Open Access. Powered by Scholars. Published by Universities.®

Navigation, Guidance, Control and Dynamics Commons

Open Access. Powered by Scholars. Published by Universities.®

Mechanical Engineering

Institution
Keyword
Publication Year
Publication
Publication Type
File Type

Articles 31 - 60 of 75

Full-Text Articles in Navigation, Guidance, Control and Dynamics

The Effect Of Store-To-Store Energy Transfers On The Global Dynamics Of Aircraft, Guilherme Mainieri Eymael Mar 2022

The Effect Of Store-To-Store Energy Transfers On The Global Dynamics Of Aircraft, Guilherme Mainieri Eymael

Honors Program: Senior Projects (Public)

This study analyzes the energy transfer mechanisms when nonlinear devices (stores) are attached to a linear model airplane. For that, a reduced-order model (ROM) was derived to simulate the first two flexible modes of vibration of the primary structure (aircraft) with one store in each wing. Each store can either be locked or unlocked. When locked, it only contributes as mass-effect, and when unlocked, it adds nonlinearity to the system. Simulations were then performed with either both stores locked, one store unlocked, or both stores unlocked. It was found that the attachment of nonlinear stores in the ROM changes the …


Design, Development, And Testing Of Near-Optimal Satellite Attitude Control Strategies, Giovanni Lavezzi Jan 2022

Design, Development, And Testing Of Near-Optimal Satellite Attitude Control Strategies, Giovanni Lavezzi

Electronic Theses and Dissertations

Advances in space technology and interest toward remote sensing mission have grown in the recent years, requiring the attitude control subsystems of observation satellites to increase their performances in terms of pointing accuracy and on-board implementability. Moreover, an increased interest in small satellite missions and the recent technological developments related to the CubeSats standard have drastically reduced the cost of producing and flying a satellite mission. In this context, the proposed research aims to improve the state of the art for satellite attitude control methodologies by proposing a near-optimal attitude control strategy, simulated in a high-fidelity environment. Two strategies are …


Formation Control With Collision Avoidance For Fixed-Wing Unmanned Air Vehicles With Speed Constraints, Christopher Heintz Jan 2022

Formation Control With Collision Avoidance For Fixed-Wing Unmanned Air Vehicles With Speed Constraints, Christopher Heintz

Theses and Dissertations--Mechanical and Aerospace Engineering

Advances in the miniaturization of powerful electronic components and motors, the democratization of global navigation satellite systems (GNSS), and improvements in the performance, safety, and cost in lithium batteries has led to the proliferation of small and relatively inexpensive unmanned aerial vehicles (UAVs). Many of these UAVs are of the multi-rotor design, however, fixed-wing designs are often more efficient than rotary-wing aircraft, leading to a reduction in the power required for a UAV of a given mass to stay airborne. Autonomous cooperation between multiple UAVs would enable them to complete objectives that would be difficult or impossible for a single …


Precise Landing Of Vtol Uavs Using A Tether, Jeremy W. Rathjen Jan 2022

Precise Landing Of Vtol Uavs Using A Tether, Jeremy W. Rathjen

Graduate Theses, Dissertations, and Problem Reports (ETD)

Unmanned Aerial Vehicles (UAVs), also known as drones, are often considered the solution to complex robotics problems. The significant freedom to explore an environment is a major reason why UAVs are a popular choice for automated solutions. UAVs, however, have a very limited flight time due to the low capacity and weight ratio of current batteries. One way to extend the vehicles' flight time is to use a tether to provide power from external batteries, generators on the ground, or another vehicle. Attaching a tether to a vehicle may constrain its navigation but it may also create some opportunities for …


3-Axis Reaction Wheel System For Cubesats, Alexandra Mae Lee, Daniel Leon, Christopher Pablo Casillas, Rose Mccarver Jun 2021

3-Axis Reaction Wheel System For Cubesats, Alexandra Mae Lee, Daniel Leon, Christopher Pablo Casillas, Rose Mccarver

Mechanical Engineering

Reaction wheels are a common, but expensive, component used in CubeSats, that can accurately position a satellite using an imparted momentum (or impulse) from a rotating flywheel to adjust a satellite’s attitude. This document serves as the final design review and report for the 3-Axis Reaction Wheel Senior Design Project in the Mechanical Engineering Department of California Polytechnic State University, San Luis Obispo. The goal of this project is to produce a functional, low-cost 3-axis reaction wheel system based on previous research done by a master’s student at Cal Poly to be implemented in future CubeSats in the Cal Poly …


Accelerated Controller Tuning For Wind Turbines Under Multiple Hazards, Aly Mousaad Aly, Milad Rezaee Mar 2021

