ABSTRACT
The Paris Gun was an engineering marvel of many
firsts: first supergun, first object to fire a projectile
into the stratosphere, and one of the first explosive
projectile weapons to hit its target from so far
away, its victims could not hear its report. This
report examines the friction and wear principles
behind how the power of this gun was its own
downfall, its projectiles travelled so fast through so
long of a rifled barrel that only 60 shots could be
fired before a new barrel was required.
Max Willer
THE PARIS GUN
A TRIBOLOGICAL STUDY
FWLM Spring 2015 Final Report
TABLE OF CONTENTS
List of Tables .................................................................................................................................. 2
List of Figures ................................................................................................................................. 2
Purpose............................................................................................................................................ 3
Lessons in History ....................................................................................................................... 3
Weapons of a World War ............................................................................................................ 4
The Paris Gun .............................................................................................................................. 5
Theory and Methodology................................................................................................................ 7
Fundamentals of the Paris Gun Design ....................................................................................... 7
Fundamentals of Friction and Wear ............................................................................................ 9
Wear Mechanicsms in the Paris Gun .............................................................................................. 9
Types of Rifling Erosion ............................................................................................................. 9
Mechanical Wear in the Paris Gun ............................................................................................ 10
Volumetric loss ..................................................................................................................... 11
Force of the Gun ................................................................................................................... 11
Brinell Hardness.................................................................................................................... 12
Material Study....................................................................................................................... 13
Conclusion .................................................................................................................................... 14
References ..................................................................................................................................... 16
Appendix ....................................................................................................................................... 18
1
LIST OF TABLES
Table 1: Brinell hardness numbers (ASTM E10-12 2012) ........................................................... 13
LIST OF FIGURES
Figure 1: German Spring Offensive, 1918 (From the History Department of the US Military
Academy West Point 2006) ............................................................................................................ 4
Figure 2: The Paris Gun (Todd n.d.) ............................................................................................... 6
Figure 3: Gun Barrel Internal Geometry (Hasenbein 2004) ........................................................... 7
Figure 4: View of a New Rifled Barrel (Hasenbein 2004) ............................................................. 8
Figure 5: Design of the German Long-Range Projectile (Miller 1921).......................................... 8
Figure 6: Volume Removed from Rifled Bore per Shot ............................................................... 11
Figure 7: Image of Paris Gun Shell and Detail of Rifling Angle (Todd n.d.) .............................. 12
2
PURPOSE
The purpose of this paper is to take a look at an engineering marvel, the Paris Gun and how the
engineering principles of friction, wear, and lubrication effected the design, use, and eventual
ineffectiveness of the largest gun ever constructed at the time. This paper will take a brief look
into the history of cannon barrel designs and how this specific gun fit into the world stage near
the end of World War I. This paper will then summarize the general principles of gun barrel and
projectile design and introduce the fundamental aspects of friction and wear that come into play.
We will then take a more detailed look at the tribological contact scenarios seen in gun barrels
and specifically in the Paris Gun. There are an exceeding number of factors present in what
causes friction and wear in a gun barrel, especially one as extreme as the Paris Gun, so it will be
difficult to accurately quantify the exact effects of each friction and wear mechanism. Hopefully,
however, this examination of the Paris Gun will illustrate the complexity of accounting for
friction and wear in engineering projects, especially in a time predating modern analytical
techniques.
Lessons in History
At 7:17 in the morning of March 21st, 1918, Europe was at war. A tangle of alliances and
ultimatums turned what should have been a small conflict between Austria-Hungary and Serbia
into a global conflict. After the assassination of Archduke Franz Ferdinand pit Austria-Hungary
against Serbia, Russia mobilized to assist its ally Serbia, Germany mobilized against Russia her
ally of France. England joined the war due to an obligation to France and the invaded Belgium.
