<< Page 19 Page 20: Page 21 >>   The Envelope Often, in movies about flying, in books, or even in everyday language, one might hear the expression “pushing the envelope”. This idea, of exploring or testing the limits of what is possible, is derived from aviation (more specifically, from test-flights at Edwards AFB as described in The Right Stuff). Now that you know about the forces that act on an airplane, it would be interesting to learn about the envelope, and to see how these forces change at different speeds and altitudes. Thrust, Drag and Lift (but not weight – not significantly, anyways) change at different speeds and altitudes. Therefore, they influence the airplane in different ways at different speeds and altitudes. Because of this, there are many combinations of speeds and altitudes that an airplane simply cannot reach. The group of combinations of speeds and altitudes that an airplane CAN reach is its flight envelope. More accurately, the flight envelope is the “edge” of this area, it is the boundary between the possible and the impossible. (In mathematics, the “envelope” describes the maximum and minimum values of a function or group of functions. For example, say I can throw a baseball at no more than 25 meters per second. Now, say I am standing in the middle of a very wide, flat field. There is a maximum distance that I can throw the ball – the range of my throw – because of the limited initial speed. Do the math (projectile motion), and you will find this is just under 64m. There is also a maximum height that I can throw the ball. Do the math and you will find this is just under 32m. Can I throw the ball at a point 64m away horizontally and 32m high? No. The only point 32m high that I can throw the ball is right overhead, and all the points that I can throw the ball that are 64m away are at 0 altitude. Therefore, given all possible throw angles and speeds (up to 25m/s), the points in space that my ball can reach form a “dome” around me, 64m in radius at the bottom, and 32m high: The envelope of the possible trajectory of my ball is the “ceiling” or “shell” of this dome Or here’s a simpler example: The envelope of the places on the ground my ball can land at, which is the envelope of points that are 64m or less from me on the surface of that field, is a circle 64m in radius with me at its center. Sorry about the mathematical digression. But now that we know what an envelope is; What defines the envelope of flight speeds and altitudes of an airplane? To start off, an airplane’s envelope usually looks something like this: The shape of this envelope – which shows what altitudes the plane can reach at different speeds, and what speeds the plane can reach at different altitudes – is determined by how the generation of lift, drag and thrust changes at different speeds and altitudes. The larger the envelope, the higher the ranges of speeds and altitudes the airplane can achieve. From the envelope, one can find out the maximum speed (and at what altitude it can be reached), the maximum altitude (and at what speed it can be reached), the stall speeds at different altitudes (useful if you want to land somewhere not at sea level), the maximum low-altitude speed (useful if you’re a fighter or bomber on an attack mission trying to stay under radar), and more. To simplify things, let us split the envelope into three edges: The slow edge, the fast edge, and the ground. We will see why the airplane cannot pass these three lines. The ground is a pretty obvious one: You can’t fly at less than zero altitude. As many aerobatic pilots will tell you: You can’t break the record for minimum altitude, you can only tie it. The slow edge is determined by the stall speed. As we have seen, a wing will stall more easily at higher altitudes. This is because air is less dense at higher altitudes, so 1) It is less viscous and thus stalls more easily and at higher speeds given a certain angle of attack, and 2) less lift is generated at a given angle of attack, so the angle of attack used in higher altitudes must be higher than at sea level, thus making the stall even easier. In other words, if you go higher, your minimum speed increases, and if you go below this speed, your wings stall and you fall (and in the process pick up more speed and un-stall, unless you hit the ground first). The fast edge is determined by how drag and thrust change with altitude. Because the air is thinner at higher altitudes, the drag goes down - but because the air becomes thinner, the thrust also goes down. So why is maximum speed reached at some intermediate altitude? At low altitudes, drag and thermal effects are much more severe than they are at high altitudes, because of the higher air density at low altitudes. An airliner flying at 650 miles per hour at sea level, or a fighter flying at MACH 2.5 at sea level, would probably be torn apart by the denser air. (In fact, at least