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Posted (edited)

I’ve been reviewing a lot of the historical data on the various 50 caliber bullets used in World War 2. The DCS values for muzzle velocity and weight are different from data in the historical and contemporary sources in some instances.

 

In the first part of this post I will present data showing the muzzle velocities, weight and dispersion for these bullets.  All the data presented will be for the 36 inch Barrel Aircraft Machine Gun version of the Browning 50 caliber. 

 

In the second part, we’ll get a little more in depth with data.  We will also construct firing tables and compute the trajectories of the bullets using historical methods and data.  

 

With that out of the way. Let's begin by comparing the DCS data in the CoreMods\WWII Units\Weapons\Weapons.lua file to some contemporary and historical data.   

The table Below shows the values In game Vs the historical data.  I’ve also added some data for the M1 incendiary bullet, which was one of the most commonly used in American aircraft.

 

DCS M2 AP 

DCS M8 API 

DCS M20 APIT

M2 AP Historical Data

M8 API Historical

Data

M20 API Historical Data

M1 Incendiary

V0 (Muzzle Velocity MPS)

V0 (Muzzle Velocity MPS)

V0 (Muzzle Velocity MPS)

V0 (Muzzle Velocity MPS)

V0 (Muzzle Velocity MPS)

V0 (Muzzle Velocity MPS)

V0 (Muzzle Velocity MPS)

830

860

875

864

899

899

912

Bullet Weight Kg

Bullet Weight Kg

Bullet Weight Kg

Bullet Weight Kg

Bullet Weight Kg

Bullet Weight Kg

Bullet Weight Kg

0.0458

.0403

0.0410

0.046

.042

.0396

0.040049

Da0

(Dispersion) 

Da0

(Dispersion) 

Da0

(Dispersion)

Da0

(Dispersion) 

Da0

(Dispersion) 

Da0

(Dispersion) 

Da0

(Dispersion) 

0.00085

0.00085

0.00085

0.001

0.001

0.001

0.001

100% Dispersion: Mils

100% Dispersion: Mils

100% Dispersion: Mils

100% Dispersion Mils

100% Dispersion: Mils

100% Dispersion: Mils

100% Dispersion: Mils

6.8

6.8

6.8

8

8

8

8


 

Below is a table of muzzle velocities for the .50 Caliber M2 AP, M8 API and M1 Incendiary in the various historical and contemporary documents.The table also includes a link to the source material. 


 

Bullet:

Muzzle Velocity: 

FPS

Muzzle Velocity 

MPS:

Source:

Link To Source

M2 AP

2835

864.07

Terminal Ballistic Data 1945

https://cgsc.contentdm.oclc.org/digital/collection/p4013coll8/id/2373/rec/8

M2 AP

2845

867.11

Terminal Ballistic Data 1944 /43

https://cgsc.contentdm.oclc.org/digital/collection/p4013coll8/id/2327/rec/1

M2 AP

2845

867.11

Test Method Standard V50 Ballistic Test For Armor MIL STD-662F 1997

https://www.abbottaerospace.com/downloads/mil-std-662f-v50-ballistic-test-for-armor/

M2 AP

2845

867.11

NDRC Study Effects Of Weapon Impacts

https://www.loc.gov/resource/gdcmassbookdig.effectsofimpacte01unit/?sp=421

M2 AP

2840

865.59

TM 9-225 Browning Machine Gun .50 Caliber AN-M2 Aircraft

https://www.google.com/books/edition/Browning_Machine_Gun_Caliber_50_AN_M2_Ai/nXySRue3QAYC?hl=en&gbpv=1

M2 AP

2845

867.11

TM-9-2200 Small Arms 

https://archive.org/details/TM9-2200/page/n203/mode/2up

M2 AP

2840

865.59

TM 9-219 AN M3 Basic Aircraft Machine Gun

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=7268

M8 API & M20 APIT

2946

897.89

AFM 51-44 Fighter and Fighter Bombers Employment in Tactical Air Operations 

https://archive.org/details/fighter-fighter-bomber-employment-in-tactical-air-operations-usaf/page/55/mode/1up

