A method and system for testing wave drag of a free-running model in all wave directions at a constant speed
By using a constant-speed wave drag increase test method for a free-roaming model in all wave directions, and by adjusting the propeller speed and using least-squares linear fitting, the accuracy and applicability issues of all-wave direction testing in existing technologies have been solved, and efficient and convenient wave drag increase testing has been achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANGHAI SHIP & SHIPPING RES INST CO LTD
- Filing Date
- 2026-03-25
- Publication Date
- 2026-05-29
Smart Images
Figure CN122108530A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of wave drag increase testing for ships, and in particular to a constant-speed wave drag increase testing method and system applicable to free-roaming models in all wave directions. Background Technology
[0002] Wave drag is one of the key performance indicators faced by ships navigating at sea. Accurately measuring the wave resistance and drag increment of a ship model at a target speed is of great significance for optimizing ship hull design and improving navigation economy and safety. Wave drag testing of free-roaming, all-wave-direction self-propelled models (also known as ship models) is a core means of simulating the complex navigation environment of a real ship, and the scientific validity and reliability of its testing methods directly determine the reference value of the test data.
[0003] Existing wave drag enhancement testing technologies mainly fall into two typical categories, both of which have significant technical shortcomings and are difficult to meet the practical requirements of omnidirectional, high-precision, and engineering applications:
[0004] Firstly, there is the conventional constrained model wave test scheme. This scheme focuses only on wave-facing conditions, using constraint devices to limit the sway and roll motions of the model, and towing the model in a pool to maintain a constant speed. Wave forces and motion data are measured using sensors on the seaworthiness instrument. However, a real ship sailing at sea is unconstrained and can freely perform sway, roll, and other multi-degree-of-freedom movements. This scheme forcibly restricts the model's motion freedom through mechanical constraints, resulting in a fundamental difference between the model's motion state and the actual sailing state of the real ship. The flow field interference effect is significant, and the measured wave resistance data has a high degree of distortion, failing to accurately reflect the force characteristics of the real ship in waves. At the same time, due to the limitations of the constraint structure and towing system, this scheme can only conduct wave-facing tests and cannot cover all wave directions such as cross waves and oblique waves, making its applicability extremely limited.
[0005] Secondly, some free-roaming model aircraft test schemes. To improve the realism of constrained model schemes, some studies have attempted to use free-roaming models for testing. However, they face insurmountable problems in speed control and data acquisition: One type of scheme attempts to achieve precise control of the target speed by dynamically adjusting the propeller speed through real-time monitoring of the free-roaming model's speed. However, wave interference on free-roaming models is random and instantaneous, causing real-time fluctuations in the free-roaming model's speed. The speed adjustment inevitably has a response lag, easily triggering an oscillating cycle of "speed fluctuation - speed adjustment - secondary fluctuation." This not only makes it difficult to achieve precise and stable speed control but also causes severe fluctuations in key data such as propeller thrust and torque, resulting in poor test data quality that cannot be used for subsequent resistance calculations. Another type of scheme uses manual judgment to control the speed in real time, requiring a long wait for the model speed to reach a stable range. However, most test pools have limited length, failing to meet the space requirements for long-term stable testing, leading to low test efficiency. Furthermore, the subjectivity of manual operation easily introduces additional errors, further reducing data reliability.
[0006] In summary, existing solutions either suffer from distorted motion simulation, limited applicability to a single wave direction, or difficulties in speed control, poor data quality, and stringent testing conditions, all of which prevent the effective and convenient testing of wave drag enhancement for free-roaming models across all wave directions. Therefore, there is an urgent need to design a wave drag enhancement testing method that can accurately reproduce the real motion of a ship, reduce implementation difficulty, cover all wave directions, and ensure data accuracy, thereby addressing many of the shortcomings of existing technologies. Summary of the Invention
[0007] To address the problems of traditional techniques, such as applicability to only one wave direction, high implementation difficulty, and poor test data quality, this invention proposes a constant-speed wave drag increase testing method for free-roaming model aircraft operating in all wave directions. By adjusting the propeller speed to obtain test data, and combining this with interpolation in a linear fitting equation established using the least squares linear fitting method, the target propeller speed and target propeller thrust corresponding to the target speed are obtained. Based on the engineering assumption that thrust reduction in waves is the same as thrust reduction in still water, the wave drag increase corresponding to the target speed can be calculated. This method does not strictly require the free-roaming model's speed in waves to be the target speed, reducing the requirements for testing equipment, simplifying operation and facilitating engineering applications, while ensuring high test data accuracy. This invention also relates to a constant-speed wave drag increase testing system for free-roaming model aircraft operating in all wave directions.
[0008] The technical solution of the present invention is as follows:
[0009] A method for testing wave drag at constant speed on a free-roaming model aircraft operating in all wave directions includes the following steps:
[0010] S1: Under all-wave conditions, the free-roaming model maintains linear motion along the length of the pool using its autopilot system; the propeller speed of the free-roaming model is adjusted so that it is linearly correlated with the speed and thrust, and the average speed and thrust during the stable period corresponding to each propeller speed are measured and calculated; the average speed during the stable period is the average speed of the free-roaming model during the stable navigation time at the given propeller speed; the average thrust during the stable period is the average propeller thrust of the free-roaming model during the stable navigation time at the given propeller speed.
[0011] S2: Using the least squares linear fitting method, establish linear relationship models between the average speed in the stable section and the propeller speed, and between the propeller speed and the average propeller thrust in the stable section, respectively. Combine the measured propeller speeds and their corresponding average speeds and average propeller thrusts in the stable section, solve for the linear fitting equations of speed-propeller speed and propeller speed-propeller thrust.
[0012] S3: Based on the linear fitting equation of speed-propeller speed, the target propeller speed corresponding to the target speed required for constant speed test is obtained by interpolation calculation; the target propeller speed is substituted into the linear fitting equation of propeller speed-propeller thrust, and the target propeller thrust corresponding to the target propeller speed is obtained by interpolation calculation.
