"One of the really nice features of underwater testing of models is that the water ordinarily is quiet and free of turbulence. For this reason glides made underwater are truly a measure of the performance of the model. The method measurements is quite simple. Take two marks about 36 inches apart on the bottom of the tub, either with a wax pencil or some adhesive tape. Then release the model from a point in the water above the first mark so that it slides to the bottom at the second mark. The glide ratio is easy to calculate: it is 36 divided by the altitude in inches at which the model is released. Quite consistent results can be obtained if you take a little care to launch at the correct glide and with the model's normal flight speed. Enterprising modelers may wish to time the flight speed with a stop \watch. From this speed and the wing loading, engineers are able to compute the lift coefficient. Using the lift coefficient and the glide ratio, it is possible to compute the drag coefficient.

"You can even hold flight competitions in the bathtub. The authors had such a competition, using 10-cellt models of a P-40 and a Spitfire. The object was to see who could get the better glide angle out of his model by cleaning it up. The hollow fuselages were filled with wax, the props filed off, the spinners smoothed with sandpaper, the landing gear removed, all sharp corners rounded and rough edges filed down. The canopy was filled flush with wax and the under camber of the wing also filled with wax (modeling clay may be used instead. When all this was done, the glide ratio was improved from two to one to three to one–a 50 per cent gain. The Spitfire won the competition with a glide ratio of 3 to 1.

"The same process of drag reduction can be applied to the larger plastic models. Propeller-driven models should have the propeller blades removed and the spinner filed smooth. All joints should be smooth and the leading edges nicely rounded. Embossed insignia should be filed off or sanded smooth.

"Another really fascinating and instructive experiment is to make the flow of water around the model visible. In a wind tunnel this is done by injecting smoke into the tunnel. In the bathtub you merely attach a small crystal of potassium permanganate to the model with soft soap. As the model flies, the permanganate dissolves, leaving a clearly visible trail of purple. If you place the crystal of permanganate on the very end of the wing tip you will see the trail curl up into the tip vortex [see drawing at the top of illustration above left]. If you launch the model so that it will stall, you will note the first indication of loss of lift in the weakening of the tip vortex. When the model recovers from the stall, the tip vortex again rotates strongly. The lift is directly proportional to the strength of the tip vortex.

"Place a crystal of permanganate in the wing root on the top side at the leading edge. Now fly it under water, preferably with the water a little warm in order to get a more dense purple color in the flow line. You will notice that as the model approaches a stall the flow line separates from the surface of the model [drawing at lower left in illustration above]. The lift in a region which has a separated flow is very much weaker than when the flow is attached. On large models in wind tunnels or in full-scale flight tests, the regions of separated flow are commonly indicated by tufts of wool attached in the right places.

"You can see what happens when a plane approaches a stall by placing a crystal in the middle of the wing on the upper side. In the stall the flow there is inward toward the fuselage. This shows that the pressures on a stalled wing are lower on the root than toward the tip.

"You can also observe the effect of surface disturbances on the flow around a wing. If you place a wire on the upper surface of the wing, lying spanwise near the 25 per cent point of the chord, you will see an early separation. If you put the wire on only one wing, you will force the model into a spin, for the wing with the wire will lose lift earlier than the other. The wire acts as a lift spoiler. A wire placed ahead of the wing will make the flow over the wing turbulent. The flow line will spread like a diffuse jet. But you will notice that the flow does not separate as early as it does on a plain wing, A turbulent boundary layer does not separate as soon as a laminar one does.

"In these days of high technology even in modeling, one must know something about the regime in which his flight tests are taking place. One thing you want to know is the Reynolds number, which is a measure of the boundary-layer flow around the plane at a given speed. At a Reynolds number of about 60,000 (in the air) most model airplanes perform poorly because of the increase in drag. If your model flies slightly below this number, you can improve its performance by adding a wire or by roughening the leading edge to increase turbulence.

"In the air the Reynolds number is the speed in miles per hour times the chord in feet times 10,000. In water the Reynolds number is found by multiplying the speed in miles per hour by the chord in feet by 150,000; that is, the number is 15 times higher in water than in air. But of course the models fly much more slowly under water than in the air.

"You can easily compute the Mach number of their underwater flight. The Mach number is simply the ratio of the speed of the flight to the speed of sound in the medium. In water the speed of sound is 5,000 feet per second. Thus when your model flies at one foot per second (e.g., the Grumann F9F), the Mach number is 1/5000. You do not have to worry about the sound barrier or shock effects!

