Aerodynamics空气动力学.doc

Aerodynamics空氣動力學Basic Principles基本原理The popularity and accessibility of paragliding has compelled theoreticians to simplify the fundamentals of aerodynamics so that it can be more comprehensible to everyone. In my attempt to follow this spirit in my book, I will explain Bernoullis general law or principle, along with the concepts of glide ratio and polar curve, all of which will be outlined shortly. It is thanks to its aerodynamic wing that a paraglider is able to fly, and flying speed depends on the shape of the wing, which is specially designed and manufactured. During the launching procedure, as the wing is pulled overhead, air entering from the front fills the wing and internal pressure is built up, thus enabling it to take on its intended shape. The air enters the central part of the wing and circulates to build up pressure in the closed wing tips making a semi-rigid, more or less solid, wing.飛行傘（滑翔傘）的普及性和可及性使得理論家們不得不簡化空氣動力學的基礎原理，以便於每個人易於理解。我在書裡將試著沿用這種精神，我將跟滑降比率和性能曲線一起解釋伯努利一般定理或者原則，而上述幾個名詞亦將會簡短的說明。感謝空氣動力的翅膀使得飛行傘得以飛行，而飛行的速度取決於被特別設計並且製造的翅膀的形狀。在起飛階段，因為翅膀被拉在頭頂，由於自前面填充進入翅膀的空氣和內部的壓力的增加，使得它能夠呈現預計的形狀。而那些進入傘翼中央部分並且循環的空氣增加了傘翼封閉端壓力，並使其成為半硬式（多少是固態的）的傘翼/，At this point, the wing is inflated and aloft. While the wing is flying the air that meets the leading edge (front edge) is forced to separate into two airflows. Due to its design, the wing is almost flat underneath whereas it is curved above. 此時，傘翼膨脹並且位於高處。當傘翼在飛行中碰上前沿(前緣)的空氣時 空氣被迫分成兩道氣流。 由於設計的關係，傘翼的下緣相對於他的上緣是平坦的。 The lower portion of the separated airflow continues its course smoothly below, while the upper flow follows a larger course over the curved upper surface. The two flows meet simultaneously at the rear of the wing. 被分開的氣流中的較低的部份繼續沿著下面的路線順利的流動，而上面氣流沿著上緣彎曲的表面上的較長路線流動。兩道氣流同時在傘翼的後緣接觸。According to Bernoullis law of physics, accelerated air reduces the pressure the air exerts on a surface, thus there is less pressure on the upper wing side and more pressure on the lower side. Thus due to this difference in pressure the wing acquires lift, an upward force that enables the wing to fly. 根據物理學上的伯努利定律，加速的空氣會降低壓力空氣並施加於表面，因此上緣傘翼會有較低的壓力而下緣的傘翼會有較高的壓力。所以傘翼會因為這種壓力差而得到昇力（使傘翼能夠飛行的一個向上的力量）。If we take the analysis a little further, we can distinguish an other force. The opposite force to lift, which is gravity. 如果我們稍微更進一步的分析，我們能區分出一種其他力量。 昇力的相反的力量，即重力。According to Newtons law, all objects fall to Earth at a rate of acceleration of 9.8 meter per sec2 (32 ft/sec2), which in the case of our wing, is opposed or slowed down by the aerodynamic forces.根據牛頓定理，所有的物體皆以每秒9.8米(32英呎/秒)的加速度的比率下降到地球。而我們傘翼情況，則是被空氣動力學的力量抵消或者減速。The aerodynamic forces can be separated into those that work to offset gravity and those that impede forward progress. These latter forces are called drag. Added to this drag is friction, which also impedes the glider. 空氣動力學的力量可以被區分為：抵銷重力的力量以及阻礙向前的力量。後面力量被稱為阻力，施加阻力是磨擦力，這也同時妨礙著飛行傘There are 3 sources of friction and drag: 磨擦和阻力的3個來源1. Friction on the wing surface from air passage. 2. Resistance of the wing, lines and pilot as solid bodies blocking the airflow. 3. Vortices or swirls on the tips of the wing. 1. 來自空氣流過的傘翼表面的磨擦。2. 傘翼，傘繩和飛行員像固體般堵塞氣流產生的阻抗。 3. 在傘翼上方的渦流或氣旋。The result of all the forces balancing on the wing is the capacity of the paraglider to fly steadily in a gradual downward sloping direction. The only way we may gain altitude is if the surrounding air current is ascending enough to offset our gradual sinking. As we fly along, our forward motion creates an airflow called the relative wind, which is the wind we feel blowing in our face. Our forward motion through the air and relative wind have the same speed. In practice, the wing starts to move through the air when we begin loading it and aerodynamic forces build up. 