M8 API & M20 APIT

2950

899.12

TM 9-225 Browning Machine Gun .50 Caliber AN-M2 Aircraft

https://www.google.com/books/edition/Browning_Machine_Gun_Caliber_50_AN_M2_Ai/nXySRue3QAYC?hl=en&gbpv=1

M8 API & M20 APIT

2950

899.12

TM 9-219 AN M3 Basic Aircraft Machine Gun

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=7268

M8 API (45 Inch Barrel)

3045

982.07

FT 0.50AA-T1 1946 Firing Table M8API Heavy Barrel

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=3561

M1 Incendiary

3100

944.83

TM-9-2200 Small Arms

https://archive.org/details/TM9-2200/page/n203/mode/2up

M1 Incendiary

2990

911.31

TM 9-225 Browning Machine Gun .50 Caliber AN-M2 Aircraft

https://www.google.com/books/edition/Browning_Machine_Gun_Caliber_50_AN_M2_Ai/nXySRue3QAYC?hl=en&gbpv=1

M1 Incendiary

2990

911.31

TM 9-219 AN M3 Basic Aircraft Machine Gun

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=7268

 

Below are images from the sources On Muzzle Velocity.

Images 

Spoiler

Terminal Ballistic Data 1945:

Tf3XpfPnmgSazR1HQ7nGZL4suwRYnRQpT0RVY5uo

 

Terminal Ballistic Data 1944/1943:

EbBkQ-Sjq51L4obXgNy4sZoudaNyiQpJ6ZkMiUTC

VD_175tlMYT4avZTcbb40fWqKy83c5rEppPktHlF

 

TM-9 2200 Small Arms, Light Field Guns, 20MM Aircraft Guns 

scQ8YHb04L98S_4ub3v-IlXqOBDpH6myNGy50RjXvccYmgQWRdnTmmF6Vy3PFWQr9mKMA_xHxV9nVKaL

 

Test Method Standard V50 Ballistic Test For Armor MIL STD-662F 1997

 

HPRWh6ARnTe0gAf2aTYcjG7EReFDNOALNompZiPM

The formatting of the table above can be confusing. It gives the impact Velocity in FPS for ranges in Yards and meters. I’ve added the table below to clarify the data.

 

Range: 

Meters

Velocity Remaining: FPS

0

2845

100

2700

200

2555

300

2430



 

TM 9-225 Browning Machine Gun Caliber .50, AN-M2 Aircraft, Basic. 

 

Bv2ZQ8gZcw7EIcG-fV7J5pqYa8psFTsQnLN4XJCq

 

NDRC Study Effects Of Weapon Impacts

 

xay_TRSfQLdya_DXS5ZJCKqYnQVk4csI8aggpoDs

B0GkwaJdkoY7VMDfeekTkVKqLHuwuDRE1wthi9VL

 

FT 0.50AA-T-1 Firing Tables For 50 Caliber M8 API.

 

dcFD4tDwfVmlAT0k8UVgGIFJ69_7c0p333VwEoTd

 

TM9-219 Basic Aircraft Machine Gun Cal .50, AN-M3.

 

HnCFkMIRVmufpdEjFwT7b1VN0savzXIsz_tnJF6d

 

AFM 51-44 Figher And Fighter Bombers

 

Fcso4-aBbgJRaxeS68DQHNwrAcic_Z5d0WOAFEjw

 

 

Projectile Weight:

For the weight data we’ll use one source, the blueprints for the projectiles. The blueprints for the projectiles have two different weights. The Standard weight and the Alternate weight. We’ll be using the Alternate weight of the projectiles, where applicable, the M2 AP, M8 API and M20 APIT. The reason for this is explained below the table. 
 

