stick & rudder
flight advisor The Envelope, Please Knowing how the flight envelope is formed will help you stay inside H.C. “Skip” Smith
T
est pilots are famous for “pushing the envelope.” No movie or TV show involving flight testing would be complete without the hero risking his neck to push the envelope in some dramatically dangerous scene. This term, which has crept into everyday vocabulary, really means exceeding, by some small margin, the limits for which the airplane was designed. Such maneuvers are sometimes necessary for verifying the safety of new experimental designs, but those who fly already proven designs should have a goal to stay within the envelope. But, just what is this envelope, and how do we ensure that we are, indeed, keeping inside it? The envelope can refer to the enclosure of the possible altitudes and airspeeds, but for light airplanes it usually means a plot of the allowable vertical accelerations, or g-loads, as a function of airspeed. When we are flying straight and level, the aircraft is subject to 1g, or the acceleration due to gravity. The lift in this case, of course, is equal to the weight. If, however, you dive the airplane and then pull up, you encounter more than a 1g load. The lift on the wing is then that number of g times the weight of the airplane. The wing can only be built to take so many g’s before it fails. Hence, there’s a limit on the number of g’s that can be imposed on the airplane. This number depends 88
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on the category in which the airplane is certificated. For light airplanes, the positive vertical limits are 2.5g to 3.8g for the normal category, 4.4g for utility, and 6g for aerobatic. The range in normal category loads is due to variations in weight. Most light singles have to be at the top of this range (3.8), but heavier airplanes more than about 4,000 pounds can be designed for lower g’s. Negative, or inverted flight, vertical loads are a fraction of the positive number: half for aerobatic, and four-tenths for the other categories. Let’s invent a fictitious airplane and construct the envelope. This envelope is referred to by engineers as a VN diagram, N being the symbol used for load factor. Since N is expressed in so many g’s, the diagram is also sometimes called a VG diagram. This term seems more comfortable to pilots, so we will use it here. The airplane is a normal category airplane (the most popular) of 2,500 pounds maximum gross weight. The limit loads would thus be 3.8 positive, and 1.52 negative. The upper limit on speed is our allowable dive speed. Hence, in its simplest form, the VG envelope would be a rectangle of these limits. With acceleration plotted vertically against velocity across the horizontal axis, the top edge would be at +3.8, the bottom at -1.52, and the right side at the specified dive speed, similar to the limits shown in
the diagram in Figure 1. What’s wrong with this picture, though? Well, we can’t fly at zero airspeed, so the left side can’t be zero. There must be a minimum speed line added to the chart. By now you have probably figured out this is the stall speed. The stall speed you normally think of, though, is for 1g. At higher g-loads the stall speed goes up. Remember the increased stall speed in a bank? At 60 degrees, for example, the stall speed increases by 1.4 times that of level flight and the airplane
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Figure 1 is pulling 2g. If we bank even more (not recommended for normal category), the forces will be even higher. The stall speed actually goes up as the square of the g-load. To accurately determine this line of lower limits on airspeed, assume the airplane has 165 square feet of wing area and a conventional cambered airfoil. Using typical values of wing characteristics, the stall speed curve would then appear as the left side of the diagram in Figure 1. The inverted stall curve is also included. These stall speeds would be a little higher (negatively) than positive ones for a normal cambered airfoil. Both curves are cut off at the 1g lower limit. The limit dive speed (VD) is 1.4 times the design cruise speed (VC), which is specified in terms of the wing loading. Design cruise speed is normally the same as maximum structural cruise speed (VNO), the upper end of the green arc on your airspeed indicator. For this fictitious airplane, VC comes out to be 129 knots and VD then is 181 knots. The diagram also gets chopped off with a straight line on the negative limit from cruise to
dive speed, resulting in the complete maneuver envelope of Figure 1. Since pilots are normally very conscious (or should be) of their airspeed, it is not too hard to recognize when the airplane is below the limit dive speed. Determining the exact acceleration is more difficult, unless, of course, you have a g-meter. Usually,
only aerobatic aircraft have these, but, even then, when doing high-g maneuvers, you could momentarily exceed the g limit before recognizing it. To preclude such an event, designers have a magical speed called the “maneuvering speed,” where the airplane will stall before exceeding the limit load factor.
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flight advisor Figure 2 In reality, this speed is not that magical. It is the speed associated with the upper left corner of the diagram. It is termed VA in more technical references, and this corner of the diagram is called point A, as shown. Note that, at this point, the stall speed curve crosses the maximum g limit line. This means that, at VA (110 knots for this airplane), the pilot can yank back hard on the stick and the airplane will stall at 3.8g. The loading will not go any higher because the lift drastically diminishes at the stall. Hence, a pilot cannot overstress the airplane at this speed. Going slower than 110 will cause the airplane to stall at correspondingly lower g. So much for maneuvering. We all know, however, that the airplane can be flying along straight and level in a lazy 1g mode and suddenly get one heck of a kick in the pants from Mother Nature. This effect is from turbulence, or what engineers call gust loads. Gust loads arise from vertical currents pushing the relative free airstream up or down.