two 737 accidents involved “frozen” rudder mechanisms which caused the jets to go into full-speed powered nosedives, and both 737s came apart before hitting the ground). So drag is much higher at lower altitudes, making it harder – and more dangerous – to fly at top speed through the denser air. Not only that, but engines having all that dense air shoved into them (if they were flown very fast at low altitudes) would get dangerously hot. Remember how, when we talked about ramjets, we said that the turbine inlet temperature was just about the most important restriction that limits the thrust an engine can put out. The air at lower altitudes is hotter and at higher pressure than high-altitude air. If you compress that low-altitude air, it becomes even hotter. Engines have a much easier time working with high-altitude air: When the engine takes in air that is colder and less dense to begin with, it can be compressed more before reaching those limiting temperatures. This means that the colder and less-dense air at higher altitudes allows a jet engine to run at higher RPMs and at higher compression rations, which make it more efficient. It also means that the engine intake can swallow more of that air per second and compress it properly, and thus burn more fuel and generate more thrust. So as you go higher, the engine can make more thrust and there is less drag, so you can go faster. But this only works up to a point. Remember that engines work by taking some amount of air per second (whatever flows into the intake) and accelerating it backwards. As air becomes less dense, there is less air to be accelerated backwards, so the thrust force decreases. (For a similar reason, the thrust put out by a small boat’s outboard motor decreases dramatically when the propeller (screw) is pulled out of the water and into the air; Air is much less dense and, when pushed back, does not supply an “opposite reaction” as strongly as the water does. Humans can use paddles and oars to move around on water but not in air). In other words, the thrust is the flow rate of air through the engine per second, times the added speed the engine gives to that air. When air is too dense, the engine cannot give the added speed it could with less-dense air, so very low-altitude air is not best for high speed. But with very thin air, the air flow rate through the engine per second is small, so the thrust decreases at very high altitudes even though the air is being pushed out as fast as the engine can push it. So, as you go up, air changes from “too dense to be compressed at full power” to “just dense enough to compress as hard as the engine can without getting too hot” to “so thin that, even though it’s being compressed and used to burn fuel, there’s not much stuff to push out of the back end”. Other considerations also limit thrust when the air is very thin. For example, the ratio of fuel burned to engine air flow must stay within a certain range; Too little air, and you can’t burn as much fuel. (This is why your car engine produces less power at altitude). Also, the compressor blades may stall when the air is too thin (See previous page, just after the graph, for reasons why wings stall easily at altitude); If the blades try to squeeze the thin air into the engine (as they must), the air can separate (stall), the compressor no longer compresses, and the flame in the combustor dies out. You then have no thrust at all! So the top of the envelope – max altitude – is either 1) An altitude where your engine is working as hard as it can AND your wings are on the verge of stalling, or 2) An altitude where your engine is on the verge of flaming out (the compressor is on the verge of stalling). What about piston-powered planes? They have no problem taking in the denser air, so they get more thrust at low altitudes, and less and less thrust as they go up. So their best speeds and efficiencies are usually at fairly low altitudes. With turbochargers and superchargers (which compress thin air before feeding it to the pistons), they can maintain high thrust into altitudes where the drag starts to get lower, so those might be able to go a little faster at these middle-altitudes (say, several thousand feet) than at lower altitudes. Like the jet compressor, though, the prop stalls if you get too high. Unlike jet compressors, though, props face the fullspeed slipstream (rather than air slowed down by a diffuser/intake) so they stall even more easily than jet compressors. A prop plane’s slow speed at altitude (due to low thrust) also causes the wings to stall easily. Both these reasons keep prop planes from wandering into the altitudes where jet aircraft perform at their best, and also from going much faster at any altitude than they do at very low altitudes. The exact speed at which this maximum altitude can be reached (the engines delivering all the thrust they can AND the wings about to stall), and