[0013] S4: Based on the still water speed test, determine the still water drag and thrust reduction corresponding to the target speed required for the constant speed test; based on the engineering assumption that the thrust reduction in waves is consistent with the thrust reduction in still water, take the thrust reduction as the equivalent thrust reduction under all-wave conditions; calculate the wave drag corresponding to the target speed according to the equivalent thrust reduction and the target propeller thrust; and then obtain the wave drag increase corresponding to the target speed according to the difference between the wave drag and the still water drag.
[0014] Preferably, in step S1, under all-wave conditions, the free-roaming model maintains its linear motion along the length of the pool by relying on its automatic steering system, and records the heading angle of the free-roaming model in real time.
[0015] The steps of adjusting the propeller speed of the free-flying model, and measuring and calculating the average speed and average propeller thrust during the steady-state period corresponding to each propeller speed include:
[0016] Multiple sets of different propeller speeds are set and adjusted sequentially within a preset range, so that the free-roaming model can continuously sail for a preset time at each propeller speed. During this period, the speed and propeller thrust data of multiple free-roaming models corresponding to each propeller speed are recorded in real time.
[0017] For each group of propeller speeds, data segments are selected where the free-running model's speed fluctuation range is less than a preset fluctuation threshold and the corresponding heading angle deviation is less than a preset heading angle deviation threshold. The average speed and average propeller thrust within each data segment are calculated to obtain the average speed and average propeller thrust in the stable segment corresponding to each group of propeller speeds.
[0018] Preferably, in step S2, the linear relationship model between the average speed during the stable phase and the propeller speed is as follows:
[0019] ,
[0020] Where V represents the average speed during the steady-state period, N represents the propeller speed, and a and b represent the fitting coefficients;
[0021] Based on the measured propeller speeds and their corresponding average speeds during the stable period, the fitting coefficients a and b are obtained by minimizing the sum of squared errors between the measured average speeds during the stable period and the average speeds during the stable period calculated by the linear relationship model, and then the linear fitting equation of speed-propeller speed is obtained.
[0022] Preferably, in step S2, the linear relationship model between the propeller rotational speed and the average propeller thrust during the stable phase is as follows:
[0023] ,
[0024] Where T represents the average propeller thrust during the steady-state phase, N represents the propeller speed, and c and d represent the fitting coefficients.
[0025] Based on the measured propeller speeds and their corresponding average propeller thrust in the stable section, the fitting coefficients c and d are obtained by minimizing the sum of squared errors between the measured average propeller thrust in the stable section and the average propeller thrust in the stable section calculated by the linear relationship model, and then the linear fitting equation of propeller speed-propeller thrust is obtained.
[0026] Preferably, in step S3, based on the calculated fitting coefficients a and b, the target speed required for the constant speed test is substituted into the linear fitting equation of speed-propeller speed obtained from the linear relationship model between the average speed of the stable section and the propeller speed, and the target propeller speed corresponding to the target speed is calculated.
[0027] Preferably, in step S3, based on the calculated fitting coefficients c and d, the target propeller speed is substituted into the propeller speed-thrust linear fitting equation obtained from the linear relationship model of propeller speed and average propeller thrust in the stable section, and the target propeller thrust corresponding to the target propeller speed is calculated.
[0028] Preferably, in step S4, the wave resistance corresponding to the target speed is calculated based on the equivalent thrust reduction and the target propeller thrust, using the following formula:
[0029] ,
[0030] in, This represents the wave resistance corresponding to the target speed. The target propeller thrust is represented by t, and the equivalent thrust reduction is represented by t.
[0031] Based on the difference between wave resistance and still water resistance, the wave drag increase corresponding to the target speed is calculated using the following formula:
[0032] ,
[0033] in, R represents the wave resistance, and R represents the hydrostatic resistance.
[0034] Preferably, in step S1, the Qualisys motion capture system is used to record the speed of the free-roaming model in real time, forming a speed time series curve, and the data segment in which the speed fluctuation range of the free-roaming model is less than a preset fluctuation threshold is determined based on the speed time series curve.
[0035] A constant-speed wave drag increase testing system for a free-roaming model aircraft operating in all wave directions includes a wave condition free-roaming model parameter measurement module, a measurement data linear fitting relationship modeling module, a target speed correlation parameter interpolation solution module, and a wave drag increase calculation module connected in sequence.
[0036] The wave-condition free-roaming model parameter measurement module is used to maintain the free-roaming model's linear motion along the length of the pool under all-wave conditions, relying on the model's autopilot system; it adjusts the propeller speed of the free-roaming model so that the propeller speed is linearly related to the speed and propeller thrust, and measures and calculates the average speed and average propeller thrust during the stable period corresponding to each propeller speed; the average speed during the stable period is the average speed of the free-roaming model during the stable navigation time at the given propeller speed; the average propeller thrust during the stable period is the average propeller thrust of the free-roaming model during the stable navigation time at the given propeller speed.
[0037] The linear fitting relationship modeling module for the measurement data is used to establish linear relationship models between the average speed during the stable period and the propeller speed, and between the propeller speed and the average propeller thrust during the stable period, respectively, using the least squares linear fitting method. It also combines multiple sets of measured propeller speeds and their corresponding average speed and average propeller thrust during the stable period to solve for the linear fitting equations of speed-propeller speed and propeller speed-propeller thrust.
[0038] The target speed correlation parameter interpolation solution module is used to calculate the target propeller speed corresponding to the target speed required for constant speed testing by interpolation based on the linear fitting equation of speed-propeller speed; and to calculate the target propeller thrust corresponding to the target propeller speed by substituting the target propeller speed into the linear fitting equation of propeller speed-propeller thrust.
[0039] The wave drag calculation module is used to: determine the still water drag and thrust reduction corresponding to the target speed required for constant speed testing based on still water speed tests; based on the engineering assumption that the thrust reduction in waves is consistent with the thrust reduction in still water, use the thrust reduction as the equivalent thrust reduction under all-wave conditions; calculate the wave drag corresponding to the target speed based on the equivalent thrust reduction and the target propeller thrust; and obtain the wave drag increase corresponding to the target speed based on the difference between the wave drag and the still water drag.
[0040] Preferably, in the wave condition free-roaming model parameter measurement module, under all-wave conditions, the free-roaming model's automatic steering system maintains the free-roaming model's linear motion along the length of the pool, and records the free-roaming model's heading angle in real time.
