This information is also outlined in the enclosed DSS Table for typical maneuvering speeds and model scale factor (K factor). I have also included other typical aircraft class examples for additional general comparisons.

MODEL
SCALE "K"
FACTOR

SQUARE
ROOT
FACTOR

FULL-SIZE SPEED & MODEL DYNAMIC SIMILITUDE SPEED IN MPH
FIRST-ROW SPEEDS BELOW ARE THOSE OF FULL-SIZE

1/1

1.000

75

100

125

150

200

250

300

350

400

450

1/2

0.707

53

71

88

106

142

177

212

247

283

318

1/3

0.577

43

58

72

87

115

144

173

202

231

260

1/4

0.500

38

50

63

75

100

125

150

175

200

225

1/5

0.447

34

45

56

67

89

112

134

156

179

201

1/6

0.408

31

41

51

61

82

102

122

143

163

184

1/7

0.378

28

38

47

57

76

95

113

132

151

170

1/8

0.353

27

35

44

53

71

88

106

124

141

159

1/9

0.333

25

33

42

50

67

83

100

117

133

150

1/10

0.316

24

32

40

47

63

79

95

111

126

142

1/12

0.289

22

29

36

43

58

72

87

101

116

130

1/16

0.250

19

25

31

38

50

63

75

86

100

113

TYPICAL AIR SHOW

MANEUVER SPEEDS:       LOW MODERATE  HIGH   VERY HIGH
TYPICAL AIRCRAFT:        WW-I  GENERAL AV.  WW-I I  JETS

FIGURE 3. TABLE FOR DYNAMIC SIMILITUDE SPEED (DSS) vs. SCALE SIZE.

Listed model speeds provide identical flight maneuver features as full size

(such as bank angles in turns) for realistic scale-size maneuvers.

The Table reflects what most scale modelers are already achieving for prototypical maneuver results, particularly if monitored accurately with radar. There may be one or two example areas where competitive scale modelers have recognized handicaps and have also been improving. These may be worthy of comment and further description.

The upper end of typical maneuvering speeds for WW-II scale fighters is sometimes lacking, particularly for high-performance prototypical vertical maneuvers such as loops. On the other hand, jets may sometimes fly only on the upper end of their prototypical maneuvering speed range rather than police themselves in throttle control during maneuvers that would usually not require high speed. These include low-performance horizontal maneuvers like figure eights. Excessive bank angle in scale-size turns reveal excessive speed very easily as described earlier, particularly if high-g stresses are not typical to the aircraft being flown for such maneuvers.

When scale WW-2 fighter models are equipped for adequate speed performance to include vertical maneuvers, it eliminates the problem of only flying in a narrow speed range that has sometimes handicapped overall-flight realism. In the DSS table, many WW-2 fighters have a broad range of maneuvering speeds such as 150 to 300 mph (or 2:1 margins) that should also be reflected in models for optimum overall maneuver selections. However those modelers achieving these capabilities (including jets) must also use that performance wisely, since selection of such an aircraft and well-equipped model is not an inherited license to speed through all maneuvers unnecessarily.

WW-II VERTICAL MANEUVERS AND DSS

Lets examine a full size P-51 flying at 300 mph. At this relatively high maneuvering speed, it is capable of entering a full-round loop of 2000 ft diameter (as also described by Steve Hinton). If we model a P-51 in the scale of 1/6, this would imply a DSS speed of 122 mph at loop entry. This is what well-equipped 1/6 scale WW-II fighter models have been monitored at with radar to enter round-scale-size loops approximating 330 feet diameter. Those not capable of these entry speeds either struggle through smaller loops or avoid a loop entirely. They may also become deformed or "egg shape" from inadequate speed at the top depending on initial entry speed and loop size. Having a lower performance fighter may equate to flying an F4F in a smaller realistic loop with lower entry speed.

Somewhat larger examples of 1/5 scale WW-2 fighters have sometimes been described with flying capabilities only in the vicinity of 65 to70 mph for their maneuvers. This also suggests they would be handicapped in prototypical options such as the 2:1 speed maneuvering range earlier described for WW-2 fighters. Although a 70 mph model speed equates to a scale speed (LSS) for full-size of 350 mph or 350 x 1/5 = 70, the DSS Table indicates 65 to 70 mph in 1/5 scale has a performance equivalent of only approximately 150 mph in full size. These relatively large 1/5 scale size WW-2 fighter models (with typical wingspans of 7 to 8 ft) will still fly at 65 to 70 mph and provide simple maneuvers such as horizontal rolls, but only with minimal or sluggish looking performance options compared to full size. Perhaps another perceptive magazine scale writer associated with the Top Gun scale competition stated it best..."You notice that a fighter that flies like a slug isn't scoring so well".


