BYOE: Activities to Map Intuition to Lumped System Models

The objective of this series of experimental activities is to create a stronger qualitative connection between observed behaviors of simple systems and the equations, terminology, and graphical methods used to describe and represent them. This work is motivated by an observed inability of students to qualitatively model and predict how a real-life system will behave, despite an understanding of such models in homework and lecture settings. Thus, there is a disconnect between understanding how real-life physical behaviors map to the elemental and system equations of idealized models. The experiments, presented herein, and corresponding qualitative discussion among peers are designed to precede and pair with subsequent course discussion of the concepts involved. During the follow-on lectures, the instructor references, and may repeat, these demonstrations to link the student’s observations to the appropriate terminology, equations, and graphical representations being taught. The four short experiments presented in this paper are described briefly below; a selection of these activities will be demonstrated at the ASEE conference. Canoe Coast-down: Students study video taken of a canoe in “coast-down”, as its velocity decays. The canoe exhibits a first-order response to this initial condition. Students hypothesize models for their observations, and thus begin developing the skill of system identification. During a subsequent class the instructor leads the students through a more complete analysis. Playdough Hot Potato: Students are given playdough that represents a “hot potato” and asked to come up with ways to make it cool down as fast as possible. In a follow-on lecture the instructor introduces the parameters of thermal resistance, thermal capacitance, time constant, and step input size; and links the cooling methods proposed by students to the corresponding parameter(s). The open-ended rich solution set of this challenge offers to open discussion in many directions, including the limitations of lumped system modeling. Fluid in a Tube: This experiment illustrates the step response of a second order fluid system as a function of its damping ratio. Students are asked to observe fluid oscillations in a tube and explore how the size and duration of oscillations varies with restrictions to air flow at the end of the tube. During a follow-on lecture the instructor shows plots of the oscillations observed in this activity for both high and low damping ratios. This provides a lead-in for more extensive discussions on the characteristics and behavior of second order systems. Slinky and Mass: A small mass attached to a mini-slinky forms a simple spring-mass system which is used to map the observed time domain response of a minimally damped second order system to the graphical representation of its frequency response. Students move one end of the spring up and down, observe the response of the mass on the other end, and qualitatively describe the system behavior for a range of frequencies. Introduction, Background and Motivation Observing students working on projects for general design classes, both introductory and capstone, and as a part of extracurricular student design teams, reveals that many students do not apply the analytical techniques learned in earlier coursework. Our goal is to better prepare students to integrate such analysis with the everyday engineering problems they face, outside of the classroom. Two possible explanations for failing to apply previously learned analytical techniques are: 1. students did not retain the knowledge, and 2. students do not recognize when it is appropriate to apply the “tools” in their analytical “toolbox” [1]. The importance of repetition in learning retention is well documented within the literature [2-4] and can be summarized using the forgetting curve [5]. The forgetting curve indicates that to maximize retention, any key concept must be repeated multiple times over the course of a term, beginning with repetition intervals of high frequency and gradually decreasing in frequency [6]. Therefore, the key concepts must be introduced and then reviewed several times within the first few weeks of the term to maximize long term retention. Unfortunately, some of the key concepts in an introductory lumped systems modeling class, such as frequency response and the behaviors of second order systems, are analytically complex and are typically taught after students have acquired the necessary mathematical skills, which is often very late in the term. This traditional approach does not provide adequate time for the necessary repetition within the course timeframe to maximize retention of these critical concepts. The human capacity to recognize cause and effect relationships, and to associate a name to those observed behaviors, precedes our ability to create a physics-based mathematical model to precisely predict behavior. For example, a young child quickly develops an understanding that if you throw a ball up it will always fall down; that if you throw it harder it will stay in the air longer; and the angle you throw it at, combined with how hard you throw, determine how far the ball travels. This mental mapping of behaviors, termed “constructivism” [7], happens many years before a student can understand the equations for projectile motion. This same sequence of learning in young children, where the capacity for qualitative learning significantly precedes the ability to form a quantitative model, can facilitate learning at any age. Research in active learning through techniques such as model-eliciting activities, hands-on teaching, and predictobserve-explain, supports the value of qualitative experiential learning to enhance understanding [8]. Recognizing that topics can be understood qualitatively allows even the most complex topics to be brought to the beginning of a course allowing for more repetition and therefore a greater likelihood of retention. In addition, developing and checking conceptual understanding early in the term provides an opportunity to identify and address misconceptions that could otherwise persist throughout the course. Assuming students retain the knowledge of what analytical “tools” they have available in their “toolbox” the next question is: Do they recognize when it is appropriate to use them [1]? For a lumped systems modeling course this requires the skills of system identification and model formation. Arguably, the skill of deciding how to model a system such as recognizing energy flow pathways and identifying what simplifying assumptions can be made, is a skill that takes years to develop, but a greater emphasis on developing these skills could be incorporated throughout such a course. The intent of this series of experimental activities is to help students in an introductory lumped systems modeling course to create a simple mental model of system behaviors very early in the term [7], so later that term, when the mathematical modeling and graphical representation of the system behaviors are taught, students can relate this to the qualitative framework they have already formed [1]. This paper proposes that these simple activities presented early in the term will improve retention and understanding, and also improve utilization of course concepts in post-course design work. Experiential learning techniques can be time consuming and thus challenging to incorporate into collegiate courses with a packed syllabus. Lab equipment can be expensive to purchase and maintain. Further, instructors may presume that students have already formed simple mental models of system behaviors from earlier coursework or life experiences. To minimize these possible implementation barriers, the criteria used to create these activities are that all students can experience the hands-on activity concurrently, within a traditional lecture hall. Thus, the experiments must be inexpensive, simple to set-up, and brief. Also the activities are purely qualitative and use common language, in addition to traditional systems terminology, so the activities can precede formal lessons on the topic. The intent is not to replace traditional quantitative modeling labs but rather to provide additional early-term concept exploration. These experiments have been tested and are in the process of being implemented into an existing lumped systems modeling course. The efficacy of these activities will be measured and monitored over several years, with the outcomes presented in a follow-on paper. This paper is organized into 4 distinct experiments. For each experiment we include an overview, instructions for the students, teaching cues for incorporating the activity into the lecture, and some ideas for revisiting the experiment later in the term as a more traditional lab. Experiment 1: “Canoe Coast Down” First Order System Identification from Observed Step Response Overview The outcome of this activity is an introductory understanding of system identification. A video is presented where a canoe is paddled to a target speed and then coasts down, traveling perpendicular to a stationary on-shore video camera (Figure 1). The canoe exhibits the response of a first-order system, and in this case, the students are viewing its initial condition response. Small groups of students work together to hypothesize models for this system. This activity can be combined with the other activities in this paper as an introductory “mini-lab”, used alone as a breakout activity within a lecture, or as a group homework assignment. In a follow-on lecture the instructor revisits this exercise using it as a basis for simple system identification, and analysis of a first-order system. Figure 1: “Canoe Coast-down” video screenshot Student Instructions Watch the video provided [9]. Working with your group discuss why the canoe slows down, what parameters determine how quickly it slows down, and what the shape of the velocity verses time