所有力量在傘翼上平衡的結果，是提供飛行傘一種沿著逐漸向下的傾斜方向穩定飛行的能力。唯一能夠使我們獲得高度的方式，是我們周遭的氣流上昇力的足夠抵銷我們逐漸下沈的力量。當我們獨自飛行時，我們前進的動作製造了一種空氣的流動，稱之為相對風（是一種我們覺得吹在臉上的風）。我們前進通過空氣的動作和相對風有著一樣的速率。實際上，當我們對傘翼進行負重時他就開始移過空氣，而空氣動力學的力量使他增強。Paraglider designers have been trying to achieve greater lift and lower drag, thus improving performance. This is, however, a balancing act since wings enjoying large spans and little chord (depth) produce better performance but are more susceptible to collapse and require greater piloting skills. In other words, designers can create the perfect wing in terms of performance but safety may be compromised. The important factor is always safety and this is where experienced test pilots assist in development. Theory and practice have improved the gliders to a high level compared to the older gliders. 飛行傘設計者早已試著獲取更大的昇力及更低的阻力，如此方能改進性能。假如傘翼有著較大的翼展及較小的翼弦（深度、寬度）則會製造更好的性能，但也更易於潰傘也就需要更好的飛行技巧，這兩者之間必須要取得平衡。換句話說，設計者可以製造一個在性能上完美的傘翼，但在安全上就必須被妥協。而安全永遠是一個重要的因子，這也就是試飛員在開發過程中能有所幫助的地方。相對於舊的飛行傘，新的飛行傘在理論與實務方面已經有大幅度的改善了。Let us now analyze forces and the angles that result from them: 現在讓我們分析各種力量的的角度及結果：Description of Terms 名詞解釋R: Attitude angle is the angle between the chord of the wing and the horizon. It is positive above and negative below the said horizon. R：姿態角：介於翼弦跟水平面間的角度。他高於水平面時是好的，低於則是不好的。A: The angle of attack is the angle between the chord line of a wing and the relative wind (which is exactly opposite to the flight direction). Angle of attack typically ranges from 3 to 12 for a paraglider. Below 0 a negative lift is produced, and above 15 or so a stall occurs. A：攻角：是介於翼弦線及相對風（飛行方向的反方向）間的夾角。典型的飛行傘攻角範圍由3度到12度之間。低於0度時昇力就產生，而高於15度時就發生失速。F: The flight angle is the angle between the horizon and the flight direction or path. F：飛行角：是介於水平線跟飛行方向間的角度。RW: Relative wind is produced by our wing during forward motion in the air. It has the same axis but opposite direction to the flight path. RW：相對風：是傘翼向前移動過空氣時所產生的，他與飛行路徑有相同得軸線但相反的方向。Glide Ratio: Horizontal distance traveled divided by height loss. Glide Ratio = Distance/Height. Glide Ratio：滑降比：高度損失時所移動的水平距離。滑降比距離/高度。The angle of descent is the angle your path makes with the horizon and is the same as flight angle. The angle of descent：下沈角：是你所製造的路徑與水平線間的角度，大小與飛行角一樣（為飛行角的對角）。The mean camber line is the line from the leading edge to the rear edge of the wing, each point of which is of equal distance below and above the wing. The shape of this line determines a wings aerodynamic featuresThe mean camber line：平均弧線：是一條由傘翼前緣到後緣的線，此線上的任一點到傘翼的上、下緣有相等的距離。這條線的形狀會決定傘翼的空氣動力學特性。Angle of attack 攻角The angle of attack changes the aerodynamic balance of a wing. At higher angles of attack the airflow must alter its path more to move past the wing. Thus lift and drag increase and the wing slows down. If we reduce our angle of attack, lift and drag will drop and the weight will accelerate the wing downwards and forwards. Acceleration will cease eventually because lift and drag build back up since they depend on the speed of the airflow over the wing. Thus, at a lower angle of attack, constant speed is attained which is greater than that at a higher angle of attack. We can conclude that adjusting the angle of attack will result in our wing speed being altered. Pulling on the brakes or applying the speed bar is what modifies the angle of attack on a paraglider. By the same logic, a constant angle of attack is equivalent to a constant flying speed. 