BB weight and range: WHAT is the truth?

[Ragnarok]

I guess the drag on a bb of that size has a pretty set value for a certain speed, but a speed vs. Time graph wouldn't be too easy because of the fact that air resistance decreases as speed decreases, so we'd have a few too variables for my skills.

It's actually easier (and in this case, more useful) to calculate it as velocity vs. distance, because that follows a simple logarithmic relationship. In other words, you lose x% of velocity for every metre travelled, in a similar way to compound interest.

So, if you start at 100m/s and have got a velocity retention of 90% per metre, then you'll have a velocity of 90 m/s after one metre, and 81 m/s after the next... and so on and so forth.

Calculating the velocity retention is a bit harder to do from scratch, but there is actually an equation for the job: 1/e^{Cd*D^2/(2078*m)}
Where D is the diameter in millimetres, and m the mass in grams.

Anyway, that gives your velocity coefficient, and for 0.2g BB, it's approximately 0.962. So, to work out the velocity at any given distance, you raise that coefficient to the power of the number of metres, then multiply by the muzzle velocity.

So, for 10 metres, a 100 m/s muzzle velocity 0.2g BB would be defined by:
100 m/s * 0.962^{10 metres} = ~ 68 m/s

You can get time to a given distance by integrating appropriately.

Maybe you are looking at an old version?

Absolute latest, version 2.1.2 - downloaded it off the guy's site today. It's scarcely more than a week old (if that).

Whatever is happening at your end, if I put in 1 metre drop, and 100 m/s muzzle velocity, it's giving me a ~10.2m range - a two metre drop gives a ~20.4 m range...

[Davidvaini]

hey rag, you think its time that you and me make another computer application??

[Ragnarok]

Hey Rag, you think its time that you and me make another computer application??

Possibly... how far are you going to want to go with it?

[Davidvaini]

well, with your knowledge in the calculations, and my knowledge of airsoft and programming, It would be nice to make a better version of the one that is out there.

It would be done over time of course, just like the other program.

[lozz08]

(That sounds good to me)

How odd, I have an older version and it is far better. The new version won't even let me input bb weight to two decimal places!

1/eCd*D^2/(2078*m)
What did the cd there stand for?
And thanks for the formula, that's great. Would the time of flight be 0.675 sec. over 50 meters for an 0.2g bb travelling 167 m/s at the muzzle? (550fps)

[psycix]

Cd = drag coefficient
Which is a value to express the aerodynamic shape as a number. Bad shapes have a high drag coefficient (>1), super smooth shapes have a low one. (<0,3)

More information.

[Hidden Guest]

Much Like an MMPI, the answer to:"WHAT is the truth?" remains completely subjective; left to endless debate.
The "truth" you seek is not going to be dolled out to you by any of the Individuals here-in. They can only dispense to you the hard data as they have it. The "truth" you seek is only going to be what you alone decide: No-one can decide that for you, nor tell you WHAT it is... you'll decide that for yourself. Your perception of the facts and how you handle your self in battle will be your only guide... assuming you want your BB's to have enough knock-down power to stop that pesky varmint.

[Ragnarok]

1/e^{Cd*D^2/(2078*m)}
What did the cd there stand for?

As psycix said, Drag Co-efficient. I tend to use 0.45 for BBs.

And thanks for the formula, that's great. Would the time of flight be 0.675 sec. over 50 meters for an 0.2g bb travelling 167 m/s at the muzzle? (550fps)

No, I make it 0.918 seconds.

For comparison, a 0.25g BB of the same muzzle energy would make it there in 0.801 seconds. It'll also have 32% more velocity at that distance, and 2.2 times the remaining energy.

@Hidden Guest: Call it subjective if you will.

As I've already shown, any minuscule advantage the velocity of lighter BBs gives them at short range are outweighed by the advantage the ballistic co-efficient of heavier BBs gives them at longer ranges, because they retain velocity dramatically better - and therefore, keep both energy and lift, as well as resist wind drift better.

Personally, having done the maths, I can only say that people who think lighter BBs are better are expecting them to be better, and are therefore seeing improvements that really aren't there. Or equally, their guns have hop-ups that don't really agree with heavy BBs.

I still say, go as heavy as your hop-up will allow.

[lozz08]

yeah, I was using 0.47 Cd, explains the difference.
Really useful formula again, thanks. I'm thinking I'm going to set up a graph with curves for each bb weight velocity vs. distance, and time of flight vs. distance, and make a different graph for energy levels 0.8, 1, 1.5, 2, 2.5, 3, 4, and 5 joules muzzle energy. That should be enough info to make a decision on at least what weight range you should be using for a given muzzle energy.

[Ragnarok]

yeah, I was using 0.47 Cd, explains the difference

Not really. If anything, using 0.47, you should get a higher number than I did.

I'm not even entirely sure how you've reached your number.

[lozz08]

How were you calculating the time of flight? I did integral of the graph of velocity vs time over 50m divided by 50, should give average velocity, then calculated it from there.

Oh and I got 0.968 for velocity retention using CD= 0.47

[jackssmirkingrevenge]

Much Like an MMPI, the answer to:"WHAT is the truth?" remains completely subjective; left to endless debate.
The "truth" you seek is not going to be dolled out to you by any of the Individuals here-in. They can only dispense to you the hard data as they have it. The "truth" you seek is only going to be what you alone decide: No-one can decide that for you, nor tell you WHAT it is... you'll decide that for yourself. Your perception of the facts and how you handle your self in battle will be your only guide... assuming you want your BB's to have enough knock-down power to stop that pesky varmint.

Why do I have visions of BBs suddenly stopping mid-flight and dropping harmlessly to the ground...

Ah, right.