15-10-2012, 05:41 PM
Haftka’s Helicopter Project: Combined Theoretical/Experimental Design
[attachment=36452]
Abstract
A helicopter design project is described that combines computational modeling, optimization,
design of experiments theory, fabrication, test, and analysis of the results, including statistical
analysis. This is all done in a classroom environment in a reasonable number of class periods.
Originally introduced by Professor Rafi Haftka at the University of Florida, this paper describes
the version of the project carried out in the Fall of 1997 at Virginia Tech. The purpose of this paper
is to expose a wide spectrum of educators to this project. Our experience with this project was very
good and we provide enough details to allow easy implementation elsewhere.
Introduction
Real world product development efforts require analytic models, analytical/computational
design and an experimental development program to produce a quality product. It is a challenge to
find a class project that simulates the flavor of this process. At the University of Florida, Professor
Raphael Haftka has introduced a project that serves this purpose in his senior/graduate level course
“Experimental Optimum Engineering Design”.1 In the Fall of 1997 a simplified version of the
project was used in the “Introduction to AOE Design” course at Virginia Tech after Professor
Haftka sent us a draft version of a paper describing the project .The project is perfectly suited for
use in engineering design and product development classes, and the ASEE Conference provides an
opportunity to make a wide spectrum of educators aware of this project. One of the key
components in the class is the use of statistical methods. Although industry has been requesting
more use of statistics in the engineering program, many aerospace engineering courses are still
weak in the use of statistical methods. This project builds on previous projects used in the statistics
community to illustrate design of experiments theory and process variation.2,3 The project is also
multidisciplinary, an aspect of engineering we have been stressing at Virginia Tech for several
years.4 I am aware of one other similar project. The U.S. Air Force Academy has used design of
experiments theory to develop a test matrix for gliders.
The Course
The Aerospace and Ocean Engineering Department gave a one credit pass/fail, elective,
nominally-sophomore class that provided an introduction to design methods and aerospace and
ocean engineering. Typically the class had 20-25 students, and eventually attracted a mix of
students from other majors. It met once a week for two hours. The class was introduced at the
request of students for two reasons. First, the seniors complained that they weren’t ready for the
capstone senior design and it was hoped this would help them. Second, we started using some
freshmen in the second semester of the senior design class to help them get some insight into the
engineering process, and motivate the need for the engineering science classes.6,7 Those students
wanted to continue some sort of design activity. This course is now being replaced by a more
traditional three credit required introductory course. Two aspects are worthy of note. The mix of
seniors and freshman worked well, a class of same year students is not nearly as good (What if
companies segregated their workers by number of years of experience? Would that make sense?).
Also, the freshman-senior program has been expanded by Prof. Marchman to include sophomores
and juniors, as well as seniors from other majors and an international element.
Experimental Design
After we’d flown the helicopters obtained from the math model and optimization, we started
the experimental development program. We gave the students an admittedly superficial introduction
to design of experiments methods, and a typical sheet generated by JMP IN to use to construct the
range of experiments. Figure 2 is the visualization of the matrix of designs that were built and
flown. We pointed out that not all of the possible combinations of designs were included. And
gave an example showing how with the addition of more design variables it quickly becomes
impossible to consider every combination of design variables. The design illustrated in Fig. 2 is a
Box-Behnken design, which was selected because it resulted in making the smallest number of
designs. Note that it “trims off” the corners of the design space. Table 1 shows the output from
JMP IN, that we actually used, together with the results from one of the groups to be presented
below. Here, the design variables are given in terms of their upper and lower bounds, which we
provided for the students.
Results
Working in teams of from two to four students, they worked in our design lab, as shown in
Fig. 3, to obtain the optimum from Excel. Figure 4 shows them making the helicopters. They then
timed the flights for a drop of 18 1/2 feet, typical of atriums found in modern buildings. For our
case, the students found that the flight time for the optimum case was predicted to be 5.33 seconds.
Teams obtained average values from five helicopter flights of 5.2, 6.1, 7.3, and 7.4 seconds. This
was a remarkable range of times for the flights of helicopters that were supposed to be identical,
and set the stage for the next part of the project.
Conclusions
This project combines a number of key aspects of the design process. The students are able to
develop theoretical models of the system, develop a rational experimental development program,
and then make and test the designs. Software such as Excel and JMP IN allow the students to
carry out the math easily. It is a good way of introducing statistics into the educational process. In
doing the test, it was hard to control the students. One of the lessons was that the students wanted
to undertake ad hoc improvements. They immediately wanted to start cambering and twisting the
rotor blades. Finally, helicopters can be flown in a variety of locations. I have always had
problems finding a place to fly model airplanes in the late fall or winter time in Blacksburg.
