BB science - distance & time:

this is an artical written by Jared, Mechanical Engineer and Airsoft Player published March 2005 and offers some intersting results for the players that love technical stuff:

So you finally bought your first AEG, gas, or bolt airsoft gun and the next thing on your mind is shooting it. Before you can do that, you’ll need some bbs, but which weight should you buy? There are numerous weights of bbs out there available for purchase starting with weights as low as .12 gram all the way up to .88 gram carbon steel bbs. The majority of the bbs sold today are .20 gram. As you go up in weight, you will go up in price and down in quantity of your bag of ammo. But who cares about the weight of the ammo you buy? Most people want the most for their money, so why not go with the cheapest .20 gram bbs you can find?

There have been numerous field studies performed that deal with specific bb weights related to accuracy, fps, and range. Since these are the three main areas of study for airsoft ballistics, we should look at them more in depth than just recording data trends from the field. Although this method of using statistical data to form a trend best represents actual effects in these three areas, is it possible to apply science and physics behind these findings to further knowledge in these specific areas?

The answer is yes. The study outlined in the following paragraphs shows the effects of three variables on airsoft ammo. These three variables are time, fps, and distance. The main reason for this study was to find downrange velocities of certain bb weights at varying distances and specific time intervals. This particular study uses a theoretical airsoft gun firing at 85m/s (278.87 fps) and compares the relations between .20 and .25 gram ammo. It can be altered to any muzzle fps as well as any ammo to show the desired results on the tables and graphs from only two inputs (bb weight and initial m/s). This study not only includes the effect of specific bb weights and initial muzzle velocities but also uses an exponentially changing drag coefficient and corresponding interval velocity to account for the drag forces that act on the bb during flight. Without these drag forces, the bbs velocity at every distance would be constant. We know this is now true because it hurts much worse to be hit by a bb from 10 feet versus 100 feet away.

The spreadsheet below has many columns of numbers and formulas that are important to the study, but not directly relevant to understanding the final result. They are all in SI units, not English, so do not be confused. The final results are in English units since most of us prefer and understand a measure in feet versus meters. This first sheet shows a .20 gram bb fired at a theoretical stock fps of 85 m/s (278.87 fps). For those interested in details, the variables from left to right are mass of bb in grams, initial velocity in m/s, time, total distance traveled in meters, coefficient of drag, area of bb perpendicular to velocity flow, the density of air at STP (standard temperature and pressure), force of drag in Newtons, acceleration in meters per second^2, velocity in fps, time, and total distance traveled in feet.

INPUT		OUTPUT
m (gram)	v (t) (m/s)	t (sec)	x(t) (m)	Fd (drag force N)	a (m/s^2)	v (t) (fps)	t (sec)	x(t) (ft)
0.20	85.00	0.0	0.00	0.03062363	153.118	278.87	0.0	0.00
0.20	69.69	0.1	6.97	0.02058435	102.922	228.63	0.1	22.86
0.20	59.40	0.2	12.91	0.01495317	74.766	194.87	0.2	42.35
0.20	51.92	0.3	18.10	0.01142559	57.128	170.34	0.3	59.38
0.20	46.21	0.4	22.72	0.00904956	45.248	151.59	0.4	74.54
0.20	41.68	0.5	26.89	0.00736398	36.820	136.75	0.5	88.22
0.20	38.00	0.6	30.69	0.00612044	30.602	124.67	0.6	100.69
0.20	34.94	0.7	34.18	0.00517435	25.872	114.63	0.7	112.15
0.20	32.35	0.8	37.42	0.00443643	22.182	106.14	0.8	122.76
0.20	30.13	0.9	40.43	0.00384893	19.245	98.86	0.9	132.65
0.20	28.21	1.0	43.25	0.00337302	16.865	92.55	1.0	141.90
0.20	26.52	1.1	45.91	0.00298176	14.909	87.02	1.1	150.61
0.20	25.03	1.2	48.41	0.00265597	13.280	82.13	1.2	158.82
0.20	23.70	1.3	50.78	0.00238165	11.908	77.77	1.3	166.60
0.20	22.51	1.4	53.03	0.00214837	10.742	73.86	1.4	173.98
0.20	21.44	1.5	55.17	0.00194825	9.741	70.34	1.5	181.02
0.20	20.47	1.6	57.22	0.00177523	8.876	67.14	1.6	187.73
0.20	19.58	1.7	59.18	0.00162458	8.123	64.23	1.7	194.15
0.20	18.77	1.8	61.05	0.00149257	7.463	61.57	1.8	200.31
0.20	18.02	1.9	62.86	0.00137621	6.881	59.12	1.9	206.22
0.20	17.33	2.0	64.59	0.00127311	6.366	56.86	2.0	211.91
0.20	16.69	2.1	66.26	0.00118131	5.907	54.77	2.1	217.38
0.20	16.10	2.2	67.87	0.00109919	5.496	52.83	2.2	222.67
0.20	15.55	2.3	69.43	0.00102545	5.127	51.03	2.3	227.77
0.20	15.04	2.4	70.93	0.00095896	4.795	49.35	2.4	232.71
0.20	14.56	2.5	72.39	0.00089879	4.494	47.77	2.5	237.48
0.20	14.11	2.6	73.80	0.00084417	4.221	46.30	2.6	242.11
0.20	13.69	2.7	75.17	0.00079443	3.972	44.92	2.7	246.60
0.20	13.29	2.8	76.50	0.00074900	3.745	43.61	2.8	250.97
0.20	12.92	2.9	77.79	0.00070739	3.537	42.38	2.9	255.20
0.20	12.57	3.0	79.04	0.00066919	3.346	41.22	3.0	259.33

