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The success of the SES mission—to manage government Note particularly the diversity and breadth of SES projects. systems programs for General Telephone & Electronics, the You may advance in a technical or administrative capacity in parent corporation—depends on the professional and intellec- any of these areas: ground electronics equipment for Minute- tual growth of its personnel. In every respect, SES has created man missle sites...research and development in electronic an environment to foster that growth. Be sure that any prospec- warfare field...electronic security systems... tive employer you consider has established a ASW systems...special purpose airborne com- growth climate of like specifications. putersforincoporationintoU.S. Air Force large Making promises is one thing. 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In your hands, man's most daring IBM Corporate Headquarters, Armonk, a mbetter world. dreams can become reality—to make a better life for more people. New York 10504. IBM is an EquaL The key is IBM computers. They're Opportunity Employer. helping medical researchers learn If that sounds like an exciting more about cancer and factors prospect, it's because it is. A career associatedwithit.Helping educators with IBM will give you both personal developnewtechniquesforinstructing and professional fulfillment. culturallt deprived children. Helping Your placement officer can tell you about career opportunities with IBM. engineers plan flood-prevention See him, too, for an appointment program. with our interviewers. Before you Computers are helping to do a conquerlot of new worlds, try your hand at goodthingsfor a lot of people. But reshaping the old one. Knowledge of the familiar 3-4-5 right triangle TRIANGLES dates back through untold centuries to the ancient civilization of the Egyptians and the Chinese. It In all, several hundred separate proofs have served the purpose of helping man lay out squarely been drived that state this remarkable property his plots and tracts of land, his villages and towns, of the right triangle. The story is told that! his highways and canals, and his buildings and humble Hindu mathematician of several centuries monuments. ago once etched in a stone wall a geometric B| All hough these ancient men commonly employed ure similar to Figure 2, at right. Before passing the 3-4-5 principle for the construction of aright on his way, he adorned his handiwork with jM angle, it is believed they were satisfied with the single word, BEHOLD! We leave it to you to dis- results so obtained and considered not why they cover the proof of the Pythagorean Theorem were so. The knowledge was simply handed down contained in the following construction. along with the other arts and crafts necessary for the continuity of their civilizations. Pythagoras, a frequent visitor to Egypt in the Sixth Century, B.C., picked up much of the math- ematical learning and lore of that country and was the first man history records as having stated the proof that has become a classic in Euclidian geom - etry. We recall a simple proof derived from the right triangle, abc, appearing in Figure I, below: By similar triangles", Have astronauts made pilots old hat? Sure, the boys who III most advanced research and develop- is at the office of the Professor of Aero- go off the "pads" get the big, bold head- ment organizations, we have a continu- space Studies, if there is an Air Force lines. But if you want to fly, the big op- ing need for scientists and engineers, as ROTC unit on your campus. If not, con- portunities are still with the aircraft that well as administrators. tact the nearest Air Force recruiter for take off and land on several thousand Young college graduates (both men information on all Air Force officer op- feet of runway. and women) in these fields will find that portunities. Or mail the coupon below. Who needs pilots? TAC does. And they'll have the opportunity to do work MAC. And SAC. that is both interesting and important. There's a real future in Air Force fly- The fact is, nowhere will you have greater ing. In years to come aircraft may fly latitude or responsibility right higher, faster, and farther than we dare from the start than on the dream today. But they'll be flying, with men who've had Air Force flight training at the controls. Of course the Air Force also has Plenty of jobs for those who won't be Aerospace Team—the U.S. Air Force. flying. As one of the world's largest and Interested? The place to find out more Degrees —temperature as well as engineering —really matter at Union Carbide's Linde Division. LINDE, a leading commercial producer of industrial gases for over 50 years, is now engaged in many diverse industrial activities. Heat, cold, pressure, vacuum, and engineering talent are the basic creative tools used in continuing efforts to develop new products and ad- vanced technological capabilities. Temperatures uti- lized may run as hot as 30,000°F., to as cold as -452°F. This work particularly requires the skills of Mechanical, Chemical, Metallurgical, Electrical, and Civil engineers. There are excellent opportunities in programs in Cryogenics, Plasmas, Flame-Plating, Industrial Gases, Electronics, Molecular Sieves, Bio-Chemistry, Crys- tallography, and other technical areas. You can look forward to a rewarding career in Re- search, Development, Engineering, Production, Sales Engineering. LINDE is a nationwide organization with offices, plants, factories and laboratories throughout the coun- try. Where you work will largely depend upon the work you do. Research and Development: LINDE has four tech- nical centers at Buffalo, N. Y., Newark, N. J., Indianapo- lis, Ind., and Cleveland, Ohio. Production Facilities: LINDE operates production facilities in nearly every state of the Union. General Offices and Sales Offices: LINDE'S general offices are located in New York City; region sales of- fices are located in major cities throughout the country. LINDE offers a progressive employment benefit pro- gram: relocation; Educational Refund Plan for ad- vanced study in your field of interest. Promotion from within is a basic company policy. If you'd like to know more about your opportunities with us, contact your College Placement Office. A campus interview can be arranged with one of our representatives. Or write to: Union Carbide Corporation, Linde Division, Recruiting Department, 270 Park Avenue New York, N. Y. 10017. CONTINUED FROM PAGE « triangles. Given the x and y components of two or Now, if tan 0 - a/b, an integer fraction, then more vector quantities, the situation often arises ran 2B«_2a/b - 2a/b ,-P_ that the sum of the vector components along one o( j I a2/b2 1 - a2/ h 2 b2 the axes will predominate. An example is an al- - 2ah ternating-current electrical circuit analysis with some reactance, but largely resistance prevailing. ThuH tan 20 d is still an integer fraction, and 2ab Another problem is a turbine stage velocity dia- ,,' i" h (b2 - a2) may be used to form the two gram where either the x or the y component of fig" of • iMger right triangle as represented in the steam velocity may be small, depending upon S S i r e I I•MMh-r. upon obtaining the square root whether inlet or exit conditions are in mind. There are countless tractive, friction and conveying the hypotenuse, is (b^ * a*), another problems where a small grade or incline is in- ,n three Bides of any right m a n g l e de- volved. Other problem solutions of this nature ied In this manner are integer values. concern the boat crossing a river with a current (,iv,n any Integer fraction, a/b, leas than unity, or an airplane flying with a cross wind. i,.iii triangle follows automatically from these We know, of course, with precision that the [impli in mipiil.itlons. solution of a right triangle involves solving an Hi,- following form, with a few examples, is sug- equation of the form gested foi the m.iss production of these special c2 - a 2 + b2. , which .ire now known to permeate the for one of its parts, a, b, or c. We may elect to n | a tuggi iced thai the investigation pro- rearrange the above equation in the form , ,-,ti syst. matically with Integer fractions such as c2 - a 2 = b2. 