Separating by vectoring on crossing traffic by TURNING BOTH AIRCRAFT ( No wind case ) 
Vectoring on crossing tracks is a trickier business in radar vectoring because it demands some good evaluation of various parameters from the controller . We will divide our study to 2 parts . This one refers to the case where BOTH aircraft are turning , a case more often encountered in areas of short dimension as in APP and ACC within airways . For the case where only one aircraft turns , please advise the pertinent topic from the Radar Techniques main page
Parts :
1. Mathematical analysis
2. The daily "RulesofThumb"
3. Practical verification with a simulator
4. What if the track angle is less than 90 degrees ?
Mathematical analysis
This is why we would like to analyse mathematically the problem and then get out of it some practical and simple ‘rulesofthumb’ , properly justified from theory and easily applicable to daily life !
We initially assume :
A No wind case
A crossing traffic at 90 degrees with aircraft of equal speeds at equal distances from the crossing point
For practical purposes , we assume that the new headings are established 30 NM before the crossing point  a more appropriate distance practically to start vectors in typical ACC operations
Both aircraft are turned , to achieve more in less airspace
The turns should always be on the same sense for both aircraft so it is either both to the pilots' left or both to the pilots' right
We will measure the evolution of their separation while both move towards the crossing point having as a variable the distance run by aircraft while on vectors . Distance is probably easier for a controller to understand than talking about time , when dealing with radar separation
We delegate all our calculations to the MS Excel and we simply study the results to identify the practical rules . Lets study the following table produced:
Angle of vector (a) 
Distance (S) run by aircraft moving from 30 NM away the conflict point 

5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 

5 
Separation (NM)

35 
28 
21 
14 
8 
4 
8 
15 
22 
29 
36 
10 
35 
29 
22 
15 
10 
7 
11 
17 
23 
30 
37 

15 
36 
29 
23 
17 
12 
11 
14 
19 
25 
32 
38 

20 
36 
30 
24 
19 
15 
15 
17 
22 
28 
34 
41 

And here in a graph form :
The immediate simple results are :
§ The minimum separation is achieved when aircraft have run, on their headings, a distance equal to the one they started vectoring from the crossing point ( 30 NM in our case ) .
§ The minimum separation achieved is related proportionally to the vectoring angle .
The results indicate that :
Vectoring Angle degrees 
Minimum Separation NM 
5 
34 
10 
7 
15 
11 
20 
15 
The separation is almost the 70% in NM of the value of the vectoring angle in degrees . Some people prefer to say that every 5 degrees of angle will increase by 4 NM the minimum separation achieved
So :
The daily "RulesofThumb"

In case headings are established in a distance of less than 30 NM then you should accordingly increase the vectoring angles proportionally to get the same separation . For example if headings are established 20 NM before the crossing point you should increase by a 30% ( as 20 is less by 30% to 30 ) the previous values . So 10 degrees go up to 13 , practically 15 and 15 or 20 become 20 or 30
For safety never start vectoring closer than at 10 NM distance before the conflict point . If forgotten or at an emergency consider at this point very strong turns , up to 4060 degrees and above all NOTIFY PILOT IMMEDIATELY on instruction . You may also consider to vector by relative turns and not by a heading , to avoid the calculation , like : " Turn immediately 40 degrees to the right ... + traffic information ….) " .
The pilot can do a lot for you :
An informed pilot reacts faster and …
He may be in visual conditions and escape the danger with less than standard separation
He might even have an early TCAS/ACAS advisory to help additionally . Note : In the case of TCAS/ACAS II resolution , however , there is a gray area considering a vectoring situation , as these resolutions suggest only vertical maneuvers and not horizontal ones . The early information to the pilot and his/her understanding will save probably a lot of a very probable confusion
Practical verification with a simulator
Let us use the ATC2k simulator of Vic Day which can easily animate some example scenarios and then additionally calculate certain parameters to us . Note that you may use this programme freely to get as much of practical experience as you want
Drawing 1 :
The 2 aircraft here are KLM231 on track 180 and the AFR2912 on track 090 . Their distance from the crossing/conflicting point is very close to 30 NM . Aiming say at 10 NM minimum we try a vectoring angle of 15 degrees : Say both to their left
Drawing 1 :
Drawing 2 :
After the new headings are established we ask the simulator to draw the new paths . The rollingball cursor measures 10 NM between the points of the minimum separation . Watch the heading instructions on the bottom line of the labels , 075 (=090015) for AFR2912 and 165 (=18015) for KLM231
Drawing 2
Drawing 3 :
When AFR2912 has run 30 NM from the point it established the new heading (075) as measured with the rollingball cursor the minimum has been reached . The same is true for the KLM231 . Watch the position of the 2 aircraft relative to their tracks around the crossing point
Drawing 3
Drawing 4 :
When beyond that distance the separation will only increase . Then you may RESUME NAVIGATION for the pilots to their next point
Drawing 4
Drawing 5 :
What If , however , the vectors are late …?
In drawing 5 aircraft start vectors later ( and they are vectored now both to the left ) : AFR2912 around 15 NM and KLM231 20 NM from the crossing point and the simulator calculates that to achieve 10 NM as before , AFR2912 had to be vectored from heading 090 to 120 and KLM231 from 180 to 205 , that is the vector angle necessary is now 2530 degrees !
Drawing 5
Drawing 6
On the same occasion as in Drawing 5 but by using only 10 degrees then you get some 6 NM only because you started vectors later than 30 NM from the crossing point !
Drawing 6
What if the track angle is less than 90 degrees ?
The answer is coming a bit more natural almost as a sequence from the present experience : You should accordingly increase proportionally your angle . Let us take in Drawing 7 where the conflicting traffic at tracks of 60 degrees is the EIN3344 on vector heading 140 and the DLH101 on 080 . They will have a minimum separation of 5 NM and not 7 as suggested by a 10 degrees vectoring angle when at 90 degrees tracks . Reasonable , isn’t it ? It should have been so because with 60 degrees traffic is more close in space and since 60 track degrees are less by 30% from 90 , so your vectoring angle should increase by 30% and make the 10 degrees 13 or practically 15 !
Drawing 7
Guess what ! If we have 30 degrees track angle then at 30 NM before the crossing point you need not 10 degrees to make 7 NM ….but how much ? Well , since 30 degrees is 60% less than 90 degrees we will increase the 10 degrees by 60% and make it 16 practically 20 . Will that work ? Have a look at Drawing 8 :
Drawing 8
The BA022 and COA011 at initial headings of 145 and 120 are turned both 10 degrees to the right to make just 4 NM of separation – and maybe less ? Our analysis is suggesting that with 20 degrees vectoring angle , that is headings for BAW022 = 165 and COA011 = 145 they could have done 10 NM separation !
§ You may note that in angles less than 90 degrees it takes more distance until you arrive to the separation , aircraft stay close for longer but you are not deviating much from the neighborhood of the crossing point keeping easily within airway area limits
§ For angles less than 30 degrees , say 20 or even 10 , it is better to avoid vectoring as aircraft are practically on same track where a different technique works better