Linear Regression for Heavy Artillery. M109A7 Paladin case
Alexander Levakov, Senior Research Fellow, Ph.D
June, 2020
Paladin M109A7
1 About M109A7
The M109 is an American 155 mm turreted self-propelled howitzer, first introduced in the early 1960s to replace the M44. It has been upgraded a number of times, most recently to the M109A7. The M109 family is the most common Western indirect-fire support weapon of maneuver brigades of armored and mechanized infantry divisions.
For more see: https://en.wikipedia.org/wiki/M109_howitzer
https://fas.org/man/dod-101/sys/land/m109a6.htm
2 Data
All data for long range guns (LRG) is here: https://en.wikipedia.org/wiki/List_of_railway_artillery
Some interesting statistics is here:http://rpubs.com/alex-lev/357849
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(DT)
lrg <- read.delim("lrg.txt")
#datatable(lrg)
lrg## Name Country WW Weight_t Barrel_M Caliber_mm Range_M
## 1 Modele1893 France 1 7.00 7.40 164.7 18000
## 2 17KE Germany 2 80.00 NA 173.0 27000
## 3 180Pattern Russia 2 18.50 8.20 180.0 38500
## 4 20.3KE Germany 2 86.10 11.60 203.0 37000
## 5 M188 USA 1 15.30 12.30 203.0 21900
## 6 MkVIM3A2 USA 2 19.00 9.37 203.0 32300
## 7 K12VE Germany 2 318.00 33.30 211.0 115000
## 8 Theodore_Kanone Germany 2 95.00 8.90 238.0 26750
## 9 Mortire1884 France 1 31.00 6.70 240.0 17300
## 10 Type90 Japan 2 136.00 12.83 240.0 50000
## 11 Nathan Germany 1 55.50 6.33 149.1 22675
## 12 Samuel Germany 1 61.50 6.90 172.6 24020
## 13 Peter_Adalbert Germany 1 110.44 8.40 209.3 25580
## 14 Theodor_Otto Germany 1 103.00 7.14 238.0 18700
## 15 Theodor_Karl Germany 1 116.90 8.87 238.0 26600
## 16 Kurfürst Germany 1 149.00 10.40 283.0 25900
## 17 Bruno Germany 1 156.00 10.40 283.0 27500
## 18 Max Germany 1 267.90 16.13 380.0 47500
## 19 Paris_Gun Germany 1 256.00 34.00 238.0 130000
## 20 Kanone_E Germany 2 74.00 20.10 149.3 22500
## 21 BrunoKE Germany 2 118.00 11.08 283.0 35700
## 22 Kanon5E Germany 2 218.00 21.54 283.0 64000
## 23 OrdnanceBL12 GB 1 50.00 12.19 304.8 29900
## 24 OrdnanceBL9.2 GB 1 NA NA 233.7 20000
## 25 ObuhMK312 Russia 2 51.00 14.40 305.0 31000
## 26 M1890M1 USA 2 13.20 3.58 305.0 13360
## 27 BL13MKV GB 2 NA 15.39 342.9 37120
## 28 MKII USA 1 NA 17.78 355.6 38000
## 29 M1920 USA 1 104.30 18.10 355.6 44090
## 30 SiegfriedKE Germany 2 286.00 18.40 380.0 55700
## 31 Cannone381 Italy 1 93.50 15.24 381.0 24000
## 32 BL18 GB 2 85.70 16.00 457.2 20400
## 33 Obusier France 1 263.00 11.90 520.0 17000
## 34 Gustav Germany 2 1350.00 32.50 800.0 47000
## 35 Modele1893/96 France 1 48.00 12.20 305.0 12000
## 36 Mk.1 GB 1 NA 5.00 305.0 14000
## 37 BL14 GB 1 248.00 16.00 355.6 34750
## Velocity_MPS Elevation
## 1 775 25
## 2 875 45
## 3 900 50
## 4 925 47
## 5 NA 42
## 6 840 45
## 7 1650 55
## 8 810 45
## 9 575 38
## 10 1050 50
## 11 840 45
## 12 815 45
## 13 790 45
## 14 640 45
## 15 810 45
## 16 715 NA
## 17 785 45
## 18 1040 55
## 19 1640 NA
## 20 805 45
## 21 860 NA
## 22 1120 50
## 23 796 30
## 24 NA 40
## 25 815 NA
## 26 460 NA
## 27 787 40
## 28 853 43
## 29 808 50
## 30 1050 52
## 31 770 NA
## 32 570 40
## 33 500 60
## 34 820 48
## 35 780 15
## 36 447 65
## 37 792 403 Linear Regression Model
Here we fit linear regression model for data with Range_M < 70000. For more about linear model see: https://rpubs.com/alex-lev/360385
lrg2 <- lrg%>%filter(Range_M<70000)
fit.lrg.2 <- lm(Range_M~Velocity_MPS+Barrel_M+Elevation,data = na.omit(lrg2))
summary(fit.lrg.2)##
## Call:
## lm(formula = Range_M ~ Velocity_MPS + Barrel_M + Elevation, data = na.omit(lrg2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -14153.6 -1985.0 -60.7 2916.1 7010.3
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -44325.420 6863.817 -6.458 2.69e-06 ***
## Velocity_MPS 59.200 7.428 7.970 1.24e-07 ***
## Barrel_M 736.305 182.142 4.042 0.000637 ***
## Elevation 411.624 116.034 3.547 0.002020 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5075 on 20 degrees of freedom
## Multiple R-squared: 0.8804, Adjusted R-squared: 0.8624
## F-statistic: 49.06 on 3 and 20 DF, p-value: 2.096e-094 Predicting M109A7 Range
Here we apply open source data on M109A7 Paladin.
predict(fit.lrg.2,newdata = data.frame(Velocity_MPS=800,Barrel_M=6.05,Elevation=60),
interval = "conf",level = 0.99)## fit lwr upr
## 1 32186.87 24720.34 39653.39\[P(24720.34<Range<39653.39)=0.99\]
5 Conclusion
- Linear regression model
Range_M~Velocity_MPS+Barrel_M+Elevationis the best for fitting historical long range guns data (\(Range < 70 km\)). - Applying model on real heavy artillery gun M109A7 Paladinon we have got nice result for the range of fire.