1/2, 1/3, 1/4, 1/5, etc., until it becomes evident The lefthand side begs of factoring just What further types will appear from that (c + a) (c - a) = b2 rhen begin 2 3, 2 4, 2/5, e t c . u n t i l a new Dividing through by the term, (c +a), yields Bach numerator, when used in (c - a) = b2/(c+a) combination with the successive integers as a c = a + b2/(c + a) = a + b^/2a. lOminatOr, will produce a series of triangles Where c is unknown, we may get a first approx which nuy be found by inspection after the first imation for the hypotenuse of a right triangle b thn o foui examples. solving the approximate expression on the right above. Similarly, if a short side and the hypor TABLB 1. RlKht Triangles with Integer Sides are known, we may approximate the long side a; from Double-Annie Formula follows: a = c - b 2 /2c. li k^ 2ab b2 - a? b 2 - a2 Triangle We will see later how we can improve upon tin T 2 1 4 t 3 5 3 - 4- 5 results of these approximation methods. 2 4 40 28 43 53 28-48-5:-! The ancient civilizations used these methods - 9 ol 48 55 73 48-55-73 in their approximate solutions of right triangle before methods of extracting square roots wen li may be well h e i v i<> take a m o m e n t in t r y i n g invented. It is interesting to observe how closely to c o m p r e h e n d the infinite. We Learned f i r s t t h a t interrelated are the problems of square roots am may be used to g e n e r a t e a l i g h t t r i - right triangle solutions. We learned to appro" angle combination, yielding in the process two new mate square roots in FUN WITH RECIPROCAL larger Integers, to spur us on. Now we see thai each by using a method that is virtually synonymou. integer may be used with the Infinite array of In- with the derivation above. ..Q tegers to produce Pythagorean triples. Moreover, As an example assume a resistance, Rx 0* " ' this infinite nr.iv nuy be performed an infinite ohms, and the net reactance, Ry • ^ ^ ' number of linns. Finally, each of these infinity of Applying methods learned in FUN WITH SQUAKW, infinities of operations produces three new in- we recognize immediately that R 2 = I 5 = " teger* that form three possible combinations of y nn2 a b that feed new numbers to the formulation units. We also know that the interval between li"(i for our purposes faster than they can be consumed. and 1112 comprises some 221 "square units. I he preceding discussion is largely purely the- We adopt the convention of putting quotes arouiL oretical and may appear to have little practical the 221 "square units"2 so that it is possible application. Yet, it has been passed along to spur work in terms of a, b , and c at the same tim an interest in these phenomena and has been pre- without becoming confused. We may thereto sented with the hope that you will come into closer simply state that if, working contact with the readily available network Z 2 = R 2 t R 2 ohms, of facts and data which are number theory. x y thcn Long usage is what 'nakes the old shoe fit , Z s 110 + 225 comfortably, and it takes usage to make the in- 221 formation contained in this and the preceding = 111 + _ £ = 111 +1/55.3. parts worthwhile in everyday practice. 222 I here are problems everywhere throughout studies in physics and engineering that involve Now, we should recall from FUN WITH REClp' the addition of vector quantities in a two-dimen- ROCALS that sional system. Every one of these problems can 1/18 - (1/2) (1/9) -(0.5X0.1111 )=O.05555;...- be reduced to the solution of one or more right Turn about being fairplay, 1/55.5 = 0.018. We ma. CONTINUED ON P* G If I join Every man with any job hunting experience knows not to ask that question. And yet, we think it has some validity. After all, a man's growth can depend as much on the company he works for as the company's growth the Timken depends on the man (remember, there are no statues to committees). So to invest in your growth, and ours, every young graduate engineer who joins the Timken Company spends up to four years in one of 22 in- Company dividualized training programs. Extensive training after Instruction takes place on the job and in the classroom. Later on there are executive development programs at leading universities. graduation, But don't misunderstand us. The Timken Company is not a graduate school. With us, you earn as you learn. As one of our engineers, you'll learn much of what we know about tapered what roller bearings, or fine alloy steel, and their infinite applications. Hopefully, you'll teach us something, too. You can be an indoor-type working on straight application engineering, will they do research, testing and production. Or you can be an indoor-outdoor-type and work in sales engineering. It doesn't matter—choice of assignment is for me? up to you. Challenging assignments If you choose the latter group, you'll work in automotive, industrial, and railway bearing sales—or steel sales—helping customers solve their engineering problems, which are also ours. Some of our recent efforts: bearing engineering for a telephone cable-laying ship now crossing the Pacific, the Alweg Monorail, the world's tallest crane and biggest strip mining shovel, Craig Breedlove's Spirit of America, a moveable grandstand for the new District of Columbia stadium. Steel prob- lem solving for Atlas missile silos, Project Mohole, the latest Kaman Heli- copters, a 400-foot crane boom and hundreds of automotive gear and die applications. We won't forget you Advancement is not restricted to one department or division. A steel sales engineer may be transferred to automotive sales and from there to Inter- national. Whatever your job, we'll never forget where we've put you. This is one of the advantages of working for a company that is the world's largest producer of tapered roller bearings and a foremost producer of seamless steel tubing, but is not the world's largest corporation. We employ about 20,000. The Timken Company has three products: Bearings, Steel, Rock Bits. Uses for these products number in the growing thousands. And there is always something new stirring. The dramatic switch of the nation's railroad freight cars to roller bearings, a field we pioneered, is an example. An international company There are 31 Timken Company sales offices in the United States and Canada. Practically every major city has one. We serve markets in 119 countries from 14 manufacturing plants located in Australia, Brazil, Canada, England, France, South Africa and the U.S. And we're still growing strong. If you are, too, we'd like to hear from you. Write to Department MC for Career booklet. An equal opportunity employer. CONTINUED FROM PAGE 10 proportionately small side, and determine the now State Z to a greater degree of precision than other leg. For example, given: any laboratory measurements of resistances al- F2 =Fx2 + F y 2 , Lowi ^ ^ j , 4 ,, where F - 2,000 pounds , Fy " 600 pounds; find F x . Nearly 4000 "square units" in terms of Fy2 arc- ,t to scale.) . ^ ^ required to yield F x a single pound less than F, itself. As it happens, F y 2 - 360,000 "sq Z - 111.018^^^* Ry-15 units," or enough for 90 such intervals. Now we ^&' md 1132, Including three significant figures, n - 90. tin- solution of V4 - 413 Feet per second is c o m - Recall now FUN WITH SQUARES and recognize plete. that the sum of the accumulated error represented by the series above is nothing more than the square of 90! That is, the sum of the first n odd / ^ " 29 numbers is n2, itself! Therefore, the accumulated error after 90 intervals totals 8,100 units. These, (Not to Bcale.) /S ^/^1 in turn, suggest that two additional intervals may V4 - 4 H . O 4 / ^ 3 > / < ' 8 2 5 " | be included, of F = 1,908 pounds. This solution now agrees with the calculated answer referred to above. As a matter of fact, we may tabulate the prob- lem as below and eventually arrive at any desired degree of accuracy. ^ ^ — "2500"( F x = 1,910 - 8,100 3,819 Vx> 410 - 1,909 - 4,281 Figure 5. Solution of a 50-410-413 Right Triangle 3,817 = 1,908 - 464 It Is within our capability to carry the above 3,815 solution out to 413.04 if we dared introduce the = 1,908 - 0.12 implied significance and accuracy in the velocity ... " 1,907.88. determinations. Although we started with 3-4-5 as a right tri- Assume a new circumstance in which the hypo- angle, we now also recognize 6OO-L£QLJ8-2JK tenuse or a right triangle is known, along with a as being another, where the 1907 88 is as accurate as we please to make it! (Republication rights reserved.) Professor Paul J. Grogan, Chairman Madison, Wisconsin Department of Engineering March 13, 1964 University Extension Division The University of Wisconsin Figuring an Getting Ahead? Sound good? If you're our kind of person it should. We're We need aggressive, imaginative, well-trained men. In getting big—and getting big fast, but we haven't forgotten chemistry,chemicalandmechanical engineering, physics, what it's like to be young. And one more thing —our world- marketing, accounting. If you're one of them you'll be wide divisions and affiliates provide the opportunity for challenged to your limits because we're growing so fast. Our1964saleswereupm o r e t h a n 2 5 % t 0 o v e r $ 7 0 0 m i l - movement to