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Displaying results 1 - 30 of 32 in total
Conference Session
Innovations in Mechanical Engineering Education Poster Session
Collection
2007 Annual Conference & Exposition
Authors
Nihad Dukhan, University of Detroit Mercy; Michael Jenkins, University of Detroit Mercy
Tagged Divisions
Mechanical Engineering
functionality. They also had to provide a technical report ofthe design and construction of it. In addition, they were required to create complete experimentalprocedure, data sheets, and analysis and to describe the requirements for a lab report based on theexperiment that future students can complete and turn in for a grade in the heat transfer lab. Thelast part of the project that challenged the students to reflect on their own learning and the wayfuture students may learn the concepts. The reflection component may not be present in typicalprojects, and/or may not be probed. The learning of the students was probed via a survey of afew questions. The questions asked the students if the project increased their understanding ofthe technical concept they
Conference Session
Innovations in Mechanical Engineering Education Poster Session
Collection
2007 Annual Conference & Exposition
Authors
Cindy Waters, North Carolina A&T State University
Tagged Divisions
Mechanical Engineering
Lifelong learning.The basic premise is that an individual learner must actively "build" knowledge and skills 3. Weknow that technology changes with time and an engineer must be motivated to continue to learnand stay current with technology. Constructivism is a method of teaching and learning based onthe principle that cognition (learning) is the result of mental construction, and this construction inquite individual. Knowledge is formed by reflecting on our experiences, by putting informationtogether with what we already thereby we construct knowledge in our head. Thus, we create ourown understanding of the world we live in. Learning is the process of adjusting our mentalmodels to fit with new experiences. Constructivist theorists maintain that
Conference Session
Improving ME Instructional Laboratories
Collection
2007 Annual Conference & Exposition
Authors
Samuel Yang, Troy High; Mariappan Jawaharlal, California State Polytechnic University-Pomona
Tagged Divisions
Mechanical Engineering
alongwith a writing diagram and a picture. Instructional sheet for each sensor (Fig. 12 though Fig. ) isshown below. Page 12.43.7 Fig. 12 – Ultrasonic Sensor 6Sensor: Ultrasonic RangerDiagram:Principles of Operation: An ultrasonic burst of sound is emitted and reflects off the nearestsolid object. The time it takes for the wave to return is directly proportional to the distance of theobject.Specifications: Range: 2 – 300 cmFeatures: Ultrasonic range sensors offer a relatively wide detection beam and high degree ofsensitivity.How it’s Used: The microcontroller sends out a trigger
Conference Session
Innovations in Mechanical Engineering Education Poster Session
Collection
2007 Annual Conference & Exposition
Authors
Jeffrey Marchetta, University of Memphis; Edward Perry, University of Memphis
Tagged Divisions
Mechanical Engineering
assessment. Thisself-administered online tool poses 40 conjectures to the student. Upon completion of theinstrument the student’s learning style is characterized and reported to the student in terms ofeach of the following learning style pairs: ‚ Active vs Reflective Learning Style ‚ Sensing vs Intuitive Learning Style ‚ Page 12.1126.3 Visual vs Verbal Learning Style ‚ Sequential vs Global Learning Style Figure 1. Sample homework assignment using an online learning object.For this study, the Visual vs Verbal learning style was used to compare the learning styles of thestudents populating these courses.Material related to
Conference Session
Innovations for the Senior Year of the ME Curriculum
Collection
2007 Annual Conference & Exposition
Authors
Steven Trimble, Arizona State University; Ronald Bengelink, Arizona State University; Valana Wells, Arizona State University
Tagged Divisions
Mechanical Engineering
experience ‚" Present a Unifying Engineering Profession Model ‚" Integrate industry speakers into the lectures ‚" Encourage multiple ways of learning - Case Studies - Group Discussions - “Hands-On Contests” - Reflection - Papers - Oral PresentationsCulminating Experience: Team Microturbine Development ProposalAll the course lectures, speakers, exercises, readings, and homework areselected and tailored to prepare the students for their final project. In thisproject, a fictitious company’s board of directors tasks the student teamsto
Conference Session
What's New in Dynamics?