[0041] The steps of adjusting the propeller speed of the free-flying model, and measuring and calculating the average speed and average propeller thrust during the steady-state period corresponding to each propeller speed include:
[0042] Multiple sets of different propeller speeds are set and adjusted sequentially within a preset range, so that the free-roaming model can continuously sail for a preset time at each propeller speed. During this period, the speed and propeller thrust data of multiple free-roaming models corresponding to each propeller speed are recorded in real time.
[0043] For each group of propeller speeds, data segments are selected where the free-running model's speed fluctuation range is less than a preset fluctuation threshold and the corresponding heading angle deviation is less than a preset heading angle deviation threshold. The average speed and average propeller thrust within each data segment are calculated to obtain the average speed and average propeller thrust in the stable segment corresponding to each group of propeller speeds.
[0044] The beneficial effects of this invention are as follows:
[0045] This invention provides a constant-speed wave drag increase test method for all-wave-direction free-roaming model aircraft, also known as a high-precision constant-speed wave drag increase test method applicable to all-wave-direction free-roaming model aircraft. This method adjusts multiple sets of different fixed propeller speeds, collects and calculates the average speed and average propeller thrust during the stable phase at each speed, thus reproducing the real operating conditions of a real ship with a fixed propeller speed and small-range speed fluctuations during normal operation. It also eliminates interference data from unstable phases, ensuring the reliability and validity of the measurement data. Furthermore, the method of obtaining the average parameters during the stable phase simplifies the test process and can compensate for instantaneous fluctuation errors caused by waves, providing a high-quality data source for subsequent linear fitting and ensuring the accuracy of the entire test process. The method utilizes least squares... A linear fitting method is used to establish linear relationships between the average speed during the stable phase and the propeller speed, and between the propeller speed and the average propeller thrust during the stable phase. This method fully utilizes the characteristics of propeller speed variation within a small range and the relatively weak nonlinearity of propeller speed, speed, and thrust. While ensuring computational accuracy, it significantly reduces the complexity of data processing and avoids the high demands on equipment and algorithms imposed by traditional nonlinear fitting methods. Furthermore, by quantifying the correlation between parameters (including the correlation between the average speed during the stable phase and the propeller speed, and between the propeller speed and the average propeller thrust during the stable phase) through the linear fitting equations, it effectively offsets random errors in experiments, improves data stability and repeatability, and provides a scientific and reliable mathematical basis for subsequent interpolation calculations of the target speed. This approach achieves the transformation from discrete data to a usable model. Through interpolation calculations using linear fitting equations, it precisely addresses the core challenge of maintaining a strictly constant speed for free-roaming models in waves. It eliminates the need for forced control of the free-roaming model to maintain the target speed in waves, significantly reducing the operational difficulty and equipment requirements of the experiment. The target propeller speed is obtained by back-interpolating the target speed into the linear fitting equation of speed-propeller speed, and then further derived by interpolating into the linear fitting equation of propeller speed-propeller thrust. This achieves precise matching between the target speed and the target propeller thrust required for constant speed testing, bypassing the impact of wave interference on speed control while ensuring the accuracy of key parameters at the target speed. Based on still-water speed tests, it determines the... Based on the still water resistance and thrust reduction corresponding to the target speed of the self-propelled model, and the engineering assumption that the thrust reduction in waves is consistent with the thrust reduction in still water, the equivalent thrust reduction under all-wave conditions of the free self-propelled model is determined. Wave resistance is calculated by using the equivalent thrust reduction and the target propeller thrust, and the wave drag increase is obtained by the difference between wave resistance and still water resistance. This directly achieves the core objective of the experiment and provides key data support for ship hull optimization and navigation economics assessment. The reasonable application of the engineering assumption that the thrust reduction in waves is consistent with the thrust reduction in still water balances the calculation accuracy and implementation difficulty. Its error is completely within the engineering allowable range, which not only meets the actual needs of ship design, but also ensures the convenience and efficiency of the method, making it suitable for engineering applications in various laboratories.This invention utilizes wave-condition free-roaming model parameter measurement, linear fitting relationship modeling of measurement data, target speed correlation parameter interpolation solution, and wave drag calculation. Combined with the least squares linear fitting method and the engineering assumption that thrust reduction in waves is consistent with thrust reduction in still water, it eliminates the need for strict requirements on the free-roaming model's speed in waves to be the target speed, reducing the requirements on testing equipment. It is easy to operate and apply in engineering, while ensuring high accuracy of test data. It can simply and efficiently achieve constant-speed wave drag testing of free-roaming models in all wave directions.
[0046] This invention addresses the issue of free-roaming model aircraft being susceptible to course deviation due to wave impacts under wave conditions, which can lead to distorted speed measurements and abnormal thrust consumption. It employs a course angle filtering mechanism at the same time point to accurately eliminate invalid data from unstable course states, ensuring that the retained speed and thrust data correspond to the free-roaming model's straight-line navigation in a preset direction. This makes the measurement data more aligned with the experimental design requirements and avoids the impact of course deviation on subsequent fitting accuracy. Waves cause high-frequency instantaneous fluctuations in the speed and thrust of free-roaming models. By using a "speed fluctuation range filtering + stable segment averaging" approach, the core data segment for force balance and motion stability of the free-roaming model can be accurately identified, resulting in more accurate calculated stable segment average speed and stable segment average propeller thrust. Multiple speed settings cover the speed range corresponding to the target speed, providing sufficient sample support for subsequent linear fitting.
[0047] This invention precisely quantifies the relationship between the average speed and propeller speed during the stable phase by explicitly defining a linear expression for these two parameters. This perfectly aligns with the core premise that the nonlinear relationship between parameters (speed and propeller speed) is weak under small-range propeller speed conditions. Simultaneously, by minimizing the sum of squared errors between the measured average speed during the stable phase and the average speed calculated from the linear relationship model—that is, constructing an error function using the sum of squared residuals—it comprehensively reflects the deviation between discrete experimental data and the fitted line, providing a clear quantitative judgment target for optimizing the fitting parameters and avoiding the subjectivity and blindness of manual fitting. Based on the parameter calculation formula derived from minimizing the error function, the precise solution for the fitting parameters is achieved. This derivation process strictly follows the core principle of the least squares method, directly establishing the fitting coefficients a (slope), b (intercept), and the measured data (N) through mathematical operations. i V i The one-to-one correspondence between the fitting parameters and the experimental data does not require complex algorithms or multiple iterations. This ensures the accuracy of the fitting parameter calculations and avoids the additional errors caused by complex numerical iterative calculations, allowing the fitting results to truly and accurately reflect the inherent correlation patterns of the experimental data.