"Although motorless flight is fascinating enough, you will want before long to try some propulsion on your water model. You can easily equip the plastic P-51 with a suitable motor: Install a small thrust bearing on the spinner, drill the prop spinner for a prop hook of piano wire, thread a double strand of 1/8-inch rubber through the fuselage and hook it to the rear with a wire clip. Now wind up your motor and release the model– preferably from the bottom of a swimming pool. You will get a nice flight, in some cases even reaching the 'ceiling' (pool surface) from a depth of six feet. Don't be surprised if the model pops to the surface, but if by any chance the model should take off into the air, let us know!

"For jet propulsion of a jet model, place a few pieces of dry ice inside the jet, seal the jet intakes with scotch tape, fill the fuselage with water and then launch the model. The carbon dioxide gas evaporated from the dry ice emerges under pressure from the jet exhaust and thus gives propulsion.

"The authors wish you many pleasant and interesting evenings with bathtub aerodynamics. Archimedes long ago made a famous discovery in a bathtub. You may not make any great discoveries, but you will learn some aerodynamic fundamentals and find a lot of entertainment–which has proved challenging enough to interest a number of scientists, professional and amateur. Perhaps you will even invent some new variations on these fascinating experiments."

AMONG the thousands of amateur telescope makers, some are mechanics by vocation as well as by avocation. Michael Spacek, Jr., of Royersford, Pa., whose telescope is illustrated in the drawing on the opposite page, is a toolmaker. He enjoys the great advantage of access to shop equipment which is not available to the average amateur.

Spacek's telescope rests on a pier made of heavy angle iron welded into a rigid unit and covered with tempered Masonite. The polar axis is sloped parallel to the earth's axis in the latitude of Tampa, Fla., where the telescope is used by Malcolm Maner. It is made of solid shafting 1~ inches thick, and turns on roller bearings of the needle type. The declination axis has the same diameter and bearings, plus a thrust bearing. It turns in a cast-iron housing 3~ inches in diameter. The housing was line-bored on a large lathe to obtain alignment.

The drive is basically the same as the friction-disk drive described in Amateur Telescope Making–Advanced, page 311. A roller on the shaft of a 1/60 horsepower Bodine synchronous motor drives a leather-faced disk by friction. A "rate adjustment" knob on the side of the pier adjusts the motor shaft axially to select the correct ratio for the change from the standard time of the synchronous motor to the desired sidereal time, or to the rate for the moon or a planet, or for guiding the telescope. This type of drive avoids the use of gears.

The time-indicating device is a separate electrical unit consisting of two selsyn motors on a single circuit. The first shown in the illustration on the next page, is driven from the polar axis by a rubber belt and two accurately matched V pulleys. The second, or slave, selsyn is inside the pier and has on its shaft a dial pointer which extends through the pier wall to the sidereal time dial. This is calibrated by hours–1 to 24. Whenever the master motor is moved, the slave motor precisely imitates its movements. whether large or small, quick or gradual.

A third electrical unit, separate from the others, is the magnetic clutch, which is leveled to the polar axis shaft by a spline and can move only!, endwise. This may be clamped to the steel disk on the worm gear by closing or opening a switch. It is powered by direct current of four amperes at six to eight volts from a selenium rectifier battery charger. The magnet has several hundred turns of No. 22 insulated wire. The energy of a single flashlight cell magnetizes it so powerfully that it cannot be pulled away from the disk. The clock drive in the pier rotates the worm gear on the polar axis by a vertical shaft. When the observer closes the control switch energizing the magnet, the drive rotates the polar axis shaft also, and the telescope starts tracking.

The telescope tube is made of seamless aluminum tubing with an inside diameter of 6-1/4 inches and a 1/8-inch wall. The objective was made by Stanley Brower of the Laboratory Optical Co., Plainfield, N.J. Spacek says it performs excellently. He found, however, that the leather-covered friction disk on the drive did not work well. Whenever the telescope lay idle for several days, this disk became indented by the drive pulley and the drive bumped badly. Means had to be provided to relieve the pressure from the leather during such periods.

Spacek made all the patterns and did all the machining. He has also built a coating equipment. He is building a new telescope which will have a 10-inch Zeiss objective on the mounting just described.

After studying the telescope for his illustrations, Roger Hayward commented: "The Spacek telescope is noteworthy. The clamps are ingenious, the selsyn timepiece is plushy. But the right-ascension slow motion, independent of the drive, might be bothersome. Having set the instrument on an object, you have to unclamp the slow motion and then clamp the drive, unless you let the clock push it through the slip ring." Spacek replied: "By adjusting the current fed into the magnetic clutch the tube can be moved, and slow motion in right ascension may be operated, without unclamping it and without gear damage. However, Hayward's idea is better."

