There will be times where you will see a character reacting to, or sometimes outright dodging various projectiles, such as arrows, bullets, and even something much, much faster. Thus, in order to calculate how fast one must move in order to dodge incoming projectiles, there are a couple of things you must know beforehand.
- What is the speed of said projectile?
- How far was the projectile away from the person before he/she dodged said projectile?
- How much distance did he/she cover when the projectile was dodged?
- How much distance did he/she cover when the projectile was deflected?
Speed of Various Projectiles
- Longbows (Medieval): 149-183 feet per second or 45.4152-55.7784 m/s (Though higher speeds have been mentioned)
- Longbows (Modern): 214 ft/s or 65.2272 m/s
- Recurve bow: 225 ft/s or 68.58 m/s
- Compound Bows: 338.5-354 ft/s or 103.1748 to 107.899 m/s, with the absolute legal limit being 400 ft/s or 121.92 m/s
- Compound crossbows: 350 to 460 ft/s or 106.68 to 140.208 m/s (Low-end models like the Mission Sub-1 can hit speeds of 106.68 m/s, but faster models have speeds reaching upto 410 ft/s or 124.968 m/s, with many other models being capable of easily exceeding 400 ft/s or 121.92 m/s with heavier bolts, with the absolute fastest models hitting 460 ft/s or 140.208 m/s)
- Ballista Projectiles: 190 mph, or 85m/s
- Cannonballs: 381 to 518 m/s
- Flintlock Musket: 400 to 550 m/s (As confirmed by renowned gunnery scientist Benjamin Robins in 1742 in his book New Principles of Gunnery, with muskets from earlier periods like the 16th and 17th century also being proven to be capable of shooting at similar speeds)
- Flintlock pistol: 253 to 385 m/s (Though averages between 305 to 610 m/s were also achievable and common)
- Wheellock rifles: 427 to 533 m/s (The Doppelhaken rifles have muzzle velocities ranging from 483 to 533 m/s, with more common wheellock arquebus rifles having speeds exceeding 427 m/s)
- Arquebus: 300 to 500 m/s
- Wheellock pistol: 438 m/s
- 9x19mm Parabellum: 390 to 426 m/s
- AK-47 Rifle: 715 m/s
- Barrett M82: 853 m/s
- Browning M2 Machine Gun: 890 to 1219 m/s
- M16 Rifle: 960 m/s
- M4 Carbine Rifle: 910 m/s
- RPG-7: 300 m/s
- Tank Cannons: 1580 to 1750m/s. This is the cannon that our modern tank, the M1 Abrams, uses.
- Lightning: 440,000m/s
- Laser: 299,790,000m/s
- Angsizing may be involved in some of the steps.
- Angsizing equation = 2atan(tan(70/2)*(Object Size in pixels/Panel Height in pixels)). This lets you find the field of view of angle for an object in the panel, which is in degrees.
- Angsize Calculator = Plug your angle and size of object shown in this calculator, and you will get the distance.
You can read more about it here
Steps to Calculate Speed
STEP 1. Find the distance the bullet covered.
STEP 2. Find the distance the character covered.
STEP 3. Find the ratio between the distance the character covered and the bullet covered. Multiply this ratio by the speed of bullet.
The formula is:
- (Distance the character moved in meters) x (Speed of projectile in meters/s) / (Distance the projectile was away from the character when he/she started to move in meters)
This will get you the speed of character in meters/s
Note. Keep in mind that if said character was shown to move BEFORE the bullet was fired, this would be classified as Aim Dodging, and thus, would not be a valid reaction feat for said character.
1: Standard Dodging Feat 1
A standard rifle is fired, with the muzzle velocity of the bullet said to be 370m/s. Character B notices the bullet when the bullet is 32m away, and quickly dives to the right to dodge it. Character B lunged about 5.2m to the size; at the same time, the bullet had pierced the ground. Find the speed of Character B.
- STEP 1: Find the distance the bullet covered. In this example, the bullet had traveled 32m before it pierced the ground, thus the bullet covered 32m in distance.
- STEP 2: Find the distance said character covered. Here, the "Character B" moved 5.2m by the time the bullet managed to pierce the ground.
- STEP 3: Find the ratio of distance covered between the character and the bullet. So, we do...
- (Distance the character moved = 5.2m) x (Speed of projectile = 370m/s) / (Distance the projectile was away from the character = 32m)) = 60.13m/s; Subsonic
2: Standard Dodging Feat 2
A ranger on a dirt road notices that there is a tank turned backwards in front of him. In the screen, the height of the panel was shown to be 800px high, and the width of the tank to be 246px wide. The tank was shown to be about 6 meters in width/size. We are in the ranger's point of view, seeing the tank directly in front of him.
As soon as the tank fires the ranger dashes; only a tenth of a second had passed after the bullet was fired when the ranger immediately dashes ahead of the tank, catches the ammo and stops it in its tracks. Find the speed of the ranger. The velocity of the tank round is 1750m/s in this case.
- STEP 1: Find the distance between the tank and the ranger. Using the angsizing equation 2atan(tan(70/2)*(246px/800px)), you get an angle of 24.3 degrees. Plug the angle as well as the size of tank into the angsize calculator, and you get a distance of 13.934m.
- STEP 2: Find the timeframe. In this case, only 1/50th of a second had passed in this case, thus we have a timeframe of 0.1 seconds.
- STEP 3: Find the distance the tank round covered in the given timeframe. In this case, the velocity of the tank round is 1750m/s, and the timeframe is 1/50th of a second. Since Distance = Velocity x Time, Distance = (1750m/s) x (0.02 s), which turns out to be 35m.
- STEP 4: Find the ratio between the distance the character covered and the bullet covered. Multiply this ratio by the speed of bullet. So, we do...
- (Distance the character moved = 13.934+35 m) x (Speed of projectile = 1750m/s) / (Distance the projectile was away from the tank = 35m)) = 2446.7 m/s; Hypersonic