[0048] This invention establishes a linear expression for the relationship between propeller speed and average propeller thrust during the stable phase. This precisely addresses the experimental premise where the nonlinear correlation between propeller speed parameters (propeller thrust and speed) is weak within a small range, complementing the linear fitting logic of speed-speed, and constructing a complete mathematical model for parameter correlation. By minimizing the sum of squared errors between the measured average propeller thrust during the stable phase and the average propeller thrust calculated by the linear relationship model, i.e., constructing an error function using the sum of squared residuals, this invention comprehensively and quantitatively reflects the deviation between discrete experimental data and the fitted line. This provides a clear quantitative judgment target for optimizing the fitting parameters, avoiding biases caused by subjective judgment during the fitting process, and ensuring that the fitting results truly reflect the inherent correlation between the two. Based on the parameter calculation formula derived from minimizing the error function, accurate and efficient solutions for the fitting parameters are achieved. This derivation process strictly follows the mathematical principles of the least squares method, directly establishing the fitting parameters c (slope) and d (intercept) and the measured data (N... i T i The formula establishes a definite correspondence between propeller speed and average thrust in the steady-state phase, eliminating the need for complex iterative algorithms or high-end data processing tools. Researchers can quickly calculate the values of c and d by directly substituting multiple sets of measured data on propeller speed and average thrust in the steady-state phase into the formula. This ensures the accuracy of the fitted parameters calculations while avoiding the additional errors introduced by complex numerical calculations, significantly improving data processing efficiency.
[0049] This invention employs the Qualisys motion capture system to record the speed of a free-flying model aircraft in real time, generating a speed time series curve. Based on this curve, it identifies data segments where the speed fluctuation of the free-flying model aircraft is less than a preset fluctuation threshold at the current propeller speed. The Qualisys motion capture system boasts core advantages of high precision and high refresh rate, enabling it to capture instantaneous changes in the speed of the free-flying model aircraft in real time and accurately. The generated speed time series curve realistically reproduces the dynamic speed process of the free-flying model aircraft at the current propeller speed. The speed time series curve visually presents the trend of speed change over time, clearly distinguishing between the acceleration, stable, and fluctuating segments of the free-flying model aircraft, significantly reducing the difficulty of identifying stable data segments.
[0050] This invention also relates to a constant-speed wave drag increase test system for a free-roaming model in all wave directions. This system corresponds to the aforementioned constant-speed wave drag increase test method for a free-roaming model in all wave directions. It can be understood as a system that implements the aforementioned constant-speed wave drag increase test method for a free-roaming model in all wave directions. It includes a free-roaming model parameter measurement module under wave conditions, a linear fitting relationship modeling module for measurement data, a target speed correlation parameter interpolation solution module, and a wave drag increase calculation module. These modules work together and have the following advantages: First, the accuracy and reliability of test data are significantly improved: By using least squares linear fitting to extract the regularity of discrete data, random errors in the experiment are effectively offset, and the correlation between test data is quantified; through precise interpolation, the target speed and target propeller thrust are accurately matched. Combined with the linkage of engineering assumptions and still-water speed test data, the high accuracy of the wave drag increase calculation results is ultimately guaranteed. The error is completely within the engineering allowable range, which can provide reliable data support for ship design. II. Significantly Reduced Difficulty and Cost of Experimentation (Testing): This system abandons the rigid requirement of "forced constant speed" in traditional solutions. Through the core logic of "fixed speed acquisition + linear fitting interpolation," it bypasses the technical challenge of dynamically adjusting the speed in waves, eliminating the need for high-precision, high-response dynamic control. The engineering assumption that thrust reduction in waves is consistent with thrust reduction in still water avoids the complex flow field testing equipment and cumbersome algorithms required for dynamic thrust reduction measurement under wave conditions, simplifying the calculation process. III. Realistic Reproduction of Ship Motion in Waves: The design with fixed propeller speed and small-range speed fluctuations accurately reproduces the core operating conditions of a real ship during normal operation. The method is scientifically sound, easy to implement, and has good prospects for widespread application. Attached Figure Description
[0051] Figure 1 This is a flowchart of the constant-speed wave drag increase test method for a free-roaming model aircraft of the present invention.
[0052] Figure 2 This is an example diagram of the free-flying model's speed time series curve according to the present invention.
[0053] Figure 3 This is an example diagram illustrating the speed variation along the length of the pool in the stable segment of the free-flying model's speed time series curve of the present invention.
[0054] Figure 4 This is an example diagram of the speed change of the stable segment in the time series curve of the free-flying model aircraft of the present invention, perpendicular to the length of the water tank.
[0055] Figure 5 This is an example diagram illustrating the linear relationship between the ship's speed and the propeller speed according to the present invention.
[0056] Figure 6 This is an example diagram illustrating the linear relationship between propeller speed and propeller thrust according to the present invention.
[0057] Figure 7 This is a structural block diagram of the constant-speed wave drag increase test system for a free-roaming model aircraft of the present invention. Detailed Implementation
[0058] The present invention will now be described with reference to the accompanying drawings.
