Predict Aircraft Roll Rate: Aerodynamic Data Guide

by Viktoria Ivanova 51 views

Hey guys! Ever wondered how aircraft roll and how we can predict their roll rate at different speeds? This article dives deep into predicting an aircraft's roll behavior using aerodynamic data. Whether you're an aviation enthusiast, a student, or an engineer, understanding these principles is crucial for designing and analyzing aircraft performance. We’ll explore the key factors influencing roll rate, the necessary aerodynamic data, and how to create a spreadsheet calculator to predict roll performance across a wide range of airspeeds, from a crawl at Mach 0.01 to a speedy Mach 0.99. Let's get started!

Understanding Roll Rate and Its Significance

Roll rate, simply put, is how quickly an aircraft can rotate around its longitudinal axis. Think of it as how fast the wings can move from level to a banked position. This is a critical performance metric for aircraft, influencing maneuverability, responsiveness, and overall flight characteristics. A high roll rate allows for quick changes in direction, which is vital in situations ranging from evasive maneuvers to performing aerobatics. Understanding and predicting roll rate is essential for several reasons:

  • Aircraft Design: Engineers need to know the roll performance of an aircraft to ensure it meets handling qualities requirements. A well-designed aircraft should have a roll rate that is both responsive and controllable, avoiding excessive or sluggish behavior.
  • Flight Simulation: Accurate prediction of roll rate is crucial for flight simulators, allowing pilots to train in realistic scenarios and experience the aircraft's handling characteristics firsthand.
  • Flight Testing: Predicted roll rates serve as a benchmark for flight testing. Actual flight data can then be compared to predictions, validating design models and identifying areas for improvement.
  • Safety: A predictable and controllable roll rate is important for safety. Unexpected or insufficient roll performance can lead to accidents, especially in critical phases of flight like takeoff and landing.
  • Performance Optimization: Understanding the factors that influence roll rate enables designers to optimize the aircraft's aerodynamics and control systems for maximum performance. This can involve adjusting wing geometry, aileron size, or control system characteristics.

To accurately predict roll rate, we need to delve into the aerodynamic forces and moments acting on the aircraft. The primary control surface responsible for roll is the aileron. When the pilot deflects the ailerons, they create a differential lift force on the wings. One aileron goes up, decreasing lift on that wing, while the other aileron goes down, increasing lift on the opposite wing. This difference in lift generates a rolling moment about the aircraft's longitudinal axis, causing it to roll. However, it's not just the ailerons that affect roll. Factors like airspeed, wing geometry, and the aircraft's overall aerodynamic configuration play significant roles. At higher airspeeds, the same aileron deflection will generate a larger rolling moment due to the increased dynamic pressure. Wing geometry, such as wingspan and aspect ratio, also influences roll performance. An aircraft with a longer wingspan generally has a higher rolling moment for the same aileron deflection. Furthermore, the aircraft's overall shape and the presence of other control surfaces, like spoilers or flaps, can affect the airflow over the wings and, consequently, the roll rate. Predicting roll rate accurately requires a comprehensive understanding of these interacting factors and their influence on the aircraft's rolling motion.

Key Aerodynamic Factors Influencing Roll Rate

Predicting aircraft roll rate involves considering several key aerodynamic factors. These factors interact in complex ways, and understanding their influence is crucial for accurate predictions. Let's break down the primary elements:

  • Aileron Effectiveness: The most direct influence on roll rate comes from the ailerons. Aileron effectiveness refers to how much rolling moment is generated for a given aileron deflection. This is influenced by factors such as aileron size, shape, location on the wing, and deflection angle. Larger ailerons, or those with more aggressive deflection, will generally produce a greater rolling moment. However, there are practical limits to aileron size and deflection due to factors like hinge moments (the force required to move the aileron) and potential for flow separation (where airflow detaches from the aileron surface, reducing its effectiveness). The shape of the aileron also matters; for example, frise ailerons, which protrude slightly into the airflow when deflected upwards, can help to balance the aerodynamic forces and improve control effectiveness. Aileron effectiveness is also affected by the overall wing design, including its chord length (the distance from the leading edge to the trailing edge) and taper ratio (the ratio of the wingtip chord to the wing root chord). Wings with a larger chord length provide more surface area for the ailerons to act upon, while a higher taper ratio can influence the spanwise distribution of lift and rolling moment.
  • Airspeed: Airspeed plays a critical role because it affects the dynamic pressure acting on the control surfaces. Dynamic pressure, which is proportional to the square of the airspeed, is a measure of the force exerted by the airflow. As airspeed increases, the dynamic pressure also increases, resulting in a greater rolling moment for the same aileron deflection. This means that an aircraft will typically roll faster at higher speeds. However, the relationship between airspeed and roll rate is not always linear. At very high speeds, factors like aeroelasticity (the deformation of the wing structure under aerodynamic loads) and compressibility effects (changes in air density due to high speeds) can influence the aircraft's response. For instance, at transonic speeds (around Mach 0.8 to 1.2), shock waves can form on the wing surface, altering the pressure distribution and potentially reducing aileron effectiveness. Similarly, aeroelastic effects can cause the wing to twist or bend under load, which can either enhance or diminish the rolling moment generated by the ailerons.
  • Wing Geometry: The wing's geometry, including wingspan, aspect ratio, and wing sweep, significantly impacts roll performance. Wingspan is the distance from wingtip to wingtip, and a longer wingspan generally results in a higher rolling moment for a given aileron deflection. This is because the lift forces generated by the ailerons have a larger moment arm (the distance from the force's line of action to the aircraft's longitudinal axis). Aspect ratio, which is the ratio of the wingspan squared to the wing area, is another important parameter. A higher aspect ratio wing (long and slender) tends to have a lower induced drag (drag created by the generation of lift) and a greater rolling moment for the same aileron deflection compared to a lower aspect ratio wing (short and stubby). Wing sweep, the angle at which the wing is angled backward from the fuselage, also influences roll performance. Swept wings are often used on high-speed aircraft to reduce drag at transonic and supersonic speeds. However, wing sweep can also affect the spanwise lift distribution and aileron effectiveness. Highly swept wings may experience aileron reversal, a phenomenon where the ailerons produce an opposite rolling moment at certain speeds due to wing aeroelasticity.
  • Aircraft Inertia: The aircraft's inertia, particularly its moment of inertia about the roll axis, affects how quickly it responds to the rolling moment. Moment of inertia is a measure of an object's resistance to rotational acceleration. An aircraft with a higher moment of inertia about the roll axis will be more resistant to rolling and will have a lower roll rate for the same applied rolling moment. The distribution of mass within the aircraft significantly influences its moment of inertia. Aircraft with heavy components located far from the roll axis will have a higher moment of inertia compared to those with mass concentrated near the axis. For example, an aircraft with heavy engines mounted on the wings will have a higher roll inertia than one with engines mounted closer to the fuselage.
  • Other Aerodynamic Effects: Several other aerodynamic effects can influence roll rate. These include factors such as wing dihedral (the upward angle of the wings from the fuselage), which provides roll stability, and the presence of other control surfaces like spoilers, which can be used to augment or replace ailerons. Dihedral creates a restoring rolling moment when the aircraft is disturbed from a wings-level attitude, helping to stabilize the aircraft in roll. Spoilers, which are hinged plates on the upper surface of the wing, can be deployed to disrupt the airflow and reduce lift, creating a rolling moment. Spoilers are often used in conjunction with ailerons to improve roll control, especially at high speeds where aileron effectiveness may be reduced due to aeroelastic effects. Furthermore, the interaction between the wings and the fuselage, as well as the presence of external stores or nacelles, can affect the airflow and influence the roll rate. Accurately predicting roll rate often requires considering these complex interactions and using computational fluid dynamics (CFD) simulations or wind tunnel testing to assess their impact.

Aerodynamic Data Needed for Roll Rate Prediction

To accurately predict an aircraft's roll rate, you'll need specific aerodynamic data. Gathering this data may involve a combination of methods, including wind tunnel testing, computational fluid dynamics (CFD) simulations, and theoretical calculations. Here's a breakdown of the essential data points:

  • Aileron Hinge Moment Coefficient (Chδa): The aileron hinge moment coefficient is a crucial parameter representing the force required to deflect the aileron. It's influenced by the aileron's shape, size, and deflection angle, as well as the airflow conditions around the wing. This coefficient is essential for determining the control forces a pilot needs to exert to achieve a desired roll rate. Wind tunnel testing and CFD simulations are common methods for obtaining accurate hinge moment coefficients. These tests involve measuring the forces acting on the aileron at various deflection angles and airspeeds. The data is then used to generate a graph or table of hinge moment coefficient values as a function of aileron deflection and airspeed. Understanding the hinge moment characteristics is critical for designing control systems that provide the pilot with the appropriate level of control feel and prevent over-control or under-control situations. Additionally, the hinge moment coefficient is an important input for flight simulators, ensuring that the simulated control forces accurately reflect the real-world aircraft behavior.
  • Rolling Moment Coefficient due to Aileron Deflection (Clδa): This coefficient, Clδa, quantifies the rolling moment generated by the ailerons for a given deflection. It's a primary factor in determining the aircraft's roll effectiveness. Higher Clδa values indicate a more responsive roll behavior. The rolling moment coefficient is influenced by several factors, including the aileron's size, shape, and location on the wing, as well as the wing's overall geometry. Wind tunnel testing is a common method for measuring Clδa. During a wind tunnel test, the model aircraft is subjected to various airflow conditions, and the rolling moment generated by different aileron deflections is measured using force sensors. CFD simulations can also be used to estimate Clδa. These simulations solve the governing equations of fluid dynamics to predict the airflow around the aircraft and the resulting aerodynamic forces and moments. Theoretical calculations, based on simplified aerodynamic models, can provide an initial estimate of Clδa. However, these calculations often need to be validated with experimental data or more detailed simulations. The rolling moment coefficient is a critical input for flight dynamics analysis and control system design. It allows engineers to predict the aircraft's roll response to pilot inputs and to design control systems that provide the desired handling characteristics.
  • Rolling Moment Coefficient due to Roll Rate (Clp): This coefficient, Clp, represents the damping effect on roll caused by the aircraft's own roll rate. It's typically a negative value, indicating that the rolling motion creates a moment opposing further roll. This damping effect is crucial for stability and prevents excessive oscillations. The rolling moment coefficient due to roll rate is primarily influenced by the wing's geometry, particularly its span and chord distribution. Wings with a larger span tend to have a greater damping effect on roll. CFD simulations and wind tunnel testing are common methods for determining Clp. In wind tunnel tests, the model aircraft is forced to oscillate in roll, and the resulting aerodynamic forces and moments are measured. The data is then used to calculate the rolling moment coefficient due to roll rate. CFD simulations can also be used to estimate Clp by simulating the airflow around the aircraft as it rolls. Accurate knowledge of Clp is essential for predicting the aircraft's roll stability and for designing control systems that provide a smooth and predictable roll response. A large negative Clp value indicates strong roll damping, which can improve stability but may also reduce the aircraft's responsiveness to control inputs. Conversely, a small negative Clp value indicates weaker roll damping, which can make the aircraft more agile but also more susceptible to oscillations.
  • Aircraft Inertia (Ix): As discussed earlier, the aircraft's moment of inertia about the roll axis (Ix) is crucial. This value represents the aircraft's resistance to rolling motion. Accurate determination of Ix is essential for predicting roll acceleration and overall roll response. The moment of inertia depends on the aircraft's mass distribution and can be calculated using detailed weight and balance data. This data includes the weight and location of all components of the aircraft, such as the fuselage, wings, engines, and payload. The moment of inertia can be calculated using the parallel axis theorem, which allows the moment of inertia about any axis to be determined from the moment of inertia about a parallel axis through the center of mass. In practice, the moment of inertia is often determined experimentally using methods such as pendulum tests or oscillation tests. These tests involve suspending the aircraft or a scale model and measuring its period of oscillation. The moment of inertia can then be calculated from the period of oscillation and the dimensions of the aircraft. Accurate knowledge of the moment of inertia is essential for flight dynamics analysis and control system design. It allows engineers to predict the aircraft's response to control inputs and to design control systems that provide the desired handling characteristics.
  • Air Density (ρ): Air density varies with altitude and temperature and directly affects dynamic pressure. Accurate air density values are necessary for calculating aerodynamic forces and moments at different flight conditions. Air density can be calculated using standard atmospheric models, which relate air density to altitude and temperature. These models are based on empirical data and provide a good approximation of the atmospheric conditions. Alternatively, air density can be measured directly using weather instruments or sensors on board the aircraft. Accurate knowledge of air density is crucial for predicting the aircraft's aerodynamic performance at different altitudes and temperatures. For example, at higher altitudes, the air density is lower, which reduces the dynamic pressure and, consequently, the aerodynamic forces and moments. This means that the aircraft will require a higher airspeed to generate the same amount of lift or rolling moment at higher altitudes compared to lower altitudes.

