The BFM You’ve Learned Is Wrong: One-Circle and Two-Circle Fights
Hello everyone, this was originally posted on the Falcon BMS Forum, but I thought I’d tweak it a bit and share it on Reddit as well.
Introduction
For far too long, whenever we discuss BFM or dogfighting, we always come back to the One-Circle and Two-Circle concepts. But unfortunately, the whole idea behind One-Circle and Two-Circle is wrong, and we have been repeating the same mistake over and over again.
In case the images fail to load, you can find all of them on Google Drive here: https://drive.google.com/drive/folders/1N5cbB_juJQKk-CC-C6KV4HYP_6Bln44M?usp=share_link
The Wrong Lesson: One-Circle and Two-Circle Fights
For beginners who aren't familiar with the One-Circle and Two-Circle concept, here’s a good video that explains it: https://youtu.be/At3qlnd_Ugo?si=MhTZ3EAEyIAukuDs
The One-Circle and Two-Circle concept has been taught by the US military for decades—perhaps more than half a century. Since then, we simmers have been learning the same theory without ever questioning it.
Based on the theory, after the merge, if both fighters turn in the same direction, it results in a One-Circle fight, also known as a “Radius Fight”. If they turn in opposite directions, it results in a Two-Circle fight, or a “Rate Fight”.
In a Two-Circle fight, you're chasing your opponent in a nose-to-tail position. While in a One-Circle fight, you're heading toward your opponent nose-to-nose.
Then there is the Vertical fight. If both fighters go up, it essentially turns into a One-Circle fight, as they’ll meet nose-to-nose at the top. But if one goes up while the other dives down, it becomes a Two-Circle fight, with both aircraft ending up chasing each other in a nose-to-tail position.
Problem One: Two-Circle but it’s a Radius fight
The easiest way to understand the problem with this theory is by looking at the Rolling Scissors and the Defensive Spiral.
Once again, here are two good videos that explain the maneuvers:
https://youtu.be/D4wxj-Wd9jg?si=W-OthFY7fPDxgBGE
https://youtu.be/wwwxpDeKFZE?si=euF1-gEr94GRU7IY
In both the Rolling Scissors and the Defensive Spiral, the rear fighter is chasing the front fighter in a nose-to-tail position, which makes it a Two-Circle fight. But in both cases, the front fighter is actually trying to slow down and force an overshoot. So even though both maneuvers follow the Two-Circle flow, they are actually Radius fights.
Problem Two: One-Circle and Two-Circle don’t work in a 3D world
If two fighters merge, one goes up Vertically while the other turns Horizontally to the right. What kind of circle flow is this? One-Circle or Two-Circle?
Or what if one of the fighters dives down Vertically while the other turns Horizontally to the right? What kind of circle flow is this then? One-Circle or Two-Circle?
So here’s the second problem with the Circle theory: if both fighters aren’t turning on the same 2D plane, then you can’t classify the engagement as either a One-Circle or a Two-Circle fight. In other words, the Circle theory doesn’t work in a three-dimensional world.
Problem Three: Gravity was not considered in the Circle theory
Continuing from the previous example: when two fighters merge, one goes up while the other turns right. The climbing fighter converts its speed into altitude, which leads to a smaller turn radius and allows it to get inside the turn circle of the Horizontally turning fighter. As a result, the engagement becomes a “Radius Fight”.
In the case where one fighter dives down while the other turns right. For the diving fighter, Gravity also pulls the aircraft downward, further increasing its speed during the descent. This acceleration allows the diving aircraft to bleed less airspeed during the high-G turn, enabling it to sustain a higher turn rate for a longer period. As a result, the engagement becomes a “Rate Fight”.
As you can see, an aircraft’s turn rate and turn radius are heavily influenced by Gravity. In many cases, Gravity is the deciding factor in whether a fight becomes a “Rate Fight” or a “Radius Fight”. Yet despite this, the traditional Circle theory never takes Gravity into account.
Higher G Force = Faster Turn Rate and Smaller Turn Radius
If an F-16 and an F/A-18 are both flying at 500 knots at 20,000 feet. They merge head-on and enter a dogfight. Who’s going to win?
Answer: The F-16 will win the fight.
At 500 knots, the F-16 can pull 9 G, while the F/A-18 is limited to 7.5 G. It doesn’t matter whether it’s a “One Circle”, “Two Circle”, “Rate Fight” or a “Radius Fight”, when the F-16 is pulling more G, it will achieve both a higher turn rate and a smaller turn radius. So regardless of the engagement type, the F-16 always win.
To better understand this, we can refer to any EM chart for analysis. To keep things simple, let’s compare turn rate and turn radius at Mach 0.8 at sea level, and see what happens at 9 G versus 7 G.
As you can see, when a fighter is pulling 9 G at Mach 0.8, it will have both a higher Turn Rate and a smaller Turn Radius compared to pulling 7 G. Therefore, when both fighters are flying at the same speed and altitude, the one that can pull more G will have the advantage in both “Rate Fight” and “Radius Fight”.
And of course, if the dogfight starts at 350 knots, the F/A-18 will actually have the advantage in G capability over the F-16. At such low speeds, the F-16 becomes limited by its AOA limiter, which reduces the amount of G it can generate. Meanwhile, the F/A-18 maintains excellent nose authority and can still produce higher G forces. As a result, in a low-speed merge, the F/A-18 will beat the F-16 every time.
