## On Ideas and Engineering Education

**Great Ideas:**

Engineering is a collection of great ideas. A good example is the idea of modeling an airfoil by a single point-vortex (lumped vortex method). Knowing the Kutta-Joukowski theorem (or simply following a physical intuition), we conjecture that a vortex is essential to describe a lifting flow, and hope that a flow over a point vortex will provide us with useful information in studying the lift of an airfoil. Then, passion takes over. We struggle to figure out where to place the vortex and how to determine its strength. Finally, we arrive at a remarkable result: a highly accurate lift curve for a thin airfoil over a practical range of angles of attack. A useful tool to analyze and design an airfoil is obtained. I believe that useful engineering tools such as analytical formulas or numerical algorithms have been developed based on ideas and passion of engineers and scientists. An engineering textbook is a collection of stories of great ideas. These wonderful stories inspire students with enthusiasm and excitement, and the spectacular progress in engineering continues.

**Learn with Ideas:**

The above example of a lumped vortex model illustrates an important combination of an idea and passion, or a principle and skills. Ideas are free. Anybody can come up with from anything smart to absurd. But it is not enough. One needs to turn ideas into realities, or simply, to express them: e.g., pictures, novels, songs, equations, etc. Only then can the value of the idea be evaluated. In engineering, to be a great idea, it must yield something useful. For this, skills are required: mathematics, programming, or manufacturing. To learn skills can be boring, but it can be quite exciting if recognized as a means to turn ideas into useful engineering tools or products. Homework can be a good opportunity for students to experience the process of getting ideas to work in engineering applications. For example, they may apply the lumped vortex method to explore tandem airfoils by a pair of vortices or an airfoil in a wind tunnel by the method of mirror images. Through such exercises, students acquire skills as needed and develop an engineering insight. At the same time, these applications will serve as convincing examples that the simple idea of the lumped vortex model is indeed a great idea.

Poor ideas can also be useful in learning. A popular explanation of lift based on a false concept of ‘equal transit time’ and the Bernoulli theorem is a good example. I myself attempted to calculate the lift coefficient of a parabolic airfoil based on this idea, and obtained the result that the lift coefficient at zero angle of attack is proportional to the square of the maximum thickness (See “False Theory of Lift”). The thickness being a small value, the resulting formula significantly underestimates the lift: the lift coefficient is well known from the thin-airfoil theory to be directly proportional to the maximum thickness. It can also be easily proved wrong by experiments. This example shows that there are good ideas and poor ideas in terms of successful engineering applications. Examples of poor ideas are valuable to students who are likely to go through such experiences in future when they deal with real world engineering problems for which the solution cannot be found in textbooks. That is, they can learn how to examine ideas for engineering applications. In this context, it would be a highly educational exercise to let students propose an idea and examine it by themselves.

**Achieve with Ideas:**

Students who have gone through such a learning process are expected to become creative engineers. Given a goal, they would try to come up with ideas and examine them one by one to find the best approach, acquiring skills as needed. In doing so, they continue to strengthen their skills, intuition, and knowledge. A goal of engineering education is to educate such creative engineers and scientists.

Katate Masatsuka

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