。
In order to separate the different friction resistance components of ships without and with bulb in accordance with Froude's method, the total delivered power
为了根据弗劳德的方法分离没有和有球泡的船舶的不同摩擦阻力成分，总交付功率

is regarded as composed of a frictional part (index ) and a residual part (index ). If the propulsive efficiency is known, the residual power can be calculated as the difference
被认为由摩擦部分（索引 ）和残余部分（索引 ）组成。如果已知推进效率 ，则残余功率可以计算为两者的差值。

Fig. 10 Dependence of the residual power reduction coefficient on the length/beam ratio, the volumetric parameter, and the length parameter, respectively. Curve parameter is the Froude number. The parameters , , and are constant
图 10 残余功率减少系数对长度/梁比、体积参数和长度参数的依赖关系。曲线参数为弗劳德数。参数 、 和 为常数。

Fig. 11 Dependence of the residual power reduction coefficient on the beam/draft ratio, the volumetric parameter, and the depth parameter, respectively. Curve parameter is the Froude number. The parameters ,
图 11 残余功率减少系数对波束/吃水比、体积参数和深度参数的依赖关系。曲线参数为弗劳德数。参数 ，
and are constant
和 是常量
between total and frictional power, and a residual power reduction factor
在总功率和摩擦功率之间，以及一个剩余功率减少因子

can be defined. 可以被定义。
The relationship between effective and delivered power is
有效 与输出功率之间的关系是

With the frictional power calculated by the International Towing Tank Conference (ITTC) 1957 line
根据国际拖曳水池会议（ITTC）1957 年线计算的摩擦力

the residual power is 剩余功率是

With equations (16) to (18), the residual power reduction factor becomes
通过方程（16）到（18），残余功率减少因子变为

A separation of the various bulb effects is not possible in this way.
以这种方式无法分离各种灯泡效果。

The propulsive efficiency is a function of hull form and speed and should be known for the analysis of the model test results. Moreover, for ships without and with bulb, the propulsive efficiencies are generally not equal, but it is in the beneficial speed range of the bulb ship. Unfortunately, from most of the propulsion test results, could not be estimated. Therefore, as a first step in simplification of the reanalysis, a constant has to be chosen for ships without and with bulb. The mistake is small if in the calculation of the residual power reduction factor by equation ( ), the condition is assumed. In general, the relations
推进效率 是船体形状和速度的函数，应该在模型试验结果分析中已知。此外，对于没有和有球鼻的船，推进效率通常不相等，但在球鼻船的有利速度范围内是 。不幸的是，从大多数推进试验结果中， 无法估计。因此，作为重新分析简化的第一步，必须为没有和有球鼻的船选择一个常数 。如果在通过方程（ ）计算剩余功率减少因子时假设条件 ，则错误很小。一般来说，关系

Fig. 12 Influence of different propulsive coefficients on the residual power reduction coefficient, shown with the ship-bulb combination No. 7 of Table 2
图 12 不同推进系数对剩余功率减少系数的影响，显示为表 2 中的船舶-灯泡组合第 7 号

Fig. 13 Comparison of the residual power reduction coefficients from full-scale and model-scale measurements (for main particulars, see Table 1)
图 13 全尺寸和模型尺寸测量的剩余功率减少系数比较（主要参数见表 1）