Never thought of that! Sure, just move the Battery back beneath the Bellcrank where the CG is located!
Damn! Just tried that and now the CG isn't at the BC mount anymore. Is that OK? Should I fly it anyway? Will it fly better now? What'd I do wrong?
Ted
Nah just add 10 ounces to the belly.
According to the Netizban writings the bell crank should be behind the CG anyway. But is dont matter as everyone has said in the past anyway.
Control-Line Aerodynamics Made Painless
By Bill Netzeband
Originally published in 'American Modeler', July/August 1966.
Crewcut Bill goes long-hair! And he has conspirators, many of the nation's leading designers.
Line rake angle is an all-important factor, they agree.
-----oooOooo-----
Since the beginning of control-line models, back in the 40's, the design phase, viewed from published information, has been a "black art" relying on phases of the moon, superstition, etc. "Designers" appeared to ignore, or misunderstand, the unique effects of flying in circles tied to a pilot in the center.
We were told to balance the model on front leadout; or balance it on the belicrank pivot; or to balance one thumb-print forward of the main spar, or any other such nonsense that popped into a designer's head. All we really knew was that his model balanced there and he liked it! Always they were half right - and half wrong.
Actually, we lived by the "Flea Fright" practice of adjusting each ship to tailor out the kinks, ii it survived the first flight! Ultimately, we were subjected to a lot of marginal designs (mine, too) flown by talented pilots who took it upon themselves to explain phenomena they didn't understand. Luckily, we do not wipe out pilots during crashes.
Back in 1951 I started serious investigation into miniature aerodynamics. It is simply a matter of applying classic aerodynamics to our size whenever we could. The principles, happily enough, apply directly; the problems are in the constants. Guess and test methods were used to back-up mathematical correction of lift, drag and lnertia factors, finally coming up with "numbers" useful to our size airplanes. One slight point irks me. Only a scale model of a man-carrying airplane qualifies for the name "model." If we design an airplane for a specific performance criterion, then it's an airplane, no matter how small!
In future issue we'll present a generous portion of concentrated CL aerodynamics; concentrated meaning, any mathematical procedure will be explained in English and useful equations will be reduced to simple nomographs We will be shooting for those of you Interested in knowing Why and How, but who have not elected to follow a career in engineering or science. We assume that Math and Aero majors will be reading very critically looking for mistakes!
Basic Physical Facts: This installment covers a phenomenon not recognized in any other branch of science, at least not in books I've been able to read. So we had to develop our solution. We tie our airplane to a handle, pick up that handle and stand there while the airplane zooms around us. The physical reactions caused by moving a body (object) in a hemispherical plane, supported by thin flexible lines; with motive power applied at the object, are unique to CL airplanes.
Roger Wudman with his Invader, one of several aerobatic aircraft used to check out calculations.
Weighs 60 ozs., Mccoy .40, 600 squares, 48 mph.
Flying above the handle introduces forces not covered in classic aerodynamic work, and the effects of the lines themselves are interesting. Our phenomenon is the curve that appears in the lines: How do we measure it accurately, its effect on the airplane, and what do we do in the design of the airplane to achieve the best performance? Where should the line-guide be located?
Since Isaac Newton discovered that an object pulled by a force tends to move in a straight line, we must apply another force to make that object move in a circle. This is called Centripetal Force, which you apply at the handle. There then exists an equal and opposite force to balance it called Centrifugal Force. (EQ 1) These two keep the circle round because, if imbalanced, like a broken line, the object heads back toward its straight line. The amount of centripetal force is determined by the weight of the airplane, the angular rate at which it moves around the circle, and the length of the lines. For our purposes we convert angular velocity to tangential velocity and call this the airplane speed (V) generally in miles per hour (mph).
By convention, we make lines to a length which will give standard distance from handle to airplane centerline. The center of gravity (CG) of the airplane is very close to centerline, so we now state that airplane speed (V) is that of CG. To simplify matters let's assume the Thrust of the prop passes through the CG. This done we could throw away the airplane and use a dimensionless lump, same weight, at the CG. If it were possible to mount the bellcrank pivot exactly on the CG and the load of each line didn't change (it does) we could fly without a line guide.
Since precise location is not practical, we add some form of line support between the belicrank and the handle. After adding the line-guide one problem is solved, another created. For years we were fooled into believing that the position of the bellcrank in the airplane controlled its attitude. Not so. The beilcrank can be almost anywhere in the airplane.
A simple cardboard outline of an airplane will show this relation (photograph in continued portion) (See note). Place an eye (U-shaped bent pin) in one wing tip and tie a pin on the end of a thread. Run the thread through the eye and stick a pin anywhere in the cardboard. Observe how the thing hangs and then move the pin (string end) to some other location. Right! Anywhere you stick that pin the airplane hangs the same. Now move the eye (line-guide). The airplane assumes some new position. The CO of the airplane will line up with the linc-guide. (Note: It would be nice to mount the bellcrank on a line between the CG and the line-guide, because the control lines could lead straight through the line-guide, therefore operating with the least stiffness.)
Crux of the matter. Behind the charts stands years of flight testing.
We must qualify the above facts by stating that the line must be very flexible compared to the weight of the airplane. A perfectly flexible wire can carry no side load without bending. Misplaced bellcrank side load is reacted inside the airplane, not appear as an aerodynamic force. Notice that this effect is factual for the fore-and-aft. and also the vertical position of. the CG. Were you to use say 1/16-in. diameter leadouts on a ½ A ship, running them beyond the line guide 4 or 5% of the total line length, and then placing the belicrank at a kooky position, you have established an exception. All practical cases so far.
The next problem is line ahape. Closest parallel in engineering mechanics is the Catenary, a curved line between two points similar to a slack flexible oord hanging between two poles. This cord is assumed to be carrying only its own weight (uniformly distributed load) and it hangs in a mathematically predictable shape. The point of maximum deflection from a straight line between the support points is in the exact center of the wire. The deflection is inversely proportional to the tension in the line (more tension, smaller deflection), and directly proportional to the weight of the lines. You can demonstrate this one with a piece of control line, so we'll not describe the experiment. It will prove that in horizontal flight your lines will droop from gravity causing a slight vertical angle leading into the airplane CG. For most airplanes "going around flat and fast" this angle is too small to measure.