more than 70 plants, or laboratories, around lion. Compacent? Not on your life! We're already planning the world. forthesecond billion. Why not start now? Talk to your faculty and Placement Director, then arrange to see our representative when he What does this mean to you? lts a chance to Prove y ° u r s e l f visits your campus. Or write to: Matthew Park, Jr., Super- andberewaredwithprofessionalrecognition , recognition, responsibil- visor of University Recruitment, Celanese Corporation of ity, authority-not to mention money. And a chance to work America, 522 Fifth Avenue, New York, foracompanyyouknowisascommitted to growing a n d br°adening itself as you are. ON PLANETARY LANDINGS BY SPACECRAFT I In Part 1 of this discussion, (5) Drag force of an atmosphere fo being the initial radial veloc- pullshed in the January issue of on a ship at any time: ity. the magazine, we derived and dis- (9) Radial distance traveled by cussed certain preliminary re- F d = l / 2 PU 2 SC D sults. T h e s e results are ex- the ship whose radial drag force U is the ship's airspeed, S the obeys Eq. (8): r = r 0 ^ tremely Important; the e n t i r e surface area exposed to the air- discussion of the specifics of a - 1 In cosh c vGt'. stream, and Op the ship's co- planetary landing, as presented in efficient of drag. this article, can be carried on (10) Velocity of a ship whichis within the framework of these re- (6) Reduction in airspeed as a moving vertically and is firing sulta and their I m p l i c a t i o n s . result of drag in a constant- rockets: Therefore, we will restate them density atmosphere: v = X In Mo - gt - v 0 , at this point. Ui fi Mo- /ft U- (1) Variation of atmospheric where T is rocket thrust (and is density with altitude: (1/2U.PSCD/M)t + 1 not to be confused with the f p - p o e -< m / RT )gy where M\ is the ship's initital air- Eq. (1), M o and v o are the ships where m is molecular weight of speed, M the mass of the ship, initital mass and velocity, arum the atmosphere, R the universal and t is time. is the rate of mass ejection Dy gas constant, T the Kelvin tem- the rockets. . perature, g the acceleration due (7) Angular distance traveled by the ship while decelerating Having restated these results, to gravity, y the altitude. we may now go on to discuss the under atmospheric drag: (2) Shape of a Keplerian orbit: specifics of a planetary landing 1•E r M -I We need consider only those min 1 + E cos $ 0-0 o+ |_l/2PSC D r eff J portions of a landing approach where r is radial distance from which lie in the atmosphere, for the planet's center, E the orbital x[ln (1 + l/2UjPSCDt/M)j when a ship is outside the at- eccentricity, r m in the perigee, where 0o is the angular position mosphere its orbital motion is and sS the angular distance from of the spacecraft on entering the governed explicitly by the laws the perigee. atmosphere (which is of constant of Kepler. In particular,ifthe (3) Eccentricity of orbit, when density), and reff is half the dis- ship's velocity and direction of ship's motion is approximately tance between R and the upper motion are known atagivenpoint, parallel to the planet's surface: limit of the atmosphere. then the eccentricity may be foun E - t (v 2 r/gR 2 - 1) (8) Radial velocity of a ship from Eq. (3) or from^ its gener- where v is the ship's velocity which is under the effect of grav- alization which wasdiscussedin ity, "centrifugal force", and a Part I of this paper. Further, relative to the planet's center the perigee may befound,bydif- radial drag force which obeys Eq and R the planet's radius. (5): ferentiating Eq. (2) with respect (4) Velocity of a ship falling to 0. setting the derivativdr/d toward a planet: f = c tanh c \fG~t' where we have equal to thedirectionofmotion made the following changes of of the ship at the given point, v - v0 + V2gR 2/r variable: and proceeding to solveforrmin where vQ is the velocity relative If a ship is passingthroughan to the planet's center of the ship G = (g -v2r ef f);c2 = l / 2 p s c D / M ; when it is very far (at least 250 R) atmosphere there are two cases l> from the planet. =t • 1 In VG,.7,gq , to consider. The first isthatthe 2c V£ VC - cf 0 ship is undergoing a series of braking ellipses and will there Find your "occupatibility" at Du Pont It won't take much looking. We realize, you see, that with this year's What's "occupatibility"? graduating technical men, "occupatibility" is a pretty important thing. It's a term we've invented to express the opportunity Du Pont offers you as a tech- Learn more about Du Pont. Send this coupon for a subscription to the Du Pont magazine. nical man* to find the job that best matches your interests and abili- ties. You may find it could be in research, or scientific marketing, product development, or plant operations. At the moment, y o u m a y n o t be sure exactly what it is that y o u want to do. We'll help you find out, by giving you actual experi- enc e on different jobs. You'll find, too, that we have plenty of "This year, our recruiters will be at your room for you to move around. Many school looking mainly for: Ch.E., M.E., DuPont technical men have changed jobs, I.E., E.E., C.E., chemistry, physics and even switched from one discipline to an- mathematics graduates. DuPont is an equal other right within the company. opportunity employer. CONTINUED FROM PAGE 1< Theorem I is motivated by the vo fore leave the atmosphere again; fact that the idealized orbit dis- 1 + Qt. the second is that the ship will cussed above is, ordinarily, (i.e. Let T be the time required to remain in the atmosphere and will for moderate reductions in vel- reduce v from v 0 to ve; then this land directly. These cases cor- ocity) very nearly symmetrical, equation implies that Q » 1 - k respond respectively to Steps 1 with the perigee lying near the n ' and 2 and to Step 3 of the gen- middle of the flight path. This Then we have: eralized landing approach dis- theorem states: Let one space- v vo cussed in Part I of this paper. ship follow the idealized orbit, Suppose a ship is passing so as to enter the atmosphere at l+[U-k)/kT]t through the atmosphere in a brak- a point 0o and leave at a point To find v a v we must integrate ing ellipse (as opposed to a ter- 0 e , 0O «#0 e , reducing its veloc- this expression from 0 to T and minal descent). It is a well- ity in the process from v 0 to v e . divide by T: known fact that the ship will not Let an identical spaceship fly at v be strongly braked along the en- a constant altitude which has av - V£ / dt tire length of its flight, but will been so chosen as to insure that T / o 1 +[(l-k)/kTJt undergo a rather short period of this ship will also reduce its v o k / I 'r(l-k)/kT]dt Intensive deceleration about mid- velocity from v 0 to v e while ~ ttj 0 1 + L(l-k)/kfjt way through its atmospheric traveling from position 0O to 0 e . flight, this short period being Then the average velocities for bracketed by much longer peri- the two flights will be very nearly vok ods In which the deceleration is equal, and furthermore will be ' 1-k In (1/k) rather small. Thus we may ideal- given approximately by: Consider now In (1/k). Let 1 - ize the situation as one of flight k v down to perigee with velocity av " Ifcfo where k = v /v 1+x so that x = ljc. If we ex- unchanged, with a sudden de- k+1 e/ o. 1-x 1+k crease in velocity in the im- To prove this, it is necessary pand in a Taylor series about mediate vicinity of the perigee, to consider the two situations. the point x - 0 we have: In Jjti * followed by flight up from the In the idealized orbit the ship 1-x perigee to the atmospheric limit travels half the flight path at vel- 2(x -x3 + x5 -...) Butfork>l/2 at constant velocity (the reduced ocity v 0 and the other half at velocity). velocity v e . Let s be the length 3 5 of the flight path. The time for we can easily neglect higher A physical system described traversing the first half = s/2 v o . powers of x. Then, making ap- by this model is that of a stone Likewise, the time for traversing propriate substitutions, we have: skipping over water: it flies at the second half is s/2v e or In (1/k) = 2(ldS), or, multiplying nearly constant velocity, but its s/2kv . Thus the total time is 1+k velocity is reduced very suddenly 0 by the coefficient vok, vav - ^ during the time of contact with (s/2v 0 f s/2kv0) = s(k + l)/2kv 0 . l^k ^ the water. Now it is a remark- Then the average velocity is as But this is precisely the expres- able fact that if a spacecraft given in the theorem, 2kv o /k + l. sion for v a v found for the ideal- has the proper shape and enters For the constant-altitude sit- ized orbit. Thus the theorem is the atmosphere at the proper uation the mathematics is not so angle, it will