Collection
2007 Annual Conference & Exposition
Authors
El-Sayed Aziz, Stevens Institute of Technology; Sven Esche, Stevens Institute of Technology; Constantin Chassapis, Stevens Institute of Technology
Tagged Divisions
Mechanical Engineering
-freedom free and forced vibrations. In addition, theremote control of real instruments through the Internet was integrated into the vibrationlaboratory experience.Keywords: Virtual Learning Environment; Simulations; Web-based laboratory; Online LearningEnvironmentIntroductionFive categories of learning style models have been recommended in the educational literature1,2,3:sensing/intuitive, visual/verbal, inductive/deductive, active/reflective and sequential/global. Mosttextbooks and classroom teaching are intuitive, verbal, deductive, reflective and sequential, butthis environment does not meet the needs of the second-tier students who are sensing, visual,inductive, active and global learners. Engineering educators have been reshaping the
Conference Session
Innovations in Mechanical Engineering Education Poster Session
Collection
2007 Annual Conference & Exposition
Authors
Jesse Maddren, California Polytechnic State University
Tagged Divisions
Mechanical Engineering
- fourthsof the programs surveyed utilized some sort of commercial software for solving equations and amajority of the respondents indicated that they required extensive use of the application insubsequent courses. Therefore, it appears that the commercial software applications had moreutility in problem solving.Genik and Somerton1 describe their work in a senior level capstone course in thermalengineering. "Among the topics covered were power system analysis, refrigeration systems,psychrometrics, combustion, heat exchangers, and numerical conduction. Though the list oftopics may seem to be a hodgepodge, it is somewhat reflective of the eclectic nature ofengineering." To combat the perception of this "hodgepodge" of subjects they designed a set
Conference Session
Thermodynamics and Fluid Mechanics Instruction
Collection
2007 Annual Conference & Exposition
Authors
Michael Maixner, U.S. Air Force Academy; James Baughn, University of California-Davis
Tagged Divisions
Mechanical Engineering
various lines change as sliding bars are moved. • This reflects changes in cells which calculate humidity ratio • The cells are color coded to correlate to the color of the associated line on the psychrometric chart • For each of these lines, the independent property is dry bulb temperature (Tdb), and the dependent property is humidity ratio, ω.o Lower part: provides an initially blank range where the cadets construct their own psychrometric chart, based on the prevailing atmospheric pressure. Figure 3 provides a view of the lower portion of the worksheet after completion. When completed, this portion of the worksheet is used in conjunction with
Conference Session
Innovations in Mechanical Engineering Education Poster Session
Collection
2007 Annual Conference & Exposition
Authors
Louis Everett, University of Texas-El Paso; Arunkumar Pennathur, University of Texas-El Paso
Tagged Divisions
Mechanical Engineering
these puzzles has had demonstrated success in student learning yet twochallenges remain. The first challenge is to develop robust puzzles that revealmisconceptions. The second is to find enough colleagues to critically assess thework. The project recently received additional NSF funding (DUE-0618861) and* This material is based on work supported by the National Science Foundation under Grant No.DUE-0618861. Any opinions, findings, and conclusions or recommendations expressed in thismaterial are those of the authors and do not necessarily reflect the views of the National ScienceFoundation. Page 12.37.3† The student confessed this long after the
Conference Session
Meeting ABET Requirements
Collection
2007 Annual Conference & Exposition
Authors
Michael Ward, California State University-Chico
Tagged Divisions
Mechanical Engineering
Survey results analyzed - results reported to Department Chairs1 Week Before Assessment Committee present assessment results to faculty, set actions if needed.*Classes BeginFall Reporting ActivityOctober Annual Assessment Report from Department Chairs to College Deans summarizing assessment results, actions.** Department assessment results are to be shared, analyzed, and reflected with appropriate constituent Page 12.842.5groups including advisory boards or student groups at regularly scheduled meetings.Annual Reporting of ResultsThe results from most of the assessment activities previously mentioned
Conference Session
Improving ME Education: Trends in Mechanical Engineering I
Collection
2007 Annual Conference & Exposition
Authors
Wayne Whiteman, Georgia Institute of Technology; Brian Mathews, Georgia Institute of Technology
Tagged Divisions