Gathering this data can be a complex process, often involving specialized equipment and expertise. However, having accurate aerodynamic data is the foundation for building a reliable roll rate prediction model.

Building a Spreadsheet Calculator for Roll Rate Prediction

Now that we understand the key factors and data required, let's discuss how to create a spreadsheet calculator to predict roll rate. This tool will allow you to input aerodynamic data and airspeed values to estimate the aircraft's roll performance. Here’s a step-by-step guide:

  1. Set Up Input Cells: In your spreadsheet software (like Microsoft Excel or Google Sheets), designate specific cells for inputting the required aerodynamic data and flight conditions. These cells should include:

    • Aileron Hinge Moment Coefficient (Chδa)
    • Rolling Moment Coefficient due to Aileron Deflection (Clδa)
    • Rolling Moment Coefficient due to Roll Rate (Clp)
    • Aircraft Inertia about the Roll Axis (Ix)
    • Air Density (ρ)
    • Airspeed (V)
    • Aileron Deflection Angle (δa) – typically in degrees or radians
    • Wingspan (b)

    Label these cells clearly so that the user knows what data to input. You can also add units to the labels (e.g., “Airspeed (m/s)”, “Aileron Deflection (degrees)”). Providing clear labels and units will help prevent errors and ensure that the user inputs the correct data.

  2. Calculate Dynamic Pressure (q): Dynamic pressure is a critical parameter that relates airspeed and air density. Create a cell to calculate dynamic pressure (q) using the formula:

    q = 0.5 * ρ * V^2

    In your spreadsheet, this would translate to a formula like 0.5 * [Air Density Cell] * [Airspeed Cell]^2. Dynamic pressure is a measure of the kinetic energy of the airflow and is a key factor in determining the aerodynamic forces acting on the aircraft. As airspeed increases, the dynamic pressure also increases, resulting in greater aerodynamic forces. This means that the same control surface deflection will generate a larger rolling moment at higher airspeeds. Dynamic pressure is also affected by air density, which varies with altitude and temperature. At higher altitudes, the air density is lower, which reduces the dynamic pressure and, consequently, the aerodynamic forces.

  3. Calculate Rolling Moment (L): The rolling moment (L) generated by the ailerons can be calculated using the following formula:

    L = q * S * b * Clδa * δa

    Where:

    • q is the dynamic pressure
    • S is the wing area
    • b is the wingspan
    • Clδa is the rolling moment coefficient due to aileron deflection
    • δa is the aileron deflection angle

    In your spreadsheet, create a cell to calculate the rolling moment using this formula. You’ll need to input the wing area (S) into a designated cell. The rolling moment represents the twisting force that causes the aircraft to roll. It is directly proportional to the dynamic pressure, wing area, wingspan, rolling moment coefficient due to aileron deflection, and aileron deflection angle. A larger rolling moment will result in a higher roll rate, assuming other factors such as aircraft inertia remain constant. The formula highlights the importance of several factors in achieving a high roll rate. A larger wing area and wingspan provide more surface area for the ailerons to act upon, while a higher rolling moment coefficient due to aileron deflection indicates a more effective control surface. Increasing the aileron deflection angle will also increase the rolling moment, but there are practical limits to deflection due to factors such as hinge moments and potential for flow separation.

  4. Calculate Roll Rate (p): The steady-state roll rate (p) can be estimated using the following equation:

    p = L / (Ix * Clp)

    Where:

    • L is the rolling moment
    • Ix is the aircraft's moment of inertia about the roll axis
    • Clp is the rolling moment coefficient due to roll rate

    This equation represents a simplified model of the aircraft's rolling motion, assuming that the aircraft is in a steady-state condition (i.e., rolling at a constant rate). In your spreadsheet, create a cell to calculate the roll rate using this formula. Note that Clp is typically a negative value, which means that the roll rate will have the opposite sign to the rolling moment. This is because the rolling moment coefficient due to roll rate represents the damping effect on roll caused by the aircraft's own rolling motion. A larger negative Clp value indicates stronger roll damping, which will reduce the steady-state roll rate. The formula also highlights the importance of the aircraft's moment of inertia about the roll axis (Ix). A higher moment of inertia means that the aircraft is more resistant to rolling, which will result in a lower roll rate for the same rolling moment. Accurately predicting roll rate requires considering the interplay between these factors and using appropriate aerodynamic data and formulas. The spreadsheet calculator provides a convenient tool for estimating roll performance, but it's important to recognize that it is a simplified model and may not capture all of the complexities of aircraft rolling motion.