glance off in a simple. The relevant equations proved. manner precisely analogous to are Eqs. (6) and (7). These, From this theorem wehavetwu that of the skipping stone; this however, are written for air- extremely useful equations: was first shown by Sanger and speed, or velocity relative to the Vav~2v Q k - 2vove Bredt in 1944. This analogy lends surface of the planet. The air- " " 1 + k vo+ve credence to the model. speed U j n d velocity v differ by voTheorem *1 + l^PUiSCBTTM II states: If two idenj a factor wX rgfj, where UJ is the The corresponding idealization planet's angular velocity and X of the orbit is a "piecewise" represents the cross product. tical spaceships reduce their v Keplerlan conic, the first part, ocity from v 0 to v e solely cy extending down to perigee, hav- However, the difference between mospheric drag, then they mjs ing the eccentricity associated U and v is ordinarily quite small, encounter the same mass or g • with the ship when it enters the amounting in the case of Earth The proof stems from the-W atmosphere and the second part to about 5% at most, in the case extending up from the perigee) of Mars to no more than 8%, and that if the two ships reduce in having the eccentricity associ- in the case of Venus to very nearly velocity from v 0 to v e tnen ^ ated with the ship when it leaves zero. Thus we may modify Eq (6) must lose the same amount the atmosphere. slightly and the modification will momentum. The only wayatney jt still be quite accurate. Themod- lose momentum is to tr "L s {he The key to analysis of the prob- fified equation will read: to the gas encountered. one lem, then, lies in determining mass of gas encountered uy the proper perigee. There is no v- vi ship be mi and the mass oi» explicit solution to this problem d/2 UjpSCD/M)t 4 1. encountered by the other ce in the form of an equation but it Then we require that ™l(Vo ..£ is possible to set up an iterated This equation is not exact, as - m 2 (v 0 - ve), from which we process which will lead to the de- U n m d i f i e d (6 but immediately that mi * m 2- ee sired solution. This p r o c e s s ^ n values small 1 °of t such >- ^ as we will rests upon two theorems, which Now we may find the perw be concerned with it is accurate The process is as follows: " ^ we will now consider. enough Call the term in paren- theses Q; then we have that v«* a value of the perigee. Sine .... cn ON P » G E up to a more than 2-billion-dollar business in POWER — C L I M B W I T H U S Go with Internationa, mechanical power for a world moving faster every year. Harvester. We're a major company on the move in every We need engineers. Now. We need mechanical, industrial, a rea f r o m f a r m and construction equipment to marine en- agricultural, metallurgical, general, civil and electrical en- gines to utility vehicles. Illustrated is the new Sportop ver- gineers. At IH, you will find an exceptional combination of sion of the famous International® SCOUT. Equipped with opportunity, responsibility and individual treatment. 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All this adds CONTINUED FROM PAGE 16 pression that must be put in the(7), (8), and (9) may be applied and v e are known, it is possible exponent of (1) in the place of y, successively to each layer, the to calculate the Idealized orbit. the resulting expression being in- conditions of the ship at the bot- Now calculate the mass of gas t e g r a t e d between appropriate tom of any given layer furnishing which lies along this orbit; to do limits. This integration cannot be initital conditions for the appli- this it will be necessary to com- carried out except by computer, cation of these equations begin- pute the value of the line integral for the integrals involved cannot ning at the top of the next layer of Eq. (1) along the path of this be reduced to known functions, as the ship descends. It is even orbit; this computation is d i s - functions which have been tabu- possible to account for the useof cussed further on in this article. lated. dive brakes or parachutes, for Now under the above two the- As a point of interest, however, these will change the values ofS, orems it follows that the ship there are special cases for which the exposed surface area (and could travel along an "artifici- the integration is simple indeed. perhaps also the value of Cj)), but al", purely mathematical, con- These are the cases for which 0O it is a trivial matter to arrange stant-altitude orbit so chosen as or # e ^ rather small — less than the boundaries of layers so that to reduce its velocity from v 0 to 0.4 radian. For such cases (1 + these changes will occur at such v e while traveling from 0O to 0 e ; E cos 0)^(1 -t E),and from the a boundary. In this fashion the if It were to do so it would en- Taylor expansion,coser»l-l/2e(2. ship may m a t h e m a t i c a l l y be counter the same mass of gas as it would along the Idealized orbit, Putting these approximations tracked on down until it is rather and would require very nearly the into the general expression for near the surface of the planet, same time, T. Let the mass of y(0), we have the approximation for near the surface it may well gas that must be encountered be y(0)~y m in + REg2 . This ex- be desirable to fire retrorockets iii^, and let s be the distance in 2U4E) for the final touchdown. This is linear units (not radians or de- pression can then be substituted especially true if the planet In . n ' .) between a0 and efe, meas- for y in Eq. (1). Then we may set question is Mars; it is fairly ured along the orbit. Find mg/s; up the line0 integral for mg: certain that the final descent must this would be the density of gas nig* P o / i e - ( m g / K T > be made by rocket, rather In In the constant-altitude orbit, p . the manner of the Russians' re- We find v a v from F.q. (11) and (ymin + cent Luna 9. knowing s, we can easily findT: 2lUE) ) d* KT It may reasonably be assumed T « s/v a v . This T and p can be f 0 i mgRE__02 that through the use of appropri- put into F.q. (12); the implied Jo e~2KT(}+E) d 0 ate aerodynamic braking devices equality will hold if and only if the ship has greatly reduced the proper value of the perigee where we are calling the univer- its airspeed so that it is moving was guessed at the start. For if sal gas constant K, not R, to avoid only slightly with respect to the the value guessed was too low, confusion with the R that repre- surface. Further, it is reasonable then p will be too high, and the sents planetary radius. to suggest that there are two pos- value computed from (12) will be But this integral can easily sible cases. In the first case tne too low; if the value of the per- be evaluated, for it is of the form rocket would have been slowed igee was guessed too high, the r x _t2 by parachute to Just over a saie value computed from (12) will be J o e dt. This i n t e g r a l , or touchdown speed, and only a sllgm too high. rather a variant which is mul- "kick" would be needed for a sate This therefore makes possible tiplied by 2 / N / W , is called the landing. An example of this case an Iteration which will converge "error integral" and has been is to be found in a series oi ex- eventually. It should be noted, tabulated extensively, for exam- periments recentlycarriedoutin however, that the process is la- ple, in Jahnke and Emde's Tables Texas on the landing of Gemini borious and is best carried out of Functions with Formulae and capsules on land. The main brak- by computer. In particular, the Curves. ing was by parachute; onlyinthe calculation of mg by computing Now let us consider the termin- last few feet of descent were the line integral of Eq. (1) along al landing phase, in which the ship rockets needed, and these were the path of the orbit will proceed enters the atmosphere and does quite small.