SCALE SPEED EPILOG

"Model does not fly at a scale-like speed." These were the words earlier used in the AMA Competition Regulations for Radio Control Sport Scale (Sportsman and Expert) as an itemized error for flight. Despite the implications to scale speed, earlier inquiries with AMA officials suggested these words had no specific definition. Judges and contestants were then left with deciding what they meant.

The original author of these words for the AMA Competition Regulations had indicated "scalelike speed" was never intended for interpretation as a requirement to fly at scale speed. He further stated, "Never was such a rule and there should not be!" That was probably a wise statement to make since scale speed had also been repeatedly demonstrated by modelers to be in conflict with the immediately following sentence in the AMA rules that further described the error of "Attitude in flight is unrealistic." Using various practical monitoring methods such as radar as well as the physical sciences, scale modelers had recognized that correct flight attitudes and a number of other realistic features and maneuvers could not be performed at scale speeds. They also recognized that scale speeds were dangerous if not impossible to achieve. As a result, the words "scale-like speed" were in serious question.

In retrospect, these "fuzzy words" implying scale speed were likely used to simply discourage flying arbitrarily fast beyond that needed for many other realistic flight features. Nevertheless, these words remained troublesome for a critical listed error in scale competition. Not surprisingly, there were many "solar flares" for almost 20 years as to their meaning prior to their recent removal from the AMA Competition Regulations starting in 1999 for RC Sport Scale (Sportsman and Expert).

Well-defined rules normally bring an order and harmony to competitive events, rather than introduce more questions than they answer as did this notable example. In some cases, judges had interpreted "scale-like speed" in the specific manner not intended by penalizing a contestant for not flying at scale speed. This has also been called Linear Scale Speed (LSS) since it is scaled like the dimensions for our models in a linear manner (1/4, 1/5, 1/6, etc.) compared to full size. Most have realized the problems with scale speed and its conflicts, but some have not. This article may serve as added background on this subject or as future reference material when needed.

Knowing that definition was lacking, it stimulated further efforts by many modelers to achieve improved judging uniformity as also encouraged by the AMA. In these investigations, it was recognized scale speed contradicted other important realism features also found in AMA Competition Regulations. These included prototypical maneuver attitudes, stability, g-loading appearance, and ability to select various flight options for scale-size maneuvering characteristics of aircraft modeled. We will explore these further to avoid such conflicts and define a speed relation offering a level-playing-field for small and large-scale models of different vintages competing together. This had also become important since Giant Scale was earlier combined with Sport Scale in 1992.

It does not require much imagination to realize scale speed would immediately provide advantage to large-scale-size models over small ones if that had been the primary criteria in "scale-like speed". For RC scale modelers, any notable competition should play no favorites with size alone. Otherwise it primarily becomes a race as to who can build the largest model with its added cost ramifications and counterproductive total participation effects.

Since realistic flight attitudes are among the most basic and visibly apparent features for realism in AMA and other notable Scale Competition rules, it will also play an important role for optimum speed consideration herein. For a basic realistic turn, this translates to prototypical bank angles in scale-size turns that we can all identify with realism. In our discussion, this basic feature is important since it can be demonstrated this prototypical appearance in turns is very sensitive to speed. It will also be found scale speeds do not provide correct turning bank angles!

At the U.S. Scale Masters Championships in 1993, all those attending an initial evening pilots meeting believed they were already performing with optimum speeds to provide both scale-size maneuvers along with prototypical bank angle turns compared to the full-size aircraft. If these and many other notable pilots are also flying in this same manner, what is this so-called "Maneuver Realism Speed" (particularly if it is not scale speed)? In historical definitions, it has often been called Dynamic Similitude Speed or "DSS" herein. If more palatable to you, just continue to think of it as "Maneuver Realism Speed" as we proceed further into this article.