攻角會改變一個傘翼的空氣動力學平衡。在高攻角時，氣流必須更加的改變它的路徑以移動過傘翼。如此昇力和阻力會增加而傘翼就會減速。如果我們降低攻角，提升和阻力會下降，而重量會使得傘翼向下且向前加速。因為昇力及阻力會隨著傘速增加，所以加速度最終會停止。因此，在一個較低的攻角下，會比高攻角下更容易取得恆定的速度。我們能斷定調整攻角將會導致我們的傘速被改變。拉煞車或踩加速器是改變飛行傘攻角的方法。透過相同的邏輯，一個固定的攻角可以獲固定的傘速。（註：依據黑點大師的意見，拉煞車或踩加速器是改變飛行傘攻角的方法這一句話有點過於簡化。嚴格的說，應該是拉煞車或踩加速器會改變姿態角，進而改變飛行傘的攻角）A wing does not necessarily have the same angle of attack in the middle and at its tips, due to the way it is designed. This is the wings washout, meaning the wing tips have a progressively different angle of attack from the center of the wing. Usually the wingtips have a lower angle of attack due to the towings shape, and when we change the angle of attack by pushing the speed bar the edges are affected more. In flight, the angle of attack can only be adjusted to a small degree, as the wing is highly pliable and subject to collapse. If we try to fly at too high an angle of attack the wing proceeds too slowly and a stall will result. If we lower the angle of attack beyond a certain limit the wing flies much faster, but will be subject to collapse. 由於設計的關係，一個傘翼不必在中間及翼尖都有固定的攻角。傘翼的除洗（WashOut），指的是傘翼的翼尖較中央的部分以更大的攻角。通常翼尖由於是後拖的形狀，所以會有一個更低的攻角，當我們透過推加速器改變攻角時，邊緣的攻角會改變更多。在飛行時，當傘翼變的極度容易折灣及崩潰時，攻角只能被調整至一個非常小的角度。如果我們試著在高攻角下飛行，則傘翼會前進的太慢，失速也就產生了。如果我們降低攻角到某個限度之下，傘翼會飛得快很多但更容易潰傘。 Stalls 失速A paraglider has a very limited speed range. Below the minimum speed the wing enters a stall. This happens if the angle of attack is increased too much so the airflow over the upper of the wing is unsteady and the forward motion of the wing is stopped. A stall is a result of an error performed by the pilot. In SIV Maneuvers we describe how a stall can be produced by the pilot and the procedure to recover from it. 一頂飛行傘有著非常有限的速度區間。低於最小速度傘翼會進入失速狀態。如果攻角變的過大以致流過頂端的氣流變的不穩定，同時飛行員操作錯誤所形成的結果。在SIV Maneuvers中我們會說明如何由飛行員造成失速，以及排除、回復的程序。In flight a stall can occur if the pilot is flying at low speed and encounters a sudden ascending air mass. This upward moving air will momentarily increase the wings angle of attack possibly beyond the stall angle of attack. The stall speed is the specific speed point where the wing stops flying. This occurs at one angle of attack for the same wing loading of a paraglider (or any aircraft). When the wing enters a stall the pilot maintains the control and altitude is lost. The recovery from a stall depends on the reaction of the pilot. He should gradually release the brakes to normal position (about shoulder height). Most of the training wings will recover in 2-3 seconds. Stalling close to the ground can lead to an accident if sufficient recovery altitude is not available. Flying at low speeds near the ground is dangerous. 如果飛行員在低速飛行時遭遇瞬間消失的空氣亂流，亦會發生造成失速。在越過失速攻角時，上層流動的空氣會暫時的增加傘翼的攻角。失速速度是指：當傘翼停止前進的一個特定的速度點。這種情形會發生於飛行傘（或任何的航空器）的翼負載相當於攻角時。當傘翼進入失速狀態時，飛行員依然能保持對傘的控制，但是飛行高度會嚴重損失。若要從失速狀態中改出，則有賴於飛行員的反應操作。飛行員應該逐漸的釋放煞車到正常位置（大約是肩膀的高度），多數的訓練傘會於2-3秒內回復。如果沒有足夠的高度進行失速的排除，在$接近地面時發生的失速可能會造成意外。所以，在接近地面時的低速飛行是非常危險的。Flying Speeds 飛行速度Manufacturers usually quote minimum and maximum flying speed for a design. Speed will be affected by altitude, but for now lets not concern ourselves with that since comparisons must be made under similar conditions. 製造商通常會強調一個傘具的最低及最高速度。速度會受到高度的影響，而是我們所重視的是那些在相同條件下產生的結果。When we talk of flying speed called V trim, we mean the wings speed without applying any pressure on the brakes or speed bar. This speed relates to the trim angle of attack and it is the flying condition a wing will return to when the pilot releases the controls in smooth air. 