* For this case the in the following manner: not leave but spirals to a landing. mass of the system is very nearly Suppose the orbit has been cal- The solution to this problem will constant, and the problemofthe culated; it is in two "branches", yield only to a computer, but the altitude at which retrofire must either of which is given by Eq. (2): key lies in a relatively simple begin for there to occur a de r -r . * + £ ] where Ei is iterated process. Let the atmos- sired velocity reduction can b min , 1 • Ei cos tt phere be divided into a large num- solved quite easily by a single the eccentricity corresponding to ber of equally-spaced l a y e r s , application of Newton's laws. either v 0 or v e , as the case may each layer being only a mile or In the second case the ship be. It will be necessary to find the so thick so that density in each must be slowed a great deal- variation of altitude with si; this is Iyer is very nearly constant. As 100 feet per second, or more. r - R, i.e. vtoud+Eprmjn -R a ship traverses an individual as a reasonable estimate, Here 1 + Ejcos 0 layer its tangential velocity will the ship will have to cut loose or y(«0 » y m l n 1 ^ . £ j not change by very much; hence from its parachute and effect the nr,.,, 1+EJCOS0 the " c e n t r i f u g a l force" will remaining d e s c e n t solely on + fTE^^ Where Vministhe change little, and G of Eqs. (8) and (9) may be taken as constant for altitude at perigee. This is the ex- a given layer. Then, remember- ing that v - U + £ X R, Eqs. (6), Ten years ago we were making only a handful of relatively simple semiconductor devices for a limited number of applications. Today, with highly advanced and exotic processes, we are pro- ducing hundreds of different and sophisticated semiconductors — for thousands of applications. Our technicians can now control material composition down to the molecules with precise regu- lation of impurity levels-and on a daily production line basis. This we call PERFORMANCE. Five years ago we produced semiconductor packages the size of a pencil eraser that replaced the big glass vacuum tubes in your radio. Today we're making sophisticated semiconductors that per- form giant-sized tasks-yet fit on a soupspoon like grains of rice. We call this MINIATURIZATION. Drop the old time vacuum tube and it would smash. Its parts wore out pretty regularly too. Shake it or shock it beyond rela- tively modest limits and you were in trouble. Now you can launch a space vehicle with thousands of semiconductor components to go all the way to the moon and back . . . and make it go back around all over again. And a couple of times more after that. That's RELIABILITY. Shake 'em, shock 'em, squeeze 'em or freeze 'em-today's elec- tronic devices have got to be able to take it . . .and perform. Motorola makes them as though they're a matter of life or death. Sometimes they are. The Company's first engine, the Wasp,I* to the air on May 5, 1926. Within a jurt, Wasp set its first world record and mm v to smash existing records and setsUndi" for both land and seaplanes for , t come, carrying airframes and pilots - fanner, and faster than they had evergr before. ship in fields such as gas turbines, liquid hydrogen Take a look at the above chart; then a good long look at Pratt & Whitney Aircraft—where technical careers technology and fuel cells. offer exciting growth, continuing challenge, and lasting Should you join us, you'll be assigned early responsi- stability—where engineers and scientists are recog- bility. You'll find the spread of Pratt & Whitney Aircraft's nized as the major reason for the Company's con- programs requires virtually every technical talent. You'll tinued success. find opportunities for professional growth further en- hanced by our Corporation-financed Graduate Educa- Engineers and scientists at Pratt & Whitney Aircraft tion Program. Your degree can be a BS, MS or PhD in: are today exploring the ever-broadening avenues of MECHANICAL • AERONAUTICAL • ELECTRICAL . CHEMICAL energy conversion for every environment.. .all opening ENGINEERING • PHYSICS • CHEMISTRY • METALLURGY up new avenues of exploration in every field of aero- • CERAMICS • MATHEMATICS • ENGINEERING SCIENCE OR space,marineand industrial power application. The APPLIED MECHANICS. technical staff working on these programs, backed by For further information concerning a career with Pratt In recent years, planesPoweredbyprat Management's determination to provide the best and & Whitney Aircraft, consult your college placement & Whitney Aircraft have goneontoset most advanced facilities and scientific apparatus, has officer—or write Mr. William L. Stoner, Engineering new standards ofPerformanceinmuchthe same way as the Wasp haddoneinthe already given the Company a firm foothold in the cur- Department, Pratt & Whitney Aircraft, East Hartford, 192O's.The 727 and DC-9 are indicative of rent land, sea, air and space programs so vital to our Connecticut 06108. the new family ofshort-to-mediumrange country's future. The list of achievements amassed jetliners which are poweredbythehighest by our technical staff is a vertable list of firsts in the successful JT8D turbofan.Examplesofdevelopment of compact power plants; dating back to current military utilizationsaretheJ58 the first Wasp engine which lifted the United States powered Mach 3 YF-12Awhichrecently established four worldaviationrecordsand to a position of world leadership in aviation. These the advanced TF30-poweredF-111variable engineering and scientific achievements have enabled geometry fighter aircraft. the company to obtain its current position of leader- CONTINUED FROM PAGE 18 tion about the descent under rock- surface. Now that it has landed, rocket thrust. Drag forces will et thrust. If the parameters of it is well to look back and note be quite small, and the velocity the retrorockets are known then that this analysis is not exact, of the ship at any time after in- these equations will give the time but is only a resonable approx- itiation of retroflre will be given required for descent and the alti- imation. It is relevant to note by Hq. (10). Also, by integrating tude at which retrofire must be- that an exact analysis was worked this equation with respect to gin; if a retro system is under out by Stuhlinger about ten years time, the distance traveled at any design then these equations can ago; a key feature of his work time past the time of retro igni- be used to determine If a partic- is an exact description of the tion can be calculated. This dis- ular design will be adequate. motion of spacecraft in an at- tance is given by: Of course, there is the possi- mosphere. Our analysis is lim- y * y 0 - v ot - i/2gt 2 bility that the ship can make the ited in its accuracy by two as- + J . [t(l + ln__Mp_ ) descent entriely by parachute. sumptions, namely, that the vel- A M 0 -/»t This is the case for all Mercury ocity can be treated as dropping + Muln(M0- /*t)l and Gemini flights to date; it will off very rapidly in the vicinity also be the case for a landing on of the perigee, remaining es- n d3) Venus, which has exceptionally sentially constant elsewhere, and Moreover, the time required for dense atmosphere. Thus, a soft that the increase in velocity which the descent may be calculated landing on Venus is a great deal results from falling inward to from F.q. (10) since, for a par- easier than a soft landing on the lower altitudes, an increase pre- ticular rocket whose parameters moon, and this fact is borne out dicted by Kepler's Second Law, are known, v is a function of t by recent history: the Russians is negligible. However, in cases alone. The time required cannot had to try several times before where these assumptions are jus- be found from an explicit equa- they succeeded in a soft landing tified, our analysis can serve as tion, since it is a root of a trans- on the moon, but seem to have a first approximation. cendental equation. It can be very nearly succeeded on the first found, however, by trlal-and-er- attempt at a soft landing on Venus. ror. Thus i:qs. (10) and (13) will So it is that the ship touches provide all necessary informa- down and comes to rest on the John Lauritzen wanted further knowledge He's finding it at Western Electric when the University of Nevada awarded John Lauritzen ment for the Bell System's revolutionary electronic SB telephone switching system. his ;S.E.E. in 1961, it was only the first big step in the learning Program he envisions for himself. This led him If you set high standards for yourself, educationally to western Electric. For WE agrees that ever-increasing and professionally, let's talk. Western Electric's vast communications job as manufacturing unit of the Bell knowledge is essential to the development of its engi- System provides many opportunities for fast-moving neers-and is helping John in furthering his education. careers for electrical, mechanical and industrial engi- John attended one of Western Electric's three Grad- neers, as well as for physical science, liberal arts and uateEngineeringTrainingCenters and graduated with the business majors. Get your copy of the Western Electric honors.Now,through Company-paid Tuition Refund Career Opportunities booklet from your Placement Plan, John is working toward his Master's in Industrial management at Officer. And be sure to arrange for an interview when Brooklyn Polytechnic Institute. He is the Bell System recruiting team visits your campus. currently a planning engineer developing test equip- Twenty-five hundred dollars Ford Motor in cash awards Company is: to engineering and metallurgy students. recognition