飛機在飛行航線上，若一架飛機逐漸靠近另一架飛機時，距離過近就會有可能產生碰撞的危險，此時，若兩架飛機在相距較遠的時候，如能預測在未來特定時間區間會產生碰撞，就可以提早做出有效的閃避動作或者規劃新的航線。本研究目標裡，希望在只知道彼此的速度情況下，利用相對速度找出以一架飛機為參考點，當另一架飛機位在哪邊時在未來會產生碰撞，而上述發生碰撞的位置集合即為碰撞危險區域(Danger Zone)。利用當參考點飛機之初始位置與兩架飛機的速度，伴隨著時間所行進的距離，可推導出空間中的碰撞危險區域，此區域會根據時間的長短，分別會有不同大小的碰撞危險區域，當所需要的時間越長，或者定義為碰撞的距離越大，此分部的區域就會越大。但利用此方法在計算過程中，必須針對每一個時間點做積分計算出位置，才能找出碰撞區域，較為繁瑣複雜，本研究的計算方法為利用空間集合的概念，把位置與時間的關係轉換成限制的條件，再利用所定義之碰撞距離形成數個子集合，僅需要檢查上述子集合是否符合，即可交集找出整體的碰撞區域。利用此集合的觀念，即可在僅知道兩架飛機的位置及速度變化的情況下，藉於限制條件的判斷，兩架飛機在未來是否會發生碰撞，在計算及判斷上較為快速方便。

The potential collision danger increases if an aircraft gradually moves closer to another aircraft. If we are able to predict the collision time before the aircraft dangerously close it will help us to devise an effective evasive maneuver (EEM), or re-routes the plane, thus avoiding the collision.
This research focuses on determining safety with the velocity and acceleration. We set the Evader as the reference point and determine the collision range. The two aircraft collide if the Blunder enters the collision range. The collision range is called the Danger Zone (DZ).
First, we use the aircraft’s initial position and velocity to calculate the distance between the two aircrafts, it is necessary to do integral for each time point to calculate positions, to extract the DZ. The DZ range is based on the time and in direct proportion. Second, if the distance between two aircrafts is smaller than a design value, then it is called collision. So the DZ’s range is based on the collision distance between two aircrafts and direct proportion, too.
In this research, the calculation method is as followed, transforming the relationship between the position and time into the constrain conditions by the concept of semialgebraic set, then re-using defined collision distances to form several subsets, it only need to check whether the subsets fit , so that the intersection will be the overall Danger Zone. By the concept of using semi-algebraic set, in the case of only knowing the position and velocity of the two airplanes, it can be judged whether the two airplanes collision in the future by constrain conditions; the calculation and judgment is relatively quick and easy.

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