Battling Blowhards An upward push would yield a sudden higher angle of attack before the airspeed could change. At a higher angle of attack, the wing suddenly develops more lift, and the result is the same as a sudden pullback on the stick. Such loads can put high stress-
es on the airplane. To prevent overstressing, the FAA requires design for certain limit gust loads. These limits are specified in terms of gust velocities rather than g-force. For light airplanes, the requirement is for 50 feet per second at VC, and 25 feet per second at VD. These velocities are not
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considered to hit instantaneously, but to onset over a small amount of time. This effect is accounted for in a “gust alleviation factor,” which is a function of the mass of the airplane. It is important to recognize that a certain value of gust velocity puts different g-loads on the airplane at different forward airspeeds. This load drops off in a straight line from a maximum at design cruise speed to 1g at zero velocity. Thus, just as with maneuver loads, slowing down lessens the blow to the airplane. The question is, how much? Transport category aircraft have a certain speed called “maximum gust intensity velocity.” That is their best speed for turbulent air. Light airplanes do not have such a speed specified, so maneuver speed is generally used as the speed for minimizing gust loads as well. Figure 2 shows the gust envelope plotted over the maneuver envelope. Note that, for our example airplane, the 50 fps gust imposes only 3.6g on the airplane at VC (point B), less than the maximum +3.8 that the airplane must be designed for. The gust load allowances help ensure the airplane is always inside the positive envelope, turbulence-wise, at all airspeeds. This situation is typical of many light airplanes, but aircraft with low wing loading may be exceptions. Nature may not have read the regulations and may not be aware that it is sup-
posed to limit its gusts to 50 fps. That means that slowing to maneuvering speed is a good idea because it results in a larger margin of safety. On the negative side, we do slightly exceed the maneuver limit at point C, and more so at the dive speed (point D). The aircraft would, therefore, have to be designed for these loads, since they exceed those from maneuvering.
Weighty Issues So far, all our figures have been calculated at design (maximum) gross weight, which is what is used for certification purposes. At lower weight, the airplane stalls at lower airspeed. Hence, the stall line, or lower end of the envelope, shifts over as shown in Figure 3 for a reduced gross weight of 1,700 pounds. (Note that, for simplicity, we have only shown the positive side of the envelope here.) The weight here, 1,700 pounds, is the minimum operating weight for this airplane—the empty weight plus a standard-weight pilot and a halfhour of fuel. Now you can see that, if you fly at the original maneuvering speed of 110 knots, you could exceed the 3.8g limit before the airplane stalls (point E). It would not stall until you are pulling 5.6g. To ensure that you stay within the envelope, you would have to fly at the new VA of 91 knots (point F). Some of these values are calculated from rounded-off numbers
Figure 3
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flight advisor and are, therefore, not exact. It’s interesting to note that, if we did stay at 110 knots, and pulled 5.6g’s, we would not overstress the wing. The wing lift is the weight times the g-load, and the lift for 1,700 pounds at 5.6g is the same as the lift for 2,500 pounds at 3.8. That means the wing would stay on even if we don’t reduce the maneuvering speed. Why worry about it then? Well, the attachment of fixed items on the airplane, such as the engine, battery, landing gear, etc. are designed to withstand loads of only 3.8g, and could be damaged by higher loads regardless of the overall gross weight. Hence, you really do need to adjust your maneuvering speed for lower gross weight. Since maneuvering speed is the safe turbulence penetration speed, it makes sense that the airplane needs to slow more when it’s light when the airways get bumpy. The gust line for 1,700 pounds is also plotted on Figure 3. Note that if the airplane is at the design cruise speed of 129 knots it would exceed the 3.8g limit with a 50 fps gust (point G). Slowing to the max weight VA of 110 is also not enough, since the airplane would still pull more than 3.8g with this gust intensity. Going to the new maneuvering speed of 91 knots, though, does put the airplane within the gust envelope. Here, a 50 fps gust only results in about 3.4g. The negative gust velocity line (not shown) would intercept the lower limit (-1.52g) at about 93 knots, even closer to the new VA of 91 knots. The reason that lower weights result in higher gust loads is that, for a given speed, the increase in lift from a vertical gust velocity is the same for all weights, but the original level flight lift is less for lower weight. Hence, the increase in lift from a gust is a greater percentage of the original g lift on a lighter aircraft. Most modern aircraft have maneuvering speeds specified in the pilot operating handbook for various gross weights. If yours does not, there should at least be a figure for maximum gross weight. Using this value for most operating weights would 92
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probably be a safe procedure. If, however, you were very light, it would be prudent to slow to about 85 percent to 90 percent of that speed. Flight instruction book author Bill Kershner recommends reducing maneuvering speed by half of the percentage of the reduction in gross weight below maximum. In our example, 1,700 pounds is 32 percent less than the maximum weight of 2,500. Reducing the 110knot maneuvering speed by 16 percent (half of 32) would yield 92 knots, very close to our calculated 91. Pilots don’t often have time, however, to do a lot of calculations when in a busy flight situation. It is also important to keep the airplane at a sufficient margin above stall speed when in low-level operations, such as on approach. An even simpler rule of thumb to ensure the airplane is at a safe turbulence penetration speed for all weights and still retains an adequate margin above stall is to fly at 1.5 times the flaps-up stall speed specified for maximum gross weight. This is the speed at the lower end of the green arc on the airspeed indicator. For the sample airplane, the green arc begins at 56 knots, so the all-weight turbulence penetration speed would be 84, even more conservative than the 91 knots calculated for minimum speed. Following these rather simple rules should help ensure your airplane stays in one piece, even in some of the roughest air. Remember that 50 fps is a rather hefty gust velocity. That’s about 30 knots, and you probably have a good idea of how strong a 30-knot horizontal wind is. Also, the airplane must be designed not only to not bend below the limit g loads, but also not to fail until a load 50 percent greater than that is encountered (a 1.5 safety factor is used in all aircraft design). Hence, the wing of a normal category airplane won’t actually break off until you pull at least 5.7g at full gross weight. But don’t get complacent and count on these margins. The moral of the story is: When encountering significant turbulence, slow down. At lower gross weight, slow down even more. Don’t try to push the envelope.