What does it take to gain recognition at Ford Motor Company? If you have skills that we can utilize, and if you're ambitious as well as able, you can move ahead fast at Ford! Consider the career of Eric Mangelsen: Eric came to work at our Ypsilanti Plant in February, 1961. During the initial stage of his training program, he was given the assignment to supervise the development, design and construction of special production calibrating and test equipment for auto- mobile voltage regulators. Later, he v assigned to processing and production of the transistor ignition amplifier system for our 1963 cars. He was responsible for introducing a new cleaning process for voltage regulator contact points, which substantially reduced costs. He was also instrumental in processing the refined transistorized regulator system used in our new 1966 automobiles. Now a member of management with broad responsibilities in a key Production Department, Eric Mangelsen has moved ahead rapidly with a company that believes in giving young men every opportunity to demonstrate their skill and ingenuity Why not investigate? Talk to our representative when he visits your campus. You can go far with Ford. Industrial News This simple device — a single wafer of quartz with two electrodes — is now performing a complex function of frequency selection which previously required eight individual electronic components. Developed by Roger A. Sykes and William D. Beaver of Bell Telephone Lab- oratories, the new device is a bandpass filter which cor be used in radio, narrow-band FM, and telephone com- munication systems. New plastic covering system for suspension-bridge cables - a joint development by Bethlehem Steel Cor- poration and E. I. du Pont de Nemours & Co., Inc. — has many advantages: speedy installation, handsome appear- ance, true watertight protection of the cables, and no maintenance. mating a unique " f i r s t " in the annals of bowling are (left to right) Ray R. Eppert, president Burroughs Car- poration; Joe Joseph, professional bowler, Manny Levy. president of the Bowling Proprietors' Association of America, and Howard C. Seehausen, executive director ot the association. Burroughs and BPAA joined forces to automate the reporting of results at the 1966 Silver Anniversary All-Star Bowling Tournament at Joe Joseph's Pro BoW| i n Lansing, Michigan, which was held January 18-30. A Burroughs B300 computer was on site to proc- ess results and to provide biographical and statistical information to the sports press on individual bowlers the entire field. Have you heard about all the opportunities for engineering and other technical graduates at Bethlehem Steel? You'll find a great deal more information in our booklet, "Careers with Bethlehem Steel and the Loop Course." You can ob- tain a copy at your Placement Office, or drop a postcard to Manager of Personnel, Bethlehem Steel Corporation, Bethlehem, Pa. 18016. An equal opportunity employer in the Plans for Progress Program ACCELERATED DEFENSE PROJECTS OPEN NEW OPPORTUNITIES FOR YOUNG ENGINEERS AT ALLISON In addition, an expanding volume of work in commercial Young graduate engineers will find broad new opportunities fields gives a solid base to these urgently needed military created by Allison's expanding capabilities in the defense area. Allison long has been recognized as a leader in design, programs. development and production of advanced aircraft power sys- Chances are, the opportunity of your choice awaits you at tems, as well as power transmissions for military tracklaying Allison. Talk to our representative when he visits your cam- vehicles.As the energy conversion division of General Motors, pus. Or, write for our brochure describing opportunities in Allison also is making significant contributions in advanced the creative environment at Allison. Send your request to: aerospace and nuclear technology. Mr. R. C. Martz, Director of Personnel, Allison Division, Now, with the assignment of responsibility to operate the General Motors Corporation, Indianapolis, Indiana. Army's Cleveland Tank-Automotive Plant, Allison is taking on a new dimension to its capability in the design, develop- ment and production of complex military weapons systems, Thus, Allison represents a versatile opportunity for en- gineers in the application of advanced technologies to aero- space propulsion systems, andarmored milltary vehicle sys- tems-including one of their components, power transmissions. ICE AND ITS PREVENTION AT THE ST. CLAIR POWER PLANT SUMMARY INTRODUCTION Experiences by the Company, and other or- Universally, industry requires a vast supply of ganizations, with icing difficulties were investi- water, and a steam generating power plant gated. One instance of ice difficulty was located is not unique in its great thirst for water. which was sufficient to show possibility of dif- Not the least of the power plant's water re- ficulties, but not frequency. Hence, it was as- quirements is for condenser cooling. For the sumed that frazil ice presented a significant problem for further consideration. new units, such as the main turbo-generator to be added at St. Clair, this need runs to Methods of ice prevention were investigated; nearly a quarter of a million gallons per minute. they consist of: As with smaller systems there arises vulnerabil- 1. Electric heating of the intake flow, ity of the operation to ice formation that could 2. Steam heating of the intake flow, seriously curtail the intake water flow and with 3. Compressed air bubbling through the intake that the efficient operation of the condenser. flow, and 4. Recirculation of warm condenser cooling The purpose of this report is to determine water from the overflow canal to the water the best method of ice prevention, provided intake at the screen house. ice formation is deemed a serious P roblem, It was found that the costs of preventing ice Four alternate schemes of ice preventionwillbe formation using steam or electric heat would be investigated. large and, within a short time, would exceed The consequences of ice formation arise from the cost of installing a recirculation system. plugging of the intake water screens due to the Furthermore, for the air bubbling scheme to be phenomenon of frazil ice formation in water effective there must be temperature stratifica- near thirty-two degrees Fahrenheit (32° F). fra- tion of the water ahead of the screens, and in- zil ice, commonly called "needle" ice, consists formation from the U.S. Army Corps of En- of minute particles of ice that nucleate about gineers indicated that there is no significant impurities and microscopic eddies in the water. temperature gradient in the St. Clair River. The particles, then grow at such a rate that Hence, air bubbling would be ineffectual. It is, they can accumulate on the screens and result t h e r e f o r e , recommended that recirculation in a substantial decrease in flow within a few be continued on the basis of its low cost, ef- minutes. 1 fectiveness, and reliability. The methods of elimination of frazil ice to To prove the absolute necessity for ice pre- be considered here are steam or electrical heat- vention, it is recommended that preventive ing of the intake flow, compressed air bubbling measures be ceased at St. Clair until either ice in the ice formation region, andrecirculationof difficulty is encountered, or sever winter con- condenser cooling water from the overflow canal ditions are experienced with no difficulty. into the intake flow (See Figure 1) At the con- elusion of the report a recommendationwillbe Richard F. Luxton, senior in electrical en- made in favor of the most advantageousandre- gineering, served as a student engineer this liable scheme, if one is necessary. past summer for the Detroit Edison Company inis article represents his findings compiled as a part of his summer work experience. If you still think glass is just glass, ask Woods Hole. Now glass can do what metals c a n - a n d more. Much more. properties at missile speeds. Be a heat exchanger in a gas tur- bine engine. Save weight without sacrificing strength. Con- AskWoodsH °le Oceanographic Institution. duct or insulate. Bend. Not bend. Break. Not break. Melt. For years, t h e O n l y w a y t 0 8 e t a s a m P l e o f t h e ocean's floor Not melt. Do whatever you want it to. It is the most versatile was to lower what they call a "bottom corer" on a wire and basic engineering material. thenlaboriouslyhaul it up again. Not any more. Now a For solutions to their problems, industry and government "Boomerang Corer"-made for Woods Hole by Benthos, Inc. are coming to Corning. Because Corning is the glass-master. -is simply tossed overboard and allowed to plunge freely. We are widely