To determine line shape in the horizontal plane (top view), we resort to forces shown in Fig. 1. Here the load on the line is not uniformly distributed. load is caused by aerodynamic drag which is proportional to a constant times velocity squared. The velocity of the wire is assumed to be zero at the handle end (as in a pylon) and increases directly proportional to the distance away from the handle finally reaching airplane speed (V). Therefore, each little piece of line travels at a different velocity. This dictates the process of mathematical summation to find line drag. (More later.) To move this force system we apply thrust (T) to the CG. T being just enough to carry the effective line drag (DL). To establish equilibrium in the system we need a thrust at the handle (TH). Surprised? Fact is, without a pylon, whipping is a way of life (Say it isn't so!- Ed.) At a later time we'll show how to whip best. But back to the lines.
It is conventional in vector analysis to resolve a vector (a force with a definite magnitude and direction) into two vectors 90 degrees apart, or vice vesa. Thus, vector force FA (line tension) is the combined result of T and CF. It has an angular relationship to both, but we're interested in its angular relation to the line of action for CF. This is (&omega) Eq. 2. Likewise angle (&beta) Eq. 3 is related to FH, TH and Centripetal Force (not shown). Once we know (&omega) we know where to place the line guide! The development of an exact equation for (&omega) was a laborious chore, We'll not cover every detail, but a brief history should be enlightening.
Math Solution Development: Progress started in response to my published force diagram inside the airplane during the March/April 1963 CLC column in this magazine. Basically, it referred a portion of the line drag (DL) equal to (T) applied to the line-guide. This may not be 100% valid, since the lines slide through holes, but wear on the back of such holes proves some force exists. Right or wrong, we then searched out a coupling force to keep the airplane from turning into the circle. The reacting couple turned out to be CF and Centripetal force if the CG were moved forward in space to develop an arm between them. The resultant angle turned out to be exactly the amount as (&omega) from the last paragraph.
When the bellcrank center is exactly on the CG, and if thrust is exactly through the CG the force at the line guide will disappear, if (&omega) is correct. It should be reemphasined that bellcrank pivot should be close to the CG, to reduce the bending at the line-guide which can cause stiff controls. At the time we didn't have a reliable drag coefficient for the lines, so progress ceased. Receipt of math from Rex Powell and Charles Kiabunde provided an equation for line shape and angles (&omega) and (&beta) Eq. 4. They had some trouble agreeing on drag coefficient (Cd), otherwise complete agreement existed. Their work disclosed that with proper manipulation and substitution (&omega) was indeed proportional to the ratio of DL to CF. Also they proved the centroid of line drag was at a point three-quarters of the distance out from the handle. Thus airplane thrust is three times handle thrust. It was further shown that since both DL and CF are proportional to V squared, the system angles should be independent of velocity. This turns up frequently in our aerodynamics and, when estimating, we take advantage of it. However, Mom Nature wasn't so kind as all that there. (Figures - Ed.) Enter the villain in this piece, Mr. Reynold's marvelous number.
Osborne Reynolds was first to discover, understand and define the effects of object size, shape, speed of flow and viscosity of medium. Crudely put, he found that if two objects have the same shape but different size they will not have the same drag coefficient (or lift coefficient), unless speeds of flow and viscosity are varied to make their Reynolds numbers equal. (Eq. 5) is a simplified version of this with the viscosity held constant for air under NACA standard conditions of pressure and temperature.
When this is done, R becomes proportional to V and "some dimension defining length in the direction of flow." This dimension in our case is (d) the dia. of our lines in inches. Our lines are the same diameter from handle to airplane, the same shape, and air viscosity is constant, but (V) varies. So we can't completely ignore velocity because Cd does not remain constant from handle to airplane.
Reverting to experimental data, by old timers, it was found that, over our range of interest in R, Cd wandered from 2.4 or higher , to around 0.98. Three ditferent people ran experiments that appeared to agree well enough to believe. Unfortunately, the variation wouldn't nicely convert to an equation so we could plug it in. We were held for the moment to saying "Let's use CD = 1." This gave a fairly reasonable number considering we were looking at thin, dirty, vibrating lines. But there was more to come.
Ed Fort sent along a complete line drag equation using an approximate equation for Cd as estimated by F Eisner (Eq. 6). By substituting for R in terms of V and d, and solving a definite integral he allowed as how total line drag was per Eq. 7. One glitch in this Cd, it continued decreasing where experimental data proved an increase occured. This would cause error in large lines and high-speed airplanes like C-speed ships. But it was the best yet.
We made a nomograph of this one, congratulating ourselves and all concerned. Meanwhile Pete Soule confirmed Rex's and Charles' work tying in nicely with my stuff and picking Cd = 1. (We were going to publish the results but job changes, flres etc. short-stopped that.) We tried it out on several models with reasonable experimental results. (It was close!)
Pete Soule showed up one evening with a solution giving "effective line drag" based on thrust horsepower used to pull a portion of the lines (Eq.
. He had also resolved the Cd problem by finding an "effective drag coefficient" based upon the Reynolds number of a line traveling at airplane speed. This bit involved complex curve fitting by Gaussian Quadrature (Who he?- Ed.), and I'll leave it lying right there. The validity is unquestionable so we constructed the final nomographs which appear here: You think that part was tough? Those are the answers. You should have been around for the questlons!
Two other gentlemen got in hot licks. Piper Mason went at the problem with a jet model and careful observations, outlining a good test method. Bob Ormiston's observations pretty well concurred with what we finally got. What did we get, you ask?
We Got Results:
1. An angle between the CG and the line-guide which if built into an airplane will fly that airplane squarely tangent to the circle; theoretically providing least drag, most thrust and good line tension.
2. If you don't want to fly squarely tangent to the circle, you can correctly bias the angle to suit your whim. No Guesswork when yawing in or out.
3. An exact method of determining the line drag the engine has to move. This will lead down the musty corridors to finding airplane drag coefficients, measuring the effect of streamlining, engine hop-up, prop thrust etc. We still need 1% accurate engine Bhp characteristics and any kind of propeller thrust data.
4. A basis for evaluating the best techniques for "whipping."
And we finally opened a door that was closed.
Practical Considerations: For about two years we subjected the calculated results to flight testing. Speed work by Roger Theobald, TR by Pete Soule, Rat and TR by John Barr. Stunt by Roger Wildman and "lil ole linemaker me" dashing around with Combat, Carrier and 1/2A - bugging all concerned. Each time we carefully adjusted speed and CG-to-line-guide relation to airplane weight we confirmed the accuracy of the calculations.
