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