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Ratios INSTRUCTIONAL OBJECTIVES Students will • Use ratios to compare quantities NATIONAL MATHEMATICS STANDARDS Understand numbers, ways of representing numbers, relationships among numbers, and number systems • Understand and use ratios and proportions to represent quantitative relationships Algebra • Generalize patterns using explicitly defined and recursively defined variables • Interpret representations of functions of two variables Problem Solving • Solve problems that arise in mathematics and in other contexts • Apply and adapt a variety of appropriate strategies to solve problems INTRODUCTION Many different types of mathematics are used in the evaluation of propulsion. One way that engineers describe different characteristics of a plane is by using ratios. The ratio of a scalar quantity a to a scalar quantity b is equal to a divided by b: ratio = ab. Recall that a scalar quantity has only a magnitude, not a direction. Below are just some of the ratios that engineers use when studying aircraft. Visit http://www.grc.nasa.gov/WWW/K-12/airplane/ratio.html for many more types of ratios, additional examples, and interactive simulations on these topics. • The Mach number M is the ratio of the speed of an object to the speed of sound in a gas. The Mach num- ber defines the various flight regimes of an aircraft and the importance of the compressibility of the flow. Note that because the temperature and density of the air decreases with increasing altitude, the speed of sound also decreases with altitude. Classifications of high-speed flight: – Subsonic, M < 1 – Transonic, M = 1 – Supersonic, 1 < M < 3 – High supersonic, 3 < M < 5 – Hypersonic, M > 5 – High hypersonic, M >> 25 • The thrust-to-weight ratio of an aircraft determines the climb rate and performance of an aircraft. The thrust to-weight ratio of an aircraft determines the g-loading on the payload and structure; g-loading refers to how many times the force of gravity a structure can withstand. • The aspect ratio of a wing is equal to the square of the wingspan divided by the wing area. This factor influ- ences the induced drag and downwash effects on the lift of a wing. High-aspect-ratio wings are more efficient than low-aspect-ratio wings, as first discovered by the Wright brothers in 1901 to 1902. • Other ratios include glide ratio, lift-to-drag ratio, engine’s fuel-to-air ratio, and compression ratio. Pushing the Envelope: A NASA Guide to Engines 59 PHYSICS AND MATHPDF Image | NASA Guide to Engines
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