[0059] This invention discloses a constant-speed wave drag increase test method for a free-roaming model boat operating in all wave directions. The method involves using a free-roaming model boat (also known as a boat model) to conduct all-wave tests. The test tank must be equipped with an L-shaped wave generator capable of generating waves at different angles. The free-roaming model only needs to move along the length of the tank. Since the free-roaming model is not connected to a shore-based trailer system, its built-in propulsion and autopilot systems are used to achieve a stable speed, maintaining the model in a straight line along the length of the tank. Data such as the thrust generated by the propeller during this state are recorded. Before the test, the equipment integration, assembly, and preliminary calibration of the free-roaming model need to be completed. First, a complete propulsion system needs to be installed on the free-roaming model, including a propeller, a power meter for measuring propeller thrust, a servo motor for driving the propeller and controlling its speed, a servo motor driver, and a battery unit that provides independent power to the entire propulsion system. In addition, an autopilot system needs to be installed on the free-roaming model, including a rudder, servo motor, yaw angle gyroscope, servo motor control module, and power module for the autopilot system. Then, the model's displacement, center of gravity height, and radius of inertia parameters need to be adjusted to ensure that the free-roaming model meets the test requirements. Finally, all equipment signals need to be tested before the free-roaming model is launched to ensure that all equipment is working properly, and the thrust sensor (i.e., the power meter) needs to be calibrated in advance.
[0060] After completing the above preparations, the all-wave-direction constant-speed wave drag increase test can be carried out, such as... Figure 1 As shown, the constant-speed wave drag increase test method for a free-roaming model aircraft of the present invention includes the following steps:
[0061] S1: Under all-wave conditions, the free-roaming model is given initial kinetic energy through rigid towing by a trailer or other acceleration devices. Then, the autopilot system is activated, maintaining the model's linear motion along the length of the pool, and the heading angle is recorded in real time. The propeller speed is adjusted to be linearly correlated with speed and thrust. The average speed and thrust during the stable phase are measured and calculated for each propeller speed. The average speed during the stable phase is the average speed of the free-roaming model during the stable navigation period at the given propeller speed; the average thrust during the stable phase is the average propeller thrust during the stable navigation period at the given propeller speed.
[0062] This invention employs a constant rotational speed method to conduct wave drag increase tests at a constant speed in all wave directions. The principle is that, under a fixed propeller speed, the speed of a free-running model fluctuates within a small range; therefore, the average speed during the stable phase is used to characterize its sailing speed. In normal operation, excluding the influence of extreme weather, the propeller speed of a real ship mostly remains constant, with speed fluctuating only within a certain range under the influence of external waves. Therefore, this constant rotational speed test method can accurately simulate the actual motion of a real ship, providing a realistic experimental basis for wave drag increase tests at a constant speed in all wave directions.
[0063] The specific steps include:
[0064] Sequentially set and adjust multiple sets of different propeller speeds within a preset range (the propeller speed settings should vary within a small range so that the corresponding speeds cover the target speed. For example, if the target speed is 0.8 m / s, four propeller speeds can be set so that the corresponding speeds include values less than 0.8 m / s and values greater than 0.8 m / s). Allow the free-roaming model to continuously sail for a preset time at each propeller speed. During this period, record in real time the speeds, propeller torque, and propeller thrust of multiple free-roaming models corresponding to each propeller speed.
[0065] For each group of propeller speeds, data segments are selected where the free-running model's speed fluctuation range is less than a preset fluctuation threshold, and the heading angle deviation at the same time point is less than a preset heading angle deviation threshold. The average speed and average propeller thrust within each data segment are calculated to obtain the average speed and average propeller thrust in the stable segment corresponding to each group of propeller speeds.
[0066] Furthermore, embodiments of the present invention can employ the Qualisys motion capture system to record the speed of the free-flying model in real time, generating a time-series curve of speed corresponding to each propeller rotation speed (e.g., Figure 2 As shown, the x-axis represents time, and the y-axis represents speed. Based on the speed time series curve, the data segment where the speed fluctuation range of the free-roaming model is less than a preset fluctuation threshold at the current propeller speed is determined. Figure 2 The data segment from 20.1s to 39s represents the free-flying model's speed fluctuation range being less than the preset fluctuation threshold.
[0067] Specifically, by decomposing the speed direction of the selected data segment, we can analyze the speed variation of the free-roaming model along the length of the pool within that data segment (e.g., Figure 3 As shown, the x-axis represents time, and the y-axis represents the speed of the free-roaming model along the length of the pool and the speed change perpendicular to the length of the pool (e.g., ...). Figure 4As shown, the x-axis represents time, and the y-axis represents the speed of the free-roaming model perpendicular to the length of the pool; then according to... Figure 3 Determine the time period during which the speed fluctuation range of the free-flying model along the length of the pool (set as the x-axis) is less than a preset straight-line speed fluctuation threshold (e.g., 5%); then, based on... Figure 4 Determine the time period during which the speed of the free-roaming model perpendicular to the length of the pool (set as the y-axis) is less than a preset lateral speed threshold (e.g., 0.02 m / s). Figure 4 As shown, when V y =-0.01215m / s, when the amplitude is extremely small, it can be assumed that only the speed in the x-axis direction exists); take the intersection of the two time periods, and in Figure 3 Calculate the mean speed of the ships within the time range corresponding to the intersection. Figure 3 The average speed is 0.81044 m / s, which is used as the average speed during the steady-state period corresponding to the propeller speed of this group. The average propeller thrust within the time range corresponding to this intersection is calculated as the average propeller thrust during the steady-state period corresponding to the propeller speed of this group.
[0068] Furthermore, embodiments of the present invention can utilize the propulsion system to acquire and record the propeller speed and propeller thrust collected by the thrust sensor.
[0069] S2: Using the least squares linear fitting method, establish linear relationship models between the average speed in the stable section and the propeller speed, and between the propeller speed and the average propeller thrust in the stable section, respectively. Combine the measured propeller speeds and their corresponding average speeds and average propeller thrusts in the stable section, solve for the linear fitting equations of speed-propeller speed and propeller speed-propeller thrust.
[0070] The theoretical relationship between the speed, propeller thrust, and propeller speed of a free-flying model aircraft is nonlinear, but this is the rule under the condition of "large-range variation of propeller speed". When the propeller speed fluctuates only within a small range, the nonlinear curve will be approximately flattened, just like cutting a very short segment from a curve. This segment of the curve looks almost straight. The error brought by this "linear approximation" is much smaller than the measurement error of the test equipment. Therefore, in engineering, it can be considered that the "nonlinearity is not strong", that is, the propeller speed is approximately linearly related to the speed and propeller thrust.