the exact altitude where maximum speed can be reached (where the air density and speed lead to the best relationship between drag and engine thrust), are hard to predict exactly. This is why you hear about test pilots “pushing the envelope” – part of their job is to fly around these areas of the envelope where the top speed and top altitude are suspected to be. They try different speed and altitude combinations until they find the right one that delivers maximum altitude or speed. The hard part is doing this without stalling (for altitude) and without burning up your engine (for speed) in the process… Also crucial is finding where in the envelope the plane gets the best fuel economy. I should not fail to mention the more abstract and philosophical meaning of “pushing the envelope”, the one you are probably more familiar with. For example, if I am designing an airplane: Given my stiffest and lightest of materials, my best engines, and my knowledge of aerodynamics… How fast an airplane can I make? What is the maximum range I can squeeze out of a plane of a certain size? How high can I get a plane to fly? In other words, given some initial restrictions, What is possible? Pushing technology – or any pursuit, even personal improvement – to new limits and new realities is “pushing the envelope” of your initial limitations and restrictions. And while we’re on the subject – have you noticed how much “leading edge” has been used to refer to cuttingedge technologies, knowledge, and research? Even outside the aeronautical world (where it’s almost a cute pun to say “leading-edge” instead of “cutting-edge”), it seems to be catching on, like with computer technologies and so on. Yet another expression from the world of aeronautical engineering making it out onto the real world. And I wonder how many people know what “streamlining” really means… But I digress. Back to work. Here is an interesting comparison of envelopes: One for a turboprop plane (like a C-130 Hercules), one for a Helicopter (Like the HH-60 Blackhawk), and the one for the V-22 Osprey tilt-rotor aircraft (which is both a turboprop and a helicopter, in a way). The tilt-rotor clearly has the best of both worlds: it can fly at extremely low speeds like the helicopter but unlike the turboprop, and it can fly at high speeds and altitudes like the turboprop but unlike the helicopter. Its envelope is bigger, so it is more flexible when it comes to flying at different speeds and altitudes. Remember how we said heating gets to be a problem at high MACH numbers? For this reason, many supersonic airplanes (especially modern ones which use composite materials) may be able to reach a speed with their thrust and drag, but would not structurally be able to stay in one piece at that speed (their structures would heat up and soften, i.e. start to melt). For example, the F-22 envelope: Here we see two F-22 envelopes (non-afterburning, and afterburning) compared with two F-15 envelopes (nonafterburning, and afterburning). Note that an area to the right, possible given the F-22’s aerodynamics and engine, is “cut off” due to high temperatures (“Airframe temperature limit”). Also note some other interesting facts, like: The F-15 cannot break the sound barrier without using afterburner, or: The F-22 without afterburners can do everything the F-15 can WITH afterburners and more. This is true even when it comes to maneuvering (climbing and turning), which is not discussed in the graph above. It should also be noted that envelopes can be drawn for more than just “staying in the air”. So far our envelopes (specifically, level flight envelopes) have shown in what speed-altitude combinations the wing can produce enough lift to keep the plane in the air (i.e. 1X plane weight). A valid question, especially for a fighter design, would be what in speed and altitude (and power) combinations the plane can pull 5-g turns (i.e. when the wings can generate 5X plane weight as lift). Here, an envelope shows this information (5g flight, not just 1g flight), and again we see the F-22 is superior to the F-15 even without afterburners.   - - - - - - - - - - - - - - - - - -   Summary: the Envelope: -Level Flight Envelope defines how high an airplane can fly at different speeds, and how fast it can fly at different altitudes. Also reveals details like the maximum low-altitude speed, stall speeds at different altitudes, max speed, max altitude, etc. -Minimum/stall speed increases as altitude goes up. -Max speed increases to a point, then quickly decreases, as altitude goes up. Max speed is at this “point”. -Max altitude is the tricky place at a unique altitude where the wings are on the verge of stalling and the engine can’t produce any more thrust. -An envelope can also be drawn to define when/where an airplane is capable of performing turns and other maneuvers. This maneuvering envelope would lie within the Level Flight Envelope.