DYNAMIC SIMILITUDE SPEED

Dynamic Similitude Speed and motion study has been used extensively by NASA and aircraft designers to predict flight response characteristics with scale-size models much like our own. Ironically it has also been used in zoology for animal motion studies including predicting speed and motion qualities of different size animals including dinosaurs as portrayed in the filming of Jurassic Park.

Dynamic Similitude Speed (DSS) for a model is that which best duplicates full-size performance in similar attitude-motion effect through any prototypical scale-size maneuver when accelerating qualities are not altered. This is the added reference for "similitude" effect, since our gravitational acceleration of 32.2 ft/s2 does not have any scaling factor "K" as would linear dimensions on our scale models (K= 1/4, 1/5, 1/6, etc). Other accelerating qualities on scale models will also not be different when compared to full-size. With this definition, DSS also provides the viewer with the same "g-factor" loaded flight maneuvers as full size for realistic effects. In contrast, scale speeds do not. Scale speeds are also generally found inadequate to safely sustain flight since the accelerating pull of gravity does not scale.

Some of us may ignore the technical understanding of DSS, but we cannot ignore its common influence on the motion effect for all objects in our constant gravity environment. When acceleration remains unaltered, it can be demonstrated that DSS results in a square-root relation to scale K factor as summarized in Figure 3 later in this article. For those wishing to know why DSS varies in this manner, the following is briefly provided.

Relatively simple and immediate observations can be made with high-school physics and algebra when objects are scaled in size for similar attitude-motion effect without altering their accelerating qualities. Acceleration "A" is the rate in change of velocity "v" with time "t", or A = v/t. Velocity is the rate in change of distance with time. Distance will be expressed as "d", so we can then describe velocity as v = d/t. Therefore acceleration may be further expressed as A = d/t/t = d/t2. This is often measured in units of ft/sec≤. Rearranging terms using simple algebra, time squared is equivalent to t≤=d/A. We can then solve for time as t=÷ (d/A).

When acceleration is not changed and distance is scaled as "ds", we find something interesting happening with the period of time involved to provide the same motion effect in a scaled environment. We will call it scaled time or "ts". When then providing for the scaled distance "ds" into the last equation above (where ds = K x d for any desired scale factor K), we substitute and determine the "scaled time" as: ts = ÷ (ds/A) = ÷ (Kxd/A), or ts = (÷ K) x ÷ (d/A). Since the initial time t = ÷ (d/A) from above, we can again substitute this and simplify to have the "scaled time" of: ts = (÷ K) x t, or the scaled time for similar motion effect scales as the square root of scale factor K.

The concept of scaled time ts may be puzzling without explanation or examples. It simply indicates time intervals for smaller objects are somewhat shorter to achieve similar motion effect, or their tempo is at a faster pace. It can be observed in such events as small birds flapping their wings in shorter time cycle than large birds and why small children (or a very small pilot) would move or walk with a quicker cadence in walk or shorter time cycle of each step. If we scale up in size, it also suggests why larger objects comparatively move at a slower tempo or longer time interval than small ones. This includes slower-tempo-motion activity for an elephant (or of a large dinosaur) and why a large Boeing 747 looks very slow upon landing compared to a smaller general aviation aircraft, despite the fact the 747 is still going faster. These are the scale considerations in time or prototypical motion effect for similar activity. Now let's complete the same study with velocity.

Velocity "v" is distance divided by time or v = d/t. We can then also determine that scaled velocity vs = ds/ts. Substituting for ds and ts from above, we have: vs = K x d / [(÷ K) x t]. Since K = (÷ K) x (÷ K), we can simplify the K terms and have: vs = (÷ K) x d/t. With the initial velocity v = d/t from above, we can again substitute and determine the scaled velocity of: vs = (÷ K) x v, or scaled velocity also scales as the square root of scale factor K for similar motion effect. This is Dynamic Similitude Speed or "DSS" that is also tabulated in Figure 3 later in this article for a variety of different scale model sizes.

