BatesCalc2K

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Bates Grain Kn Calculator Version 2K Enter your values in the blue box. The rest is calculated by the spreadsheet

Any units of distance measurement may be used: inches, mm, furlongs...whatever, as long

Number of Grains: 4 This sample is in millimeters, in case you were wondering

Grain OD: 31.75 Progression of Kn ratios will appear in last column to the right

Core Diameter: 9.525 (Feel free to delete my silly arrows once you have "got it.")Grain Length: 52.3875

Nozzle Throat Diameter: 7.9375

Burn OD-Initial Length Core dia Outside End area Core End

Increment Interval area* full disk area

Burn Increment: 0.7664 (See Note 1) 0 0.0000 31.75 52.3875 9.525 5225.42 791.73 71.26

Initial burn surface: 12034.3026 (See Note 2) 1 0.7664 31.75 51.6211 10.291 5148.98 791.73 83.18

Nozzle throat area: 49.4832 (See Note 3) 2 1.5328 31.75 50.8547 11.058 5072.54 791.73 96.03

Initial Kn: 243 3 2.2991 31.75 50.0884 11.824 4996.09 791.73 109.81

Kn Max: 290 4 3.0655 31.75 49.3220 12.591 4919.65 791.73 124.50

Final Kn: 243 5 3.8319 31.75 48.5556 13.357 4843.21 791.73 140.12

6 4.5983 31.75 47.7892 14.123 4766.76 791.73 156.66

"Ideal" Bates length: 52.3875 (See Note 4) 7 5.3647 31.75 47.0228 14.890 4690.32 791.73 174.12

8 6.1310 31.75 46.2565 15.656 4613.88 791.73 192.51

9 6.8974 31.75 45.4901 16.422 4537.43 791.73 211.82

10 7.6638 31.75 44.7237 17.189 4460.99 791.73 232.05

11 8.4302 31.75 43.9573 17.955 4384.55 791.73 253.20

12 9.1966 31.75 43.1909 18.722 4308.11 791.73 275.28

13 9.9629 31.75 42.4246 19.488 4231.66 791.73 298.28

14 10.7293 31.75 41.6582 20.254 4155.22 791.73 322.20

15 11.4957 31.75 40.8918 21.021 4078.78 791.73 347.04

16 12.2621 31.75 40.1254 21.787 4002.33 791.73 372.8117 13.0284 31.75 39.3591 22.553 3925.89 791.73 399.50

18 13.7948 31.75 38.5927 23.320 3849.45 791.73 427.11

19 14.5612 31.75 37.8263 24.086 3773.01 791.73 455.65

20 15.3276 31.75 37.0599 24.853 3696.56 791.73 485.10

21 16.0940 31.75 36.2935 25.619 3620.12 791.73 515.48

22 16.8603 31.75 35.5272 26.385 3543.68 791.73 546.78

23 17.6267 31.75 34.7608 27.152 3467.23 791.73 579.01

24 18.3931 31.75 33.9944 27.918 3390.79 791.73 612.16

25 19.1595 31.75 33.2280 28.684 3314.35 791.73 646.23

26 19.9259 31.75 32.4616 29.451 3237.90 791.73 681.22

27 20.6922 31.75 31.6953 30.217 3161.46 791.73 717.13

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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Burn Interval

Kn


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28 21.4586 31.75 30.9289 30.984 3085.02 791.73 753.97

Jimmy Yawn 29 22.2250 31.75 30.1625 31.750 3008.58 791.73 791.73

[email protected]

Recrystallized Rocketry

6/12/2005
mailto:[email protected]://www.jamesyawn.com/index.htmhttp://www.jamesyawn.com/index.htmmailto:[email protected]


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s you use the same units for all values.

BurnA1 BurnA2 Each grain

End area Core burn Total burn Area x number Web Kn Ratio

minus core area (each gr area Of Grains Thickness

720.47 1567.63 3008.58 12034.30 22.23 243.20

708.55 1668.98 3086.07 12344.29 21.46 249.46

695.70 1766.64 3158.03 12632.14 20.69 255.28

681.92 1860.61 3224.46 12897.84 19.93 260.65

667.23 1950.90 3285.35 13141.41 19.16 265.57

651.61 2037.49 3340.71 13362.83 18.39 270.05

635.07 2120.39 3390.53 13562.11 17.63 274.08617.61 2199.60 3434.81 13739.24 16.86 277.65