Accelerated Controller Tuning For Wind Turbines Under Multiple Hazards, Aly Mousaad Aly, Milad Rezaee

Faculty Publications

During their lifecycle, wind turbines can be subjected to multiple hazard loads, such as high-intensity wind, earthquake, wave, and mechanical unbalance. Excessive vibrations, due to these loads, can have detrimental effects on energy production, structural lifecycle, and the initial cost of wind turbines. Vibration control by various means, such as passive, active, and semi-active control systems provide crucial solutions to these issues. We developed a novel control theory that enables semi-active controller tuning under the complex structural behavior and inherent system nonlinearity. The proposed theory enables the evaluation of semi-active controllers’ performance of multi-degrees-of-freedom systems, without the need for time-consuming …


Electromagnetic Formation Control Using Frequency Multiplexing, Zahra Abbasi Jan 2021

Electromagnetic Formation Control Using Frequency Multiplexing, Zahra Abbasi

Theses and Dissertations--Mechanical and Aerospace Engineering

This dissertation addresses control of relative positions and orientations of formation flying satellites using magnetic interactions. Electromagnetic formation flight (EMFF) is implemented, in which each satellite is equipped with a set of electromagnetic coils to generate an electromagnetic field. Traditional EMFF technique applies DC magnetic fields which lead to a nonlinear and highly coupled formation dynamics that allow for only position or orientation control of the satellites. We present a new frequency multiplexing method, which is a technique that uses multi-frequency sinusoidal controls, to approximately decouple the formation dynamics and to provide enough controls for both position and orientation control. …


Evaluation Of Murrell’S Ekf-Based Attitude Estimation Algorithm For Exploiting Multiple Attitude Sensor Configurations, Sharanabasaweshwara Asundi, Norman Fitz-Coy, Haniph Latchman Jan 2021

Evaluation Of Murrell’S Ekf-Based Attitude Estimation Algorithm For Exploiting Multiple Attitude Sensor Configurations, Sharanabasaweshwara Asundi, Norman Fitz-Coy, Haniph Latchman

Mechanical & Aerospace Engineering Faculty Publications

Pico- and nano-satellites, due to their form factor and size, are limited in accommodating multiple or redundant attitude sensors. For such satellites, Murrell's implementation of the extended Kalman filter (EKF) can be exploited to accommodate multiple sensor configurations from a set of non redundant attitude sensors. The paper describes such an implementation involving a sun sensor suite and a magnetometer as attitude sensors. The implementation exploits Murrell's EKF to enable three sensor configurations, which can be operationally commanded, for satellite attitude estimation. Among the three attitude estimation schemes, (i) sun sensor suite and magnetometer, (ii) magnetic field vector and its …


Design And Testing Of A Feed-Forward Control System For Deployable Vortex Generators Dependent On Angle Of Attack, Solomon B. Whitmire, Christopher J. Chapanar, Kirklin M. Anderson, Nickalus R. Amon, Daniel W. Chech Jan 2021

Design And Testing Of A Feed-Forward Control System For Deployable Vortex Generators Dependent On Angle Of Attack, Solomon B. Whitmire, Christopher J. Chapanar, Kirklin M. Anderson, Nickalus R. Amon, Daniel W. Chech

Williams Honors College, Honors Research Projects

A vortex generator (VG hereafter) is a common feature of an aircraft wing that disturbs the flow on the leading edge of the wing, thus energizing the boundary layer and reducing flow separation. For an aircraft experiencing flow separation, VGs can increase the lift-to-drag ratio of the wing and prevent stall; however, if flow separation isn’t an issue, the unnecessary frontal area of the VGs has the potential to produce parasitic drag. This study seeks to determine whether the use of a deployment system can improve the performance of VG’s by raising or lowering them depending on the angle of …


Dji Drone Modification, Sean Lacey, Seth Mancuso, Bryce Mckenzie Jan 2021

Dji Drone Modification, Sean Lacey, Seth Mancuso, Bryce Mckenzie

Williams Honors College, Honors Research Projects

For this project, we set out to create a lightweight carrying case that would be mounted to a DJI Phantom 3. This case is designed to transport small packages, such as medications, from a delivery vehicle to their final destination. Based on our maximum drone lifting capacity of 600 grams, our case, servomotor, and contents had to weigh less than or equal to that value. The coronavirus pandemic has led to an increase in contactless delivery options along with the push for immunocompromised people to avoid contact with people that may be sick. Our product would help transport necessary supplies …


