1 공학입문설계 서강대학교 전자공학과

Chapter 7: Length and Length-Related Parameters The important dimensions of a BMW Z3 Roadster are shown in the illustration (page 137). The fundamental dimension length and other length-related variables, such as area and volume (e.g., seating or trunk capacity) play important roles in engineering design. As a good engineer you will develop a “feel” for the relative magnitude of various length units, area units, and volume units. It is also important for you to know how to measure, how to calculate, and how to approximate length, area and volume. 2

Every physical object has a size. –Length is one of base dimensions that we use to properly express what we know of our natural world. Thousands of parts that are manufactured by various companies in different parts of the world. Coordinate systems –Used to locate things with respect to a known origin. –Rectangular, cylindrical, spherical. Length as a Fundamental Dimension 3

4

5

Case study: 화성 탐사선의 사고 원인은 단위 –1999 년 9 월 화성궤도에 진입하려던 1 억 2500 만 달 러짜리 미국의 ‘ 화성 기후 궤도선 ’(Mars Climate Orbiter) 이 파괴되었음. – 원인 : 어이없게도 단위 문제임. 제작을 담당한 록히드마틴 사 : 야드파운드법으로 탐사 선의 제원을 작성함. 탐사선을 발사한 미국항공우주국 (NASA) 제트추진연 구소 : 미터법 단위로 착각함. – 결과 : NASA 가 탐사선의 추진력을 킬로그램이 아닌 파운드로 잘못 계산하는 바람에 탐사선은 화성에서 예정 궤도보다 100 ㎞ 아래인 60 ㎞ 지점의 낮은 궤도 에 진입함. 결국 화성 탐사선은 대기와 마찰을 일으 켜 파괴되었음. 6

Measuring devices –Finger length, arm span, stride length –Ruler, yardstick –Vernier caliper, micrometer –EDMI (electronic distance measuring instruments –GPS (global positioning system) Measurement of Length 7

Case study ( 에라토스테네스 - 지구둘레 구하기 ) 8 시에네알렉산드리아 ① 지구는 완전한 구형이다. ② 태양 광선은 지구에 평행하게 도달한다. ( 지구둘레 ) : 5,000 stadia = 360˚ : 7.2˚ 지구둘레 = 250,000 stadia = 46,250 km 1 stadia = 185 m 에라토스테네스의 측정값 실제 지구의 둘레 ( 적도 ) 46,250 km40,077 km

Indirect measuring using trigonometric principles Measurement of Length sine rule cosine rule 9

Manufacturers of engineering parts use round numbers so that it is easier for people to remember the size and thus more easily refer to a specific part. –Nominal size: 2 x 4 piece of lumber –Actual size: approx 1.5 in. x 3.5 in. Nominal Sizes vs. Actual Sizes 10

Nominal Sizes vs. Actual Sizes 11

The relationship among the arc length, S, radius of the arc, R, and the angle in radians, θ, is given by –2π radians is equal to 360 degrees, and 1 radian is equal to degrees. Radians as a Ratio of Two Lengths 12

Stress and strain information is used in engineering analysis. The deformation by a tensile load: strain –Normal strain Strain as a Ratio of Two Lengths 13

Area is a derived, or secondary, physical quantity. –The rate of heat transfer from a surface is directly proportional to the exposed surface area. –Many leaves of trees instead of one big leaf. Area 14

Relationship between a given volume and exposed surface area. –crushed ice vs. big ice chunk Area volume: 1 m 3 exposed surface area: 6 m 2 volume: 1 m 3 exposed surface area: 12 m 2 15

Cross-sectional area plays an important role in distributing a force over an area. –Why edge of a sharp knife cuts well? –High-heeled shoes are designed poorly. Area 16

Area calculations Area 17

Approximation of planar areas –The trapezoidal rule Area 18

Approximation of planar areas (cont.) –Counting the squares –Subtracting unwanted areas –Weighting the area An example on p171 Area 19

In a three-dimensional world, volume would be an important player in how things are shaped or how things work. –Buoyancy force as an example This principle can be used to measure the unknown volume of an object. Underwater Neutral Buoyancy Simulator (p174)) Volume 20

Volume calculations –Examples 7.2 & 7.3 Volume 21

Area moment of inertia: –a property of an area that provides information on how hard it is to bend something. In construction site, are the beams laid out in the orientation shown in Fig. 7.20(a) or Fig. 7.20(b)? Second Moments of Areas 22

An experiment for understanding the role of the second moment of area –Which way is it harder to bend the yardstick? Second Moments of Areas 23

Definition of the second moment of area Second Moments of Areas 24