當我們談到速度（傘速）時我們稱之為V trim（V型調整），指的是沒有施加任何壓力於煞車或加速器上時的狀態。此時的傘速會與攻角的調整變的相關連，而這就如同飛行員在平順的空中方開雙手時的傘翼一樣。Glide Ratio in Relation to the Ground 對地速度中的滑降比This factor is the ratio between the ground distance covered divided by height loss. See the drawings below. For example, when a manufacturer refers to a glide ratio as say, 8:1 (read eight to one), this means that for every distance of 800 m covered, there will be a loss of a height of 100 m at a constant speed in the absence of wind. However, if at 30 km/h airspeed and in no wind the glide ratio is 8:1, with a headwind of 15 km/h a distance of 400 m over the ground will be covered, thus the glide ratio over the ground will be reduced to 4:1. On the other hand, in a tail wind of 15 km/h 1200 m will be covered and glide ratio will be 12:1. 滑降比是指對地距離除以高度損失所得的比率。舉例而言，當製造商提到滑降比為8:1（讀作八比一） 時，這是指以恆定的速度每前進八百公尺時，高度將會因為相對風的關係下降一百公尺。無論如何，假如在空速三十公里的無風狀態下，滑降比是八比一。而在頂著時速十五公里的風的狀態下將會前進四百公尺，此時滑降比將降低為4:1。換句話說，順風十五公里時則會前進一千兩百公尺，此時的滑降比會變為12:1。So you see, that while our glide ratio through the air only depends on our angle of attack, our glide ratio over the ground also depends on the wind speed and dire-ction. More about glide ratio will be discussed in the section on polar curve. 所以你可以瞭解，當我們在談純粹的空中的滑降比時僅與攻角相關，當我們考慮到對地速度時就與風向有關了。更多有關於滑降比的討論，我們將會在polar curve（性能曲線）一結中討論。Steady State Speed and Speed in Equilibrium 穩態速度與平衡速度This is an appropriate moment to discuss a paragliders steady state speed in the air. This speed is the speed given (by an earnest manufacturer) for a particular angle of attack and altitude. It can be read from an accurate airspeed indicator while in the air. Remember that in flight we can feel relative wind only, not the actual wind moving in relation to the ground. Only through such measurements can we laculate accurate airspeeds. 我想這是一個提及飛行傘的穩態速度（steady state speed）的合適章節，這種速度是在製造商所保證的特定攻角及高度下所產生的速度。他可以透過准確的空速計在空中時讀取。記住，在飛行時我們僅能感覺到相對風，而不是實際上相對於地面的風速。只有透過這樣的測量，我們才能夠取得準確的空速。Thus, there are two important and distinctive speeds: 因此有兩種重要而不同的速度1. Airspeed (our relative motion through the air) and 2. Groundspeed (our speed relative to the ground). When flying speed is 30 km/h in a 30 km/h head wind, then our groundspeed is zero. As a result, the paraglider has no forward motion and will descend vertically. If a 10 km/h tail wind exists, flying speed will be 30 km/h as measured by an airspeed indicator, while groundspeed will be 30+10 = 40 km/h. To clarify, imagine that we are walking along an escalator in a direction opposite its movement. If both speeds are the same (our walking and the escalator motion) we make no progress forward unless we increase our walking speed; then we progress at the rate of the difference in speed. When both motions go in the same direction, the speeds are added together. (See drawings on page 114.) 第一、空速（我們在空中的相對運動）以及第二、地速（相對於地面的速度）當我們以時速三十公里飛行但是頂著時速三十公里風時，此時我們的對地速度為零。結果飛行傘會沒有前進的動作而且將會垂直的下降。而在時速十公里的順風而空速計量測到的速度為三十公里的狀態下，我們的對地速度將會是時速四十公里（30+10公里）。為了弄得更清楚，想像一下我們沿著電扶梯運行的相對方向前進。如果兩者速度相同時（我們行走的速度及電扶梯前進的速度）我們將不會有任何的前進，除非我們加快走路的速度，而我們的前進速度是兩者之差。當兩者以相同的方向前進時，其速度為相加之總和（請看第XXX頁的圖）。On a paraglider, wind strong enough to give us a backward ground motion would be a serious matter. In the vicinity of a hill side or mountain slope the problem is more severe if we end up moving backwards over the peak and then on the leeward side of the hill, where we will be confronted with turbulence. High wind speed is a complicated and dangerous factor in flying. We must learn to evaluate the conditions carefully and remain within the limits of our gliders capabilities and our flying skill level. In the chapter on cross-country flying we will see that long distance flights are sometimes performed with the aid of high-speed winds at great height. Your instructor will provide valuable information to help you build an evaluation of wind conditions (also see the section on meteorology). 