Hayward and others have urged the use on telescopes of needle bearings, made by the Torrington Manufacturing Company in Connecticut. Spacek's were manufactured by the Roller Bearing Company of America, Trenton, N.J. He says: "I chose needle bearings because they are compact, rugged and will carry a heavy load. With them you can use a heavier shaft in the same or a smaller telescope axis housing."

IN THE December issue of the Journal of the Optical Society of America P. R. Yoder, Jr., F. B. Patrick and A. E. Gee of the Frankford Arsenal made public the results of an investigation of the new Dall-Kirkham spherical secondary Cassegrainian telescope. This instrument has almost wholly supplanted the classical form of Cassegrainian among amateurs who build compound telescopes (chiefly because of their high magnification) for planetary observation. By trigonometric ray tracing, the most exact method, the investigators found that the off-axis images in the new telescope are appreciably poorer than those given by the classical Cassegrainian. For example, an f/11 true Cassegrainian of 130-inch effective focal length gives excellent images over a field of about 1.7 degrees, while a telescope of the modified type with the same optical dimensions has less than one fourth as wide a field.

Amateur astronomers are anxiously inquiring whether this news spells the doom of the Dall-Kirkham form, which is much easier to make than the old form. The question was submitted to the investigator Gee, who is a professional optical worker but retains the amateur's point of view. He replied:

"The increased coma in the Dall-Kirkham form of the Cassegrainian telescope has little significance for the average amateur. Unless the telescope is to be used for direct photography of star fields at the secondary focal point (a rare case for the amateur), the coma is usually within acceptable limits. R. T. Jones of Palo Alto, Calif., reports in a paper not yet published that the increase in coma in the Dall-Kirkham form is dependent (among other things) upon the magnification of the secondary mirror. The coma worsens in proportion to the increase in secondary magnification.

"To illustrate, the f/11 telescope of 130-inch effective focal length used as an example in the paper by Yoder, Patrick and myself had a secondary magnification of approximately three times. Its coma was approximatelv four times as bad as would have been the case for a classical Cassegrainian, although still within acceptable limits. Had the secondary magnification been four times, while still retaining the 130-inch effective focal length at f/11, the coma would have been six times as bad as in the classical form. This merely indicates that trouble from coma may be expected in severe forms of the Dall-Kirkham Cassegrainian; that is, those with very fast primaries. high-magnification secondaries and fast over-all systems.

"Coma varies inversely as the square of f ratio in either form of the Cassegrainian. Consequently the slower the over-all system, the less the coma. For example, if our 11.8-inch telescope had a secondary giving, 177-inch effective focal length (f/l5) instead of 130-inch (f/11), its coma in the classical form would be reduced by a factor of approximately two. In this case (assuming the same f ratio primary), the secondary would magnify approximately four times. As pointed out above, this would mean that the Dall-Kirkham form would have approximatelv six times the coma of the classical form, rather than the four times it had at f/11. However, the coma in the classical form was improved by a factor of two, while increasing the magnification due to the secondary only worsened the proportional coma by 6/4, or 1-1/2. Thus our f/15 Dall-Kirkham telescope of practically the same physical dimensions as the f/11 has about 30 per cent improvement in coma.

"To sum up, an amateur need not worry about increased coma in the Dall-Kirkham Cassegrainian if he designs telescopes of conventional dimensions. (A secondary magnification of three to four times and an effective f ratio of f/10 or less are considered conventional.) Secondary magnifications can be increased if the f ratio of the system is made slower. Stick to primary mirrors of f/4 or slower and I promise you won't be bothered by the coma."

A NEW 93-page illustrated book titled Astrophotographe D'Amateur, by Jean Texereau of the Paris Observatory and Gérard de Vaucouleurs of the Astrophysical Institute, covers compactly the testing of camera lenses and the building, mounting and use of short-, medium- and long-focus lenses. It is available for 800 francs (approximately $2.32) from La Revue D'Optique Théorique et Instrumentale, 165 rue de Sèvres, Paris 15, France.

Bibliography

AERODYNAMICS FOR MODEL AIRCRAFT. Avrum Zier. Dodd, Mead and Company, 1942.

EXPERIMENTS WITH AIRPLANE INSTRUMENTS. Nelson F. Beeler and Franklyn M. Branley. Thomas Y. Crowell Co., 1953.

AMATEUR TELESCOPE MAKING. Edited by Albert G. Ingalls. Scientific American, Inc., 1952.

AMATEUR TELESCOPE MAKING – ADVANCED. Edited by Albert G. Ingalls. Scientific American, Inc., 1952.

AMATEUR TELESCOPE MAKING–BOOK THREE Edited by Albert G. lngalls. Scientific American, Inc., 1953.

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