How to calculate scale speed on a model & If scale speed is inappropriate, how do you make a model perform scale-like?

From : Don Stackhouse

This is the subject of much debate, almost as heated as the infamous downwind turn.

There's an article that discusses some of this in the "Ask Joe and Don" section of our website. The specific article is at: CLICK ME! It discusses some of the aerodynamic effects that a scale model has to deal with when attempting to fly at "scale speeds".

A good deal of the controversy is because there are several different definitions of "scale speed".

From a dynamic scaling standpoint, such as when determining the speed for testing a wind tunnel model so that it has the same Reynolds numbers as its full-scale counterpart, the speed needs to be multiplied by the inverse of the scale factor. For example, if you were testing a quarter-size model and want to have the same Reynolds numbers and with normal air density, you need to set your wind tunnel speed at FOUR TIMES the full-scale aircraft's flying speed. This is not the type of "scale speed" us modelers are normally looking for.

There are some that try to argue in favor of a speed based on the square root of the scale factor. This is based on the fact that lift is proportional to the square of the airspeed. There are various other rationalizations based on similar lines of reasoning, all fundamentally based on the assumption that since lift doesn't scale linearly with speed, it's somehow "unfair" or "impossible" or "unreasonable" to expect the model to fly at a linearly scaled airspeed. Some of these have been proposed as definitions for the term "scale speed" in the scale competition rules. While I agree that getting a model to fly at a "visually scale" speed (i.e.: a linearly scaled airspeed, more on that in a moment) can be very difficult, even impractical, there is nothing in the "laws of physics" that says they have to be "fair". Physics is not a democracy, and the laws of physics are rarely (if ever) subject to negotiation.

For the "scale-like" visual appearance in flight of scale models, the only "scale speed" that truly makes sense is linearly scaled speed.

In other words, multiply the speed of the full scale aircraft by the model's scale factor. For example, a full-scale J-3 Cub cruises at about 70 mph. Therefore, a quarter-scale Cub should cruise at about 18 mph. The model and the full-scale aircraft will both move the same number of fuselage-lengths-per second, and therefore will both appear to the eyes of the spectators to be flying at the same speed. A 1/6 scale Cub (70" span) should cruise at about 12 mph. A 1/12 scale Cub (35", like some of the park fliers) should cruise at only 6 mph, and its stall speed should be about 3.5 mph. Is that tough to achieve? Probably, at least in most cases, especially the smaller models. However, if you want the model to really look like the full-scale article in flight, that's what's required. And no, contrary to what some of the ads claim, it's a rare indoor model that can actually fly that slow. In most of the cases I've studied, with very few exceptions, the ones that claim to have 4 or 5 mph stall speeds are probably more likely to have stall speeds of about 6-8 mph.

The other problem here is the wind. When we scale the model down, we don't scale the wind down with it. If your 3" Cub really does have a stall speed of 4 mph and a cruising speed of 6 mph, that means its top speed is probably only about 7 mph. It will be very difficult to fly in winds greater than about 3-4 mph. In other words, if you can feel any breeze at all (which means for most humans that there's at least 3-5 mph of wind), it's too windy to fly. For small models, flying at truly scale speeds isn't really practical unless you're flying indoors.

Because of this constraint, and because of the difficulties in keeping the weights low enough, very few outdoor models actually fly at scale speeds, unless it's a model of a very fast full-scale aircraft. The next time you're at a local small airport, watch a small aircraft flying in the landing pattern, and note how many fuselage lengths per second it moves. Now go to your local model airplane field and measure the same thing for typical models. See what I mean?

As modelers we've gotten used to seeing models fly at some typical airspeed where they perform well. This is usually considerably greater than a truly "scale speed", but it looks normal to us because it's what we're used to seeing FROM A MODEL. For us to actually achieve truly scale airspeeds, we usually need to have either a very large model of a fairly fast full-scale aircraft, or else an extremely light indoor model.

For example, I did a study a while back of a scale model I was designing. It was a model of a fairly large turboprop business aircraft (74' span), and I wanted to be able to fly at a truly (linearly) scale airspeed, but with a practical model structure. I estimated the flying weight of several different sizes of model, all the way down to 6' span, and the linearly-scaled flying speed and the resulting necessary lift coefficients. I found that the model needed to be at least 11.5' span to have adequate allowance for flying weight and scale speed, without hanging on the edge of a stall to do it. Even so, it needed functional Fowler flaps to get the landing speed low enough.

Another example is our Roadkill Series indoor models. The single-motor warbirds typically cruise at about 13 mph, which equates to about 250-270 mph in their full-scale counterparts, probably a reasonable cruise speed for a WW II fighter. However, they don't slow down much below that for landing, so their landing speeds are quite a bit faster than scale. They're still great fun to fly though, and that's what matters.

Scale speeds are tough to achieve, although not impossible. Even if we can achieve them, it's not always wise to do so. You need to figure out what's possible, what's practical, and how much you're sacrificing in other parameters to achieve these scale speeds. Only then can you determine if they're not only possible, but also desirable.

Don Stackhouse
DJ Aerotech