Optimum flight and maneuver realism examples with DSS are extensive. Lets look at a few that scale modelers may recognize. But first lets introduce ourselves to our reduced scale-size pilot and his smaller world in activity before we also fly his smaller airplane.

MOTION STUDY OF A SCALE PILOT

As previously described, the time expected for a similar activity or comparable event to occur is somewhat shorter when scaling objects down in size. A good example can be made for a scale pilot with the fundamental manner in which he would walk or move in all his activities (if we could find such a little critter). An initial clue is available by simply watching small children walk naturally compared to an adult. It quickly becomes evident that their tempo or cadence of walk is quicker, or each step requires a shorter time cycle to achieve than an adult. Their step distance remains a linear-scale distance compared in size to adults that might approximate 1/2 scale, but the time to take each step is somewhat shorter. If you want to demonstrate this to yourself, this can be observed more clearly by the following experiment using the pendulum principle.

Get a yardstick which has a hole drilled at one end so you can allow it to freely swing on a short hand held pivotal rod. As it swings, walk along side it with a normal stride and you will find it has a tempo of natural frequency swing remarkably similar to your own walk. This is simply because most adults have a leg approximately three feet in length from hip joint to their foot. A normal comfortable stride exerts the least amount of added energy, so we let our legs act as "natural pendulums" to do the walking for us (as much as possible). Now do the same with a free swinging cut-off ruler of 9 inches for a 1/4 scale man, and another one cut off at 4 inches for a 1/9 scale little guy. You will then better recognize the tempo of walk is correspondingly quicker. Furthermore if you time the interval of swings, you will find the 1/4 scale man has a step or swing interval in time 1/2 that of the full-scale man and the 1/9 scale little guy has 1/3 the time interval. This indicates time intervals for dictating "scale mechanics of motion" is a square root of the scale factor used in our constant gravity environment.

This is exactly as predicted by the earlier derivation for "scaled time" using a little bit of algebra and the premise that acceleration does not change with scale objects for similar natural motion effect. Such is the real world we all reside in with constant gravity and accelerating effects.

Since the 1/4 scale man takes a corresponding 1/4 size step at 1/2 the time interval as we would, his velocity of walk is 1/4 distance divided by 1/2 the time as we would walk. This equates to 1/2 our own walking speed. The same exercise for the 1/9 scale man would produce a natural walking speeds 1/3 of our own. This is simply revealing a scale man or pilot walks and moves at the previously described square root relation in velocity for his scale factor size compared to us in full size. As you may have already guessed, this is equivalent to Dynamic Similitude Speed (DSS)! A slower linear-scale-speed walk would have dictated that only step distance change by a scale factor, and not the time interval when compared to each step experienced by us in full size. This uncomfortable "scale-speed walk" forces a scale man to restrain his natural movements in our world unless we could scale gravity for him as well.

Just as the pilotís tempo in walk is shorter in time cycle, so might we also expect a similar shorter time for his aircraft to displace its own length with DSS speed to achieve various correct attitudes in flight. Unless we could scale the accelerating pull of gravity, flying with scale speed may otherwise be dangerously slow and unrealistic to perform prototypical maneuvers as we will see in further examples. These "mechanics in motion" qualities also have little or no control by model (or pilot) weight.

There are a number of Dynamic Similitude comparisons that could be made beyond scale pilots (or scale aircraft) with remarkable predictability. It applies to small and large people and various size animals for time cycle of motion and speed for walking or running as demonstrated in the successful filming of Jurassic Park. Serious scale enthusiasts interested in this "big-picture perspective" can explore it further. But let's return to our subject of how DSS relates to optimum overall flight realism for a variety of maneuvers when fully documenting prototypical motion for a scale aircraft and pilot.