[0071] Among them, the linear relationship model between the average speed during the steady phase and the propeller speed is as follows: Figure 5 As shown, Figure 5 The x-axis represents the average speed V during the steady-state phase. x The y-axis represents the propeller speed N, such as... Figure 5As shown, the blue hollow circle data points corresponding to the three sets of test data are approximately distributed on a straight line. Therefore, the linear relationship between the average speed during the steady-state and the propeller speed can be expressed by formula (1):
[0072] Where V represents the average speed during the steady-state period, N represents the propeller speed, a represents the slope, b represents the intercept, and a and b are the fitting coefficients to be solved.
[0073] Based on the measured propeller speeds and their corresponding average speeds during the stable period, the fitting coefficients a and b are obtained by minimizing the sum of squared errors between the measured average speeds during the stable period and the average speeds during the stable period calculated by the linear relationship model. This leads to the linear fitting equation between the propeller speed and the speed of propeller rotation. Specifically:
[0074] The error function of the linear relationship model is shown in formula (2):
[0075]
[0076] in, Indicates the error value. This represents the average speed during the i-th steady-state segment. The i-th propeller speed is represented by n, and n represents the amount of data on the measured propeller speed and the corresponding average speed during the steady-state period.
[0077] Based on formulas (1) and (2), by minimizing the error function, formulas (3) and (4) are derived as follows:
[0078]
[0079] Substituting the measured propeller speeds and the average speeds of the stable section corresponding to each propeller speed into formulas (3) and (4), the corresponding values of a and b are calculated, thus obtaining the linear fitting equation of speed-propeller speed. That is to say, a and b in the linear relationship model shown in formula (1) are the fitting coefficients to be solved. After obtaining the specific values of a and b through the least squares linear fitting method, the linear relationship model is transformed into a linear fitting equation of speed-propeller speed, which can be used to solve the target propeller speed corresponding to the target speed.
[0080] A linear relationship model between propeller speed and average propeller thrust during the steady-state phase, such as... Figure 6 As shown, Figure 6 The x-axis represents the propeller speed N, and the y-axis represents the average propeller thrust T during the steady-state phase. m ,like Figure 6As shown, the blue hollow circle data points corresponding to the three sets of test data are approximately distributed on a straight line. Therefore, the linear relationship between propeller speed and average propeller thrust during the steady-state phase can be expressed by formula (5):
[0081]
[0082] Where T represents the average propeller thrust during the steady-state phase, N represents the propeller speed, c represents the slope, d represents the intercept, and c and d are the fitting coefficients to be solved.
[0083] Based on the measured propeller speeds and their corresponding average propeller thrust during the steady-state section, the fitting coefficients c and d are obtained by minimizing the sum of squared errors between the measured average propeller thrust during the steady-state section and the average propeller thrust during the steady-state section calculated by the linear relationship model. This leads to the linear fitting equation for the propeller speed-propeller thrust. Specifically:
[0084] The error function of the linear relationship model is shown in formula (6):
[0085]
[0086] in, Indicates the error value. This represents the average propeller thrust during the i-th stable phase. The i-th propeller speed is represented by n, and n represents the amount of data on the measured propeller speed and the corresponding average propeller thrust during the steady-state period.
[0087] Based on formulas (5) and (6), by minimizing the error function, formulas (7) and (8) are derived as follows:
[0088]
[0089]
[0090] Substitute the measured propeller speeds and the average propeller thrust in the stable section corresponding to each propeller speed into formulas (7) and (8) to calculate the corresponding c and d values, and then obtain the linear fitting equation of propeller speed-propeller thrust.
[0091] In other words, c and d in the linear relationship model shown in formula (5) are the fitting coefficients to be solved. After obtaining the specific values of c and d by the least squares linear fitting method, the linear relationship model is transformed into a linear fitting equation of propeller speed-propeller thrust, which can be used to solve the target propeller thrust corresponding to the target propeller speed.
[0092] S3: Based on the linear fitting equation of speed-propeller speed, the target propeller speed corresponding to the target speed required for constant speed test is obtained by interpolation calculation; the target propeller speed is substituted into the linear fitting equation of propeller speed-propeller thrust, and the target propeller thrust corresponding to the target propeller speed is obtained by interpolation calculation.
[0093] Based on the fitting coefficients a and b obtained from step S2, the target speed required for constant speed testing is substituted into the linear fitting equation of speed-propeller speed obtained from the linear relationship model between the average speed of the stable section and the propeller speed. That is, the target speed is interpolated in formula (1) with the obtained a and b values, and the target propeller speed corresponding to the target speed can be calculated.
[0094] Based on the fitting coefficients c and d obtained from step S2, the target propeller speed is substituted into the propeller speed-thrust linear fitting equation obtained from the linear relationship model between propeller speed and average propeller thrust in the stable section. That is, the target propeller speed is interpolated in formula (5) with the obtained c and d values, and the target propeller thrust corresponding to the target propeller speed is calculated.
[0095] S4: Based on the still water speed test, determine the still water drag and thrust reduction corresponding to the target speed required for the constant speed test; based on the engineering assumption that the thrust reduction in waves is consistent with the thrust reduction in still water, take the thrust reduction as the equivalent thrust reduction under all-wave conditions; calculate the wave drag corresponding to the target speed according to the equivalent thrust reduction and the target propeller thrust; and then obtain the wave drag increase corresponding to the target speed according to the difference between the wave drag and the still water drag.
[0096] Specifically, based on the equivalent thrust reduction and the target propeller thrust, the calculation formula for the wave resistance corresponding to the target speed is as shown in formula (9):
[0097]
[0098] in, This represents the wave resistance corresponding to the target speed. The target propeller thrust is represented by t, and the equivalent thrust reduction is represented by t.
[0099] Based on the difference between wave resistance and still water resistance, the calculation formula for the wave resistance increase corresponding to the target speed is as shown in formula (10):
[0100]
[0101] in, R represents the wave resistance, and R represents the hydrostatic resistance.
[0102] Based on the same inventive concept, one or more embodiments of this specification also provide a constant speed wave drag increase test system for a free-roaming model in all wave directions. Since the working principle of the constant speed wave drag increase test system for a free-roaming model in all wave directions is the same as the aforementioned constant speed wave drag increase test method for a free-roaming model in all wave directions, the implementation of the constant speed wave drag increase test system for a free-roaming model in all wave directions can refer to the aforementioned implementation of the constant speed wave drag increase test method for a free-roaming model in all wave directions, and the repeated parts will not be described again.