Mechanical Engineering
. 26., No. 3, Nov 2005.2 Uden, L., An engineering approach for online learning, International Journal of Distance Education Technologies,Vol. 1, No. 1, Jan-Mar 2003.3 Maor, Dorit, Using reflective diagrams in professional development with university lecturers: A development toolin online teaching, Internet and Higher Education, Vol. 9, No. 2, Summer 2006.4 Pais, Carlos, Vitor Pires, Rui Amaral, Joao Amaral, Joao Martins, Carlos Luz, and O. P. Dias, A strategy toimprove engineering teaching process based on an e-learning approach, Proceedings of the Fifth InternationalConference on Information Technology Based Higher Education and Training, ITHET 2004, 2004.5 Cheong, Pauline Hope, Namkee Park, and William H. Dutton, New Technologies, old
Conference Session
Innovations in Mechanical Engineering Education Poster Session
Collection
2007 Annual Conference & Exposition
Authors
Hyun Kim, Youngstown State University
Tagged Divisions
Mechanical Engineering
was suggested last year and implemented with favorable results. Some students still do not get a good understanding of the material, but their grade now accurately reflects this fact.Another faculty member’s course assessment revealed that at least three quarters of students inher course achieved the course objectives and close to 100% of students demonstrated theabilities in formulating and solving engineering problems and in utilizing modern tools andskills. That was a substantial improvement over the previous years’ results. Her comments on theassessment and plan of changes in the future to improve students’ performance in the samecourse are summarized as follows8: • Design projects continued to prove difficult for students
Conference Session
Improving ME Education: Trends in Mechanical Engineering I
Collection
2007 Annual Conference & Exposition
Authors
Stephen McClain, Baylor University
Tagged Divisions
Mechanical Engineering
associated with Dr. Evil’s Secret Lair Facility.The students, in groups of three, were asked to design the boiler, one air-handling unit, and thepiping system; select an appropriate pump; and perform a Hardy-Cross system simulation toverify system operation.The project assignment for ME 455 is different from the project assignments in the basicengineering science courses in that it is divided into a letter from a fictional company and adesign packet. This division reflects the fact that most senior-level engineering studentsunderstand the importance of their design classes and their relationship to their future practice.Most senior-level students do not require fictional pretenses to engage them with their designprojects. The letter with fictional
Conference Session
Introducing Active and Inductive Learning and Improving the Learning Curve in ME
Collection
2007 Annual Conference & Exposition
Authors
Christopher Byrne, Western Kentucky University
Tagged Divisions
Mechanical Engineering
continue to reflect upon the long term growth and Page 12.1310.2competitiveness of engineering education. A focus on the academic institutes’ most importantproduct - the graduating student – should be a main factor in decisions aimed at improving theeducational experience. This should include the consideration that student satisfaction with theireducation when departing the campus, and when participating in engineering practice, can befacilitated via engagement in the scholarship of engineering with their faculty.BackgroundThe literature covering education of engineers is filled with information concerning change.This change takes many forms such
Conference Session
Software and E-learning in the ME Curriculum
Collection
2007 Annual Conference & Exposition
Authors
John-David Yoder, Ohio Northern University; Mihir Sen, University of Notre Dame
Tagged Divisions
Mechanical Engineering
access to at their home institution. 5) Giving students the opportunity to implement algorithms in the laboratory is helpful in their learning of such algorithms.The authors would be glad to work with others who are interested in developing such acourse, laboratory, or additional remote experiments. All course materials are availableupon request.Acknowledgements: "This material is based upon work supported by the National Science Foundationunder Grant No. 0410863. Any opinions, findings, and conclusions or recommendationsexpressed in this material are those of the author(s) and do not necessarily reflect theviews of the National Science Foundation." The authors would further like to thank the students in this
Conference Session
Introducing Active and Inductive Learning and Improving the Learning Curve in ME
Collection
2007 Annual Conference & Exposition
Authors