And finally the United States jointed the war 3 years later after German submarine attacks on
peaceful American vessels. (Duffy 2009) At 7:17 in the morning of March 21st, 1918, the
Germans were in the middle of their Spring Offensive, a series of attacks along the Western
3
Front that was a last ditch attempt by German to win the war before the full strength of the
Americans could arrive. This attack was a four pronged attack, the largest attack being the
Operation Michael, intended to defeat the British Army, while the other three attacks were
designed to divert Allied forces from the main offensive. (Gray 1991)
Figure 1: German Spring Offensive, 1918 (From the History Department of the US Military Academy West Point 2006)
Weapons of a World War
At 7:17 in the morning of March 21st, 1918, the war was being waged in a different fashion from
when it in 1914. Standing armies facing off against one another in decisive battles gave way to
trench warfare, long confrontations which tested the supply lines of an army as much as its
4
fighting force. Machine guns were developed to more adequately defend these trenches against
attacking armies. By 1917 armies were employing the use of tanks to get past entrenched
defenders. The nascent technology of airplanes and zeppelins were being used as the first
example of air support by dropping grenades and shells on targets from the sky. Even with all
these advances, long range artillery remained the major source of firepower on the battlefield.
These massive cannons were innovated on as well, becoming larger, easier to handle, and more
accurate in their fire. Many of these guns were also mobile, utilizing wheels, tank treads, or the
rail systems of Europe. (Llewellyn 2014)
The Paris Gun
At 7:18 in the morning of March 21st, 1918, explosions began happening in Paris around 15
minutes apart. The Parisians were used to the war by this point, but the odd part about these
explosions is that no one heard the sound of the mortar or cannon shot prior to the explosion.
Initially it was suspected that bombs were being dropped from some airplane or zeppelin too
high to be seen or heard. After investigation however, it was determined that the explosions were
caused by shells, not bombs, meaning it had to be fired from artillery. After ruling out a mortar
being fired from inside the city, the only conclusion was that the shells were being fired from a
new German long range gun coming from so far away, that no one could hear the shot being
fired. (Miller 1921)
So what was the Paris Gun? The Paris Gun was quite simply the world’s largest gun, capable of
ranges of up to 100 kilometers. Constructed by the German engineering company Krupp, they
designed the barrel to have a muzzle velocity of 1610 meters per second, which required a barrel
length of 34 meters. This massive barrel length created a number of problems. The first of which
was barrel sag, as the weight and length of the barrel could not support itself. Thus a suspension
5
bridge like truss was developed to keep the barrel straight. The second issue with the length is
that Krupp did not have a barrel rifling machine capable of creating barrels longer than 18
meters. Thus they designed the gun to only include the 18 meter rifling section and extended the
barrel with a 12 meter smooth bore extension. The massive size of the gun also required thought
as to how to even transport the gun. For this, two types of carriages were developed. The gun
was placed on a turntable on top of a rail carriage and then once it reached its destination, it was
lower onto a concrete emplacement.
Finally, the long barrel brought up the main issue with the Paris Gun that is the focus of this
paper. The temperatures, pressures, and length and speed of travel for the projectile were so high
that the gun barrel would wear away so much between shots, it would need replacement every 65
shots. This huge amount of wear meant that the ammunition needed to be 65 different sizes and
loaded in order from smallest to largest when firing.
Figure 2: The Paris Gun (Todd n.d.)
All in all the Paris Guns were not that successful. During the bombings on Paris, only 256
Parisians were killed and 620 wounded. The gun was simply too inaccurate at the distance it was
designed for to target specific installations. The projectile was too small to deliver that much
explosives to its target, and thus did little damage when it hit, with the exception of one chance
hit on the Church of St Gervais. Regardless of their effect in the war, and their obsolescence in
6
future wars thanks to the rise of aerial war technology, the Paris Gun was a massive engineering
achievement and in the following sections we look at how it works and how friction and wear
played a part in its downfall. (Todd n.d.)
THEORY AND METHODOLOGY
Fundamentals of the Paris Gun Design
At their most basic, gun barrels are designed as a “pressure vessel whose primary function is to
accurately fire projectiles at high velocities towards a target”. (Hasenbein 2004) The gun barrel
is made up of three distinct regions, the combustion chamber, the forcing cone, and the bore, as
illustrated in Figure 3.
