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otrcman -> RE: Determining weight "before" the model is built. (5/15/2008 4:32:52 AM)
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I'll try to expand on Wellss' use of the 3.5 power. First, do you want to simply build a model of this airplane and take whatever weight that comes out or do you want to determine a desirable weight and then shoot for that weight? If you want a realistic looking model you need to shoot for a specific weight range based on the weight and performance of the full scale airplane and the scale size of your model.
Here's why you would choose a target weight: The original F3F had a known speed range. Stall speed, cruising speed, and top speed. In order to look realistic in flight, your model should visually mimic the speed of the real airplane. But wait, that doesn't mean that your model should cruise at 160 mph just because the prototype cruised at 160 mph. Visually, your model will look realistic if it flys by at a speed consistent with its size. What we see in flight is the airplane covering so many times it's own length per second. Let's say the prototype was 25 feet long and cruised at 160 mph. This means the prototype travelled about 9.4 times its own length every second. So if your model is 5 feet long, it should have a cruise speed of 5 X 9.4, or 47 feet per second that's 32 mph. You can make this calculation a whole lot simpler by simply multiplying your scale by the cruising speed of the prototype, so 160 mph X 1/5 scale equals 32 mph. (surprise ! Same answer).
Unfortunately, a model scaled to look just right in level flight will be capable of very small circles when it turns. And will do incredibly tiny loops for its size. In other words, if the real airplane at 160 mph made circles in the sky of 500 foot diameter, that would be 20 times the fuselage length. Your model would need to make 500 X 1/5 or 100 foot circles to look realistic. But a model scaled to go scale speed will be capable of circles much smaller and will look funny when maneuvering.
It turns out that scale sized circles, loops, and rolls look about right if your model is quite a bit heavier and faster. To make proper maneuvers, the model would need to fly about 71 mph.
Skipping over the math, it turns out that a model will look realistic going by if its weight is scaled to the 4th power. But it will make scale sized maneuvers if its weight is scaled to the 3rd power. You can't have scale flight speeds and scale maneuver sizes in the same model unless your model is 100% scale and weighs the same as the prototype. Unfortunate fact of physics.
So what Wellss is suggesting, and is accepted practice, is to compromise between 4th power scaling and 3rd power scaling. It's 3.5 power scaling. That way your visual speed is slighty fast and your maneuvers are slightly small, but it's the best you can do and most people never notice.
Down to the numbers for weight: If you had scaled your model for scale speed, you would multiply your size scale ratio by itself 4 times to get weight. With a 1/5 scale, that's 20% or .20 of full size. Multiply .20 X .20 X .20 X .20 and you get .0016. Multiply .0016 times, say, 4000 lbs. and you get a model weight of 6.4 lbs. Too light ? Well, that's what you would have to do to make your 1/5 scale model look perfectly realistic in level flight. If you want scale size maneuvers, you would multiply your 1/5 scale by itself 3 times, or .2 X .2 X .2, and then multiply that answer by the 4000 lbs, and you have a model weight of 32 lbs. Too heavy ? Well, that's what it takes to make your 1/5 scale model do scale sized maneuvers.
You'll need a calculater to take 1/5 scale to the 3.5 power, but it works out that the model should weight 14.3 lbs to look about right in flight. Any heavier will begin to look too fast in flight, and any lighter will make unrealistically small maneuvers. Is 14.3 lbs cast in stone? No, you can go above or below that weight. But that's a good number to shoot for.
Sorry for the long winded answer. But that's the short version.
Dick
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