Just to keep it from being too simple we got "wind." Real briefly; wind, when headed directly into, causes an additional line-drag load, this one uniform (like catenary) se TH and T to balance it are equal. It can be troublesome since V is not increased and is sometimes decreased which means &omega will get larger. Upwind the nose pulls in. Downwind the effect is opposite. Jolly old experience (the resuits of poor judgment) shows us the 1/2A through .15 sport airplanes and all stunt types need increased line rake for breezy flying. Reasoning process, backed by flight work, says for large Cd, like with slow velocities and small lines, the build up of drag is more drastic. Also, slow basic speeds (around 50 mph) mean a 30-mph wind is over 50% of the base speed. So we simply provide these airplanes with extra holes in the line guide to increase rake in. 1.5 degree, intervals.
If your 1/2A is stuck with one leadout location add 15 mph when calculating DL. This about covers a 30-mph wind condition. A stunt ship should be ilown with rake as close to ideal as possible to hold down lateral glitching on tight(?) corners. Half-A's generally are marginal on basic line tension, so we must guarantee that they'll stay under controL Speed jobs are still subject to more testing, but don't bother correcting for wind. Cornbat, Rat and TR ships have worked out best with ideal calculated' angles. Carrier ships are calculated at 40 mph speed to cover the speed range accurately.
Look over Table I for some extreme values in any category. Lines used are either required by rules or "most used"' size. Weights are a little "outside" both directions. Final numbers pretty well box in each category. Numbers are "straight", no adjustment for wind.
How about engine ofiset and rudder? The facts vary widely so that each case is a new game. The CF-DL force is much larger than the combined forces of any normal engine offset or normal rudder area. Again Stunt and 1/2A sport must be evaluated each to its own. If you build-in the right &omega, bad judgment on engine offset and rudder area won't hurt much. Incidentally, the side force from engine offset isn't what we look for, unless you put in 10 degrees or more. We examine the thrust line's distance inboard of the CG (it had better be inboard) to evaluate its turning moment to keep the nose headed properly under all weird conditions.
If you want to tell me about that extreme case that shoots all this down, be very certain you send all of the facts! There are no mysteries; only a lack of complete knowledge.
We have not deliberately ignored the Scale buffs. Your problems are always very special and we recommend that you play the game straight. It was convenient to end the weight scale on Nomograph 4 at 100 ounces, but if you have something heavier, divide the weight by 2, perform the calculation and double the CF.
Nomographs and Procedures: The nomograph is a handy tool, similar in operation to a slide rule, in that logarithms of numbers are added or subtracted geometrically to perform multiplication or division. The two dimensional layout essentially. operates on the principle of similar triangles allowing answer or pivot line's location to automatically include constant factors. Each nomograph is designed to solve a specific equation, making it ideal for often-used calculations. The only other tools necessary are a straight edge, preferably clear plastic (and very straight) and a thin sharp pointed instrument (like a pencil). Throughout the Projected series we will provide nomographs for all significant mathematics.
Finally, the nomograph generally allows slide-rule accuracy, always precise enough to match our building capabilities. Our nomographs will be designed to start on outside scales (Left and Right), working through pivot lines 1 and/or 2 and the inside scales toward the answer. After you gain experience you'll flnd that they can be solved in different order to work backwards toward some independent variable. [Example - Find weight of airplane on 60' x.015" dia lines to generate 50# of CF @ 100 mph. (Ans. 4½ lb.)].
For practice you might solve the examples in Table I to see how estimates of points are handled. Let's take the "Sport 35" at 18 ounces for a trial run. Step by step: (Note - examples shown on Nomographs are to demonstrate procedure only).
A. Reynolds Number from Nomograph I
1. Place pointer on V scale (LH) at 60 mph.
2. Slide straight edge flrmly against pointer and move right end until it lines up with .015 line diameter on RH scale.
3. Read answer of 700 from center scale.
Now you have the whole basis. Hit the first point with pointer, slide straight edge to it, swing edge to other point and read.
B. (Cd).
This one is simply read from Graph I.
Note that the R scale is logarithmic, the Cd scale is linear and use your noodle when estimating. Cd in our case is 1.12.
C. Drag for One Line - Nomograph 2
1. Pointer on 60 mph (LH outside) (V)
2. Straight edge from pointer to 60' line length (r) (RH outside)
3. This time instead of readihg, lift pointer and move over to where the straight edge crosses Pivot Line 1. Place pointer there.
4. Holding edge against point on PL 1 swing edge down to 1.12 on the Cd scale (inside RH).
5. Pick up and hold point at Pivot Line 2.
6. Holding point at PL 2, swing left edge down to .015 line dia., (d).
7. Now read the answer frem Drag scale (DL) (.20 lb/line).
D. Centrifugal Force-Nomograph 3
1. Pick up model weight (18 oz) on LH scale using inside divisions.
2. Set straight edge to cross line length scale at 60'.
3. Pick up and hold crossing of Pivot Line.
4. Swing edge up to 60 mph on RH Speed scale.
5. Read answer from CF scale as 4.4 lbs.
E. Rake angle-Nomograph 4
1. Determine line drag (DL) by.multiplying DL from step (C) by the number of lines. (2 x .20 = .40#)
2. Pick up line drag on DL (LH scale) at 0.40 lb.
3. Set up straight edge to cross CF (RH scale) at 4.4 lbs.
4. FInally! Read rake either in degrees (5.5 degrees) or in inches back in 10" of span' (.98" in 10"). The latter method is a bit more accurate for layout purposes, particulary if you don't have a good big protractor.
The whole operation should take less than 5 minutes and both speed and accuracy improve with practice.
Wrap Up: One last item. The angle we calculate is partially phantom, in that it falls exactly half way between the line guide holes for a two-line. system, when the lines are equally loaded. That "equally loaded" is important. As the elevator is moved from neutral the point shifts to the line under greater tension. If you operate a limited bellcrank movement, as in combat, the load will be carried completely by either wire during maneuvers and the point of action will coincide with that leadouL These facts dictate that line-guide holes should be very close, together or through the same hole. One hole is practical only if you connect the clips inside the wing, or if you stagger the leadout ends. Otherwise the holes should never be farther apart than one inch, preferrably closer than a half inch.