Figure 3: Gun Barrel Internal Geometry (Hasenbein 2004)
The combustion chamber is as it sounds, it provides the volume for the propellant to combust in
to accelerate the bullet. The forcing cone is a short tapered hole that guides the projectile into the
bore. The bore is the rest of the gun barrel. It provides a cylinder for the projectile to travel to as
it accelerates to the muzzle velocity at the end of the gun. Sometimes the gun bore has rifling,
especially on guns where accuracy is a concern. This rifling is a machined out spiral design on
the inside of the gun barrel as seen in Figure 4. It imparts a spin to the projectile as it travels
through the bore. This spin results in increased accuracy of the projectile.
7
Figure 4: View of a New Rifled Barrel (Hasenbein 2004)
While the rifling in the Paris Gun was necessary for the gun to have any accuracy whatsoever, it
is also the most difficult part of the gun to maintain. As stated earlier, after 60 shots the rifle
needed to be re-bored to use on a different gun.
Figure 5: Design of the German Long-Range Projectile (Miller 1921)
The projectile of a rifled gun barrel must be designed with some way of letting the riddling
impart angular momentum to it. In the Paris Gun projectile design, the projectiles were ringed
8
with two splined copper bands to match the shape of the rifling. Copper was used for this
matching material since it was relatively soft compared to the steel of the bore, and when under
high temperature would expand to fit into the rifling grooves to create a seal. (Todd n.d.)
Fundamentals of Friction and Wear
Friction and wear are two of the largest contributors to requirements for gun barrel design. Once
the relatively simple ballistics equation is figured out for what mass of projectile can be fired at
what range, one knows the muzzle velocity of projectile once it has exited the gun. How to get
the projectile to that velocity is based on the design of the bore for the cannon, and is a much
more complicated problem. Getting the projectile up to speed is a balance between weight of the
projectile, chemical equations of expansion and heat, friction between the projectile and the bore,
not to mention recoil, firing angle, mounting, deflection of the combustion chamber, and so on.
To limit the scope, this paper only considers the erosion of the rifling section in the gun barrel of
the Paris Gun caused by the projectile passing through. We attempt to set up a model based on
the material removed.
WEAR MECHANICSMS IN THE PARIS GUN
Types of Rifling Erosion
Erosion of the gun barrel rifling is caused by three major processes: thermal processes, chemical
processes, and mechanical processes. Thermal processes are caused by the chemical explosion
driving the projectile forward as well as the high speed friction of the projectile passing through.
The high temperatures present in the gun barrel can cause material changes near the surface of
the gun barrel. These material changes often make the steel more brittle in those areas, allowing
for the other two types of erosion to chip away at the material.
9
Chemical processes of erosion are caused by the violent chemical reaction that generates the
force to put the projectile forward. These chemical processes are or two types: hot gases
interacting with the metals in the bore and oxidation. The hot gases interacting with the metal
can produce compounds with lower melting points than the bore itself, allowing for the other two
types of erosion to remove material. Oxidation can be caused by the reaction of the propellant,
and can cause a brittle Iron Oxide layer to form, again allowing for easier material removal.
(Johnston 2005)
Finally, mechanical forces can remove the rifling pattern in the bore as well. Mechanical forces,
alongside the chemical and thermal effects, drive the projectile along the bore causing wear
where the material is not strong enough to stay together. A steady-state wear equation was
proposed as:
𝑉=𝐾
𝑃𝐿
3𝐻
Where H is the Brinell hardness, V is the volumetric loss, L is the sliding distance, and K is the
dimensionless standard wear coefficient. (Yang 2003)
Mechanical Wear in the Paris Gun
Now that we understand the erosion process of the rifling we can apply the values we know to
the basic wear equation. This equation, as you can see, does not take into account chemical
properties, thermal properties, or even velocity. However, we should be able to capture those
properties in the general value of K, the dimensionless wear coefficient. K values are empirical
by nature and vary based on the two materials in contact, as well as other factors. Here we will
attempt to keep all other factors equal as we examine the mechanical wear on the Paris Gun.
10
VOLUMETRIC LOSS
We first start with the volumetric loss of the rifling bore. We know that the initial bore size of the
Paris Gun was 210 millimeters in diameter from Figure 5. We know from the Miller text that
after 65 rounds had been fired, the barrel was sent back to Krupp to be re-bored to 238
millimeters in diameter. (Miller 1921) We make the assumption that the bore diameter increases
linearly after each shot which means that as the projectile increases, it takes off more and more
area and volume. The tabulated calculation is included in the Appendix, and the results show that
the total volume removed per shot gets larger as the projectile gets larger as shown in Figure 6.
