Building the same plane at a different scale

A reader emailed me a question about a plan he had downloaded.  The plan didn’t have any size dimensions on it, so he didn’t know how big to build the airplane.  I’ve never had this problem myself because although I have a very large collection of plans, they are all on paper.

Traditionally, model plans are drawn on paper at a 1:1 scale, meaning what you see on the paper is the exact size of the finished model.  You don’t have to wonder how big it’s supposed to be because it’s right there in front of you.  Some builders make a copy of the plan specifically for cutting out parts, then stick these parts onto the balsa wood with contact cement for easier cutting.  Material thickness, engine size, control throw, and other data will be noted on the plans as needed.  In fact, on a traditional paper plan the wood, landing gear wire, wheels, engine, and all other parts are drawn to their exact size, so even if something isn’t specifically labeled, you should be able to measure it on the plan to determine its intended size.

Now that we have the opportunity to transmit plans electronically, and a lot of plans are generated electronically, a less experienced builder has to make sure that all of the details including wingspan, material thickness, etc, are included because a lot of designers don’t do a good job of drawing the exact sizes on the plans.  Fortunately there are some general rules of thumb that you pick up after a few building projects, which means you should be able to build a plane in whatever size you want and still give it the right amount of structural strength without adding too much weight.

Before we had scanners and large format printers available, a balsa builder would have to build the plane at whatever size it was on the paper, or design a plane of the desired size himself.  Now you can go to an office store and run a paper plan through a large format scanner, then print it out at any new size.  I’ve reprinted the famous 36″ wingspan Q-Tee and built it at 24″, and I’ve reduced the RCM Senior Telemaster from 96″ to three different, smaller sizes.  I also built the RCM Simple T-Craft for a customer in .40 size, blown up from the original .25 size.  These are not very drastic changes in scale, so I simply used whatever size material was closest to the actual size on the resized drawing.  In other words, where the Q-Tee had 3/32″ balsa I used 1/16.  Mathematically, 1/8″ balsa should have been reduced to 1/12, as this is 2/3 the original size.  1/12 is the same as 3/36, which is extremely close to 3/32, so I used 3/32.  In other words, when reducing to 2/3 of original size, I simply substituted wood one standard size smaller.  The Telemaster was easier because all materials were half of the original size and everything lined up on the plan perfectly.

At the smaller scale the Q-Tee was almost perfect, except the horizontal stabilizer.  The original plan shows this part made of 3/16″ sticks, which I reduced to 1/8″.  It turns out that tiny sticks don’t scale as well as we might want them to.  The stabilizer was very fragile and suffered damage during a landing.  A solid sheet of lightweight 1/8 balsa works a lot better in this case.  In the case of the Telemaster, the original design has lots and lots of sticks, and they are of sufficient size that the scaled down model was still very well built, even though the reduction was more drastic than the Q-Tee.

When you resize a plan it’s always a good idea to check details such as these to make sure you’re not under-building anything.  On the other hand, .40 and .60 size planes frequently have lots of hardwood in the landing gear and engine areas, which, if built as drawn, can lead to excessive weight at a smaller size.  When you shrink a plane very drastically, it’s usually best to simplify and build things out of thin sheet wood to reduce weight.

The reason you can get away with this is because of a subtle effect of scaling which can be easily explained with an analogy.  Imagine a cube that’s one inch long on each side.  It has a volume of 1 cubic inch and a surface area of 6 square inches, for a volume to surface ratio of 1 to 6.  Now imagine a cube with a 2 inch length per side.  It has a volume of 8 cubic inches and a surface area of 24 square inches.  The volume to surface ratio is 1 to 3.  Think of volume in this case as mass and landing loads, and surface area as a general gauge of airplane size.  As a result, the smaller the plane is, the less strength you need for landing, crashing, or even engine mounting.  Larger planes need more strength in the firewall, wing spars and landing gear supports.

What this means to you when you decide to change the size of an existing design, or one that has a general outline but is sparse on details, is that you can usually get away with changing the size by 20 to 40 percent without worrying too much.  But if you resize a very small plane to be very large, or vice versa, you’ll probably want to redesign the wing spars, firewall, and landing gear mounts accordingly.  The best way to do this, as always, is to look at well established designs, such as popular trainer or sport flying kits, or popular plans, and use similar sizes and thicknesses in your plane.

After you build a few planes in different sizes you’ll find that you’re able to decide how strong to build these key points instinctively.