With a three-line Robert's system it is conventional that pull on the middle line closes the throttle. It is desirable to bring this line out closer to the aft line, also arranging controls so that the aft line is "'UP". This trick will allow slow flight at maximum yaw angle. The over-and-under lendout system in Stunt is somewhat shaky, since the airplane responds in the lateral direction (roll), generally unfavorably, if you're looking for maximum smoothness in sharp corners.
If, perchance, your use of these data show's apparent errors, please try to consider every variable involved before you condemn us. Many carefully observed experiments have been performed to establish our high degree of confidence. If you still have trouble ship us every bit of information and we'll check it out
My thanks to Keith Trostle for supplying copies of the original article.
Control-Line Aerodynamics Made Painless
THE CONTROL SYSTEM
By Bill Netzeband
Originally published in 'American Modeler', September/October 1966.
For us it is difficult, for him, easy! But in this priceless discussion there are nuggets of gold strewn all over the circle.
If you dig math, you'll be miles ahead of the game. If not, even a casual reading will open many doors.
-----oooOooo-----
Because both lift and centrifugal force increase as the square of velocity, and the lift capability of a given surface increases due to more favorable Reynold's Number, an airplane should turn better at a higher speed. Yet we have all experienced the stunt or combat rig that "opened up" at high speeds.
There are also the cases of speed jobs that become uncontrollable after hitting top end, or the sport ship that "stiffens up" when the engine peaks. All of these mysteries are not mysteries at all. The control system was simply not capable of moving the elevator at those speeds. So this session should clear out the lack of science normally used in control system "design". When we're through we will have established sound calculations for: control surface loads (torque about the hinge); pushrod maximum load before buckling; correct control horn length; correct belicrank size; and correct handle line spacing. A system designed by these methods will not only operate at all practical speeds, but can be tailored to your personal control motions as a pilot.
What System? A control-line airplane achieves aerodynamic control information through a system of first class levers (Fig. 3). A handle is attached to a pilot and to a T-shaped bellcrank in the airplane via two inextensible flexible wires. The bellcrank forces are translated into push-pull forces via a rigid pushrod which connects to a control horn(s) at the elevator and/or flaps. These forces overcome aerodynamic loads on the moveable control surfaces, thus positioning them in direct relation to control handle position.
It should be pointed out that we provide positioning forces, and that ignorance of this concept has lead to some spectacular landing approaches. Look at Fig. 3 and pick up the nomenclature assigned to the various dimensions of interest. We'll begin analysis at the other end; as usual.
The Control Surface: During this discussion we will refer to a control surface, which can be either elevator or flap. With no torque applied about a control surface hinge, the surface will assume a neutral position. If a torque is applied, the surface will change angle (move) until the airloads on the surface balance the torque. The airloads are proportional to the area of the surface, (span x chord) (bc), the chord (c), theairspeed (V), the deflection from the chord line (&delta), and the angle of attack (&omega) of the fixed surface.
Precise formula is Equation 10 (Nomograph 5). Hf is the total hinge torque. From Eq. 10 we can surmise some interesting surmeece. Hinge torque increases as the square of velocity, and the cube of scale (b.c.c.), also increasing directly with (&delta & &omega). You fly a given airplane twice as fast, you need four times the control force, or build a twice-size airplane and it will require eight times the control force.
Any clues yet? A major breakthrough toward CL system analysis was finding sound data for (Ch), the Hinge torque parameter. This number plotted in Graph (2) provides a coefficient related to control surface deflection and fixed surface (&omega) for known~ratios of hinged surface chord to total chord (Cf/C). When applied in Eq. 10 it gives actual hinge torque in pound-inches, having had "q" corrected for units normally used (inches, and mph). To use Graph (2) determine (Cf/C) using average chords, maximum deflection angles and for now, estimated surface (&omega).
Nomograph 6 is a simple ratio computer, useful in several control calculations. More exact (&omega) is forthcoming. For a stabilator, estimate (&delta) as deflection angle less airplane (&omega). The two coefficients you read from the graph are applied in.Eq. 9 to get (Ch). As an example: if (Cf/C)=.40; C(&omega)=-0.01 and C(&delta)=-.015. We must watch the polarity of these functions, so: "Up" control surface (&delta) is a negative angle, Down is positive. A positive angle (&omega) of the fixed surface (airplane nose up) gets a negative sign (nose down is positive). These have more meaning to man-carrying machines since they must maintain one type of control action, "backstick, up elevator" etc'.
We are more intuitive with our numbers, since we can hook up our system in several conventions, as long as handle action. produces what we want. Back at the ranch, to get Ch for our example, let: (&delta)=30 degrees up and (&omega)=8 degrees nose up. Ch becomes (-.010) (-8) + (-.015) (-30) = + .53. For a stabilator at 30degrees deflection and airplane (&omega) of 8 degrees nose up, (&delta) becomes -30+8 = -22 degrees, and Ch=-.0l5 (-22) +.33. As we said, since we put the horn on either top or bottom the signs are important only during Ch calculation. You might browse through some of your own airplanes for practice.
To round out the first calculation let's make our elevator two different sizes with the same area, to illustrate the effect of aspect ratio. For 50 sq. in. we can go b=l0 and C=5 or b=25 and C=2. OK? At a velocity of 60 mph, Hf for Surface (1)=8.35 lb-in.; surface (2) Hf=3.35 lb-in. One blow for high aspect ratio. If you increased your velocity to 85 mph, Hf would double!
The Pushrod: This essential device, is generally overworked and underpaid. In its best geometry it should be an absolutely straight rod, but this is seldom possible. It is weakest in compression (push), and is treated mathematically by Euler's Equation for Long Thin Cylinders in compression. Failure is due to buckling, or springing out of a straight line, and having done this it can carry no larger load. It should be obvious that a buckled control rod will create no more surface deflection, generally allowing the surface to "back off" or lose angle. About a third of our problems are explained by this.
