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Investigating Impulse Loading using Model Rocketr y

Abstract

A project is presented that uses experimentally determined thrust data for a commercial model rocket engine to investigate impulse loading relations. Certain model rocket engines approach impulse loading; completely burning in a fraction of a second. Using a fixture instrumented with strain gages and a high-speed National Instruments data acquisition system, the students experimentally collect the thrust verses time response of several Estes model rocket engines. The students formulate two flight models for a rocket of known mass loaded with the specific engine being investigated. The first model uses the measured thrust data directly as input to the governing differential equation for the rocket. The students are challenged to formulate an appropriate drag model through a literature search and must justify their choice. A second flight model is formulated using an equivalent impulse, based on the experimental thrust data, as loading. The students calculate flight trajectories based on both nonlinear models using numerical methods and critically compare/contrast the results. The project has been found to engage students and to effectively provide hands-on insight in the value, and limitations, of impulse loading methods.

Introduction & Motivation

A typical mechanical engineering program will address the concept of impulse loading at multiple points within the curriculum. The mathematical definition of impulse loading and the subsequent solution of the impulse response are ordinarily addressed within the differential equation course1. The physical nature of impulse and momentum are usually covered in a classical dynamics course2,3. Yet, even with this redundant coverage (and potentially more in specific programs) students often possess little intuition regarding impulse loading. How abrupt must the loading be to approach impulse loading? Can the dynamic response to real forcing, which is never a true mathematical impulse, be accurately modeled by an impulse assumption? What are the limitations of impulse response analysis?

The project presented herein challenges students to investigate and critically evaluate the response of a rigid body subject to rapidly time varying forces. While any rapidly changing force could be considered, a readily available source is commercial model rocket engines which represent a pseudo-impulse loading scenario. Figure 1 presents the thrust profile for an Estes B6-4 model rocket engine4. Note that the peak thrust is reached approximately 0.2 seconds after ignition, and the entire burn is completed in well under one second. This is in comparison to between 6 and 10 seconds required for most rockets sized for the B6-4 engine to reach apogee.

The students are tasked with answering the following simple question, the dynamics of the model rocket be adequately simulated using an impulse model for the engine thrust? The project is included within a junior-level course entitled Experimental Mechanics taught at Oklahoma Christian University. The course focuses on experimental investigations directly related to the theory learned in Strength of Materials and Dynamics (both prerequisites to this course).

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Newberry, B. (2008, June), Investigating Impulse Loading Using Model Rocketry Paper presented at 2008 Annual Conference & Exposition, Pittsburgh, Pennsylvania. 10.18260/1-2--4233