 

M2 AP 50

M8 API

M20 API

M1 Incendiary

Weight

708

649

620

633

Alternate Core

708

649

612

643.5

std Core

718

662

624

633

Alt Core Kg

0.04588

0.0420

0.0396

 

DCS KG

0.0458

0.0403

0.041

 

DCS Grains

706.694

621.829

632.63

 

 

M2 AP  https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=13268

Spoiler

 

fYidqisYa7xHkOLdq5tiiR8tfRnmqT7sAOV2q4e-

 

 

M8 API https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=13265
 

Spoiler

 

I1ZqunlxDcXMSukE1k_bYUdlimGFzEKvSjEewM8_

 

M20 APIT

M1 Incendiary

According to a Ballistic Research Laboratory Report  and Ordnance Research and Development .In 1943, due to supply shortages. The material for all the armor piercing cores was changed in the 50 caliber bullet. This reduced the weight of all the 50 caliber projectiles which made use of an armor piercing core, the M2 AP M8 API, and M20 APIT. The majority of these bullets were assembled with the alternate core. Which is why the weights presented are based on the alternate weight of the projectile.  

 

Army Ordnance Research and Development Report 

Spoiler

 

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=13268

pAcpZHmx8H0Nd-BulOiOgGzERHaMWgGPdqRb5eKR

-3-sNP4C4o1PsTW8TwjFKVd6mDYB-czTJGhFLPcO

 

BRL Report: Ballistic Coefficients of Small Arms Bullets Of Current Production Aug 1 1944

https://apps.dtic.mil/sti/pdfs/AD0491936.pdf

jbiryz6WxIcfpbVHhzpB6OKbUpka93Oq3R4cMUrx

 

 

Dispersion:

Preface, Units of Measure. In the discussion below the data is given in the value of mils. In this case we are referring to milliradians. Where one mil is = 0.057296 degrees.  At a range of 100 feet, 1 mil = 1.2 inches. A table from the Air Force Manual Fighter Gun Harmonization provides further detail in the spoiler. 

 

Spoiler

fYbDlr-1Sveorp0Ji6y7_lIP2tZilOpb3S_-jh2z   

 

According to this comment by Yo-Yo https://forum.dcs.world/topic/207864-closed-m61-dispersion/page/2/#comment-3916757

 

The 100% dispersion, in mils, of the weapons in DCS can be computed by multiplying the value Da0 by 8000. As 0.0022 * 8 = 0.0176 radians * 1000 = 17.6 mils. Thus we can determine the game value of dispersion , Da0, of a weapon system by dividing the 100% dispersion in mils of the weapon system by 8000. 

 

In multiple documents over a period of several years. The Air Force quoted the 100% dispersion circle as 8 mills for the 50 caliber machine gun across multiple aircraft. Another value commonly used throughout the documents is the value for 75% dispersion, which is 4 mils. The dispersion rating of 8 mils 100% is the same as 4 mils 75%. Both ratings have the same standard deviation and are products of the same normal distribution. 

 

The dispersion notation of a percentage and value in mils is based around normal distribution. The equation used to compute the value is given in the National Defense Research Committee (NDRC) report Analytic Studies in Aerial War. 

 

https://www.loc.gov/resource/gdcmassbookdig.analyticalstudie02bush/?sp=38

Spoiler

 

xy0K88kQ8i9PzH7doU8rXTr6MNVn0-_-Fbm6p4Fr

X2qaL31UCajcTksW0Otr0-C1NVrTTCkD3oV8OPek     

 

 Equation 11  states:

 

 The diameter of the dispersion in mils is = the standard deviation of the distribution * the square root of 8* ln (100/(100- The percent value of the circle)

 

The equation uses whole numbers as the input to compute the diameter of the dispersion. For, example the 75% circle, where sigma is the standard deviation of the dispersion and is = 1.2 mils.

The equation is 

 

(1.2*(sqrt(8*ln(100/(100-75))) = Diameter 3.996 mils

 

By setting sigma to 1.2 and using the equation to compute we get a result that approximately matches the data in the historical sources.  