Graph (3) presents calculated buckling loads for two sizes of common pushrod wire. We built a test rig and measured several diameters in various lengths. Results were: (a) We can get only 90 percent of calculated values because our wire isn't straight enough as we buy it; (b) Unsupported rods with as little as 1/8-in. offset, buckle at such ridiculously low figures, they are almost unpredictable; (c) our salvation lies in reducing unsupported rod distances with fairleads. With any design you know pushrod length, right? We need to know pushrod load. Comes the first compromise. We attack the problem by establishing a control horn dimension (e) which will allow pushrod load (Fr) to be a "safe" value, that is, below buckling load. Take your pushrod length, assume one fairlead in the exact center, enter Graph (3) at a length equal to the longest segment of pushrod (in our case 1/2 the total length). Read the proper curve for buckling load. Now look up Equation 11, plug in Hf, Fr, and Cos (&delta). Cos (&delta) is necessary because as you move the control surface, the effective control horn force arm decreases proportional to Cos (&delta). We are still solving for maximum loads.
Continuing our example, Hf=8.35, we pick 16-in. long 1/16-dia. pushrod so that Fr for an 8-in. rod=4 lbs. At (&delta)=30 degrees Cos (&delta)=.866, so e=2.4 in. Oops! So we have a kooky elevator, but let's thrash it through.
Use a 3/32-in. pushrod, Fr=20 lbs and e=.48in. A bit more reasonable, yes? Just as a matter of f'r'instance our other elevator would have needed a .97" horn with the 1/16-in. dia. pushrod.
The Delicrank: The force to actuate the elevator is amplified by the belicrank, is transmitted by the pushrod and comes from a differential tension balance between the lines as one end of the handle is moved away from the airplane. Note, if there were no elevator load, each line would carry a load equal to 1/2 CF in all positions, assuming no stops or restrictions to movement. The maximum force which can be used to move controls is the full Centrifugal force (CF) applied to one line in tension. The other line becomes slack and exerts no load on the system (assuming the aerodynamic drag tension components to be equal). This key opens the next door in our system analysis.
To establish bellcrank dimensions we utilize two sets of requiremcnts, spiced with some individuality. Equation 12 defines the relationship of bellcrank dimensions to the already fixed "numbers". If we have a 40 ounce airplane on 65-ft. lines; CF=9.l lbs b/c=2.2. Spelled out we need a bellcrank where (b) is not less than 2.2 x (c). But we don't have (c) yet! Comes the intuition backed by experience. The proof of the following is left up to the reader.
A study of bellcrank and horn geometry will show that the best relations between bellcrank travel (&phi) and elevator travel (&delta) occur when C is equal to or smaller than e. See Eq. 18 for relationship. Note also that angles are related by trigonometric functions since we generate a linear displacement by rotary motion. When c=e, each degree of bellcrank travel produces one degree of elevator, if the approach angle of the pushrod is parallel to a line between hinge points and the pushrod holes at neutral are square with this line. Good systems are possible with c's down to 0.6e. Below this it begins to take too much belicrank travel to produce elevator motion, although it could be useful to correct a sensitive design that is not totally unstable.
In cases where (c) is larger than (e), elevator angles quickly reach 85 degrees, the action becomes too "fast" at the ends, and the system is prone to be inadequate in producing useful control forces. So, we have narrowed the selection of c to a range between e and 0.6e. For trial values try 5 steps like e, 0.9e, 0.8e, 0.7e, and 0.6e or just pick one from experience. One other point; if b/c comes out larger than 3, you're really in trouble because standard bellcranks don't provide b/c much over 3. If this is the case, your solution is to establish a longer control horn, reducing pushrod loads, thus requiring less mechanical advantage at the bellcrank. Or, you can build your own custom bellcrank.
Another significant argument for reduced pushrod loads is hole wear. The lower the Fr, the longer a system will operate without wear. The practice of bushing the bearing holes leads in this same direction by increasing the hole surface area, thereby reducing the stress level, accomplishing the same reduced wear.
To pick a bellcrank, having established a reasonable (c), use Table 2 which lists most of the commercially available bellcranks and their dimensions. A horn with the proper (e) may be found in Table 3. Note that dimensions shown for external type horns are from the base of the horn to each hole. You'll have to add on 1/2 of the elevator thickness or specifically the distance from the horn base to the center of the hinge to get the proper (e) dimension. It is highly desirable that your b/c was less than one (1.0). In this case a bellcrank can be selected that will provide a b/c larger than the required b/c allowing a large safety margin. In such a case simply establish (c) as before, pick a bellcrank to suit your whim and record its b/c ratio.
In our example we will pick c=e (.438) so b=.97" (roughly a 2-in. bellcrank). This will give a marginal system with stiff "feel". From Table 2, the TF Nylon 2-in. is about the only exact copy available. This could be used with Veco small horn, a Kurtz horn or a Veco external horn on a 1/8-in. elevator. If we were carrying an 8 lb.-in. torque, the Veco small horn would probably not hack it due to the 1/16 wire carrying the torque. In fact for such a kooky elevator, we would probably go up to a 3/4-in. horn and a larger bellcrank to reduce pushrod wear. However, we'll carry this one through to completion, since it allows us to point out critical areas for compromise. Actually we are very close to the end.
The Handle: To complete the system we must pick a handle, specifically the line spacing to correctly correlate your natural motions to full elevator travel. To this end, you'll have to do some educated guesswork. Each of us has a hand-motion computer built into our brain. We've trained it and expect (or prefer) the airplane to hit its maximum control response, at the point of handle travel we like (&theta). The game then, is to find your own preference. Studies indicate it will be between 10 degrees and 30 degrees, averaging less than 25. My own preference seems to be 22 degrees and most people who have test flown my ships, prefer "faster controls" (smaller &theta). Our sample system, using my 22 degrees &theta would use a 2.68" line spacing (h=l.34), such spacing being twice h. We have just established dimensions for a complete control system. However, this system is just exactly right for all given parameters at 60 mph. At higher speeds we would be in trouble, at lower speeds, no problem. The reasons are not readily obvious, but consist of one large fact. We set up our controls to just reach pushrod buckling under the conditions specified. This is the limiting factor in the whole system since Fr is the maximum force which can be applied to the elevator horn.
We can increase pushrod force with more speed or a larger b/c at the bellcrank, but since Hf increases in the same relation as CF, our pushrod will buckle before reaching maximum (&delta). A further problem rears its ugly head when we try to hit a square corner coming into the wind out of level flight, with a marginal system. The CF comes from velocity relative to center of circle. Heading into the breeze causes this velocity to decrease, hence CF decreases. The elevator sees actual velocity of the airstream which increases. With increased Hf, decreased CF and a marginal Fr, you can't get full control! We recommend a tentative solution which applies a bias factor to Hf for stunt, combat and sport ships "that fly on their backs." Until further notice multiply Hf by 1.4 and then design your system.