[0103] This invention also relates to a constant-speed wave drag increase test system for a free-roaming model aircraft operating in all wave directions. This system corresponds to the aforementioned constant-speed wave drag increase test method for a free-roaming model aircraft operating in all wave directions, and can be understood as a system that implements the aforementioned constant-speed wave drag increase test method for a free-roaming model aircraft operating in all wave directions. Figure 7 As shown, the system includes, in sequence, a wave-condition free-roaming model parameter measurement module 101, a measurement data linear fitting relationship modeling module 102, a target speed correlation parameter interpolation solution module 103, and a wave drag calculation module 104. Among them,
[0104] The wave-condition free-roaming model parameter measurement module 101 is used to maintain the free-roaming model's linear motion along the length of the pool under all-wave conditions, relying on the free-roaming model's automatic steering system; adjust the propeller speed of the free-roaming model so that the propeller speed is linearly related to the speed and propeller thrust respectively; measure and calculate the average speed and average propeller thrust during the stable period corresponding to each propeller speed; the average speed during the stable period is the average speed of the free-roaming model during the stable navigation time at the given propeller speed; the average propeller thrust during the stable period is the average propeller thrust of the free-roaming model during the stable navigation time at the given propeller speed.
[0105] The measurement data linear fitting relationship modeling module 102 is used to establish linear relationship models between the average speed in the stable section and the propeller speed, and between the propeller speed and the average propeller thrust in the stable section, respectively, using the least squares linear fitting method. It also combines the measured propeller speeds and their corresponding average speed and average propeller thrust in the stable section to solve for the speed-propeller speed linear fitting equation and the propeller speed-propeller thrust linear fitting equation.
[0106] The target speed correlation parameter interpolation solution module 103 is used to calculate the target propeller speed corresponding to the target speed required for constant speed test by interpolation based on the speed-propeller speed linear fitting equation; and to calculate the target propeller thrust corresponding to the target propeller speed by substituting the target propeller speed into the propeller speed-propeller thrust linear fitting equation by interpolation.
[0107] The wave drag calculation module 104 is used to determine the still water drag and thrust reduction corresponding to the target speed required for constant speed testing based on still water speed test; based on the engineering assumption that the thrust reduction in waves is consistent with the thrust reduction in still water, the thrust reduction is taken as the equivalent thrust reduction under all-wave conditions; the wave drag corresponding to the target speed is calculated according to the equivalent thrust reduction and the target propeller thrust; and the wave drag increase corresponding to the target speed is obtained according to the difference between the wave drag and the still water drag.
[0108] Furthermore, in the wave condition free-roaming model parameter measurement module 101, under all-wave conditions, the free-roaming model maintains linear motion along the length of the pool by relying on the free-roaming model automatic steering system, and records the heading angle of the free-roaming model in real time.
[0109] In the wave-condition free-roaming model parameter measurement module 101, the steps of adjusting the propeller speed of the free-roaming model and measuring and calculating the average speed and average propeller thrust in the stable section corresponding to each propeller speed include:
[0110] Multiple sets of different propeller speeds are set and adjusted sequentially within a preset range, so that the free-roaming model can continuously sail for a preset time at each propeller speed. During this period, the speed and propeller thrust data of multiple free-roaming models corresponding to each propeller speed are recorded in real time.
[0111] For each group of propeller speeds, data segments are selected where the free-running model's speed fluctuation range is less than a preset fluctuation threshold, and the heading angle deviation at the same time point is less than a preset heading angle deviation threshold. The average speed and average propeller thrust within each data segment are calculated to obtain the average speed and average propeller thrust in the stable segment corresponding to each group of propeller speeds.
[0112] It should be noted that the specific embodiments described above enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail with reference to the accompanying drawings and embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention. In short, all technical solutions and improvements that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention patent.
Claims
1. A method for testing wave drag at constant speed in a free-roaming model aircraft operating in all wave directions, characterized in that, Includes the following steps: S1: Under all-wave conditions, the free-roaming model maintains linear motion along the length of the pool using its autopilot system; the propeller speed of the free-roaming model is adjusted so that it is linearly correlated with the speed and thrust, and the average speed and thrust during the stable period corresponding to each propeller speed are measured and calculated; the average speed during the stable period is the average speed of the free-roaming model during the stable navigation time at the given propeller speed; the average thrust during the stable period is the average propeller thrust of the free-roaming model during the stable navigation time at the given propeller speed. S2: Using the least squares linear fitting method, establish linear relationship models between the average speed in the stable section and the propeller speed, and between the propeller speed and the average propeller thrust in the stable section, respectively. Combine the measured propeller speeds and their corresponding average speeds and average propeller thrusts in the stable section, solve for the linear fitting equations of speed-propeller speed and propeller speed-propeller thrust. S3: Based on the linear fitting equation of speed-propeller speed, the target propeller speed corresponding to the target speed required for constant speed test is obtained by interpolation calculation; the target propeller speed is substituted into the linear fitting equation of propeller speed-propeller thrust, and the target propeller thrust corresponding to the target propeller speed is obtained by interpolation calculation. S4: Based on the still water speed test, determine the still water drag and thrust reduction corresponding to the target speed required for the constant speed test; based on the engineering assumption that the thrust reduction in waves is consistent with the thrust reduction in still water, take the thrust reduction as the equivalent thrust reduction under all-wave conditions; calculate the wave drag corresponding to the target speed according to the equivalent thrust reduction and the target propeller thrust; and then obtain the wave drag increase corresponding to the target speed according to the difference between the wave drag and the still water drag.