在飛傘時如果風強到會使我們變成向後退的對地速度，這將是一件非常嚴重的事情。在鄰近丘陵或山邊時，如果我們停止前進而且倒退超過山頂到會讓我們遭遇亂流的背風面時，這樣的問題將更形嚴重。高風速在飛行的時候是一種複雜且危險的因子。我們必須學會小心的評估情況以及傘具性能和我們技術水準的餘裕。在越野飛行的那一章中你將會看到長途飛行有時必須藉助及高度下的高速風。你的指導者將會提供要價值的資訊來幫助你評估風況（同時參考氣象學一節）。The Polar Curve 性能曲線On a graph or diagram where descent rate and flying speed are recorded, we can create a curve which will define the glide ratio for the entire range of speeds a paraglider can achieve. Measurements should be done in the absence of wind, lifting air or sinking air. The descent rate in vertical speed is measured in meters per second (m/s) or feet per minute (FPM). We can read the descent rate as displayed on our variometer. An airspeed indicator measures our paragliders speed. By flying at a constant rate we can get a descent rate related to each distinct airspeed. Then we divide airspeed by descent rate to get the glide ratio at that airspeed. Alternatively, we can carry out a number of flights with each one being different in speed but held constant during the flight. Then, we count the distance covered and divide by height loss (takeoff to landing) and come up with the glide ratio. 在任何記錄沈降率（descent rate）以及飛行速度（flying speed）的圖表裡面，我們可以繪製一條用來定義飛行傘所能達到的所有飛行速度的滑降比的曲線。量測時必須在消除風力、上昇或下降氣流的影響狀態下進行。垂直方向的沈降率是以每秒幾公尺（m/s）或每秒幾英尺（FPM）為單位來定義的。我們可以透過升降儀來讀取沈降率，空速計來讀取飛行傘的空速。透過飛行在一個固定的速率的方式，我們可以獲得在不同空速下的沈降率。之後，我們將空速除以沈降率以獲得不同空速下的滑降比。另一種獲得滑降比的方式，則是我們可以先做許多次不同的固定速度下的飛行。然後，我們可以計算每次的飛行距離並除以所消耗的高度（由起飛到降落）來獲得滑降比。The minimum sink rate is not achieved at the same speed as the speed for best glide. （最小沈降率不是由固定速度下的最佳滑降速度計算而來的）We can record these data and then place them onto the graph. Example (note the same process yields the same results if you use English units): 我們可以記錄這些資訊並將他們畫在圖上（注意！即便使用英制單位，用相同的方法計算亦會產生相同的結果）20 km/h 1.8 m/sec. descent rate = Glide ratio of 3.08 29 km/h 1.1 m/sec. descent rate = Glide ratio of 7.3 34 km/h 1.3 m/sec. descent rate = Glide ratio of 7.26 42 km/h 1.6 m/sec. descent rate = Glide ratio of 7.29 51 km/h 2.9 m/sec. descent rate = Glide ratio of 4.88 From the chart we see that the minimum sink rate is 1.1 m/sec (216 FPM) at 29 km/h (18 mph) and the optimum glide ratio 8.1 at a sink rate of 1.3 m/sec (255 FPM) at 34 km/h (21 mph). (Drawing on page 56.)From the same polar curve we can observe that by flying at a speed that produces the smallest descent ratio we cover a shorter distance than when flying at a higher speed and a slightly greater descent rate. 從圖上可以看到最小沈降率（minimum sink rate）是1.1m/sec（216FPM）在29km/h（18mph）而最佳滑降比為8.1，是發生在沈降率為1.3m/sec（255FPM）在34km/h（21mph）時。（畫在第XXX頁）。從相同的性能曲線我們可以觀察到在最小沈降率下的飛行距離會比沈降率稍高但飛行速度較快的情況來的短。The optimum glide ratio over the ground changes with the prevailing conditions 幾種主要狀況下的最佳對地滑降比An optimum glide ratio is one that allows us to cover the greatest distance. If however, on carrying out the very same measurements in either descending or ascending air current conditions or head wind, tail wind or any combination of these factors, then we will discover that the optimum glide ratio will no longer occur at the speed we arrived at above. The speed will have to be adjusted to attain the optimum glide ratio over the ground for the prevailing conditions. 所謂的最佳滑降比指的是飛行距離最遠的狀況。如果我們用相同的量測方法