  SUMMARY

To put in order what otherwise could not be with scale speed, the AMA rules for realism features have deleted the words "scale-like speed" as a listed error in realism. This avoids making the AMA Competition Regulations a document in conflict with itself or creating misunderstandings for many other realistic-flight-feature requirements. The AMA rules for Radio Control Sport Scale (Sportsman and Expert) have now simply emphasized the following: "The model should be flown at speeds that best simulate prototypical maneuvers and overall flight. The model should not be flown excessively fast where it may result in unrealistic high bank angle attitudes and high g loads for typical turns, or excessively slow that results in unrealistic flat or shallow angle turns." The U.S. Scale Masters Championship Program had also similarly initiated these types of changes earlier to reflect what was occurring instinctively by experienced scale judges and contestants. The Top Gun Event has simply made no reference or requirement to fly at scale speed or "scalelike speed" when describing flight-realism.

The many speed-sensitive attitude features in flight maneuvers better speak for themselves when judging in an objective manner compared to the previous ambiguous implications of "scalelike speed". In addition to the physical contradictions introduced by scale speed to the other realistic qualities of flight maneuvers, the difficulties in judging scale speeds are also understandable when considering flight judges are seldom provided documentation for typical maneuvering speeds of full-size aircraft. In addition, the specific scale of a model is not provided for flight judges to presumably scale the speed in some mental capacity. In this same difficult respect, what a judge may know about speeds prior to a contest can also often become counterproductive unless it is simply related to all the other maneuver realism features expected in flight such as bank-angle attitudes in turns. As the Chairman of the US Scale Masters Association had recently indicated about this updated judging guideline, "The intent is to disarm a judge from his prior knowledge of what he thinks it should look like to a mechanical method of observing bank angles in turns for realistic supporting speeds."

Last but certainly not least, the emphasis on prototypical flight attitudes or other realistic maneuvering features have also provided means of "Accurate and Consistent Judging" as recommended by the AMA Scale RC Flight Judging Guide. When compared to ambiguous "scalelike speed" interpretations, it was also a much better way to give uniform recognition for overall flight realism qualities on a fair and equitable basis to all scale size and vintage aircraft competing together. In these many respects it can then be said, "If it looks right it is right for speed as well."

OTHER REFERENCE MATERIALS

The subject of dynamic similitude motion and dynamically similar models has been in existence for over a half century. Its technical origins by other names date back into the late nineteenth century, when a naval architect William Froude wanted to estimate the power needed to propel newly designed ships by making tests on small scale models before the ship was built. In order to make a valid comparison, he demonstrated that a model must be tested at a specific speed for similar bow-wave effects. This eventually gave rise to an expression now named after him of "Froude Number"=v/(Gxl). It is derived from the ratio of kinetic energy divided by potential energy where "l" is a reference-linear dimension on the full-size as well as for the smaller scaled model subject. Froude demonstrated this ratio Number must remain the same on the model as it was for the full size to make valid comparisons. This ratio is much like the earlier described mathematical relations where it is again found that velocity "v" must become K on the scale model compared to the full size or Dynamic Similitude Speed (DSS) when scaling the model size by the scale factor K.

In the last 50 years, numerous articles have appeared on this subject relating to DSS and the square-root-of-scale speed relation in modeling compared to full-size aviation (NASA), experimental (EAA), zoology, and RC scale modeling. A partial listing of earlier reference articles available on this subject are listed below.

1. "Radio-Controlled Dynamic Model Augments Hydrodynamic Research", by Ernest
    G. Stout, Staff Engineer, Consolidated Vultee Aircraft Corp., Aviation magazine,
    February 1946, pgs 171-173.

2. "About The Size Of It", by Bradford Powers, Model Aviation Magazine, January
    1978, pgs 8-12. It also makes reference to Consolidated research using RC flying
    boat models in 1945.

3. "Scale Flight Realism", by Kent Walters, Model Airplane News magazine, July
    1985, pgs 16, 17, 111, 112, 113, 115; and continued to August 1985 issue, pgs
    16, 17, 114, 115, 117.

4. "Dynamic Modeling", by Stan Hall, EAA 10883, Sport Aviation magazine, July
    1987, pgs 30-35.

5. "Use of Dynamically Scaled Models For Studies Of The High-Angle-Of-Attack
    Behavior Of Airplanes", by Joseph R. Chambers, NASA Langley Research Center,
    presented at International Symposium On Scale Modeling, July 1988.*

6. "How Dinosaurs Ran", by R. McNeill Alexander, Scientific American magazine,
    April 1991, pgs 130-136.

7. "Flying Lowe - Scale Speed", by Don Lowe and Ralph Grose, RCM magazine,
    August 1992, pgs 134-135.

* A long list of earlier NASA articles also relates to or makes reference to the DSS subject.

About the author: 
Kent Walters is a corporate applications and development manager in semiconductor components for consumer and military use. He has an M. S. E. E. degree from Arizona State University and several patents. Kent has been active in model aircraft RC scale competition since 1973 and has also won the U.S. Scale Masters Champion in 1980, 1982, 1985, and most recently in 2002. He was also Top Gun Chief Judge in 1991 and U. S. Scale Masters Chief Judge in 1992, 1993, 1994, 1995, 1996, & 1997. Ken is currently on the AMA Scale Contest Board representing D-X and the U.S. Scale Masters Technical Director.

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