Is Light Right?? - Ideal Weight of a HLG

The factors controlling the launch height of an hlg are very complex, but we can summarize a few of the more important ones as related to weight.

*****Warning*****

In the interest of keeping this understandable, the following contains some simplifications to a very complex subject (which the technical purists on this form will undoubtedly try to nail me on). I believe, however, that the conclusions reached are valid.

In general, more weight will reduce launch height if there are no other complications. Your arm can only impart a certain amount of energy to the model, typically measured in foot-pounds (or newton-meters for those of you outside the U.S.A.). If you impart 50 foot-pounds to a one pound model, and we pretend that none is lost through aerodynamic drag, etc., that energy can raise your one pound model to a height of 50 feet. If the model weighs 2 pounds, that amount of energy can only lift the model a height of 25 feet.

The news gets worse for your more ponderous hlg's. The energy we are talking about starts as kinetic energy ( energy in the form of mass and speed), given to the model by the accelerating force from your arm. The amount of energy available for gaining altitude depends on the difference between the velocity (squared) when it leaves your hand and the velocity (squared) where it levels off at the top of the launch. Assuming that the force your muscles can generate is more or less constant, the acceleration is inversely proportional to the mass (remember that old formula from physics class, F=Ma?), which means that the heavier model will leave your hand at a lower speed than a lighter one. Blame it on Isaac Newton! To make matters worse, that heavier model will have a higher stall speed, which means it must level off sooner at the top of the launch. Together, that means that this heavier model has LESS energy available to lift its porcine bulk to altitude. The bottom line is, the lighter model starts out faster, finishes the launch slower (for a greater total change in velocity), resulting in a greater total launch energy. And don't forget, that lighter model gets more altitude for a given amount of energy than the heavy one.

Now, just to be fair, we must admit that while the heavy model leaves your hand at a lower speed, its higher mass tends to offset that somewhat (remember my statement at the beginning that the energy from your arm is more or less constant?). Unfortunately, this doesn't do anything to help the higher stall speed, so the available energy for climbing is still less for the heavier model. The other factor involved is that the acceleration depends on the total mass of the system, including the mass of your arm. As you reduce the mass of the glider, this mass becomes a smaller and smaller percentage of the total system mass, and therefore less significant in determining the resultant acceleration. It's that old law of diminishing returns. One way to get around this is to reduce the mass of your arm, at least the portion that gets accelerated. That's the principle behind the atlatl, or "throwing stick". Instead of having to get this mass of muscle, bone, skin, r/c model, and wristwatch(for you left-handed throwers) up to launch velocity, you just have to accelerate the model plus this relatively lightweight stick. Of course, a lighter model will be an even bigger advantage if you go that route!

So is everything in favor of the lighter model? Well, if any of you have read most of my earlier postings you will know that I rarely if ever believe in such a thing as a simple cut-and-dried answer for anything. I won't disappoint you today! Because its mass is lower, the lighter model has to expend its velocity faster to overcome the energy lost through aerodynamic drag. In other words, it slows down quicker. The heavy model starts the launch at a lower speed, so it doesn't climb as fast initially, but it holds that speed longer through the middle of the launch, which partially compensates for that. Of course, this still doesn't make up for the fact that it must level off sooner due to stall speed considerations, and its faster loss of speed required to convert that speed into altitude. The balance between induced and parasite drag also comes into play here; at the beginning of launch the velocity of the lighter model is higher, and the parasite drag (which dominates at high speeds) penalizes the lighter model. At the top of launch, though, the induced drag (drag that results form the production of lift) shifts things in favor of the lighter model once again. Induced drag is a function of span loading, and since the rules limit the span to 1.5 meters, the heavy model has a higher span loading and higher induced drag at any given airspeed. One way to reduce the induced drag penalty is to hold a vertical launch path relative to the air, so that the lift of the wing is zero. No lift, no induced drag. Of course, you have to be careful that the extra induced drag created during the pullup to vertical at the beginning of launch and the push to level at the end doesn't destroy all the benefits of your zero-g vertical climb.

There are cases where the launch height of a model can be improved by adding weight. Most airfoils have a lift coefficient below which the drag rises dramatically. If this drag rise occurs at a lift coefficient significantly above the lift coefficient for the high-speed phases of launch (which because of the speed is just slightly above zero), the drag rise will cause the model to scrub-off much of its initial speed very quickly, until the airspeed is low enough to drive the lift coefficient up into the low-drag region. This is likely to be the case with many high-lift, high-camber airfoils. A model with this situation may have excellent performance at minimum sink speed, max L/D, and even at penetrating speeds, but at the extremely high speeds at the beginning of launch it runs into its own personal brick wall. If you add weight to it, and also hold an upward arc at the beginning of launch, the net effect is to increase the lift coefficient enough to get it out of the high drag region. This is one of the few cases where heavier is better, and in this case it's only to the point that the wing has enough load to keep it out of its high drag region at low lift.

One of the big keys to the improved launch performance of our new Wizard and Chrysalis hlg's was developing wings that possessed the necessary max-lift and handling for excellent thermalling, but could also stay out of this high-drag trap at zero lift for launch.

One other mitigating factor in favor of the heavy hlg is Reynolds number. For those of you not familiar with it, this is a fancy engineering term that describes the size of something from the point of view of an air molecule. It's the product of physical size (chord in the case of a wing), airspeed, and the density and viscosity of the fluid you're working in (in this case air). Generally speaking, a larger OR faster model will have better performance thanks to its higher Reynolds number. At the Reynolds numbers typical of hlg's, the differences can be quite dramatic. This is less of a factor on launch, but once you get to the top of launch, the higher L/D of the faster heavy model will give you a little more searching range per foot of altitude, and may even give you the same or better sink rate if the L/D improvement is great enough. This is mostly a function of the effect Reynolds number on the performance of that particular model's airfoils. Whether this is enough to make up for the lower launch height you will probably get depends on the design of the model.

If you are interested in altitude, so far just about everything adds up in favor of the lighter model. If you are trying to cover ground, though, and holding the model at a fairly low and constant altitude during the launch, the heavier model's ability to hold speed and penetrate better may come into play. I was at a contest recently where we had a lot of wind, and a small ridge about 70 yards (meters for you metric folks) upwind and outside of the field boundary. We had the Chrysalis prototype loaded up with 3 ounces of lead, about a 32% increase over its empty weight of 9.3 ounces, to get better penetration. Despite the 15+ knot winds, the launch height was quite noticeably lower than what we would get unballasted in light air; however, by holding the launch level at a low, constant altitude Joe was able to penetrate upwind to the ridge, slope soar to get his time, then sail home with a tail wind to land within the field boundaries. This would have been very difficult without the extra weight. I took the 3 ounces out though, as soon as I got home.

Still not convinced? If there was a significant advantage to heavier weights in our size range the free-flight hand launch glider fliers would be building 20 ounce models. They've gone through a lot more years of development and evolution than we have. You can't fool mother nature!

Don Stackhouse @ DJ Aerotech