協和飛機為什麼採用三角翼？翼型如何對於升力和激波產生有利影響？巡航中機翼如何高效產生升力？

01-02

問題屬於飛行器空氣動力學

貌似就回答了第一問，先佔個坑，剩下的考完試再答

剛考完飛行器結構力學來答一發吧，首先協和號是一架超音速客機，那麼主要圍繞兩個方面，減小波阻和提高剛度。

首先三角機翼的功用是什麼呢？「減小波阻，提高飛行速度」，在這一點上和後掠翼是一樣的，但是後掠翼有什麼缺點呢？如圖

?在相同的展弦比和梯形比下，後掠翼的真實長度比平直翼長;

?垂直於機翼剛度軸的弦較短，又採用了相對厚度較小的翼型，因此後掠翼顯得細長而薄，彎曲剛度有所降低;

?後掠翼的氣動合力作用點向翼尖靠近，使彎矩和扭矩增大。

?總的來說，後掠翼的強度、剛度特性都差，後掠角越大，這一問題越突出。

?為了保證足夠的強度剛度，必然要付出重量代價。

我們知道，機翼在根部彎矩最大，那麼對根部的彎曲剛度有很大的要求，但是後掠翼的根部長度並沒有相比比平直翼提升多少。

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而三角翼可以看作是在後掠機翼的後緣填補一塊三角面積演變而來，這樣有什麼好處呢？

1.由於根弦很長，所以根部結構的絕對高度仍然較大，承彎的結構效率高；

2.閉室面積變大大，承扭能力強；

3.翼展小，根部面積大，氣動載荷壓力中心靠近翼根，產生的彎矩小；壓心到根部剛心的距離近，扭矩也小。如下圖所示

4.機翼的根弦較長，機翼與機身對接面大，可增加多個機翼機身的連接部位，以便分散機翼傳給機身的載荷。

首先這點是符合後掠翼和三角翼的作用的，這裡我再提一點，那就是飛機的氣動彈性問題，包括彎扭顫振和彎曲副翼顫振和扭轉變形擴大等。

這一系列都要求飛機具有一個臨界速度，一般是飛機飛行極限速度的1.1倍，在這一速度下是不會發生上述問題，解決的措施之一就是提高飛機的彎曲剛度和扭轉剛度。

以上就是協和號飛機為什麼要採用三角翼，寫的比較亂，有錯誤歡迎指教。為後面考試攢攢人品

參考資料：《飛行器結構學》課件

Recently, I found an answer to explain why Concorde use delta configuration.

On highly-swept wings, flow initially detaches from the LE as AOA increases, and may roll up into
vortices that produce substantial lift (aka vortex lift)
In this case, stall is not closely linked to the onset of flow separation and lift may be further
increased by raising AOA still higher
The penalty is that drag is also large. However, the L/D ratio may be acceptable for the flight phase
considered
Typically, high-AOA effects are mainly relevant to sub/transonic flight. Supersonic aircraft may however
(and often do) exploit this effect to lift for takeoff, landing, or (subsonic) manouevering
If the wing is not highly-swept, chines or LE extensions (LEX) near the wing root can be used to
induce vortex flows

On delta wings, which are typically highly-swept, a reasonable approximation for high-! lift and
drag is obtained by assuming the lift is provided by a combination of 『potential』 and 『vortex』 lift.

The slender-wing potential
flow theory of Jones can explain this question in details.

However, I am still looking for answer to explain aerofoil section in supersonic speed. I mainly concentrate on how shock wave can be prevented or used "efficiently" on Concorde wing section.

After a few weeks, this question can be answered more specifically by using some relevant theories.

R.T. Jones adapted Prandtl』s assumptions for slender wings of high aspect ratio:

The flow around every cross-section perpendicular to the flight direction can be approximated by
the two-dimensional flow around the same section, superimposed on the original uniform stream.
This makes it possible to determine the lift distribution along the chord just as the Prandtl』 theory
gives the lift distribution along the span.
The lift at any point is only influenced by the flow ahead of the point considered and is
independent of the flow conditions downstream, unlike in Prandtl』s case of large-aspect-ratio
wings, the local lift depends largely on the influence of the free vortices downstream. Consider a delta wing flying through a stationary body of fluid, with AoA !:

The increment in velocity potential between the
two sides of the plate is given analytically by

The force is generated because in a fixed reference frame, the flow is unsteady owing to the passage of the wing. We can then use the unsteady Bernoulli equation (written in potential form)

to compute the lift force per unit length as

For a plain delta wing=const and we have

Cross-flow drag analogy for vortex lift

Consider the normal force produced by the wing-normal component of flow

Delta wing design constraints

Reference:

1 A history of aerodynamics, J. D. Anderson Jr, 1997

2 Theory of wing sections including a summary of airfoil data, I.H. Abbott IH
A.E. von Doenhoff, 1949 (online: NACA TR-824)

3 Lecture notes: Hugh Blackburn (Monash University, ), John Fulker (QinetiQ)

4 Lecture notes: , Joaquim, Imperial

簡單回答下第一問，後兩問寫完出書，不在這貼～

2馬赫的巡航速度一定要大後掠，這是阻力發散決定的。在此前提下，機翼強度的要求使得三角翼幾乎成為唯一的選擇。三角翼的低速性能非常差，所以渦升力不是主要考慮，剛好是個副產品。即使考慮的渦升力，協和和協和斯基的降落迎角還是太大，所以機頭要設計成下偏好讓飛行員能看見跑道。所以但凡有其他辦法，不會在運輸類飛機上用三角翼。

（非專業人士，歡迎指出錯誤）

三角翼可以看成是大角度的後掠翼把後面空的地方填實了，可以從這個角度來分析你提出的問題。

1. 後掠翼主要的作用就是提升超音速下的性能，但為什麼可以提升是題主問題的核心。大概地說就是後掠的角度比馬赫錐的角度更大，使得機翼躲在馬赫錐後面，這時候吹到機翼上的氣流經過減速已經是亞音速了，使得機翼不至於受激波產生的阻力影響。

我想指出的主要是，雖然搜三角翼搜不到太多信息，但因為三角翼本質上還是後掠翼，在超音速下的性能表現和未填實的後掠翼非常類似，所以可以搜swept wing：Swept wing。維基上面有定性的解釋和定量的計算。

2. 我對於填實的作用的理解是，在低速大攻角時提供基於渦旋的升力，所以即使提供升力的機翼法向空速很小，整個機翼提供的升力仍然可以保持穩定。這個題主自己的答案裡面已經解釋的比較清楚了。此外和機身更長的連接可以增加機械強度，並提高滾轉穩定性（roll stability），省略水平尾翼（stabilizer）。