Mention the phrase V-g diagram to most pilots and they immediately think of a map used by militant vegetarians to scout the location of edible but forbidden plants. In reality, the V-g diagram (sometimes called V-n diagram since technology usually refers to g-force as "n" values) is a useful tool in understandingour airplane's operating stress envelope.
Whether you realize it or not, your airplane (assuming it's certified in the U.S. under Part 23 of the FARs) is designed to withstand a great deal of stress. Unfortunately, many pilots are unfamiliar with the limits or the envelope within which that stress is allowed.
In fact, there are quite a few misconceptions in this area. For instance, some pilots believe that an airplane, flown at the top of the green arc, is incapable of exceeding the maximum allowable flight loads. Not true. Other aviators know that they should be in smooth air when flying in the airspeed's yellow arc. They don't, however, know how smooth air is defined. These and many other ideas are the topics discussed in this multipart series on the airplane's operating envelope.
Perhaps the best way to understand this operating envelope is to build one. That's exactly what we'll do. I'll walk you through the construction of the operating envelope, otherwise known as the V-g diagram. Let's get started.
The Positive-g Limit
Figure 1 shows the graph in which we'll build our the V-g diagram (Velocity/g-force diagram). We'll label the bottom axis as velocity and the vertical axis as load factor or g-force (which has nothing to do with the number of FBI men it takes to knock down a door). Let's draw a few lines representing the limits of how much our airplane may be squeezed, pulled or blown upon before it starts to look like something you find in a Dixie dumpster.
First, let's assume that our airplane is certified in the normal category. This means the engineers designed our airplane to withstand 3.8 positive g's before the airplane's wings begin to deform and structures begin to depart. Place a horizontal line at the 3.8g limit as shown in Figure 2. This line represents the upper g-force limit for normal category airplanes, otherwise known as the limit load factor.
We don't want to exceed +3.8g's for good reason. First, we'll begin losing secondary structures (flaps, gear doors, etc.), then, given enough excess g-force, we'll lose primary structures (wings, engines, etc.). The fact that you could lose anything on an airplane is very bad, even if it is a rental. You shouldn't bring an airplane back missing any of its major components. This is, after all, one of the many little ways pilots show respect for one another.
Keep in mind that positive g's are experienced when lift acts in an upward direction relative to the airplane. In other words, positive g's flex the wings upward. Negative g's, on the other hand, flex the wings downward. Perhaps you've experienced negative gs when you placed a Wrestlemania-like grip on the flight controls and shoved the elevator control forward too quickly. Unbelted passengers floating around the co*ckpit are a sure sign of negative-g's.
At this point, it's important that you have an intuitive idea about how strong airplane wings are. As an example of wing strength, take a look at a typical, older Cessna 172. The airplane has a maximum takeoff weight of 2,550 pounds. Since this airplane is certified in the normal category, its wings are capable of withstanding the stress of 3.8 times the airplane's maximum gross weight. In other words, the wings of this airplane can safely withstand a force of (3.8 x 2,550) 9,690 pounds, applied in the positive-g direction, without deforming.
To get a good idea about how much weight this really is, let's load the wings in the positive-g direction with people. First, we need to invert the airplane to apply the force as it would be felt in the positive-g direction as shown in Figure 3. Given that the average person weighs 170 pounds, the Cessna 172 could safely hold 57 people (or, approximately two small Japanese imports on each wing). Of course you don't want to try this at home, even if the airplane is a rental. Additionally, this type of static loading needs to be done professionally for obvious reasons. I hope you're convinced about the strength of airplane wings.
The Safety Factor
In addition to the normal stress limit of airplane wings, the FAA imposes an additional safety buffer in their construction. This safety buffer is known as the ultimate load factor which is 50% beyond the limit load factor. The airplane's primary structures (wings, engines, etc.) will begin departing the airplane when the ultimate load factor is reached. Unfortunately, the secondary structures (flaps, control surfaces, etc.) have probably already left. Remember, one of the most difficult tasks a pilot faces is attempting to explain to a passenger that the sizeable chunk of metal that just left the airplane isn't important.