The maximum volume removed is 0.002941 cubic meters over the length of the 18 meter rifled
bore.
Removed Volume Per Shot (m^3)
Delta Volume Per Shot (m^3)
0.003000
0.002950
0.002900
0.002850
0.002800
0.002750
0.002700
0.002650
0.002600
0.002550
0
10
20
30
40
50
60
70
Shot
Figure 6: Volume Removed from Rifled Bore per Shot
FORCE OF THE GUN
We then try to make an estimate of the force from the projectile onto the bore material. We
estimate from the Todd article that the Paris Gun accelerated the projectile from zero to 1610
meters per second over the length of the 34 meter gun. We estimate from Miller that the
11
projectile weight around 106 kilograms. We use this to estimate the acceleration and the forces
seen in the by the projectile shooting forward. (Miller 1921)
𝑣𝑓 2 − 𝑣𝑖 2 16102
𝑎=
=
= 19050 𝑚⁄𝑠 2
2𝑙
2 ∗ 68
𝐹 = 𝑚𝑎 = 106 ∗ 19050 = 2020300 𝑁
As the projectile is being pushed by this force, the rifling collar is being forced into a rotational
motion. We estimate that the angle of this rifling is about 15 degrees based on the image of the
Paris gun shell in Figure 7. 𝐹𝑟 = tan(15°) ∗ 𝐹 = 541338 𝑁
Figure 7: Image of Paris Gun Shell and Detail of Rifling Angle (Todd n.d.)
BRINELL HARDNESS
Another assumption that we make here, is that the Paris Cannon material was of a mild steel.
This correlates to a hardness value of 120 HB. Now that we have this information, we can look at
our governing equation.
12
Table 1: Brinell hardness numbers (ASTM E10-12 2012)
𝑉=𝐾
0.002941𝑚3 = 𝐾
𝑃𝐿
3𝐻
541998 𝑁 ∗ 18 𝑚
3 ∗ 120
𝐾 = 1.085 ∗ 10−7
We now have a standard wear coefficient of the system. Keeping the temperatures, propulsion
chemicals, and all other variables equal, one could extrapolate data on how the volume of
removal would change with a change of force, length or material. Since we know the force and
length that we need from our ballistics requirements, the only other thing we can change is to a
material with a different hardness.
MATERIAL STUDY
We can see how a new material (for the World War I era) may have helped the Paris Gun fire
more shells before needing re-boring. Stainless steel was just being invented during World War I
for the specific purpose of finding a material that would be more resistant to erosion within gun
13
barrels. (Peaple 2015) We can see from Table 1 that stainless steel has a Brinell hardness of 200
HB. We now look to see how much that improves the performance of the Paris Gun.
𝑉=𝐾
𝑉 = 1.085 ∗ 10−7
𝑃𝐿
3𝐻
541998 𝑁 ∗ 18 𝑚
= .00176 𝑚3
3 ∗ 200
We find that the maximum volume removed at the largest bore size would have been 40% less
than the maximum volume per shot removed from the Paris Gun made of mild steel. As the
second table in the Appendix shows, this allows the Stainless Steel Paris Gun to fire 108 shots
instead of just 65 before re-boring the barrel at 238 millimeters. By comparison, the chromium
plated 18 meter rifled barrel of the 16” caliber Mark 8 gun used on the Iowa Class US Navy
battleships have a barrel life of 290 rounds (though they only have a range of 38 km). (DiGiulian
2015) Obviously these World War II guns are more advanced in more ways than just a material
change, but it goes to show how better materials can reduce wear and lead to longer rifling life.
CONCLUSION
The Paris Gun was a marvel of engineering. It succeeded as the first gun to put a man-made
object into the stratosphere. It succeeded at bombarding a city from so far away its report could
not be heard. It completely failed as a military weapon. Its payload was too small and its
projectiles were too inaccurate to usefully aim at important targets. It was part of a last ditch
effort by Germany to win a war before Allied support grew even stronger. Even if the war didn’t
end in a year and there was time to hone and perfect the gun, use more advanced materials, and
somehow make more accurate projectiles for it, it still would have been one of the last superguns
to be created. It’s for the same reason World War I was the last war for trench warfare to play
14
such a large part: the airplane would take over as the preferred delivery method of explosive
payloads.