DSS RELATIONSHIP TO FLIGHT REALISM

There are many easily observed prototypical features for realism that are affected by speed. The most frequent example in any RC scale flight is how well a model displays a prototypical bank angle when flying through a reasonable scale-size turn radius. This example gives a great amount of credibility to the phrase, "if it looks right, it is right for speed as well!" For example, figure eights are typically performed at moderate cruise speed conditions for pilot or passenger comfort rather than at faster maximum rated speed. A scale-size figure eight with prototypical 30 to 45 degree bank angles (wind and site conditions permitting) can reveal a great deal about optimum speed control. If the model is too slow, the bank angle will be comparatively shallow. If too fast, the bank angle will be steeper than desired for optimum realism in attitudes and g loads.

Since the common coordinated turn occurs so frequently in typical model RC flying, a brief analysis of this flight maneuver for attitude, speed, and radius relationship is both desirable and revealing for overall realism.

In typical turns which maintain constant elevation without adverse yaw, the relatively simple bank-angle, velocity, and turn-radius relation for full-size airplanes and models in aeronautics is: tan q = v2/Gr

where: v is the velocity (ft/sec)

G is the gravity acceleration constant of 32.2 ft/sec2

r is the turning radius (ft)

q is the bank angle in degrees from horizontal

tan q is the tangent of the angle q

Since velocity or speed is squared, the relation between achieving a prototypical bank angle and scale-turn radius is very sensitive to speed. It is also significant this bank-angle relation has no effect from weight of the model or full-size aircraft. This relation also provides opportunity to make comparison of full-size performance at velocity v when replaced with either Dynamic Similitude Speed where DSS=(÷ K) x v, or Linear Scale Speed (LSS) where LSS= K x v for prototypical attitudes with scale-size maneuvers. With either method chosen for model velocity, the scale radius rs will be K x r for a scale-size maneuver and gravity G will remain constant for both full-size and scale model. For optimum attitude realism, the bank angle q should ideally remain unchanged. Lets see what happens when first substituting a Dynamic Similitude Speed for model velocity in the equation above where velocity or DSS =(÷ K) x v.

When DSS is squared [(÷ K) x v)]≤, this term simplifies to K x v≤ or simply the linear scale of velocity squared. Since velocity is also squared in many other important physical flight behavior relations, this same convenient mathematical feature using DSS also appears for lift, centrifugal motion, and energy when studying models in this same manner for various scale K factors. With the K x v≤ term in the numerator and a scale radius K x r in the denominator with a constant gravity G, it becomes apparent the K factors cancel and the relation is unchanged for identical bank angle where optimum realism is achieved of full size with DSS.

It can then be stated when comparing models to full-size performance that, the speed required for identical prototypical bank angle through a scale radius turn maneuver is Dynamic Similitude Speed (DSS). If you are already performing a scale-size figure eight described by the AMA scale rules, you can easily judge how well you are approximating DSS and realistic maneuvering conditions by its prototypical appearance in bank angle. So can a judge! As earlier described, most scale competitors are doing quite well with this.

In contrast when scale speed is squared (K x v)≤, this term in the numerator now is K≤ x v≤. The K factors do not all cancel with scale radius K x r in the denominator thus leaving a K scale factor in the numerator notably reducing the tan q value from that observed of full size. This will dictate a much lower (shallower) bank angle q with LSS in a scale-size turn. Similar deficiencies will occur with lift, centrifugal force, and energy as described earlier.

If you had an ultralight model of K=1/5 scale and were able to truly fly with the lower velocity of LSS without stalling, the new shallow bank angle would have a tangent 1/5 that of the prototypical bank angle in full size. If this were 35 degrees in prototypical-full-size flight, the new observed slower scale speed bank angle on the model would only be 8 degrees from horizontal in a scale-size turn. This flat looking turn is obviously unrealistic in bank angle appearance much like an ultralight would fly rather than an airplane! From the prior coordinated-turn equation involving three variables (bank angle, velocity, and turning radius), a nomograph can be generated as shown in Figure 1.

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