The chart assumes 3 constants: Drag=0.47, BB Area= 0.00001395 and Air Density=1.293

This sheet shows the effects of a .20 gram bb fired at 85 m/s (278.87 fps) over a three second time period with 0.1-second time measurement intervals. Although we know that a bb fired from a stock gun at an almost horizontal shot will not stay in the air for 3 seconds, it is important to show the trend involved with this length of time. This length of time will not affect our final results because they are located all within a 1 second time frame. The last three columns are what we are interested in. They show, from left to right, the bb velocity in fps, the time corresponding to the velocity, and the distance in feet at the same time.

The same variables are used in the sheet for .25 gram bbs. Please note that the same theoretical airsoft gun is used, so the initial velocity is reduced (from 85 m/s to 76.02 m/s) to account for the heavier bb that retains the same amount of joules of energy. If this is not easy to understand,

m (gram)	v (t) (m/s)	t (sec)	x(t) (m)	Fd (drag force N)	a (m/s^2)	v (t) (fps)	t (sec)	x(t) (ft)
0.25	76.03	0.0	0.00	0.02449870	97.995	249.43	0.0	0.00
0.25	66.23	0.1	6.62	0.01859014	74.361	217.28	0.1	21.73
0.25	58.79	0.2	12.50	0.01464983	58.599	192.88	0.2	41.02
0.25	52.93	0.3	17.79	0.01187494	47.500	173.65	0.3	58.38
0.25	48.18	0.4	22.61	0.00983926	39.357	158.07	0.4	74.19
0.25	44.24	0.5	27.04	0.00829744	33.190	145.16	0.5	88.70
0.25	40.93	0.6	31.13	0.00709929	28.397	134.27	0.6	102.13
0.25	38.09	0.7	34.94	0.00614827	24.593	124.95	0.7	114.63
0.25	35.63	0.8	38.50	0.00537989	21.520	116.88	0.8	126.31
0.25	33.47	0.9	41.85	0.00474960	18.998	109.82	0.9	137.30
0.25	31.58	1.0	45.01	0.00422578	16.903	103.59	1.0	147.66
0.25	29.88	1.1	47.99	0.00378545	15.142	98.05	1.1	157.46
0.25	28.37	1.2	50.83	0.00341157	13.646	93.08	1.2	166.77
0.25	27.01	1.3	53.53	0.00309127	12.365	88.60	1.3	175.63
0.25	25.77	1.4	56.11	0.00281467	11.259	84.54	1.4	184.08
0.25	24.64	1.5	58.57	0.00257410	10.296	80.85	1.5	192.17
0.25	23.61	1.6	60.93	0.00236350	9.454	77.47	1.6	199.92
0.25	22.67	1.7	63.20	0.00217804	8.712	74.37	1.7	207.35
0.25	21.80	1.8	65.38	0.00201384	8.055	71.51	1.8	214.50
0.25	20.99	1.9	67.48	0.00186774	7.471	68.87	1.9	221.39
0.25	20.24	2.0	69.51	0.00173716	6.949	66.42	2.0	228.03
0.25	19.55	2.1	71.46	0.00161996	6.480	64.14	2.1	234.45
0.25	18.90	2.2	73.35	0.00151435	6.057	62.01	2.2	240.65
0.25	18.30	2.3	75.18	0.00141885	5.675	60.03	2.3	246.65
0.25	17.73	2.4	76.95	0.00133219	5.329	58.16	2.4	252.47
0.25	17.20	2.5	78.67	0.00125331	5.013	56.42	2.5	258.11
0.25	16.69	2.6	80.34	0.00118129	4.725	54.77	2.6	263.59
0.25	16.22	2.7	81.96	0.00111537	4.461	53.22	2.7	268.91
0.25	15.78	2.8	83.54	0.00105486	4.219	51.76	2.8	274.08
0.25	15.35	2.9	85.08	0.00099919	3.997	50.37	2.9	279.12
0.25	14.95	3.0	86.57	0.00094784	3.791	49.06	3.0	284.03

*The chart assumes 3 constants: Drag=0.47, BB Area= 0.00001395 and Air Density=1.293