599.22 2275.12 3473.56 13894.24 16.09 280.79

579.91 2346.95 3506.77 14027.09 15.33 283.47

559.68 2415.09 3534.45 14137.80 14.56 285.71

538.53 2479.54 3556.59 14226.37 13.79 287.50

516.45 2540.30 3573.20 14292.80 13.03 288.84

493.45 2597.37 3584.27 14337.08 12.26 289.74

469.53 2650.74 3589.81 14359.22 11.50 290.18

444.69 2700.43 3589.81 14359.22 10.73 290.18

418.92 2746.43 3584.27 14337.08 9.96 289.74

392.23 2788.74 3573.20 14292.80 9.20 288.84

364.62 2827.35 3556.59 14226.37 8.43 287.50

336.09 2862.28 3534.45 14137.80 7.66 285.71

306.63 2893.52 3506.77 14027.09 6.90 283.47

276.25 2921.06 3473.56 13894.24 6.13 280.79

244.95 2944.92 3434.81 13739.24 5.36 277.65

212.72 2965.08 3390.53 13562.11 4.60 274.08

179.58 2981.56 3340.71 13362.83 3.83 270.05

145.51 2994.34 3285.35 13141.41 3.07 265.57

110.51 3003.44 3224.46 12897.84 2.30 260.65

74.60 3008.84 3158.03 12632.14 1.53 255.28


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37.76 3010.55 3086.07 12344.29 0.77 249.46

0.00 3008.58 3008.58 12034.30 0.00 243.20


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Inhibitor - prevents outer sur

Hollow core, propellant exposed.Burns from the inside out.

As the hollow core burns, it geEnds burn toward each other,

And as the core gets bigger, t

Both end surfaces are exposed.Each burns toward the middle

TermsProgressive: Thrust increases asRegressive: Thrust decreases asFlat: Thrust stays (about) the same

The Bates Grain


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face from burning

ts bigger - progressiveso the core gets shorter - regressive

e ends get smaller, also regressive

otor burn proceedsotor burn proceedsas motor burn proceeds.


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This sheet calculates Kn progressions for Bates grains.

Knratio is the ratio of the area burning propellant surface to the area of a cross-section of nozzle throat. It is a critical factor in the desi

of a solid-propellant rocket motor. Kn can be used (with other factors) to determine the pressure within the motor casing at any point in tburn. Pressure must be generated and maintained within appropriate limits for the motor to function well.

It is from German: KlemmungA German dictionary defines Klemm as "an instrument for squeezing or holding fast...a narrow pass" Sounds sorta like a nozzle to me.Not sure about "ung"... any ideas are welcomed.

If Kn is too low, the propellant does not ignite well nor burn efficiently. Think of an old automobile that is hard to crank and gets bad gasmileage. That's low Kn.

If Kn is too high: Risk of CATO, or other damage from too-high pressure. CATO is a clever rocketry term for "blows up." If CATO soundlike fun, please stay with model rocketry for a few more years.

Different propellants require different Kn levels to function well. For example, slow-burning ammonium nitrate composite propellantsrequire and allow much higher Kn ratios than fast-burning KNO3/sucrose sugar propellant

Bates grainsare hollow-cored cylinders of propellant, with an inhibitor applied to the outside surface which prevents that surface froburning. Many rocket motors use several bates grains, from 2 to 6 are common, 8 and 10-grain motors have been seen.

The core and ends burn, but the outer cylindrical surface does not burn.

The core burns progressively, getting larger as the burn continues.

The ends also burn, so that as the core gets bigger, it also gets shorter. And as the core gets bigger, the ends get smaller.

This combination of progressive and regressive traits yields a relatively "flat" burn profile which starts and ends at the same Kn ratio, andrises a little in the middle. Thus it is better described as "progressive/regressive" but that is too many syllables. "Flat" is a lot easier to s

Notes

(Note 1)"Burn Increment" is (web thickness)/(number of data points)This sheet divides the burn into 30 data points and calcluates the Kn at each of these intervals (Cells D10 through Q39).


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(Note 2)Any units of distance measurement can be used to enter the grain length, diameter, core, and nozzle throat diameter. They mube the same units, or the output will be highly irregular. The Burn Surface and any other calculations of area will be in square units ofwhatever units you have chosen to use. So if your input is in inches, areas will be expressed in square inches. If millimeters, your outpuwillbe in square mm.

(Note 3)Nozzle throat area (cell B12) is calculated from the nozzle throat diameter (cell B7) by the classic formula, "Pie are squared."This value is critical in calculating Kn ratio, so change it at your own risk.

(Note 4)Ideal Bates Length: The spreadsheet will show here (Cell B17) the length of an "ideal" Bates grain.

It is calculated from the grain diameter and core diameter you have specified in cells B4 and B5.

Length of an "Ideal" Bates grain is defined by the formula: ((Outside Diameter * 3) + Core Diameter) / 2

Enter this length into Cell B6 if you want to calculate your motor for ideal Bates grains. Then do a quick check: are the beginning andending values for Kn the same? (If not, please let me know - I made a mistake!)

This gives a grain length approximately 1.6 times the outside diameter, but that will vary somewhat for different core diameters.

Grains longer than the ideal will burn progressively, grains shorter then the ideal length will burn regressively.

This sheet provides for the calculation of non-ideal Bates grains to allow use with different motor designs. For instance, one might want tfill up a certain sized motor casing, and be willing to tolerate a slightly progressive burn. Or one might want to use 4 short grains instead3 ideal ones to generate more thrust at liftoff, at the expense of a slightly regressive burn.

Jimmy [email protected]

6/12/05


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BatesCalc2K