Emilia Bratschitsch, Joanneum University of Applied Sciences, Department of Automotive; Annette Casey, Joanneum University of Applied Sciences, Department of Automotive Engineering,; Günter Bischof, Joanneum University of Applied Sciences, Department of Automotive Engineering,; Domagoj Rubesa, Joanneum University of Applied Sciences, Department of Automotive Engineering,
Tagged Divisions
Mechanical Engineering
software • Documenting the process from research to development and finally to output • Reflecting on project management, team work and the performance of individual team members in the form of a brief written appraisal • Handing in software and documentation on a pre-defined dateThe role of the lecturers, as subject experts, is to guide the students through these stages and givethem the tools necessary for finding the missing pieces of, what for them is often a great puzzle,at least in the early stages.Project presentationFor the final step, each team is required to give a presentation approximately one week afterhanding in the software program and the project documentation. The presentation is given inplenum to the other
Conference Session
Meeting ABET Requirements
Collection
2007 Annual Conference & Exposition
Authors
Karinna Vernaza, Gannon University; Mahesh Aggarwal, Gannon University
Tagged Divisions
Mechanical Engineering
States.Published by The Accreditation Board for Engineering and Technology (ABET), Baltimore MD. 1997. Available:http://www.abet.org/EAC/eac2000.html.2. Mak, F., Frezza, S., “Process to Identify Minimum Passing Criteria and Objective Evidence in Support ofABET EC2000 Criteria Fulfillment,” ASEE Annual Conference and Exposition, Salt Lake City, Utah, June 2004.3. Cutts, Q., Carbone, A., van Haaster, K., “Using an Electronic Voting System to Promote Active Reflection onCoursework Feedback,” Proc. Of the Intnl. Conf. on Computers in Education, Melbourne, Australia, November2004.4. Vernaza, K.M., “Instructional Innovation of Mechanical Engineering Core Courses with Technology,” FacultyDevelopment Grant in Instructional Innovation with Technology, Center for
Conference Session
Innovations for the Senior Year of the ME Curriculum
Collection
2007 Annual Conference & Exposition
Authors
Gregory Davis, Kettering University; Craig Hoff, Kettering University
Tagged Divisions
Mechanical Engineering
canbe tuned to reflect the type of deceleration that occurs during an impact. A stripped-downFormula SAE chassis was fixed to the test sled and an 50th percentile male Hybrid IIIAnthropomorphic Test Device (ATD) equipped with accelerometers was used to measure theloads on the driver. See Figure 4. Page 12.1573.8 Figure 4. The car frame with test dummy just prior to impactTests were performed at the SAE specified conditions and it was found that the criteria were veryconservative. There was a very low chance of driver injury. For example, the data in Figure 5shows that the neck injury criteria are well within the ‘safe’ region
Conference Session
Software and E-learning in the ME Curriculum
Collection
2007 Annual Conference & Exposition
Authors
Ali Mohammadzadeh, Grand Valley State University
Tagged Divisions
Mechanical Engineering
50o in its rocking motion. Figure 5ConclusionThe project significantly helped students understand the abstract concepts in dynamics.This was reflected in the result of the follow up exam. Majority of the students exhibiteda very thorough understanding of Lagrange’s equations. Students enjoyed the animationpart of the project and built their models in the shop. The author received positivefeedback from the students regarding this exercise.Bibliography 1. Erdman, Arthur G., Sanders, George N., “Mechanism Design Analysis and Synthesis” Prentice Hall, 2001.2. Crespo da Silva, M. R.M., “Intermediate Dynamics”, McGraw Hills, 2004.3. Erdman, Arthur G, “Three and Four Precision Point Kinematics
Conference Session
Innovations for the Senior Year of the ME Curriculum
Collection
2007 Annual Conference & Exposition
Authors
Elvin Shields, Youngstown State University
Tagged Divisions
Mechanical Engineering
Monolingual and Bilingual Classrooms,” Creativity Research Journal, Vol. 14, Issue 3-4, pp. 373-386.6. Ghosh, S., 2003, “Triggering Creativity in Science and Engineering: Reflection as a Catalyst,” Journal of Intelligent and Robotic Systems, Vol. 38, Issue 3-4, pp. 255-275.7. Hopper, C., 2007, Practicing College Learning Strategies, Houghton Mifflin (http://www.mtsu.edu/~studskl/hd/hemis.html).8. Kim, J. and Michael, W.B.., 1995, “The Relationship of Creativity Measures to School Achievement and to Preferred Learning and Thinking Style in a Sample of Korean High School Students,” Educational and Psychological Measurement, Vol. 55, Issue 1, pp. 60-74.9. Moehrle, M.G., 2005, “How Combinations of TRIZ Tools Are Used
Conference Session
Thermodynamics and Fluid Mechanics Instruction
Collection
2007 Annual Conference & Exposition
Authors
Andrew Foley, U.S. Coast Guard Academy
Tagged Divisions