Attitude Determination And Control Of Arksat-1, Jared Gilliam Dec 2020

Attitude Determination And Control Of Arksat-1, Jared Gilliam

Mechanical Engineering Undergraduate Honors Theses

ARKSAT-1 is a nanosatellite developed at the University of Arkansas as part of NASA’s CubeSat Launch Initiative (CSLI). The goal of ARKSAT-1 is to utilize an LED emitter paired with a ground-based tracking system to perform measurements of the composition of the atmosphere using spectroscopy. As part of its function, it is imperative that the satellite is able to control its orientation so that the emitter is aligned as closely as possible with the ground tracker. To do this, the attitude control system of ARKSAT-1 uses magnetic actuators to create a torque on the satellite by interacting with Earth’s magnetic …


Low-Cost Reaction Wheel Design For Cubesat Applications, Nicholas J. Bonafede Jr. Aug 2020

Low-Cost Reaction Wheel Design For Cubesat Applications, Nicholas J. Bonafede Jr.

Master's Theses

As science instruments on CubeSats become more sensitive to the attitude of the spacecraft, better methods must be employed to provide the accuracy needed to complete the planned mission. While systems that provide the accuracy required are available commercially, these solutions are not cost-effective, do not allow the design to be tailored to a specific mission, and most importantly, do not give students hand-on experience with attitude control actuators. This thesis documents the design, modeling, and simulation of a low-cost, student-fabricated, reaction wheel system for use in 3U CubeSat satellites. The entire design process for the development of this reaction …


Fast Decision-Making Under Time And Resource Constraints, Kyle Gabriel Lassak Jan 2020

Fast Decision-Making Under Time And Resource Constraints, Kyle Gabriel Lassak

Graduate Theses, Dissertations, and Problem Reports (ETD)

Practical decision makers are inherently limited by computational and memory resources as well as the time available in which to make decisions. To cope with these limitations, humans actively seek methods which limit their resource demands by exploiting structure within the environment and exploiting a coupling between their sensing and actuation to form heuristics for fast decision-making. To date, such behavior has not been replicated in artificial agents. This research explores how heuristics may be incorporated into the decision-making process to quickly make high-quality decisions through the analysis of a prominent case study: the outfielder problem. In the outfielder problem, …


Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu May 2019

Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper presents a systematic method to analyse the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This work extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the …


Algorithm For Geodetic Positioning Based On Angle-Of-Arrival Of Automatic Dependent Surveillance-Broadcasts, Richard Allen Gross Apr 2019

Algorithm For Geodetic Positioning Based On Angle-Of-Arrival Of Automatic Dependent Surveillance-Broadcasts, Richard Allen Gross

Masters Theses

This paper develops a non-precision, three-dimensional, geodetic positioning algorithm for airborne vehicles. The algorithm leverages the proliferation of Automatic Dependent Surveillance – Broadcast (ADS-B) equipped aircraft, utilizing them as airborne navigation aids to generate an RF Angle-of-Arrival (AOA) and Angle-of-Elevation (AOE) based geodetic position. The resulting geodetic position can serve as a redundant navigation system for use during locally limited Global Navigation Satellite System (GNSS) availability, be used to validate on-board satellite navigation systems in an effort to detect local spoofing attempts, and be used to validate ADS-B position reports.

The navigation algorithm is an implementation of an Extended Kalman …


Space Dynamics Laboratory Payload Challenge: Autonomous Water Sampling Uav, Thomas Wheeler, Zachary Williams, Joseph Stack Jan 2019

Space Dynamics Laboratory Payload Challenge: Autonomous Water Sampling Uav, Thomas Wheeler, Zachary Williams, Joseph Stack

Williams Honors College, Honors Research Projects

The following report has been completed over the course of the Fall 2018 and Spring 2019 semesters at The University of Akron by Joseph P. Stack (Aerospace Systems Engineering), Thomas J. Wheeler (Mechanical Engineering) and Zachary M. Williams (Mechanical Engineering). The purpose of this project was to create a payload system for the Akronauts Rocket Design Team to use at the Intercollegiate Rocket Engineering Competition (IREC) Spaceport America Cup. The Competition as a challenge that is sponsored by Space Dynamics Laboratory specifically regarding payload systems. The challenge in very open-ended and allows student to identify their own scientific experiment and …


Immunity-Based Framework For Autonomous Flight In Gps-Challenged Environment, Mohanad Al Nuaimi Jan 2019

Immunity-Based Framework For Autonomous Flight In Gps-Challenged Environment, Mohanad Al Nuaimi

Graduate Theses, Dissertations, and Problem Reports (ETD)

