To provide realistic g-load appearance in scale-size turns for the model, the bank angle q in typical coordinated turns should also be the same as full size. This simple relation is "g-load"= 1/cos q in basic aviation study. This is also shown in a vector diagram in Figure 2. A listing of gs versus bank-angle turn is also shown on the far left side of Figure 1. We can then easily conclude that to fly at realistic g-loads we must turn at the same bank-angle attitudes as the full size. To turn with these same realistic attitudes, you must fly at Dynamic Similitude Speeds!

FIGURE 2: Coordinated turn vector diagram for g-
load without skidding, adverse yaw, or change in elevation. The g-load factor = 1/cosq when total lift provides a vertical lift vector equal to weight.

Other maneuvers also require DSS for realistic g-loads. An interesting example is "zero gs" pilots have described at the top of optimum-round loops when centrifugal force offsets gravity. This prevents falling out of the loop or becoming egg shape. Centrifugal force formulas give us G =v/r for velocity "v" at the top of a loop of radius "r" for zero g-load, where G is the gravity acceleration constant. If we scale the loop size by K x r in the denominator, the ratio v/r remains constant with G only if the DSS squared term K x v is used in the numerator as previously described. Then K factors properly cancel as earlier shown in the turn analysis for producing the same bank angles.

Notable air-show pilots like Bob Hoover have also described "energy management" in many vertical maneuvers by trading part of their kinetic energy mv/2 or speed "v" for altitude or potential energy mGh, where "m" is mass, G is gravity, and "h" is increase in height or altitude. Since the mass "m" or weight is in both forms of energy when traded in a loop, it cancels without affecting the results. For scale size maneuvers, it can be demonstrated this same type of flight-energy management for maneuver realism occurs only when we use a model velocity of DSS.

With these insights, DSS is no "thinly disguised excuse" to fly faster than scale speed. It is simply a product of the interesting unified relations in the physical sciences of motion to obtain correct prototypical flight characteristics and attitudes when compared to full-size flight. Much of this already had been instinctively recognized by determined scale modelers to match speed and maneuver for desired performance in flight realism. This is also very much like making sure the correct markings were painted on the right airplane when realistically flown in competition!

It is apparent the benefits of DSS include many overall scale-flight-realism features. In quick summary, DSS provides: improved stability in all axis, prototypical maneuver selection, prototypical g-load appearance, prototypical flight angle of attack, prototypical attitude or bank angle in turns, etc. Many of these are also outlined by the AMA for realism. These "mechanics-in-motion qualities" also have little or no control by model weight. In contrast, scale speed is a conflicting oddity and does not support the many other visible overall-flight-realism features during scale model flight in our fixed-gravity environment.
 

 
FULL-SIZE PERFORMANCE AND DSS COMPARISONS

An oversight can occur when comparing scale-model flight to full-size-combat aircraft capable of high pursuit speeds. For example, WW-II (or jet) fighter models have been used to erroneously suggest scale speed is achieved by referring only to full-size-high-speed ratings and then using them for determining scale speeds for maneuvers listed in AMA scale rules. However, these full-size aircraft do not fly such maneuvers at or near top-rated speeds! In comparison, the slower vintage models can clearly become handicapped if scale speeds were adopted with this flawed analogy. Documenting WW-II fighter aircraft typical maneuvering speeds may be of benefit to many readers, particularly since published literature usually only gives top-rated speeds at high altitudes for reference.

The following description is from Steve Hinton, who is a well-known respected pilot for the Planes of Fame Air Museum in Chino California with many WW-II vintage fighter aircraft in flying status. It is described in reference to what we would typically view from the ground near sea-level conditions for typical air-show environments. This summary also agrees with other detailed literature on this same subject for WW-II fighter maneuvers.

A stock P-47 can only do about 300 mph at sea level, and a P-51 about 350 mph. The differences relate to how slippery each aircraft is in aerodynamics through thicker air. Other fighters may be slower or vary accordingly depending on overall performance design. Horizontal rolls are typically done from 150 to 250 mph. Round loops are entered approximately at 300 mph, but lighter wing loaded fighters such as the F4F can enter them at 240 mph (210 knots). An "egg shape" loop with WW-II fighters can also generally be accomplished much lower, in some cases down to 200 mph. A round loop is optimally performed when there is zero g-factor at the top where it briefly "floats" (centrifugal force offsets gravity force) rather than exhibits a negative g or possible egg shape. For unusual maneuvers that require very high entry speeds above the level-approach capability of the aircraft at or near sea level (air shows), these are typically dived into the entry requirements such as for entering a vertical roll. He refers to "Reno style speeds" as a specialized area.

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