Mechanical Engineering
Transport Equation : the first law and then the second law as more of thesame. In a previous paper Foley (2005) describes a method of introducing the first law usingthe Reynolds Transport equation. Briefly a generic property B is considered with respectto a general ‘catch all’ control volume. (See Figure 1.)DB •B ? - Â B% net _ gen - Â (m% b) net _ in …….(1)Dt •tNote that the summation signs have been used instead of the integral sign to reflect thatmost of the problems in an introduction to thermodynamics course involve discreteinputs, outputs etc. While not to the ‘purists’ satisfaction it has worked well with studentswho later ‘ramp up’ to functional, continuous type inputs with little difficulty
Conference Session
Software and E-learning in the ME Curriculum
Collection
2007 Annual Conference & Exposition
Authors
Autar Kaw, University of South Florida
Tagged Divisions
Mechanical Engineering
mathematical procedures taught in a typical Numerical Methods course. Coupledwith other improvements, the effect of the problem-centered approach improved studentsatisfaction and student examination performance in the course.Acknowledgments - This material is based upon work supported by the National ScienceFoundation under Grant#0341468, and the Research for Undergraduates Program in the USFCollege of Engineering. Any opinions, findings, and conclusions or recommendations expressedin this material are those of the author and do not necessarily reflect the views of the NationalScience Foundation. The research problem used in the paper was funded at University of SouthFlorida by Florida Department of Transportation (FDOT) under contract#B-C008 (1998
Conference Session
What's New in Dynamics?
Collection
2007 Annual Conference & Exposition
Authors
Benjamin Liaw, City College of the City University of New York; Ioana Voiculescu, City College of the City University of New York
Tagged Divisions
Mechanical Engineering
%), exams (25%)and final group presentation and report (21%).Traditionally exams are used as the main assessment tool to evaluate a student’s progress.However, since most of, if not all, students tend to prepare for an exam seriously only a few daysbefore the exam, their learning usually is sporadic and the hastily acquired knowledge may beeasily forgotten after the exam. Hence, two exams, each counts as 12.5% toward the coursegrade, are held in the course to test students’ accumulated knowledge in the middle and at the Page 12.216.4end of the semester. On the other hand, in order to reflect the new grade distribution system, thecurrent course
Conference Session
Outstanding Contributions to ME
Collection
2007 Annual Conference & Exposition
Authors
Jeffrey Rhoads, Michigan State University; Craig Somerton, Michigan State University; Brian Olson, Johns Hopkins University Applied Physics Laboratory; Terry Ballinger, Lansing Catholic High School
Tagged Divisions
Mechanical Engineering
with the students as it once was. As this isbelieved to be reflective of the product being assembled by the students, rather than the unit conceptitself, product changes are being considered for future sessions. With regard to the lecture portionof the unit, the instructors are still concerned that the students are being introduced to modernmanufacturing via multimedia sources rather than industrial tours. While this approach does freeup an additional day for an alternative topic (such as electromechanical systems), it comes at theexpense of a ‘real world’ engineering experience. If local factory tours were to become accessibleagain, the instructors would strongly consider resuming the old manufacturing curriculum.52.7 Lesson VII: Energy and
Conference Session
Meeting ABET Requirements
Collection
2007 Annual Conference & Exposition
Authors
Anne Spence, University of Maryland-Baltimore County; Liang Zhu, University of Maryland-Baltimore County
Tagged Divisions
Mechanical Engineering
70 70 70 70 70 70 70 70 70 70 70 70 70 70Difference +10 +9 +7 +12 +10 +8 +10 +5 +9 +5 +9 +19 +17 +16 Page 12.1314.11 Figure 1. Comparison of QuACO and COS Results for the Fall 2004 SemesterThe results indicate that all of the program outcomes are meeting the critical minimum of 70%.In general, however, students perform as well as or better than their own self-evaluation. It isdifficult to determine if this is a true self-reflection or if students are simply “hedging their bets.”Students seem to over-predict their abilities in outcomes (a) An
Conference Session
Innovations for the Senior Year of the ME Curriculum
Collection
2007 Annual Conference & Exposition
Authors
Showkat Chowdhury, Alabama A&M University; Abdul Jalloh, Alabama A&M University; Ruben Rojas-Oviedo, Alabama A&M University; Mohamed Seif, Alabama A&M University; Amir Mobasher, Alabama A&M University
Tagged Divisions