diversified, internationally based, and have When it slams into the ocean floor, it drives a sample of sedi- one of the most daring, expert and imaginative engineering mentintoahollow tube inside the corer. staffs. Plus, a marketing principle that concentrates on devel- The impact releases two glass spheres that can do what oping products only in areas where a need exists and no prod- most hollow metals can't withstand the tremendous pres- sures at the bottom of the ocean. They tug the tube loose and uct does. float it to the surface. A flashing beacon inside one of the Young engineers seeking challenge, opportunity, and ad- spheres pinpoints its location for the waiting ship. vancement are invited to write to Career- Development Man- Today glass can be made to maintain constant electrical ager, Corning Glass Works, Corning, New York. circulation scheme, no history of ice difficult! at Company plants was evidenced. One instance was indicated of a frazil Ice problem at the City of Port Huron Water Supply Station during the winter of 1962-63 for a period of a few days. This instance, though not conclusive in respect to frequency, did establish the definite possibility of occurance; therefore, it is assumed that frazil ice problems are of sufficient importance to necessitate measures for its prevention. ELECTRIC HEAT One system for prevention of frazil ice for- mation would be the installation of submerged electric heaters. In considering this scheme it was thought that the heating devices could be located at a preferred depth where frazil ice would be prone to originate due to water temperature stratifica- tion. It was found, though, that such stratifica-2 tion does not occur in the St. Clair River ; hence, it is reasonable to assume that it does not occur in the turbulent flow of the intake canal. Therefore, the entire flow must be heated for the heating system to be effective. The following calculations indicate the power requirements and expense to bring about specific temperature increments to the total intake water flow based on the assumption that complete energy transfer will occur between the heaters and the water. From the tabulation, the requirements for a five degree Fahrenheit (5° F) increase (tms value to be used for effect and cost comparison) ICE FORMATION in the intake water temperature are 161,336 To determine the extent of ice problems, kilowatts at an operating cost of $363.01 per Inquiries were made within the Company and hour. Furthermore, there is a $10,486,840 ca- directed to the U.S. Army Corps of Engineers. pacity reduction cost that would be charged to Because all power plants of The Detroit Edi- the system if it operated during a peak period son Company have been provided with the re- for the total power system. 3 Cat research and engineering led the way to better lubricants.. Nobody knew how to measure lube-affecting be evaluated. New refinements and additives variables—load, speed, temperature—in a could be developed. All industry derived working gear mechanism. Thus, there was benefit, in better lubricants, because Cater- no accurate method of correlating lubrica- pillar engineers pushed back the boundaries tion failure data with actual parts. Cat engi- of knowledge a little more. neers found a way. That's one example of what we mean by They tapped Cat's accumulated experi- new frontiers. There are many others. We ence in lubrication research. Went into Cat's need engineers—mechanical, chemical, in- knowledge of metal fatigue and scoring dustrial, metallurgical, agricultural, electri- resistance—and in the end enlarged that cal, civil, and others. To work in research, knowledge. They devised the Geared Roller development, design, manufacturing, sales, Test Machine. and many other areas. If you like challenge, This machine could duplicate the entire we need you. known and anticipated range of gear loads Contact your placement office. We'll be and speeds. Reproduce, in a controlled interviewing on your campus soon. Or write: environment, any load or sliding velocity College Recruiting, Personnel Development found in the transient conditions of actual Dept.D, Caterpillar Tractor Co., Peoria, 111. machine operation. From then on, Cat engineers could pre- dict the effectiveness of any lubricant, knew when it would fail, and why. New oils could air could be heated, but any resultant effec- would be negligible considering the energy re- STEAM HEAT quired for a substantial temperature change at An alternate system would provide the energy the flow. And, without a substantial increate in the form of available energy in throttle of temperature of the water, frazil ice would steam. continue to form. Hence, the effectiveness of The following calculations Indicate energy re- this system at the St. Clair Power Plant woulc quirements and expense based on the use of be, at best, nil. throttle steam at a cost of $0.30 per million Btu of heat supplied. RECIRCULATION For the five degree Fahrenheit (5C ) Increment to the Intake flow, the operating cost is $165.18 Recirculation, which has been standard pro- per hour for steam heating. Similarly, there is cedure for The Detroit Edison Company, con- a capacity reduction incurred for this system, sists of diverting warm water from the over- but a specific dollar value is not readily avail- flow canal to the intake at the Screen House able nor easily calculated. It would be safe to where it is allowed to mix with incoming con- say, that It would represent a multi-million denser cooling water (See Figure 1) during cold dollar Investment. water periods. By following this procedure, no Company plant has suffered an outage due to AIR BUBBLING frazil ice accumulation and consequent plugging Air bubbling consists of r e l e a s i n g com- of the screens, in which event manual ice re- pressed air from a submerged location so that moval would be required and an outage of that the air may ascend to the surface of the water. section of the circulating system would beneces- since water density Is a maximum at thirty-nine sitated. degrees Faharenbeii (39 P), the ascending bub- The thermal effectiveness of the recirculation bles will transport dense and relatively warm is indicated by table 3. water to the surface where the water is coldest. From the definition of percentage or recircula- The net effect is that surface and frazil ice is tion, "Equation (6)", nineteen percent 19% prevented from forming by increased surface recirculation would be sufficient to bring water temperature. a five degree Fahrenheit (5° F) temperature. As stated previously, though, there is no increment to the incoming water. A recent water temperature stratification in the St. Clair cost estimate of a recirculating system of 25% River and a similar condition is assumed for capacity indicates that it 6would represent an the Intake canal, Furthermore, it has been installation cost of $100,000. established from technical publications that frazil Furthermore, this sytem with minor modifica- ice forms either about foreign particles or tion would offer a simple and inexpensive al- minute eddies in the water. It can be seen, ternate outlet to the river for the overflow then, that turbulence cauaed by bubbling could canal, which would be operating at near-capacity unbalance, with an adverse effect, any equili- with the addition of Main Turbo-Generator Unit brium conditions that may exist. Of course the Number Seven at St. Clair. indeed, favorable in p e r s p e c t i v e of initial cost with no operating expense and proven reliability. In com P a r i s o n , both electric and steam heat- The one inconclusively founded p r e m i s e is ing Preclude themselves from practical con- whether ice preventive measures are neces- sideration because of their huge energy r e - sary, or not. This could be answered to satis- quirements and cost. Based on a thirty year es- faction by discontinuing recirculation where it is timated life S p a n o f a m a i n turbo-generator now being used and allowing the operation of plant, 200 h ° U r S p e r y e a r o f ° P e r a t i o n , a n d a the plant to continue without recirculation. The five degree t e m P e r a t u r e increment to the water, instant availability of recirculation would serve the cost for these"two systems would be: as a "back up" in case of icing difficulties, but, 1 Electric - $2,178,060, and if no difficulties were encountered, ice preven- tion measures could be totally discontinued at 2. Steam $ 9 9 1 . 