Advance BB velocity and weight calculations
I've been on these forums for a few months now, so I feel I should contribute something that would be as useful as the input I received from the community. Therefore, I hope this guide is useful to everyone who reads it.
I've seen many threads of people, both veteran and rookies alike asking what BB weight they should use. Generally the question comes up more with snipers and DMs than other players, but it is still a common question. I've developed a mathematical formula that can determine what would be the perfect weighted BB for any rifle. It's theoretical, but from my testing, it works just as planned. However, many variables have not been taken into account, such as hop-up, barrel length, and external factors like wind and gravity. Therefore, there may be some small differences.
Calculate FPS with a simple equation:
It is very easy to find an FPS calculator online or a chart with common FPS numbers on it. However, I've yet to see an equation that you can actually calculate yourself which FPS your gun will shoot at. The problem is that the there are 3 variables to be taken into consideration, therefore it isn't a 2d graph, but a very visual 3d graph, which allows you to find the FPS of your gun at any BB weight, even some random weight such as .243 grams. I've dumbed down the equation, but I am 100% sure that it is still accurate up to the .1 FPS even at .5 gram BBs (if there is such thing).
The equation is:
z is equal to the FPS
x is equal to the Joules
y is equal to the BB weight.
Which outputs this graph:
Interactive online 3d graph here.
For those of you wondering how I did this, I used a simple function on excel that outputted a function after I inputted the following accurate data from this sit, which I found to be the most reliable so far:
Which creates this table and graph:
Using the functions that you see on the side, I was able to create a table of values, and therefore a function of that function, giving me an accurate 3rd dimension for the graph:
I did this because there are a lot more weighted BBs than the ones they used, such as .12, .32, and .4 grams. Not to mention if a company misrepresents their weight or if there is a low tolerance for the BBs. Using this function, you can predict your FPS for any weight BB you may want to try.
Difference between muzzle velocity and normal velocity:
Many people misrepresent the terms 'velocity' and 'muzzle velocity'. Both of them are measured with the same units, generally feet per second or meters per second. But the problem is that one is a constant, while the other is very dynamic. When you chronograph your rifle, you are measuring a constant muzzle velocity. Granted, it will have some variations, but overall it shouldn't have them. Velocity on the other hand, starts at the muzzle velocity, but lowers due to drag, which also gets affected by BB weight. That is the reason you need to choose your BB weight carefully. Let me use an example scenario:
Your rifle shoots at about 400 FPS with .2 BBs, or about 1.5 joules (measurement of energy). However, with .25 BBs, your gun shoots only 360 FPS. Naturally, you would want to use .2 BBs for the higher FPS, right?
Well think of this: you play a lot of woodland games, so your target is usually about 75-150 feet away. By the time a .2 BB reaches it's target, it has has dropped to about 155 FPS (.225 joules) at 75 feet, and possibly 60 FPS (.035 joules) at a range of 150 feet. The .25 BB would have dropped to about 170 FPS (.34 joules) at 75 feet, and possibly 82 FPS (.075 joules) at 150 feet.
The energy at 150 feet is twice more for the .25 BB than the .2 BB, so itís twice as likely to be felt. This is due to an important variable called 'drag'. Which is the loss of energy in the BB due to air pushing it. Taking the FPS, we can make the safe assumption that the .25 BB is 1.29 (because of 82/60) times more effective than a .2 BB at that distance. So how do we find out which BB to use for a given distance? Well I already found out the equation you would want to use. Using my above equation, you can calculate using a general drag formula for whatever kind of BB you use.
Here is a formula for drag that you can use to determine how fast a BB is traveling at almost any distance (disregarding wind and gravity of course):
Jc = Jp - .0800301944*Jp^.9986
Jc is the current Joules.
Jp is the Joule of the previous meter.
m is how far the BB is in meters.
You then repeat the equation for every meter you want to travel. This is easy in excel or a similar program that allows for you to just pull down a column and keep the equation.
<I will post a graph on this soon, but the 3d grapher is getting messed up right now>
Putting it together:
Combining these two techniques will allow you to make a decision on what kind of BB to use based on your average target's range. Especially for long ranged players such as snipers or DMs. For example, lets say we have an upgraded rifle going at a nice 550 FPS with .2 BBs, which is usually the maximum power for sniper rifles. However, you have a target at exactly 162 feet according to your range finder. Lets find out how fast the BB will be traveling by the time it reaches the target:
First we need to find out how many joules our gun has. Since we know the gun shoots 550 FPS with .2 BBs, we can find it out by using the reverse of the .2 BB equation for finding FPS:
x = .0000091369*y^2.002803925
Which, if we plug it in and calculate it, we get about 2.813 Joules.
Now that we know our muzzle energy, we can find the energy over a distance using the drag equation:
Jc = Jp - .0800301944*Jp^.9986
Which, if we plug it into Excel and calculate:
We can see at the bottom the energy and FPS that the BB will have once it hits it's target at 162 feet (about 50 meters).
Furthering that, we can then average the the FPS of the BB at each meter up until 162 meters. A tedious task, but I must add again that excel is your friend if you know what you're doing. You will actually find the best BB that you can use for the distance given:
(BB weight at 162 feet = Average FPS)
.2 = 237.39
.25 = 246.6
.28 = 249.29
.3 = 250.3
.36 = 250.53
.43 = 247.66
As you can tell from the data, it is safe to assume that the .36 gram BB will indeed, work the best at a target 162 feet.
Thanks for reading this, I hope you will all find it useful for your future games.