Still the Paris Gun is an excellent example of the effects of friction and wear. Because of its
extreme engineering, the wear of the bore required custom ammunition to be made to account for
the bore getting larger after each successive shot. Even though not much is known to an exact
degree about the materials, chemicals, and structure that went into the gun, we were able to study
the design based on its failures and do a basic study on how it could have been improved upon
today.
15
REFERENCES
ASTM E10-12. 2012. Standard method for Brinell hardness of metallic materials. Meterial
Standard, West Conshohocken, PA: ASTM International.
DiGiulian, Tony. 2015. United States of America 16"/50 (40.6 cm) Mark 7 . May 3. Accessed
May 15, 2015. http://www.navweaps.com/Weapons/WNUS_16-50_mk7.htm.
Duffy, Michael. 2009. Feature Articles - The Causes of World War One. August 22. Accessed
May 15, 2015. http://www.firstworldwar.com/origins/causes.htm.
From the History Department of the US Military Academy West Point. 2006. Map of the final
German offensives on the Western Front (World War I), 1918. May 2. Accessed May 15,
2015. http://commons.wikimedia.org/wiki/File:Western_front_1918_german.jpg.
Gray, Randal. 1991. Kaiserschlacht, 1918: The Final German Offensive,. London: Osprey.
H.C. Meng, K.C. Ludema. 1995. "Wear models and predictive wquations: their form and
content." Wear 181-183.
Hasenbein, Richard G. 2004. Wear and Erosion in Large Caliber Gun Barrels . Watervliet NY:
Weapon Systems & Technology Directorate Armament Engineering & Technology
Center U.S. Army Armament Research, Development & Engineering Center.
Johnston, Ian A. 2005. Understanding and Predicting Gun Barrel Erosion. Edinburgh, Australia:
Weapons Systems Division, Defence Science and Technology Organisation. .
Llewellyn, Jennifer. 2014. Weapons of World War I. Accessed May 15, 2015.
http://alphahistory.com/worldwar1/weapons/.
16
Miller, Harry W. II. 1921. Railway Artillery: A Report on the Characteristics, Scope of Utility,
Etc. of Railway Artillery. Washington: Government Printing Office.
Peaple, Andrew. 2015. 100 Years, 100 Legacies, Stainless Steel.
http://online.wsj.com/ww1/stainless-steel.
Todd, Roger. n.d. A Brief History of the Paris Guns. Accessed May 15, 2015.
http://www.landships.info/landships/artillery_articles.html.
Yang, L.J. 2003. "Wear coefficient equation for aluminium-based matrix composites against
steel disc." Wear 579-592.
17
APPENDIX
Table 1: Loss of Bore Material
Shot
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
Bore Size
Bore Area
(mm)
(mm)
210
34636
210.4375
34781
210.875
34925
211.3125
35070
211.75
35216
212.1875
35361
212.625
35507
213.0625
35654
213.5
35800
213.9375
35947
214.375
36094
214.8125
36242
215.25
36390
215.6875
36538
216.125
36686
216.5625
36835
217
36984
217.4375
37133
217.875
37282
218.3125
37432
218.75
37583
219.1875
37733
219.625
37884
220.0625
38035
220.5
38186
220.9375
38338
221.375
38490
221.8125
38642
222.25
38795
222.6875
38948
223.125
39101
223.5625
39254
224
39408
Total
Removed
Area
(mm^2)
0
144
289
434
580
725
871
1018
1164
1311
1458
1606
1753
1902
2050
2199
2348
2497
2646
2796
2946
3097
3248
3399
3550
3702
3854
4006
4159
4312
4465
4618
4772
18
Total