[attachment=36452]
Abstract
A helicopter design project is described that combines computational modeling, optimization,
design of experiments theory, fabrication, test, and analysis of the results, including statistical
analysis. This is all done in a classroom environment in a reasonable number of class periods.
Originally introduced by Professor Rafi Haftka at the University of Florida, this paper describes
the version of the project carried out in the Fall of 1997 at Virginia Tech. The purpose of this paper
is to expose a wide spectrum of educators to this project. Our experience with this project was very
good and we provide enough details to allow easy implementation elsewhere.
Introduction
Real world product development efforts require analytic models, analytical/computational
design and an experimental development program to produce a quality product. It is a challenge to
find a class project that simulates the flavor of this process. At the University of Florida, Professor
Raphael Haftka has introduced a project that serves this purpose in his senior/graduate level course
“Experimental Optimum Engineering Design”.1 In the Fall of 1997 a simplified version of the
project was used in the “Introduction to AOE Design” course at Virginia Tech after Professor
Haftka sent us a draft version of a paper describing the project .The project is perfectly suited for
use in engineering design and product development classes, and the ASEE Conference provides an
opportunity to make a wide spectrum of educators aware of this project. One of the key
components in the class is the use of statistical methods. Although industry has been requesting
more use of statistics in the engineering program, many aerospace engineering courses are still
weak in the use of statistical methods. This project builds on previous projects used in the statistics
community to illustrate design of experiments theory and process variation.2,3 The project is also
multidisciplinary, an aspect of engineering we have been stressing at Virginia Tech for several
years.4 I am aware of one other similar project. The U.S. Air Force Academy has used design of
experiments theory to develop a test matrix for gliders.
The Course
The Aerospace and Ocean Engineering Department gave a one credit pass/fail, elective,
nominally-sophomore class that provided an introduction to design methods and aerospace and
ocean engineering. Typically the class had 20-25 students, and eventually attracted a mix of
students from other majors. It met once a week for two hours. The class was introduced at the
request of students for two reasons. First, the seniors complained that they weren’t ready for the
capstone senior design and it was hoped this would help them. Second, we started using some
freshmen in the second semester of the senior design class to help them get some insight into the
engineering process, and motivate the need for the engineering science classes.6,7 Those students
wanted to continue some sort of design activity. This course is now being replaced by a more
traditional three credit required introductory course. Two aspects are worthy of note. The mix of
seniors and freshman worked well, a class of same year students is not nearly as good (What if
companies segregated their workers by number of years of experience? Would that make sense?).
Also, the freshman-senior program has been expanded by Prof. Marchman to include sophomores
and juniors, as well as seniors from other majors and an international element.
Experimental Design
After we’d flown the helicopters obtained from the math model and optimization, we started
the experimental development program. We gave the students an admittedly superficial introduction
to design of experiments methods, and a typical sheet generated by JMP IN to use to construct the
range of experiments. Figure 2 is the visualization of the matrix of designs that were built and
flown. We pointed out that not all of the possible combinations of designs were included. And
gave an example showing how with the addition of more design variables it quickly becomes
impossible to consider every combination of design variables. The design illustrated in Fig. 2 is a
Box-Behnken design, which was selected because it resulted in making the smallest number of
designs. Note that it “trims off” the corners of the design space. Table 1 shows the output from
JMP IN, that we actually used, together with the results from one of the groups to be presented
below. Here, the design variables are given in terms of their upper and lower bounds, which we
provided for the students.
Results
Working in teams of from two to four students, they worked in our design lab, as shown in
Fig. 3, to obtain the optimum from Excel. Figure 4 shows them making the helicopters. They then
timed the flights for a drop of 18 1/2 feet, typical of atriums found in modern buildings. For our
case, the students found that the flight time for the optimum case was predicted to be 5.33 seconds.
Teams obtained average values from five helicopter flights of 5.2, 6.1, 7.3, and 7.4 seconds. This
was a remarkable range of times for the flights of helicopters that were supposed to be identical,
and set the stage for the next part of the project.
Conclusions
This project combines a number of key aspects of the design process. The students are able to
develop theoretical models of the system, develop a rational experimental development program,
and then make and test the designs. Software such as Excel and JMP IN allow the students to
carry out the math easily. It is a good way of introducing statistics into the educational process. In
doing the test, it was hard to control the students. One of the lessons was that the students wanted
to undertake ad hoc improvements. They immediately wanted to start cambering and twisting the
rotor blades. Finally, helicopters can be flown in a variety of locations. I have always had
problems finding a place to fly model airplanes in the late fall or winter time in Blacksburg.