In this research, the artificial immune system (AIS) paradigm is used for the development of a conceptual framework for autonomous flight when vehicle position and velocity are not available from direct sources such as the global navigation satellite systems or external landmarks and systems. The AIS is expected to provide corrections of velocity and position estimations that are only based on the outputs of onboard inertial measurement units (IMU). The AIS comprises sets of artificial memory cells that simulate the function of memory T- and B-cells in the biological immune system of vertebrates. The innate immune system uses information about …


Considerations For Atmospheric Measurements With Small Unmanned Aircraft Systems, Jamey D. Jacob, Phillip B. Chilson, Adam L. Houston, Suzanne Weaver Smith Jul 2018

Considerations For Atmospheric Measurements With Small Unmanned Aircraft Systems, Jamey D. Jacob, Phillip B. Chilson, Adam L. Houston, Suzanne Weaver Smith

Mechanical Engineering Faculty Publications

This paper discusses results of the CLOUD-MAP (Collaboration Leading Operational UAS Development for Meteorology and Atmospheric Physics) project dedicated to developing, fielding, and evaluating integrated small unmanned aircraft systems (sUAS) for enhanced atmospheric physics measurements. The project team includes atmospheric scientists, meteorologists, engineers, computer scientists, geographers, and chemists necessary to evaluate the needs and develop the advanced sensing and imaging, robust autonomous navigation, enhanced data communication, and data management capabilities required to use sUAS in atmospheric physics. Annual integrated evaluation of the systems in coordinated field tests are being used to validate sensor performance while integrated into various sUAS platforms. …


Active Permanent Magnet Attitude Control For Cubesats Using Mu-Metal Shielding, Maxwell Martin May 2018

Active Permanent Magnet Attitude Control For Cubesats Using Mu-Metal Shielding, Maxwell Martin

Mechanical Engineering Undergraduate Honors Theses

Cube-Satellites (CubeSats) are nanosatellites composed of cube shaped units, each nominally 10cm to a side and around 1kg in mass. Due to their inherent size and weight limitations, it is often impractical to use conventional attitude, or rotational, control methods such as thrusters on these small satellites. Several methods, including magnetorquer rods and small reaction wheels, are often used instead of traditional methods to work around the size and weight limitations. As a new alternative to these methods, a permanent magnet mounted on a rotatable shaft could be used to achieve attitude control. In much the same way that a …


An Underwater Vehicle Navigation System Using Acoustic And Inertial Sensors, Khalid M. Alzahrani May 2018

An Underwater Vehicle Navigation System Using Acoustic And Inertial Sensors, Khalid M. Alzahrani

Doctoral Dissertations and Master's Theses

Unmanned Underwater Vehicles (UUVs) have become an essential tool for different underwater tasks. Compared with other unmanned systems, the navigation and localization for UUVs are particularly challenging due to the unavailability of Global Positioning System (GPS) signals underwater and the complexity of the unstable environment. Alternative methods such as acoustic positioning systems, Inertial Navigation Systems (INS), and the geophysical navigation approach are used for UUV navigation. Acoustic positioning systems utilize the characteristics of acoustic signals that have a lower absorption rate and a more extended propagation distance than electromagnetic signals underwater. The significant disadvantage of the INS is the “drift,” …


Some Insights Into The Migration Of Double Imaginary Roots Under Small Deviation Of Two Parameters, Dina Alina Irofti, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu Feb 2018

Some Insights Into The Migration Of Double Imaginary Roots Under Small Deviation Of Two Parameters, Dina Alina Irofti, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper studies the migration of double imaginary roots of the systems’ characteristic equation when two parameters are subjected to small deviations. The proposed approach covers a wide range of models. Under the least degeneracy assumptions, we found that the local stability crossing curve has a cusp at the point that corresponds to the double root, and it divides the neighborhood of this point into an S-sector and a G-sector. When the parameters move into the G-sector, one of the roots moves to the right halfplane, and the other moves to the left half-plane. When the parameters move into the …


Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar Jan 2018

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence …


Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar Jan 2018

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters τi, i = 1, 2, . . . , K. The characteristic quasipolynomial of such an equation is a multilinear function of e−τis. It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delay-per-scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence between …


Discrete-Time Adaptive Control Algorithms For Rejection Of Sinusoidal Disturbances, Mohammadreza Kamaldar Jan 2018

Discrete-Time Adaptive Control Algorithms For Rejection Of Sinusoidal Disturbances, Mohammadreza Kamaldar

Theses and Dissertations--Mechanical and Aerospace Engineering

We present new adaptive control algorithms that address the problem of rejecting sinusoids with known frequencies that act on an unknown asymptotically stable linear time-invariant system. To achieve asymptotic disturbance rejection, adaptive control algorithms of this dissertation rely on limited or no system model information. These algorithms are developed in discrete time, meaning that the control computations use sampled-data measurements. We demonstrate the effectiveness of algorithms via analysis, numerical simulations, and experimental testings. We also present extensions to these algorithms that address systems with decentralized control architecture and systems subject to disturbances with unknown frequencies.