The additional 40 percent should keep you out of trouble 98 percent of the time without overdesigning the system. We don't anticipate any problems with Rats, TR's, Carrier or Trainer types, unless elevators are a very large portion of the stabilizer. Design for a speed 10 mph over the highest you expect. Speed types have a problem to be covered at a later date, basically due to lack of torque at the control unit and high airspeeds.
Flaperoonies: Precision aerobatic types have a longer chore, since flaps also require force to move. Flap Hf and F are computed in the same way as the elevator. We suspect from preliminary aerodynamic checks that most contemporary ships don't change angle of attack during a maneuver, but you could assume maybe six degrees just for safety. Equation 13 is "good" only if you use a flap horn for transfer in 1-to-1 ratio (Fig. 3) (case I), or if you connect a-la late model T-Bird with direct connection between bellerank and elevator and tie your flaps to that same rod. The bellerank to flap rod must be designed to carry both flap and elevator loads for case (1).
Good design practice says use either equal flap and elevator travel or use more elevator travel than flap. So you must pick some geometric relation between (f) and (e) as well as relating both to (c). Takes a little judgment and a little more work, but you guys are in more danger than the rest, too. You might run a check for overhead maneuvers by assuming 1g (CF) and an airspeed around 40 mph. In most cases the enlarged Hf factor should cover you.
During overhead maneuvers, the lack of turning ability can be traced to low airspeed and one g unit taken away by gravity. It begins to appear that a correetly designed acrobatic airplane would fly better at 60 mph, than at the 45 to 55 we use now. At best, there is an excellent chance that the conventional design can fly better than it does right now.
Details: Graph (4) provides data to locate a set of stops at the bellcrank to provide known maximum control angles, or simply to provide enough clearance. Eq. 15 computes the bellcrank angle (&theta) for values of (&delta) and (e/c). For our test case &theta=&delta or 30 degrees. If we used the TF 2-in. bellerank, we'd locate the mounting bolt 5/8in. from a rib restricting its motion, and thus the elevator to 30 degrees. The dotted portion of each curve indicates that the pushrod arm of the bellerank must be cut down to fit.
It is interesting to note that all bellcranks except the old Kenhi unit have an unmodified minimum &theta within one degree of 40. lt is recommended that a resilient pad, such as urethane foam or foam rubber 1/4" thick, faced with shim stock, be used as stops. This will decrease the shock load on the lines during sharp action.
The sketch in Fig. 3 illustrates another critical feature of the system. For symmetrical up and down angles the pushrod end in the horn should fall on a line 90 degrees from the line connecting the horn hole and the bellcrank. If installed as shown in an aft location, the effective torque arm has already traveled a good part of its arc, and your actual (e) dimension is longer than you thought. Such placement can be used to advantage IF you desire more control in one direction. lf placed aft of the hinge you'll get fast up and slow down. Placed forward of hinge the opposite is true. Of course for the horn on top all bets are reversed!
Summary: Elevator size and maximum angle are fixed values for any given airplane and mission. So Hf is fixed. Pushrod buckling load is the first weak link, so it must be designed by computing an (e) dimension to suit the physical requirements. The pushrod can be strengthened by shortening unsupported distances with fairleads (guides) and/or increasing the wire diameter. Pushrod loads can be reduced by using a larger e at the horn, and wear can be further reduced by increasing the thickness of material at the bearing holes, either bushings or thicker material. The design b/c ratio is the second area where trouble can be eliminated (or caused). It should be set up so that the required b/c is less than one (1.0), and a bellcrank should be selected with a b/c ratio larger than 1.5. These additional mechanical advantages should prevent loss of control under almost any unexpected condition of flight. IF you find that the system gets out of hand in a practical scnsc, you can always back up closer to the exact values computed. Finally, your personal handle travel preference should be established by experiment and designed into ALL of your airplanes.
Sorry, I can't improve on this quality.
DES!GN PROCEDURE
1. For elevator-chord ratio (CF/C) and predicted maximum angle of deflection calculate (Ch), using Eq. 9 and Graph (2).
2. With airspeed, elevator dimensions and Ch calculate Hf-(Nomograph 5). (See text for Stunt and Combat.)
3. From pushrod size and geometry, determine Fr (Graph 2).
4. Establish (e) using equation 11, at the maximum angle from step 1.
5. Calculate Centrifugal Force using airplane estimated weight, line length andairspeed. Nomograph 3. [Part I]
6. Calculate b/c from eq. 12 or if flaps are used, eq. 13.
7. Browse through table 3 and pick a horn with proper e dimension.
8. As a trial c, pick out a bellcrank with a c dimension so that e/c=1. Check that bellcrank for b/c required. If the bellcrank's b/c is larger than your required b/c, you're in. If not, try another. Use Nomograph 6 to speed calculations involving ratios. As proved earlier c should be between e and 0.6e.
9. With bellcrank selected you can establish handle dimension (h), designing it with Eq. 14 to move your favorite angle (&theta). Remember (h) is 1/2 of the actual line spacing.
10. Using Eq. 15 establish bellerank travel angle (&theta).
II. If desired, a blocked system can be made using locating dimension from Graph (4), or at least guaranteeing enough clearance.
Sorry, I can't improve on this quality.
Part 3 will include data on single-line systems, aerodynamic balance of control surfaces, and the physics of flight at altitudes above the handle. These first articles cover those items which are peculiar to CL airplanes. Future articles will establish firm design data for the airplane itself from minimum turn radius to landing speeds.
My thanks to Keith Trostle for supplying copies of the original article.
In a dead-stick glide, Dave Gierke's excellentIy designed NOVI displays it's srnooth, flewing lines.
Control-Line Aerodynamics Made Painless (Part 3)
By Bill Netzeband
Originally published in 'American Modeler', December 1967.
'Your airplane is smarter than you are! It knows and obeys every aerodynamics law.' Which is to say that 'old debil' math is really a useful tool. By its careful application many 'mysterious' factors are made plain.