0 7 0 , that and similar locations. Of course, it must compared to $100,000 i n i t i a l i n v e s t m e n t , only, be remembered that such operation should be for circulation. proven through both sever and mild winter Air bubbling, by its t h e o r y of o p e r a t i o n and conditions to be conclusive. In the case of the the lack of conditions that would m a k e it effec- Main Turbo-Generator Unit Number Seven at tive, is rendered ineffectual at t h e St. C l a i r the St. Clair Power Plant, it would be advisable Power Plant. T h e r e f o r e , t h e final a l t e r n a t i v e to provide for ready availablility of recirculation of recirculation is open f o r a p p r o v a l and it i s , because of the few test seasons available before the 1968 operational date. casting also helps to make parts stronger Metal components tolerate loads better if they are designed to distribute stresses efficiently. Sharp corners or other abrupt sectional changes tend to restrict ft uniform distribution of these stresses The corner thus becomes a logical site of fatigue failure. In a casting, it is a sirr pie matter to round out corners, blen sections and taper connecting member to achieve a design which will distribute stresses. The illustration shows how stresses Casting is the simplest and most direct u p " at sharp corners. A much smoother would be prohibitively expensive to pro- transfer of stresses was achieved when wayofcreatingform and shape with metal. Casting offers almost unlimited freedom duce by any method other than casting. this part was switched to a Malleable to the designer. A cast design is not re- By using the casting process for economy, casting (shown on the right). stricted by sizes or shapes of mill stock, accessibility of tools, withdrawal allow- ances for dies, or other limitations. Complex shapes, interior cavities, and streamlined contours, which would be difficult or impossible to create with other methods, are simple with a casting. and Malleable iron for strength and ducti- For instance, consider the complexity lity, these clamps combine service and of creating the dozens of teeth, lugs, holes value. and collars on this pipe repair clamp. It The design freedom made possible by If you're looking for a career of exciting growth and accomplishment, you're also looking for a company with the same qualities. Here at LTV Aerospace Corporation, LTV Michigan Division, young engineers and the company are growing in the fields of missiles, mobile surface vehicles, weapons systems and many others. Assignments are diversified, too. They include such areas as: Structures Dynamics • Structures Stress Analysis • Aeroballistics • Guidance & Control • Electronic Systems • Propulsion • Product Design • Project Planning • Industrial Engineer- ing • and others. For complete information about a career with LTV, consult your Placement Office or write College Relations Office, LTV Michigan Divi- sion, P. 0. Box 404, Warren, Michigan 48090. LTV Michigan is a divi- sion of LTV Aerospace Corporation and is an equal opportunity employer. You might be able to avoid To quote an old-time Quaker, Crossing Grand River Avenue usual winter colds if you would "Everyone is queer except me one morning, I was mearly run avoid fatigue, loss of sleep and and thee, and even thee's a lit- down by an antiquated car lit- overcreating. tle queer." erally overflowing with about a dozen children. Since the red light has been a g a i n s t the woman d r i v e r , as she came to a halt I shouted: "Lady, don't you know when to s t o p ? " Headline of an ad in a New The engineer and his new bride Glancing back at the (mop- York bus: "For a successful were anxious not to be recog- nized as newlyweds, so the bride pets, she answered icily: ' They affair, it's the Empire Hotel." . a r e n ' t all m i n e . " removed her corsage and they both shook off the last bits a rice before entering the hotel. Then, sure that no one would ever suspect that they had just been married that afternoon, the en- gineer walked up to the desk One of the boys in the Mech. and said with studied casualness: A c a r came to a stop in the Engineering Dept. has invented "I'd like a double bed with room, what he calls the "Square Dance middle of East Lansing, and flu please." d r i v e r asked a student on W Bra"-it stays up beautifully no matter how frantic the fiddling curb, "Say w h e r e ' s MAC Av- gets. enue?" . . " I ' m a pedestrian," the studen: replied. " I don't help automo- The State Theatre is having biles." a special double feature this Definition of ecstacy-A feeling term: "In the French Style" when you feel you are going to feel & "The Fighting 69th". a feeling you have never felt before. "Daughter," said the mother, "didn't I tell you not to let s t r a n g e men come into your apartment? You know things like that worry me." "Don't be ridiculous, Mother!" laughed the girl. "I went to his apartment this time. Now, let his mother worry!" Advertiser Page Advertiser page ALLISON 29 K0DAK Inside Back Cover BETHLEHEM STEEL 28 LIND DIVISION of UNION CARBIDE 9 CATERPILLAR .33 LING-TEMCO-VOUGHT 37 CELANESE . U MALLEABLE FOUNDERS 36 CORNING . .".31 MOTOROLA 19 DELCO 40 PRATT & WHITNEY 20 & 21 DOUGLAS AIRCRAFT .' 4 SYLVANIA ! DUPONT " 15 TIMKEN 11 FORD ' *24 U. S, AIR FORCE 7 FORGING INDUSTRY ASSOCIATION . . . . . 25 U. S. RUBBER 27 GENERAL ELECTRIC Back Cover WESTERN ELECTRIC 23 IBM 5 WESTINGHOUSE Inside Front Cover INTERNATIONAL HARVESTER . . . . . . . . 17 XEROX 2 . . . is a basic management philosophy at Delco Radio employes through the popular Tuition Refund Program. Division, General Motors Corporation. Since its in- College graduates will find exciting and challenging Ceptioo in 1936, Delco Radio has continually expanded programs in the development of germanium and silicon and improved its managerial skills, research facilities, devices, ferrites, solid state diffusion, creative packag- and scientific and engineering team. ing of semiconductor products, development of labora- At Delco Radio, the college graduate is encouraged tory equipment, reliability techniques, and applications to maintain and broaden his knowledge and skills and manufacturing engineering. through continued education. Toward this purpose, If your interests and qualifications lie in any of these Delco maintains a Tuition Refund Program. Designed areas, you're invited to write for our brochure detailing to fit the individual, the plan makes it possible for an eligible employee to be reimbursed for tuition costs of the opportunities to share in forging the future of spare time courses studied at the university or college electronics with this outstanding Delco-GM team- level. Both Indiana University and Purdue University Watch for Delco interview dates on your campus,or offer educational programs in Kokomo. In-plant gradu- write to Mr. C. D. Longshore, Dept. 135A, Delc0 ate training programs are maintained through the off- Radio Division, General Motors Corporation, Kokom°, campus facilities of Purdue University and available to Indiana. An equal opportunity employer The box below permits a chemical engineer, just for kicks, to test himself for possible interest in our kind of problems. Bright M.E.s, E.E.s, and other engi- neers will pick up enough of the general idea to transpose the test to their own fields of competence. The next step would be to drop us a line about yourself and your ambitions. If mutuality of interest develops and if the mundane matter of compensation should come up, we feel that now and far into the foreseeable future we can afford the best. EASTMAN KODAK COMPANY, Business and Technical Personnel Dept. Rochester, N.Y. 14650 An equal-opportunity employer offering a choice of three communities: Rochester, N. Y., Kingsport, Tenn., and Longview, Tex. When the North American Aviation XB-70 established a mile- in jet power since the beginning of propellerless flight has stone by achieving Mach 3 flight, it was powered by six made us one of the world's leading suppliers of these prime General Electric J93 jet engines. That flight was the high movers. This is typical of the fast-paced technical challenge point of two decades of G-E leadership in jet power that you'll find in any of G.E.'s 120 decentralized product opera- began when America's first jet plane was flown in 1942. In tions. To define your career interest at General Electric addition to the 30,000-pound thrust J93's, the XB-70 carries a talk with your placement officer, or write us now. Section unique, 240-kva electrical system that supplies all on-board 699-16, Schenectady, N.Y. 12305. An Equal Opportunity Em- power needs—designed by G-E engineers. The challenge of ployer. advanced flight propulsion promises even more opportunity at G.E. GETF39 engines will help the new USAF C-5A fly more payload than any other aircraft in the world; the Mach 3 GE4J5 is designed to deliver 50,000-pound thrust for a U.S. Supersonic Transport (SST). General Electric's involvement