Mechanical Engineering
university,reflects the uniqueness of the traditional land-grant institution, which combines professional,vocational and liberal arts pursuits. The University provides baccalaureate and graduate Page 12.342.3studies that are compatible with the times to all qualified and capable individuals who areinterested in further developing their technical, professional, and scholastic skills andcompetencies. AAMU is located in Huntsville, Alabama, which is known internationally as acenter of aerospace and defense technology. Huntsville is considered as a leader in high-techresearch, engineering services, information systems design and in the manufacturing
Conference Session
Improving ME Education: Trends in Mechanical Engineering I
Collection
2007 Annual Conference & Exposition
Authors
John Duffy, University of Massachusetts-Lowell; Linda Barrington, University of Massachusetts-Lowell; Cheryl West, University of Massachusetts-Lowell; John McKelliget, University of Massachusetts-Lowell; Eugene Niemi, University of Massachusetts-Lowell; Sammy Shina, University of Massachusetts-Lowell; Hongwei Sun, University of Massachusetts-Lowell; Chris Niezrecki, University of Massachusetts-Lowell; Robert Parkin, University of Massachusetts-Lowell; Majid Charmchi, University of Massachusetts-Lowell; Peter Avitabile, University of Massachusetts Lowell
Tagged Divisions
Mechanical Engineering
difference,” value of teamwork (among others) students recorded a range ofagreement to non-agreement on a 1-9 point Likert scale. The averages were all 6 or Page 12.1274.3above, disagreement ranged from 7 % to 14% and agreement from 60 to 75%. Mostfaculty cited time as the biggest barrier to implementation. Improvements are plannedwith more student/faculty analysis of broader impacts.IntroductionService-learning is the integration of academic subject matter with service to thecommunity in credit-bearing courses, with key elements including reciprocity, reflection,coaching, and community voice in projects (Jacoby, 1996)1. Service-learning (S-L) hasbeen shown
Conference Session
Thermodynamics and Fluid Mechanics Instruction
Collection
2007 Annual Conference & Exposition
Authors
Stephen McClain, Baylor University; Christopher Smitherman, University of Alabama-Birmingham
Tagged Divisions
Mechanical Engineering
Variable Argument 2 Argument 1 Fluid Argument 1 Underscore Name Argument 2 NameFigure 1. Scheme for Naming Property FunctionsThe functions were constructed to reflect and reinforce how property information is provided intraditional property tables. Functions are provided for the saturation pressure based ontemperature and for the saturation temperature based on pressure. Saturated liquid and saturatedvapor functions are provided for specific volume (v), specific internal energy (u), specificenthalpy (h), and specific entropy (s) based on either temperature or pressure. Functions for v, u,h, and s of saturated
Conference Session
Software and E-learning in the ME Curriculum
Collection
2007 Annual Conference & Exposition
Authors
David Blekhman, California State University Los Angeles
Tagged Divisions
Mechanical Engineering
an excellent agreementin the case of the airfoil to questionable in the case of the flow over a cylinder. Nevertheless, inall cases FlowLab was an excellent tool in visualizing the flow.Adoption of the software created more work for students, which was reflected in their responses.Overall, students’ involvement ranged from low to very excited. Some students asked for morefeatures to solve real-world problems.A number of high quality publications have recently appeared on the topic, discussing theimplementation and integration of the package into existing courses and the redesign of teachingphilosophy. This paper continues the discussion, confirming that further improvements arewarranted on the instruction side as well as on the part of the
Conference Session
Thermodynamics and Fluid Mechanics Instruction
Collection
2007 Annual Conference & Exposition
Authors
Philip Gerhart, University of Evansville; Andrew Gerhart, Lawrence Technological University; Bruce Cain, Mississippi State University
Tagged Divisions
Mechanical Engineering
that may not be possible in a laboratory setting. The assigned report can be alengthy well-crafted technical paper, a brief research note, an oral presentation, or a combinationof these. The type of report assigned should be chosen to reflect the credit allotted for theexercise and the emphasis it deserves in the “big-picture” of the course. A specific example ofthe read-and-report exercise is described later in this paper. Page 12.1536.5Another potentially valuable use of PTCs is making them available as guides and/or referencematerials for student-designed experiments. In typical capstone design courses, students areoften given considerable