And this is why people often say the F-16 favors high-speed fights, while the F/A-18 excels in low-speed engagements. When you enter a dogfight, you want to be at a speed where your aircraft has a G advantage over your opponent.
G-Force, Turn Rate, and Turn Radius
To understand the relationship between G-Force, Turn Rate, and Turn Radius, we can also look at the formula for uniform circular motion.
To keep things simple, we'll assume the aircraft is flying in a circle at constant speed. Then, the formula becomes: a = v² / r = ω²r
a is the centripetal acceleration (G-Force)
v is the speed (Airspeed)
r is the circle radius (Turn Radius)
ω is the angular velocity (Turn Rate)
For example, when an F-16 is flying at Mach 0.5 at sea level, making a turn with a radius of 2,000 feet. Let’s say Mach 0.5 at sea level is about 173 m/s, and 2,000 feet is about 609.6 meters. Using the formula, we get a centripetal acceleration of 49.1 m/s². Since 1 G equals to around 9.8 m/s², so 49.1 m/s² is roughly 5 G. Given this centripetal acceleration, we can also calculate the angular velocity to be approximately 0.28 rad/s, which is about 16.3 degrees per second.
During a “Rate Fight”, if both fighters have the same turn circles (same turn radius), then the one flying faster will complete the turn sooner and thus win the fight. And from the equation: a = v² / r = ω²r, we can see that for a constant turn radius (r), a higher airspeed (v) results in a higher turn rate (ω) and also a higher G-force (a).
In a “Radius Fight”, if both fighters are flying at the same airspeed, then the one that pulls more G will have a smaller turn circle and thus win the fight. From the equation: a = v² / r, we can see that for a constant airspeed (v), a higher G-force (a) results in a smaller turn radius (r).
In other words, a higher G-force means you are turning tighter and faster, thus gaining an advantage in the turn.
Dogfight is Science, not Art
If two F-16s are both flying at 500 knots at 20,000 feet. They merge head-on and enter a dogfight. One F-16 goes up Vertically while the other turns Horizontally to the right. Which F-16 is going to win the fight?
Answer: The F-16 that climbs will win the fight.
As discussed in Problem Three, this scenario results in a “Radius Fight”. The climbing F-16 converts its speed into altitude, which results in a smaller turn radius and places it inside the turn circle of the Horizontally turning F-16. Therefore, the climbing F-16 gains a radius advantage and will ultimately win the fight.
But what if one of the F-16s dives down Vertically while the other turns Horizontally to the right? Which F-16 will win?
Answer: The F-16 that dives will win the fight.
As discussed in Problem Three, this scenario results in a “Rate Fight”. The diving F-16 will bleed less airspeed and be able to sustain a higher turn rate for a longer period of time. Therefore, the F-16 that dives will achieve a higher overall turn rate and ultimately win the fight.
And finally, if one F-16 goes up Vertically while the other dives down Vertically. Which F16 is going to win?
Answer: The F-16 that dives will win the fight.
Tacview file: Climb vs Dive.acmi
https://i.redd.it/6iltx86yliug1.gif
As we can see in the Tacview recording, the F-16 that dives is able to sustain higher G during the first half of the turn, as gravity provides additional acceleration during the descent. This allows the aircraft to maintain high-G turns without bleeding airspeed.
On the other hand, the F-16 that climbs loses most of its airspeed during the first half of the turn due to gravity. As a result, it cannot maintain high-G turns during the climb. By the time the climbing F-16 reaches the top, the diving F-16 has already gained lead pursuit on it.
As discussed in the previous section, higher G results in a higher turn rate and a smaller turn radius. Due to gravity, the diving fighter will always sustain higher G than the climbing fighter throughout the turn.
In conclusion, we can see that for an F-16 flying at 500 knots and 20,000 feet, the best move is to dive. Not climb, not left, and not right. Traditional BFM lessons may lead you to believe that you have unlimited choices or game plans during the fight, but that was never the case. In any given situation, there is always one best solution that defeats other maneuvers.
Dogfight is not an Art, it is Science. You have to calculate it.
Head on merge decision tree
We now know that there is always one best solution. But how do you find it? What is your best move when you enter a dogfight?
Below is a decision tree I use when I merge head-on with an enemy aircraft. The chart is somewhat oversimplified, but it should be helpful for beginners who want to get into BFM.
First of all, before the merge, you should check your airspeed and altitude, as well as your opponent’s airspeed and altitude.
Then, you should recall your corner speed and soft (or hard) deck. For the F-16, your corner speed is typically around 450 to 500 knots. In training, you might have a soft deck of 10,000 feet, which you should not go below. But in combat, your deck is basically the ground floor, which you should avoid hitting.
Next, based on the information you’ve just acquired, go through the chart to figure out your best move.
Finally, execute the maneuver after the merge.
After the merge
Unfortunately, you don’t always get the kill in the first turn circle. If you find yourself merging head-on again with your opponent after the turn, you should go back to step one, gather new information, and run through the decision tree again.
Keep looping through the whole process until you eventually get the kill or run out of speed and altitude.
If you have no more speed or altitude, then it’s time to disengage and escape.
Final
Dogfighting is a complicated topic, and there’s no way I can cover every detail in a single article. But I’ve done my best to explain the most important aspects as simply as possible. If I missed anything or made any mistakes, feel free to let me know.
Also, please forgive the somewhat provocative title. I am not against anyone teaching BFM on the internet, and I apologize if you feel offended. I just wanted a straightforward title, but I didn’t want it to turn into clickbait.
Aim high,
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