Removed
Volume
(mm^3)
0
2600410.368
5206232.619
7817466.755
10434112.78
13056170.68
15683640.47
18316522.14
20954815.7
23598521.14
26247638.47
28902167.68
31562108.77
34227461.75
36898226.61
39574403.36
42255991.99
44942992.5
47635404.9
50333229.18
53036465.35
55745113.4
58459173.34
61178645.16
63903528.87
66633824.45
69369531.93
72110651.28
74857182.53
77609125.65
80366480.66
83129247.56
85897426.33
Total
Removed
Volume
(m^3)
0.000000
0.002600
0.005206
0.007817
0.010434
0.013056
0.015684
0.018317
0.020955
0.023599
0.026248
0.028902
0.031562
0.034227
0.036898
0.039574
0.042256
0.044943
0.047635
0.050333
0.053036
0.055745
0.058459
0.061179
0.063904
0.066634
0.069370
0.072111
0.074857
0.077609
0.080366
0.083129
0.085897
Removed
Volume
Per Shot
(m^3)
0.002600
0.002606
0.002611
0.002617
0.002622
0.002627
0.002633
0.002638
0.002644
0.002649
0.002655
0.002660
0.002665
0.002671
0.002676
0.002682
0.002687
0.002692
0.002698
0.002703
0.002709
0.002714
0.002719
0.002725
0.002730
0.002736
0.002741
0.002747
0.002752
0.002757
0.002763
0.002768
Shot
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
Bore Size
Bore Area
(mm)
(mm)
224.4375
39562
224.875
39717
225.3125
39871
225.75
40026
226.1875
40182
226.625
40337
227.0625
40493
227.5
40649
227.9375
40806
228.375
40963
228.8125
41120
229.25
41277
229.6875
41435
230.125
41593
230.5625
41751
231
41910
231.4375
42069
231.875
42228
232.3125
42387
232.75
42547
233.1875
42707
233.625
42868
234.0625
43028
234.5
43189
234.9375
43351
235.375
43512
235.8125
43674
236.25
43836
236.6875
43999
237.125
44162
237.5625
44325
238
44488
Total
Removed
Area
(mm^2)
4926
5081
5235
5390
5546
5701
5857
6013
6170
6326
6484
6641
6799
6957
7115
7274
7432
7592
7751
7911
8071
8231
8392
8553
8714
8876
9038
9200
9363
9526
9689
9852
19
Total
Removed
Volume
(mm^3)
88671017
91450019.54
94234433.97
97024260.29
99819498.49
102620148.6
105426210.5
108237684.4
111054570.1
113876867.8
116704577.3
119537698.6
122376231.9
125220177.1
128069534.1
130924303
133784483.9
136650076.5
139521081.1
142397497.6
145279325.9
148166566.2
151059218.3
153957282.3
156860758.2
159769645.9
162683945.6
165603657.1
168528780.5
171459315.8
174395263
177336622.1
Total
Removed
Volume
(m^3)
0.088671
0.091450
0.094234
0.097024
0.099819
0.102620
0.105426
0.108238
0.111055
0.113877
0.116705
0.119538
0.122376
0.125220
0.128070
0.130924
0.133784
0.136650
0.139521
0.142397
0.145279
0.148167
0.151059
0.153957
0.156861
0.159770
0.162684
0.165604
0.168529
0.171459
0.174395
0.177337
Removed
Volume
Per Shot
(m^3)
0.002774
0.002779
0.002784
0.002790
0.002795
0.002801
0.002806
0.002811
0.002817
0.002822
0.002828
0.002833
0.002839
0.002844
0.002849
0.002855
0.002860
0.002866
0.002871
0.002876
0.002882
0.002887
0.002893
0.002898
0.002903
0.002909
0.002914
0.002920
0.002925
0.002931
0.002936
0.002941
Bore Size (mm)
240
Bore Diameter (mm)
235
230
225
220
215
210
205
0
10
20
30
40
50
60
70
50
60
70
Shot
Bore Area (m^2)
Bore Area (mm)
50000
45000
40000
35000
30000
25000
20000
15000
10000
5000
0
0
10
20
30
40
Shot
20
Total Removed Volume (m^3)
Total Removed Volume (m^3)
0.200000
0.180000
0.160000
0.140000
0.120000
0.100000
0.080000
0.060000
0.040000
0.020000
0.000000
0
10
20
30
40
50
60
70
60
70
Shot