Design Of Shape-Conforming Nosecone For Optimal Fluid Flow From Transonic To Supersonic Range, Anna Tombazzi Jan 2018

Design Of Shape-Conforming Nosecone For Optimal Fluid Flow From Transonic To Supersonic Range, Anna Tombazzi

Williams Honors College, Honors Research Projects

Modern flight vehicles, such as rockets, missiles, and airplanes, experience a force caused by forebody wave drag during the flight. This drag force is induced when the frontal point of each vehicle breaks the pressure wave during flight. Efforts to reduce this wave drag force to improve flight efficiency include modifying the nosecone profile of the flight vehicles to lower the drag force.

This project revolved around creating a design to make the transformation of nosecone shapes from a ¾ Parabolic profile to a ½ Power Series profile possible, mid-flight. Using a novel nosecone assembly, shape memory alloys (SMAs) and …


Real Time And High Fidelity Quadcopter Tracking System, Tyler Mckay Hall Dec 2017

Real Time And High Fidelity Quadcopter Tracking System, Tyler Mckay Hall

Computer Engineering

This project was conceived as a desired to have an affordable, flexible and physically compact tracking system for high accuracy spatial and orientation tracking. Specifically, this implementation is focused on providing a low cost motion capture system for future research. It is a tool to enable the further creation of systems that would require the use of accurate placement of landing pads, payload acquires and delivery. This system will provide the quadcopter platform a coordinate system that can be used in addition to GPS.

Field research with quadcopter manufacturers, photographers, agriculture and research organizations were contact and interviewed for information …


Cyber-Physical System Characterization And Co-Regulation Of A Quadrotor Uas, Seth E. Doebbeling Aug 2017

Cyber-Physical System Characterization And Co-Regulation Of A Quadrotor Uas, Seth E. Doebbeling

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

An Unmanned Aircraft System (UAS) is a Cyber-Physical System (CPS) in which a host of real-time computational tasks contending for shared resources must be cooperatively managed to obtain mission objectives. Traditionally, control of the UAS is designed assuming a fixed, high sampling rate in order to maintain reliable performance and margins of stability. But emerging methods challenge this design by dynamically allocating resources to computational tasks, thereby affecting control and mission performance. To apply these emerging strategies, a characterization and understanding of the effects of timing on control and trajectory following performance is required. Going beyond traditional control evaluation techniques, …


P26. Global Exponential Stabilization On So(3), Soulaimane Berkane Mar 2017

P26. Global Exponential Stabilization On So(3), Soulaimane Berkane

Western Research Forum

Global Exponential Stabilization on SO(3)


Autonomous Quadrotor Collision Avoidance And Destination Seeking In A Gps-Denied Environment, Thomas C. Kirven Jan 2017

Autonomous Quadrotor Collision Avoidance And Destination Seeking In A Gps-Denied Environment, Thomas C. Kirven

Theses and Dissertations--Mechanical and Aerospace Engineering

This thesis presents a real-time autonomous guidance and control method for a quadrotor in a GPS-denied environment. The quadrotor autonomously seeks a destination while it avoids obstacles whose shape and position are initially unknown. We implement the obstacle avoidance and destination seeking methods using off-the-shelf sensors, including a vision-sensing camera. The vision-sensing camera detects the positions of points on the surface of obstacles. We use this obstacle position data and a potential-field method to generate velocity commands. We present a backstepping controller that uses the velocity commands to generate the quadrotor's control inputs. In indoor experiments, we demonstrate that the …


Time-Of-Flight Based Sonic Speed Measurements For Cold Gas Thruster Development, Brandon W. Kempf May 2016

Time-Of-Flight Based Sonic Speed Measurements For Cold Gas Thruster Development, Brandon W. Kempf

Mechanical Engineering Undergraduate Honors Theses

The purpose of this thesis is to explore an experiment developed for validating the usage of a gaseous solution of water and propylene glycol for cold gas propulsion. The experiment involves a “Time of Flight” method of calculating the speed of sound in the gas and the corresponding specific heat ratio using a copper tube, two MEMS microphones, a piezoelectric speaker, and data-acquisition hardware. The experiment was calibrated using the known thermodynamic properties of air. The accuracy of the experiment was found to be within 0.6% for calculations of the speed of sound in air and within 1.0% of the …