-----oooOooo-----
Editor's Note: In the Sept./Oct. and Nov./Dec., 1966 issues were presented Parts I and II of this series. Both the editor and author lacked faith at that time that enough control-liners would seriously consider the mathematical aspects of design. Many favorable letters have been received since. Some called us "chicken" for quitting. This final article now is published with the observation that it should have been printed long ago. (Both dates are wrong - DD.)
Reviewing the introduction to this informative series we may have supplied rather shaky reasons for going to all these lengths to properly design a "rock on a string. "The fact that most published designs were "brute force" (cut-nt-crash) developed didn't always detract from their final shape.
It has become apparent that anyone, no matter how misinformed, can run down the rest of us who "roll our own" designs. So let us elevate the purpose of these reports thusly: Your finished airplane is smarter than you are! It instinctively knows every solitary aerodynamic law, and unquestionly obeys them to the letter. It therefore behooves us to learn as many of the important laws as possible so that we don't demand something which that smart lil' ole' airplane cannot do.
We will deal mostly in how, and how much with flights into why, where it is important. Mathematics are an essential part of our process, since without numbers, the principles are pretty academic and often misleading. As promised, the derivations of equations generally won't be detailed, except where the final product is clarified. It is also planned to suggest test methods and/or devices, so that ultimately we may communicate on the firm base of measured performance, rather than "Gee Whiz, it sure looked good." So much for reintroduction.
Since you've already peeked at the sketches, we're dealing with the major lateral and vertical force diagram to evaluate surface lift requirements, maximum level flight altitudes and a method for measuring the maximum lift for an airplane. Also a discussion of the propeller as a gyroscope with perhaps the answer to some of your "mysterious" crashes.
Fig. 4a illustrates the major physical forces generated by restraining a mass (our CG) in horizontal flight level with the handle. CF is centrifugal force from Part 1, Nomograph No.3. FA is line tension equal and opposite to CF. W & L are airplane weight and the surface lift necessary to just equal W. This is the simplest case, since each vector system is essentially "in line." This is the flight mode used to determine maximum line tension and trim lift.
It should be noted here that wing lift is assumed to be normal (perpendicular) to the chord line. If the airplane is banked into the circle (vector LB), the wing must generate more life to support W, buf will allow FA to decrease. For small angles, up to 10 degrees LB is almost equal to L, and the reduction of FA is W tan B, since L=W. For a heavy ship (3 lb.) at a l0-degree bank angle, line tension would be reduced almost 0.5 lb. without requiring additional lift. This effect is directly opposite if banked outward, and is not proportional to airspeed.
The use of this phenomenon is not desirable for aerobatics or combat, but could be used for in Navy Carrier (outbank) or a heavy Rat or Speed job (bank in). The most reliable method to obtain this force is to place the line(s) guide ahove (bank in) or below (outbank) the CG of the airplane. Any other method to generate a roll force (wing warping, ailerons, weight, etc.) will add detrimental side effects (no pun intended) such as added drag, an angle proportional to airspeed or adverse yawing effects.
It can be readily shown that a bank angle exists for any line length and airspeed which would give zero line tension (W tan B = CF). Actually, the amount of weight is not a factor, since CF can be reduced to its equivalent "g" factor by factoring out W. Therefore bank angle for zero line tension becomes a product of line length and airspeed. For 60' lines at 100 mph, angle B would be 85 degrees 51 minutes (11 g's) NOT too practical, but interesting. It is entirely possible that the wing cannot generate the lift necessary to do a kooky trick like that, anyway.
Points against banking in, are the landing and takeoff, where "g" factors of less than 1/2 are generated. Control can be lost, and/or the airplane could "come in" on you. Meanwhile, back to important stuff. Fig. 4b represents the real meat of this sandwich. CF is now calculated for a radius less than the line length (r cos &lambda). (&lambda) is the angle of elevation, which is somewhat easier to visualize than actual altitude (h), and is more convertible for varying line lengths. (sin (&lambda) = h/r). Under the conditions of 4b, FA is less than FA for horizontal flight (Fig. 4a) since the lift vector (L) now assumes some horizontal restraining forces. L will be shown to become tremendous at high angles, and maximum lift capability of an airplane will limit the maximum elevation angle.
Perhaps we should point out that we are dealing with level flight, not to be confused with looping and such maneuvers. It is not so difficult to prove that an airplane can be zoomed into lift factors not available in level sustained flight due to kinetic energy stored in the system.
Equations 3-1 and 3-2 were derived by conventional vector analysis and are the basis for the rest of our juggling. To simplify trial analysis we factored out weight (W), reducing the force system to "g" units, now dependent only on airspeed (V) elevation angle (&lambda) and line length (r). We then substituted the equation for CF in terms of "g" units, arriving at equations 3-3 and 3-4. By specifying (V), and (r), we can calculate line tension and lift at various elevation angles. Calculations are reduced by use of Nomograph No.3 (July/Aug. '66) and Trigonometric Functions annoted in Table 4. Simple results are plotted on Graph 5 for an airplane on 60' lines traveling at a constant 100 mph. To get actual forces, simply multiply "g" factors by W. Sample numbers would apply to a slow Rat at 26 ounces. L in "g"s are listed.
Come now the engineering compromises. We cannot get lift without drag. Increased lift causes increased drag, so without being able to increase thrust, the higher we fly. the slower we go. O.K.? Since high flying is one large bone of contention in contest judging, we should know where a "point of diminishing returns" is reached. Or. should I fly at the maximum allowed height or not? (We do uot advocate cheating!) Space does not allow complete evaluation of induced drag at this sitting, so complete analysis of actual speed reduction versus "apparent speed increase" will merely be dangled before you. right now. ("Apparent speed" is equal to V actual/cos(&lambda).)
Of immediate interest is maximum lift, since we now have most of the machinery to measure it. To evaluate a given airplane, a graph or series of point calculations leading to L versus (&lambda) are necessary. For most CL airplanes a Lift Coefficient (CL) of 0.9 is about the limit before going into hard stall conditions. Nomograph 7 will calculate L, D, or CL and CD depending on the order of procedure. (Eq. 3-5 and 3-6) If. as we have right now, values for L, we can calculate CL. The example shown on the face of the Nomoglaph can be solved for CL by proceeding as follows:
I ) Pick up wing area (S) and lift required (L) with straight edge and hold crossing point 1;
2) Holding 1, swing to V on left hand scale, reading answer CL on RH scale.