Removed Volume Per Shot (m^3)
Delta Volume Per Shot (m^3)
0.003000
0.002950
0.002900
0.002850
0.002800
0.002750
0.002700
0.002650
0.002600
0.002550
0
10
20
30
40
Shot
21
50
Table 2: Stainless Steel Bore Data
Shot
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Bore Size
Bore Area
(mm)
(mm)
210
34636
210.2616822
34722
210.5233645
34809
210.7850467
34896
211.046729
34982
211.3084112
35069
211.5700935
35156
211.8317757
35243
212.0934579
35330
212.3551402
35417
212.6168224
35505
212.8785047
35592
213.1401869
35680
213.4018692
35767
213.6635514
35855
213.9252336
35943
214.1869159
36031
214.4485981
36119
214.7102804
36207
214.9719626
36296
215.2336449
36384
215.4953271
36473
215.7570093
36561
216.0186916
36650
216.2803738
36739
216.5420561
36828
216.8037383
36917
217.0654206
37006
217.3271028
37095
217.588785
37185
217.8504673
37274
218.1121495
37364
218.3738318
37453
218.635514
37543
218.8971963
37633
Total
Removed
Area
(mm^2)
0
86
173
259
346
433
520
607
694
781
869
956
1044
1131
1219
1307
1395
1483
1571
1660
1748
1836
1925
2014
2103
2192
2281
2370
2459
2549
2638
2728
2817
2907
2997
22
Total
Removed
Volume
(mm^3)
0
1554735.212
3111406.583
4670014.112
6230557.799
7793037.645
9357453.649
10923805.81
12492094.13
14062318.61
15634479.25
17208576.05
18784609
20362578.12
21942483.39
23524324.82
25108102.41
26693816.15
28281466.06
29871052.12
31462574.34
33056032.72
34651427.26
36248757.96
37848024.82
39449227.83
41052367
42657442.33
44264453.82
45873401.47
47484285.28
49097105.24
50711861.37
52328553.65
53947182.09
Total
Removed
Volume
(m^3)
0.000000
0.001555
0.003111
0.004670
0.006231
0.007793
0.009357
0.010924
0.012492
0.014062
0.015634
0.017209
0.018785
0.020363
0.021942
0.023524
0.025108
0.026694
0.028281
0.029871
0.031463
0.033056
0.034651
0.036249
0.037848
0.039449
0.041052
0.042657
0.044264
0.045873
0.047484
0.049097
0.050712
0.052329
0.053947
Removed
Volume
Per Shot
(m^3)
0.001555
0.001557
0.001559
0.001561
0.001562
0.001564
0.001566
0.001568
0.001570
0.001572
0.001574
0.001576
0.001578
0.001580
0.001582
0.001584
0.001586
0.001588
0.001590
0.001592
0.001593
0.001595
0.001597
0.001599
0.001601
0.001603
0.001605
0.001607
0.001609
0.001611
0.001613
0.001615
0.001617
0.001619
Shot
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
Bore Size
Bore Area
(mm)
(mm)
219.1588785
37723
219.4205607
37813
219.682243
37904
219.9439252
37994
220.2056075
38084
220.4672897
38175
220.728972
38266
220.9906542
38356
221.2523364
38447
221.5140187
38538
221.7757009
38629
222.0373832
38721
222.2990654
38812
222.5607477
38903
222.8224299
38995
223.0841121
39087
223.3457944
39178
223.6074766
39270
223.8691589
39362
224.1308411
39454
224.3925234
39546
224.6542056
39639
224.9158879
39731
225.1775701
39824
225.4392523
39916
225.7009346
40009
225.9626168
40102
226.2242991
40195
226.4859813
40288
226.7476636
40381
227.0093458
40474
227.271028
40567
227.5327103
40661
227.7943925
40755
228.0560748
40848
228.317757
40942
228.5794393
41036
Total
Removed
Area
(mm^2)
3087
3177
3267
3358
3448
3539
3630
3720
3811
3902
3993
4085
4176
4267
4359
4450
4542
4634
4726
4818
4910
5003
5095
5188
5280
5373
5466
5559
5652
5745
5838
5931
6025
6118
6212
6306
6400
23
Total
Removed
Volume
(mm^3)
55567746.69
57190247.44
58814684.36