2. The method according to claim 1, characterized in that, In step S1, under all-wave conditions, the free-roaming model maintains its linear motion along the length of the pool by relying on its automatic steering system, and records the heading angle of the free-roaming model in real time. The steps of adjusting the propeller speed of the free-flying model, and measuring and calculating the average speed and average propeller thrust during the steady-state period corresponding to each propeller speed include: Multiple sets of different propeller speeds are set and adjusted sequentially within a preset range, so that the free-roaming model can continuously sail for a preset time at each propeller speed. During this period, the speed and propeller thrust data of multiple free-roaming models corresponding to each propeller speed are recorded in real time. For each group of propeller speeds, data segments are selected where the free-running model's speed fluctuation range is less than a preset fluctuation threshold and the corresponding heading angle deviation is less than a preset heading angle deviation threshold. The average speed and average propeller thrust within each data segment are calculated to obtain the average speed and average propeller thrust in the stable segment corresponding to each group of propeller speeds.
3. The method according to claim 1, characterized in that, In step S2, the linear relationship model between the average speed during the stable phase and the propeller speed is as follows: ， Where V represents the average speed during the steady-state period, N represents the propeller speed, and a and b represent the fitting coefficients; Based on the measured propeller speeds and their corresponding average speeds during the stable period, the fitting coefficients a and b are obtained by minimizing the sum of squared errors between the measured average speeds during the stable period and the average speeds during the stable period calculated by the linear relationship model, and then the linear fitting equation of speed-propeller speed is obtained.
4. The method according to claim 1, characterized in that, In step S2, the linear relationship model between the propeller speed and the average propeller thrust during the stable phase is as follows: ， Where T represents the average propeller thrust during the steady-state phase, N represents the propeller speed, and c and d represent the fitting coefficients. Based on the measured propeller speeds and their corresponding average propeller thrust in the stable section, the fitting coefficients c and d are obtained by minimizing the sum of squared errors between the measured average propeller thrust in the stable section and the average propeller thrust in the stable section calculated by the linear relationship model, and then the linear fitting equation of propeller speed-propeller thrust is obtained.
5. The method according to claim 3, characterized in that, In step S3, based on the calculated fitting coefficients a and b, the target speed required for the constant speed test is substituted into the linear fitting equation of speed-propeller speed obtained from the linear relationship model between the average speed of the stable section and the propeller speed, and the target propeller speed corresponding to the target speed is calculated.
6. The method according to claim 4, characterized in that, In step S3, based on the calculated fitting coefficients c and d, the target propeller speed is substituted into the propeller speed-thrust linear fitting equation obtained from the linear relationship model between propeller speed and average propeller thrust in the stable section, and the target propeller thrust corresponding to the target propeller speed is calculated.
7. The method according to claim 1 or 2, characterized in that, In step S4, the wave resistance corresponding to the target speed is calculated based on the equivalent thrust reduction and the target propeller thrust. The calculation formula is as follows: ， in, This represents the wave resistance corresponding to the target speed. The target propeller thrust is represented by t, and the equivalent thrust reduction is represented by t. Based on the difference between wave resistance and still water resistance, the wave drag increase corresponding to the target speed is calculated using the following formula: ， in, R represents the wave resistance, and R represents the hydrostatic resistance.
8. The method according to claim 2, characterized in that, In step S1, the Qualisys motion capture system is used to record the speed of the free-roaming model in real time, forming a speed time series curve. Based on the speed time series curve, the data segment where the speed fluctuation range of the free-roaming model is less than a preset fluctuation threshold at the current propeller speed is determined.
9. A constant-speed wave drag increase test system for a free-roaming model aircraft operating in all wave directions, characterized in that, The module includes, in sequence, a wave-condition free-roaming model parameter measurement module, a measurement data linear fitting relationship modeling module, a target speed correlation parameter interpolation solution module, and a wave drag calculation module. The wave-condition free-roaming model parameter measurement module is used to maintain the free-roaming model's linear motion along the length of the pool under all-wave conditions, relying on the model's autopilot system; it adjusts the propeller speed of the free-roaming model so that the propeller speed is linearly related to the speed and propeller thrust, and measures and calculates the average speed and average propeller thrust during the stable period corresponding to each propeller speed; the average speed during the stable period is the average speed of the free-roaming model during the stable navigation time at the given propeller speed; the average propeller thrust during the stable period is the average propeller thrust of the free-roaming model during the stable navigation time at the given propeller speed. The linear fitting relationship modeling module for the measurement data is used to establish linear relationship models between the average speed during the stable period and the propeller speed, and between the propeller speed and the average propeller thrust during the stable period, respectively, using the least squares linear fitting method. It also combines multiple sets of measured propeller speeds and their corresponding average speed and average propeller thrust during the stable period to solve for the linear fitting equations of speed-propeller speed and propeller speed-propeller thrust. The target speed correlation parameter interpolation solution module is used to calculate the target propeller speed corresponding to the target speed required for constant speed testing by interpolation based on the linear fitting equation of speed-propeller speed; and to calculate the target propeller thrust corresponding to the target propeller speed by substituting the target propeller speed into the linear fitting equation of propeller speed-propeller thrust. The wave drag calculation module is used to: determine the still water drag and thrust reduction corresponding to the target speed required for constant speed testing based on still water speed tests; based on the engineering assumption that the thrust reduction in waves is consistent with the thrust reduction in still water, use the thrust reduction as the equivalent thrust reduction under all-wave conditions; calculate the wave drag corresponding to the target speed based on the equivalent thrust reduction and the target propeller thrust; and obtain the wave drag increase corresponding to the target speed based on the difference between the wave drag and the still water drag.
10. The system according to claim 9, characterized in that, In the wave condition free-roaming model parameter measurement module, under all-wave conditions, the free-roaming model's automatic steering system maintains the free-roaming model's linear motion along the length of the pool, and records the free-roaming model's heading angle in real time. The steps of adjusting the propeller speed of the free-flying model, and measuring and calculating the average speed and average propeller thrust during the steady-state period corresponding to each propeller speed include: Multiple sets of different propeller speeds are set and adjusted sequentially within a preset range, so that the free-roaming model can continuously sail for a preset time at each propeller speed. During this period, the speed and propeller thrust data of multiple free-roaming models corresponding to each propeller speed are recorded in real time. For each group of propeller speeds, data segments are selected where the free-running model's speed fluctuation range is less than a preset fluctuation threshold and the corresponding heading angle deviation is less than a preset heading angle deviation threshold. The average speed and average propeller thrust within each data segment are calculated to obtain the average speed and average propeller thrust in the stable segment corresponding to each group of propeller speeds.