Although the ultimate load factor is a safety margin, don't even think about using it. If you do, you're just like the smoker who thinks that cutting back from five packs to four packs of cigarettes a day is going to improve his health. Exceeding the limit load factor on any airplane is simply very bad news. End of story (or it could be if you do). As you'll soon see, there is never any reason to overstress an airplane. In just a bit, I'll show you how to avoid doing so.
It is interesting to note, however, that the FAA does approve some airplanes for flight that may need to use that extra 50% margin. These are airplane approved for flight beyond their normal gross weight. Such an aircraft falls into the restricted category of airplanes.
Cropdusters are an example of such aircraft (Figure 4). Cropdusters are heavier because they've got big hoppers filled with Raid (just kidding on the Raid!). Since they're restricted, the FAA doesn't want these airplanes flying over populated areas or carrying passengers. That's why you'll never see an airline called Bob's Discount Cropdusting Airline.
The Negative-g Limit
Continuing with our V-g envelope construction, let's draw the limit load factor's negative-g limit. The FAR's require that normal category airplanes be capable of withstanding negative g's equal to not less than 40% of the airplane's positive-g loading. This equates to -1.52g's (.4 x 3.8 = 1.52). Let's draw a horizontal line at the -1.52g level as shown in Figure 5.
Before we proceed with our construction, let's see where you'll fit in on this graph. First, ask yourself how many g's you're pulling right now. That's right. You're derriere is experiencing 1 g (if we were discussing the FAR's, your derriere might feel like it's pulling 3 or 4 g's right now). Looking at the graph in Figure 5, the normal position for flight is the 1-g line, not the 0-g line. Remember, you don't operate at zero g's; if you did, you'd float away because you'd be weightless. Keep the 1-g reference point in mind.
First, it's obvious that the airplane isn't as strong structurally in the negative-g direction as it is in the positive-g direction. Why? Flight load investigators have apparently found that these negative-g limits (-1.52 for normal category airplanes) aren't likely to be exceeded under typical flight conditions. Think about it this way. If an upward gust would increase the g force by one positive g, then the same gust applied in a downward direction decreases the g-force by 1g. If you start at 1g and subtract the downward gust effect of 1g, you're now at zero g's. In other words, to experience negative g's, the airplane must first move through the zero g (weightless) position. As you'll see next week, even with a lower negative-g limit, the airplane is still capable of withstanding an equal amount of negative-g gusts as it does positive-g gusts. This further explains why the airplane's capable of safe operation even with a lower negative-g stress limit.
Maximum Speed Limit
Now that we have the upper and lower g limits established, let's take a look at the upper speed limit of our V-g diagram. Airplane speed limits are typically determined by something known as flutter. Flutter is the violent vibration of an airfoil that's usually associated with excessive airspeeds. Flutter can lead to airfoil disintegration, which is of course a very bad thing. Flutter occurs at high speeds, where the normal elastic and inertial dampening qualities of the airfoil prevent excessive vibration. In other words, if a vibration occurs in a control surface, that surface's engineered qualities will dampen the vibration, thus preventing it from increasing in amplitude. Whew! To put it simply, you want to avoid flutter at all costs.
Many years ago, before oscilloscopes and sensitive vibration measuring devices were commonly used, aerodynamicists had a very basic means of identifying an airline's flutter speed. They'd find a skilled test pilot, show him a wheelbarrow full of money, then send him aloft to dive the airplane at dazzling airspeeds. The test pilot's job was to determine the speed at which the airplane experiences flutter.
When he returned-and when his breathing slowed and he regained his ability to speak-he'd tell his tale. He'd inform the engineers about the speed beyond which the airplane experienced flutter. This speed is known as Vd or design dive speed.