  5. Create a Table for Varying Airspeeds: To predict roll rate at a range of airspeeds, create a table in your spreadsheet. List airspeeds (Mach 0.01 to 0.99) in one column. In the adjacent column, use the formula you created in step 4 to calculate the roll rate for each airspeed. Ensure that the formula references the airspeed from the corresponding row in the table.

    You can use a simple linear interpolation to fill in the airspeed values between Mach 0.01 and 0.99. Alternatively, you can use a more sophisticated approach, such as a geometric progression, to create a non-linear distribution of airspeed values. The key is to have a sufficient number of data points to capture the variation in roll rate across the airspeed range. Once you have created the table of airspeeds, you can use the formula you developed in step 4 to calculate the roll rate for each airspeed. You will need to ensure that the formula references the airspeed from the corresponding row in the table. You can use absolute references (e.g., $A$1) to fix certain cell references in the formula, so that they do not change when you copy the formula down the column. This will allow you to quickly calculate the roll rate for all of the airspeeds in the table. The table will provide a clear visualization of how the roll rate changes with airspeed and can be used to identify any potential issues or areas for improvement in the aircraft's design.

  6. Graph the Results: Visualize the results by creating a graph with airspeed on the x-axis and roll rate on the y-axis. This visual representation will make it easier to understand the relationship between airspeed and roll performance.

    Most spreadsheet software provides charting tools that allow you to easily create a graph from a table of data. You will need to select the data range for the x-axis (airspeed) and the y-axis (roll rate) and then choose the appropriate chart type. A scatter plot or a line chart is typically used to visualize the relationship between two continuous variables. You can customize the graph by adding titles, labels, and gridlines to make it more readable and informative. The graph will provide a visual representation of how the roll rate changes with airspeed. You can use the graph to identify the airspeed range where the roll rate is highest and to see how the roll rate changes at different speeds. The graph can also be used to compare the roll performance of different aircraft or configurations. By visually representing the data, you can gain a better understanding of the aircraft's roll characteristics and identify any potential issues or areas for improvement. For example, if the graph shows a sudden drop in roll rate at a certain airspeed, this may indicate a problem with aileron effectiveness or wing aeroelasticity. The graph can then be used to guide further analysis and design modifications.

  7. Iterate and Refine: Use the spreadsheet to explore the effects of different aerodynamic parameters on roll rate. You can change the input values (like aileron deflection or wing geometry) and observe how the roll rate changes. This iterative process can help you optimize the aircraft's design for desired roll performance.

    By changing the input values in the spreadsheet, you can simulate the effects of different design choices on the aircraft's roll performance. For example, you can change the aileron deflection angle to see how it affects the roll rate at different airspeeds. You can also change the wing geometry parameters, such as wingspan or aspect ratio, to see how they influence the roll performance. By iterating through different design options, you can identify the optimal configuration that meets your performance requirements. This iterative process can also help you understand the trade-offs between different design parameters. For example, increasing the wingspan may improve the roll rate, but it may also increase the aircraft's weight and drag. Similarly, increasing the aileron deflection may improve the roll rate, but it may also increase the control forces required by the pilot. By exploring these trade-offs, you can make informed design decisions that balance performance, stability, and control. The spreadsheet calculator provides a powerful tool for this iterative design process, allowing you to quickly evaluate the effects of different design choices on the aircraft's roll performance. However, it's important to remember that the spreadsheet is a simplified model and may not capture all of the complexities of aircraft rolling motion. Therefore, the results from the spreadsheet should be validated with more detailed simulations and flight testing.

By following these steps, you can create a spreadsheet calculator that provides valuable insights into an aircraft's roll behavior at various airspeeds. This tool can be a powerful aid in aircraft design, analysis, and optimization.