60441057.43
62069366.67
63699612.06
65331793.6
66965911.31
68601965.18
70239955.2
71879881.39
73521743.73
75165542.23
76811276.88
78458947.7
80108554.68
81760097.81
83413577.1
85068992.55
86726344.16
88385631.93
90046855.85
91710015.93
93375112.18
95042144.58
96711113.14
98382017.85
100054858.7
101729635.8
103406349
105084998.3
106765583.8
108448105.5
110132563.3
111818957.3
113507287.4
115197553.7
Total
Removed
Volume
(m^3)
0.055568
0.057190
0.058815
0.060441
0.062069
0.063700
0.065332
0.066966
0.068602
0.070240
0.071880
0.073522
0.075166
0.076811
0.078459
0.080109
0.081760
0.083414
0.085069
0.086726
0.088386
0.090047
0.091710
0.093375
0.095042
0.096711
0.098382
0.100055
0.101730
0.103406
0.105085
0.106766
0.108448
0.110133
0.111819
0.113507
0.115198
Removed
Volume
Per Shot
(m^3)
0.001621
0.001623
0.001624
0.001626
0.001628
0.001630
0.001632
0.001634
0.001636
0.001638
0.001640
0.001642
0.001644
0.001646
0.001648
0.001650
0.001652
0.001653
0.001655
0.001657
0.001659
0.001661
0.001663
0.001665
0.001667
0.001669
0.001671
0.001673
0.001675
0.001677
0.001679
0.001681
0.001683
0.001684
0.001686
0.001688
0.001690
Shot
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
Bore Size
Bore Area
(mm)
(mm)
228.8411215
41130
229.1028037
41224
229.364486
41318
229.6261682
41413
229.8878505
41507
230.1495327
41602
230.411215
41696
230.6728972
41791
230.9345794
41886
231.1962617
41981
231.4579439
42076
231.7196262
42171
231.9813084
42266
232.2429907
42362
232.5046729
42457
232.7663551
42553
233.0280374
42649
233.2897196
42745
233.5514019
42841
233.8130841
42937
234.0747664
43033
234.3364486
43129
234.5981308
43225
234.8598131
43322
235.1214953
43418
235.3831776
43515
235.6448598
43612
235.9065421
43709
236.1682243
43806
236.4299065
43903
236.6915888
44000
236.953271
44098
237.2149533
44195
237.4766355
44293
237.7383178
44390
238
44488
Total
Removed
Area
(mm^2)
6494
6588
6682
6777
6871
6966
7060
7155
7250
7345
7440
7535
7630
7726
7821
7917
8013
8109
8204
8301
8397
8493
8589
8686
8782
8879
8976
9073
9170
9267
9364
9462
9559
9657
9754
9852
24
Total
Removed
Volume
(mm^3)
116889756.2
118583894.8
120279969.6
121977980.5
123677927.6
125379810.9
127083630.3
128789385.9
130497077.6
132206705.5
133918269.5
135631769.7
137347206.1
139064578.6
140783887.3
142505132.1
144228313.1
145953430.3
147680483.6
149409473
151140398.7
152873260.5
154608058.4
156344792.5
158083462.8
159824069.2
161566611.8
163311090.5
165057505.4
166805856.5
168556143.7
170308367
172062526.6
173818622.3
175576654.1
177336622.1
Total
Removed
Volume
(m^3)
0.116890
0.118584
0.120280
0.121978
0.123678
0.125380
0.127084
0.128789
0.130497
0.132207
0.133918
0.135632
0.137347
0.139065
0.140784
0.142505
0.144228
0.145953
0.147680
0.149409
0.151140
0.152873
0.154608
0.156345
0.158083
0.159824
0.161567
0.163311
0.165058
0.166806
0.168556
0.170308
0.172063
0.173819
0.175577
0.177337
Removed
Volume
Per Shot
(m^3)
0.001692
0.001694
0.001696
0.001698
0.001700
0.001702
0.001704
0.001706
0.001708
0.001710
0.001712
0.001714
0.001715
0.001717
0.001719
0.001721
0.001723
0.001725
0.001727
0.001729
0.001731
0.001733
0.001735
0.001737
0.001739
0.001741
0.001743
0.001744
0.001746
0.001748
0.001750
0.001752
0.001754
0.001756
0.001758
0.001760