Let's place a vertical line representing Vd in Figure 6A. For convenience, let's use 169 knots as the design dive speed in our diagram. Of course, airplane manufacturers aren't going to let you fly the airplane right up to Vd like the test pilot did (they don't have your address and won't know where to deliver that wheelbarrow full of money). That's why, in the spirit of safety, the FAR's require marking the airspeed indicator's red line (Vne - velocity to never exceed) at a point representing 90% of Vd. In our example, Vne is (.9 x 169) 152 knots. Let's make a vertical line at this location on our diagram in Figure 6B. We'll come back to Vd a little later on.
The Stall Side
To complete the picture, we need to work on the left side-the slow speed side-of the V-g diagram. The left side of our diagram must represent a relationship between airspeed, stall and g force. Let's agree that the airplane in our example stalls at 50 knots at maximum gross weight. Draw a vertical line at 50 knots as shown in Figure 7. Keep in mind that the airplane stalls at 50 knots in a 1g condition. But what happens to stall speed when the g force changes? Yes, it must also change.
Now we need to construct a chart showing the relationship between stall speed and g force. These values are easy to determine for our airplane with just a little mathematics (Wait, come back here! I mean only a teeny-weeny bit of math). To find the stalling speed for a given load factor, we'll simply multiply the clean stall speed times the square root of that load factor. In other words, if our airplane stalls at 50 knots in the clean configuration, then it will stall at about 71 knots in a 2g condition (50 knots times the square root of 2 [or 1.414] = 71 knots). When I calculate the accelerated stall speeds for 3g's and 4g's, I obtain the graph in Figure 8.
Notice that the positive-g stall line in Figure 8 doesn't continue below 1g.
As an academic exercise, I'll continue the stall line to the left until reaching the zero g point as shown in Figure 9, line A.
Here we don't speak of stall speed, since the airplane and its contents feel weightless. After all, if you're weightless and stalled, how would you know? With just a little artist's license, I'll draw the stall speed line for negative-g flight (this involves inverted flight or outside maneuvers). We'll let the negative-g stall line be the mirror image of the positive-g stall line as shown by line B.
Now you're ready to superimpose this graph on the left side of the V-g diagram as shown in Figure 10. As you can see, the V-g diagram is nearly complete in the sense that it has four basic sides: a low speed side, high speed side, upper g-limit and lower g-limit.
To further complete the construction process, let's shade the area representing the area in which normal operations are permitted (Figure 11). There you have it. It's a completed V-g diagram, and now you know how it is constructed.
Let's examine four basic regions of the V-g diagram. Region 1A is the stall region, sometimes referred to by engineers as the region of unavailable lift. No matter how abruptly or fully you deflect the elevator, the airplane won't pull g's beyond the upper left portion of the stall speed curve.
Identify the point where the curved positive-g stall line intersects the upper g-limit line. Let's draw a line vertically downward at this intersection. This line represents a speed of approximately 97 knots. At this speed, the airplane will stall before it pulls more than +3.8 g's. This is an important speed to know. After all, if we fly at or below this speed, the airplane will stall before exceeding the airplane's limit load factor. In case you haven't guessed, this vertical line represents the airplane's maneuvering speed or Va (velocity of acceleration).
Suppose we were in extreme turbulence at 110 knots. Look at the positive-g stall line in Figure 8 and mentally project it upward. If our airplane stalled at this speed, it's obvious that it will experience enough positive-g's to put it way out of the operating envelope. This is one reason we want to be at or below maneuvering speed when encountering turbulence. We'll talk more about turbulence later in this series.
What about the other areas? Area 1B, for instance, should be avoided at all costs as we've previous discussed. This also goes for areas 1C and 1D.
Well, this is how the V-g envelope is constructed. But we're not even close to being done here. There are many, many more items to explore. For instance, next week we'll explore gust loads and what they mean to you. You'll find that a correlation exists between the different colors shown on weather radar (airborne or ground based) and the top of the green arc of your airspeed indicator. You'll definitely want to tune in for this information. And what happens to the V-g envelope when weight changes? Stay tuned for next week's article.
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