Practical Considerations and Limitations

While a spreadsheet calculator is a valuable tool, it’s essential to acknowledge its limitations and consider practical factors that may influence actual roll performance. Here are some key considerations:

  • Linearity Assumptions: The equations used in the spreadsheet calculator often assume linear relationships between parameters. In reality, aerodynamic forces and moments can exhibit non-linear behavior, especially at high angles of attack or transonic speeds. This means that the predictions from the spreadsheet may not be accurate under all flight conditions. For example, at high angles of attack, the airflow over the wing may separate, leading to a stall and a significant reduction in lift and rolling moment. Similarly, at transonic speeds, shock waves can form on the wing surface, altering the pressure distribution and potentially reducing aileron effectiveness. To account for these non-linear effects, more sophisticated analysis methods, such as CFD simulations or wind tunnel testing, may be required.
  • Aeroelastic Effects: The deformation of the wing structure under aerodynamic loads (aeroelasticity) can significantly affect roll performance. At high speeds, the wings can twist or bend, which can change the aileron effectiveness and alter the rolling moment. The spreadsheet calculator typically does not account for aeroelastic effects, which can lead to inaccuracies in the roll rate predictions. Aeroelasticity is a complex phenomenon that depends on the structural properties of the wing, the aerodynamic loads, and the flight conditions. To accurately predict the effects of aeroelasticity on roll performance, it is necessary to use specialized analysis tools and techniques, such as finite element analysis (FEA) or computational aeroelasticity (CAE).
  • Control System Dynamics: The response of the aircraft's control system can influence the achievable roll rate. Factors such as control surface actuation rates, hinge moments, and pilot input can affect how quickly the aircraft rolls. The spreadsheet calculator focuses on steady-state roll rate and does not consider the transient behavior of the control system. The control system dynamics can be particularly important for high-performance aircraft, where rapid roll maneuvers are required. The actuation rates of the control surfaces, which determine how quickly they can be deflected, can limit the achievable roll rate. The hinge moments, which are the forces required to move the control surfaces, can also affect the control system response. If the hinge moments are too high, the pilot may not be able to generate sufficient control forces to achieve the desired roll rate. To accurately predict the effects of control system dynamics on roll performance, it is necessary to use dynamic models and simulations that account for the control system characteristics.
  • Pilot Input and Handling Qualities: The pilot's control inputs and the aircraft's handling qualities significantly impact the perceived roll performance. A high roll rate is not always desirable if it makes the aircraft difficult to control. The spreadsheet calculator does not consider these subjective factors. Handling qualities refer to the aircraft's response to pilot inputs and its overall ease of control. An aircraft with good handling qualities is responsive, predictable, and stable. The pilot should be able to easily control the aircraft's roll attitude without excessive effort or concentration. Factors such as the roll damping, roll inertia, and control surface sensitivity can affect the handling qualities. To evaluate the handling qualities, it is necessary to conduct flight tests or pilot-in-the-loop simulations. These tests involve experienced pilots flying the aircraft or a simulated version of the aircraft and providing feedback on its handling characteristics.
  • Environmental Factors: External factors such as wind gusts and turbulence can affect the aircraft's roll behavior. The spreadsheet calculator does not account for these external disturbances. Wind gusts and turbulence can create unwanted rolling moments, which can make it difficult for the pilot to maintain the desired roll attitude. The effects of environmental factors on roll performance can be particularly important for aircraft operating in gusty or turbulent conditions, such as during landing or takeoff. To account for these effects, more sophisticated analysis methods, such as dynamic simulations with atmospheric disturbance models, may be required.

By keeping these limitations in mind, you can use the spreadsheet calculator as a valuable tool while understanding that it provides an idealized estimate. For critical applications, more comprehensive analysis methods and flight testing are essential to validate the predictions and ensure safe and effective aircraft operation.

Conclusion

Predicting an aircraft's roll rate at various airspeeds is a complex but crucial task in aircraft design and analysis. By understanding the key aerodynamic factors, gathering the necessary data, and building a spreadsheet calculator, you can gain valuable insights into an aircraft's roll performance. Remember to consider the limitations of the model and the practical factors that can influence real-world behavior. With this knowledge, you're well-equipped to analyze and optimize aircraft roll characteristics for improved maneuverability, safety, and overall flight performance. Keep soaring, guys!