Lift coefficient (CL) is a figure of merit defining the lift per unit area of a wing for specific conditions of Reynolds Number and angle of attack. It is necessary to introduce it, unadorned, so that we have common ground to complete this discussion. As we said, except for a high efficiency stunt wing with high lift devices, most CL wings will stall at CL=0.9. At this point drag is extremely high, and lift will decrease if you force the wing to higher angles of attack. An end point for high lift without excessive decrease in airspeed due to induced drag is closer to 0.3 or 0.4.
Having plotted or tabled L and corresponding CL versus (&lambda), pick out the CL of interest, and note the elevation angle. This is the maximum angle at which you can fly level (if CL were 0.9) or maybe the highest to fly for best "apparent speed."
During all of this, a detailed study of PA indicates a small decrease in line tension as (&lambda) increases. From Eq. 3-1, at 90 degrees line tension disappears except for airplane weight coming down. From Eq. 3-3 it appears to be different, that line tension in g units is equal to horizontal g's reduced by sin (&lambda) (which varies from 0 to 1.0). The apparent mathematical anomaly is caused by the fact that under practical circumstances CF for a zero radius is infinite, such that correct procedures require definition ot max-min values by calculus. We cannot practically reach these limits, so they are hereby ignored.
if we apply wing areas of 90 sq. in. and 140 sq. in. to our sample plot and a fixed weight of 26 ounces, we have a country fair argument for the larger area Rat Racers. F'rinstance, applying CL of 0.4 for best speed at altitude, the 90 comes in at 15 degrees, the 140 at 26. Maximum elevation for the 90 is conservatively 35 degrees as opposed to 49 degrees for the big one. Granted you can zoom maybe ten degrees higher to pass, but you won't stay up there long! Note also, that line tension is reduced by only 0.9 ,'g" even at 60 degrees, although the speed reduction we know exists will cause an actual reduction, since CF will decrease. Finally, 20' (max. racing al- titude, except passing) represents an (&lambda) of 19.5 degrees, not too encouraging for the 90, if the 140's decide to run at 20 ft!
if we had a way to measure V and (&lambda) while flying our airplane, without wind, at its highest altitude, we could calculate its maximum lift coefficient. Luckily, both can be measured with reasonable accuracy, if you want to take a little time to build a crude theodelite from Fig. 5; Using the gadget like a pistol, sighting through the eyepiece until the bullseye covers the airplane, while several laps are clocked with a stop watch, you have both angle and velocity nailed down. (V) can be calculated from Eq 3-7.
Knowing the angle (&lambda) and velocity, we can plug these numbers, along with (r), into equation 3-4 and come up with (L') in g's. By multiplying (L') by (W), we have (L max) from which CL max can be calculated from Nomograph 7 (Eq 3-5 or 3-6). This would settle manv questions, like in stunt as to just what CL is a practical maximum. The reduction in airspeed from level flight (minimum drag) will give a measure of drag increase. It is needless to tell you that this information is useless, unless you dig in and apply it, isn't it?
Particularly significant in stunt and combat is maximum lift, since this determines the minimum looping radius. It has become apparent that indiscriminant use of full-size airfoil data has led to some extremely optimistic turn radii. We seldom achieve the efficiency of a large wing at high speed. Therefore, to derive usefulI data we are using experimental measurements such as this one to write our own book.
The next phenomenon has been published before, without specifically pointing out one dangerous area. The propeller acts as a gyroscope since it is a rotating mass and numerical analysis proves that under adverse conditions it can generate enough precession torque to cause trouble. Referring to Fig. 6a we see the conventional forces associated with a gyro. The physics of the system are too complex to put down here; only the results will be presented. Essentially what occurs for conventional prop rotation (CCW when viewed from front), when the rotation axis X-X (prop shaft) is tilted, a reaction torque appears in one of the axes perpendicular to the X-X axis.
In the case shown in Fig. 6a, we are flying in the conventional direction (CCW) and move the nose down (coupling forces P-P'). This rotation is about the Z-Z axis and the precession torque appears about the vertical axis Y-Y in the direction shown. All of the forces involved here are couples (two equal and opposite forces in the same plane, but not along the same line). A couple is handled as a torque (a force on an arm causing rotation) and can be balanced only with an equal and opposite couple. or torque. These facts cause the precession force to be independent of its distance from the CG, so long or short nose lengths do not affect it. Therefore, the illustrated torque appears at the CG turning the nose into the circle.
As noted, nose up turns produce nose out torque, while the steady left hand acceleration of level flight produces a small nose up torque. These arc all real, sport fans. The amount of precession torque depends directly on the mass (weight) of the propeller, its diameter (specifically the CG location of each blade), the engine rpm and the angular acceleration (rate of airplane turning) which is in turn dependcnt on airspeed and turn radius. The larger any of these, except turn radius, the larger the precession torque.
There are several danger points in the precision acrobatic pattern, where high rates of nose.down pitch are required, the square eight and the middle two corners of the hourglass. Noting the reversal of conditions in inverted flight (Fig. 6b) one can include the second and third reverse wingover comers and bottoms of outside square loops. The effect can vary from momentary loss of control to complete loss of airplane.
In the early days with the climb and dive maneuvers we had troubles, too. To deliberately look for this force John Barr and I took his late "Lil Satan" with ST 15 diesel power, increased the stabilator area for sharper turns and performed hairy climbs with sharp pullouts. Finally with a 9-3 prop, relatively slow airspeed (low line tension) and high rpm, we started getting it every time. The nose would swing in violently, the ship would completely slack off and float to the other side. During the initial test series we were ready and could regain control before it crashed, but during a night session she pulled the bit so quickly and accidentally that the end arrived. The stunt ship with its marginal centrifugal force and a combat rig with a slight warp and high rpm mill are prime victims for this force. Since plastic props weigh about 50 percent more than wood props they will generate 50 percent more precession force.
The effect of the small nose-up or down-down precession in level flight explains the apparent stability increase while flying inverted since the effect is destabilizing in CCW flight and stabilizing in CW. This probably explains why the majority of the "developed" stunt rigs end up with a raised thrust line, to partially compensate for the precession effect on trim.
My thanks to Keith Trostle for supplying copies of the original article.
Me I just do this by what has worked for me in the past. But all this is not what this thread is about. Its about my regret not flying my second flight.
Topic: Hind sight Topic: CG discussions for IC/E power (Read 14263 times)