the Pyro Cookbook - Physics & Math

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Chamber Volume
Description Volume = pi x r² x L

Unreal Volume - 4" Bore 807.39 = 3.1415 x 2² x 64.25

Unfactored Volume - 3.5" Bore 618.16 = 3.1415 x 1.75² x 64.25

Factored Volume
618.16 = 3.1415 x 1.75² x 64.25 Remaining Chamber Volume Volume Displaced
by Barrel

522.3 = 618.16 - 95.86 1.5" Barrel
95.86 = 3.1415 x .75² x 54.25

447.73 = 618.16 - 170.43 2" Barrel
170.43 = 3.1415 x 1² x 54.25

234.69 = 618.16 - 383.47 3" Barrel
383.47 = 3.1415 x 1.5² x 54.25

Barrel Diameter Unreal Volume
807.39 = 3.1415 x 2² x 64.25 Unfactored Volume
618.16 = 3.1415 x 1.75² x 64.25 Factored Volume -
Changes per barrel

1.5" - 3:1 ratio Barrel Volume - 269.13 in³ Barrel Volume - 202.05 in³ Chamber Volume - 522.3 in³
Barrel Volume - 174.1 in³

Barrel Length - 152.29 in
12' 8 1/3" Barrel Length - 114.34 in
9' 6 1/3" Barrel Length - 98.5 in
8' 2 1/2"

2" - 2:1 ratio Barrel Volume - 403.7 in³ Barrel Volume - 309.08 in³ Chamber Volume - 447.73 in³
Barrel Volume - 223.87 in³

Barrel Length - 128.50 in
10' 8 1/2" Barrel Length - 98.38 in
8' 2 3/8" Barrel Length - 71.25 in
5' 11 1/4"

3" - 1.5:1 ratio Barrel Volume - 538.26 in³ Barrel Volume - 412.11 in³ Chamber Volume - 234.69 in³
Barrel Volume - 156.46 in³

Barrel Length - 76.15 in
6' 4 1/8" Barrel Length - 58.30 in
4' 10 1/3" Barrel Length - 22.15 in
1' 10 1/8"

Ratios of Chamber to Barrel
Factoring the Displaced Volume of the Barrel

Chamber to Barrel Ratio Volume of Chamber Volume of Barrel

3 : 1 522.3 in³ 174.1 in³

2 : 1 447.73 in³ 223.87 in³

1.5 : 1 234.69 in³ 156.46 in³

Pressures @ Muzzle
Factoring Displaced Volume of Barrel

Set Values:

Chamber Presure : P_c

Barrel Pressure : P_b (@ the muzzle)

Average Pressure : P_a

Chamber Volume : V_c

Barrel Volume : V_b

Chamber Pressure : 100 psi
P_b = (P_c x V_c) / (V_b + V_c)

Barrel Diameter Muzzle Pressure

1.5" Barrel 75 psi 52230 / 696.4

2" Barrel 66.6 psi 44773 / 671.6

3" Barrel 60 psi 23469 / 391.15

Average Pressure of Cannon
Factoring Displaced Volume of Barrel

Barrel Diameter Average Pressure P_a = (P_c + P_b) / 2

1.5" Barrel 87.5 psi 175 / 2

2" Barrel 83.3 psi 166.6 / 2

3" Barrel 80 psi 160 / 2