Originally Posted by
Top_Gunn
I am not saying any such thing. I'm not even saying anything much about what "scale speed" should be. I don't know the answer to that question; I could make guesses, but what would be the use of that? All I'm saying is that many people are assuming that it must be 1/4 of something or some combination of things for a quarter-scale model because that kind of model is 1/4 "the size" of the original, and that is wrong: it's 1/4 the length, 1/16 of the surface area, and 1/64 of the volume. There is no one number that measures "the size" of an object of more than one dimension.
I do think (but I'm not sure) that you may be right about one thing: whether a model in flight looks like a full-scale plane flying depends at least in part on how far away it is. That seems reasonable, but there may be other things that matter, too. When a model is just sitting on the runway and not moving, it seems clear enough that "scale speed" is zero: exactly the same as the speed of a full-scale plane sitting still. So if there really such a thing as "scale speed" for a model in flight, how does it go from zero to that particular fraction? Does it suddenly jump to 1/4 or 1/16 or whatever as soon as it starts moving, does it increase gradually, or what? I doubt that the answer is something we can simply calculate.
My point is based on physics (& optics), mathematics, & physiology.
Physiology. Relevant to this discussion, your only transducer able to sense the environment is your retina. What is senses is a combination of physics and optics. The mathematics of this is easy. We know that the light reflected off any object is bent by the convex lens of the eye and an image forms on the retina.
Optics. That image size is determined by the mathematics of the lens, focal length, position of the object in space (near field or far field), etc. And in the case of a single convex lens, that math is pretty easy. The size of the image in two dimensions on the retina is determined entirely by the size of the object and the distance. Assuming both are in the eye's far field vision, an object of size X & Y at distance D creates an image on the retina of size X' and Y'. Optics tells us that if you place an object 0.25X & 0.25Y at a distance 0.25D, the image on the retina is exactly the same size X' and Y'.
Physics. Since optics tells us that under the conditions above, the images on the retina are exactly the same size, then we turn to Newtonian physics and more math for speeds. Fortunately, the math there is straightforward as well. Using the observer at the center of a circle, the full scale object moves around the circle at angular velocity of Theta/second (in radians) = velocity along the circumference of the circle in feet per second divided by the radius of the circle in feet. Since we know the distance at which the 0.25 model creates the exact same size image on the retina, the radius of the model's circle is now known. All we have to do is solve for model velocity.
So a 1/4 size model at 1/4 the distance from the observer moving at 1/4 size the full scale velocity creates an image of the exact same size moving at the exact same rate on the observer's retina. As you've said people still don't perceive these as the same, so there must be other factors in play (assuming both speed and distance are correct). And I submit that it's what's happening between the ears. Namely, how the brain interprets the information fed to it by the transducer. I forget where I read it, probably in aviation safety training, but the brain processes an immense amount of other information in the "snapshot" of what the retina sends to it. You may be focused on the model, but the eye (and thus brain) are still seeing everything else in the background. Full scale items in the background of a 1/4 scale model are still perceived by the brain whether one knows it or not. And those subconscious inputs are incredibly powerful in forming the thought about whether the speed "looks scale."