 

Diameter mils

Sigma mils

% circle

3.996262134

1.2

75

8.071276938

1.2

99.65

 

Having established a standard deviation for the distribution. We can now compare our results to some of the historical data.  Below I will present the historical sources and links.

 

As a side note it looks like there may have been a typing error when the dispersion was computed. If we work backwards from the DCS dispersion value and compute the standard deviation of the dispersion, in game.  It looks like someone may hit 1.02 instead of 1.2 when they computed the value of Da0.

Da0*8000 = 100% mils

 

The DCS value for the 100% dispersion in mils = .00085. Thus Da0 *8000 = 6.8 mils 100%. If we use the NDRC dispersion equation to find the 99.65% radius the standard deviation is 1.02. As 

 

(1.02*(sqrt(8*ln(100/(100-99.65))= 6.86

 

Da0

All DCS 50 Cals

Dao * 8000 =mils 100%

DCS 50 Cal Std Dev(Sigma)

DCS 100%Radius 

NDRC Method

       

0.00085

6.8

1.02

6.8605

 

On to the sources and pics

The Standard Deviation (sigma) of 1.2 mils agrees with data on the M8 API as fired from aircraft. This was figure was published in the NDRC report Analytic Studies in Aerial War on page 105

https://www.loc.gov/resource/gdcmassbookdig.analyticalstudie02bush/?sp=123&st=image&r=-0.299,0.05,1.611,1.294,0

Spoiler

 

E5F9h5jbokHy2mKKogcjMHjWVM7F3N6ynEbjpD1X

 

The Small Arms Development Report also contains a table, which gives the mean radius of dispersion of various 50 caliber ammunition in inches at 600 yards. At 600 yards 1 mil is = to 7.2 inches. Thus, the mean radius of dispersion can be computed for each of the bullets. As the mean radius of dispersion Inches / 7.2 = Mean Radius of Dispersion mils.

 

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=13265

 

 

 

Bullet Name

Mean Radius of Dispersion at 600 yards in Inches

Mean Radius of Dispersion Mils

M8 API

12

1.666666667

M2 AP 50 Cal

10

1.388888889

M1 Incendiary 50 cal

12

1.666666667

M20 APIT Std Core

12

1.666666667

M23 Incendiary 50

12

1.666666667

M21 Headlight Tracer 

20

2.777777778

Ball M2 50 Cal

9

1.25

M10 Tracer 50 Cal

20

2.777777778

Spoiler

 

KkaTizuLyAw7mZg9ndUUFVbFq_0BceTgoiNDQzG1

 

 

The first edition of the “Fighter Gunner Manual” the dispersion is given. As has the dispersion listed as 100% 8 mil and 4 mil 75%

Spoiler

 

SSMFS5UZg_olhNu1CVl2A7huvPBOGv5eGzvUMYmi

 

This same graphic appears in the later manual. Air Force Manual 64 Fighter Gunnery

https://archive.org/details/air-forces-manual-no.-64-fighter-gunnery-firing-rockets-dive-bombing-1-may-1945/page/66/mode/1up

Spoiler

 

JDyjn6DJuEdnMTOum--YZ3gob_l-kqOvsT7fFzVu

aJcbbXC9hPXCFB10YxHdMJu2B_NMzbk2CGPCUBz5

AIZZzIJiKbEgaZYFdmH30p6TjOT-VLWbhsqSIj6Z

 

 

Boresight and alignment charts at the back of this manual confirm that almost every aircraft used by the Air Force during the war had a dispersion rating of 4 mil 75% eg 1.2 sigma. Meaning the 100% value was 8 mils.

 

The P-51b  shows the 75% dispersion is 4 mils as do all most all the fighter aircraft used by The Army Air Force at this time.

Spoiler

 

https://archive.org/details/air-forces-manual-no.-64-fighter-gunnery-firing-rockets-dive-bombing-1-may-1945/page/116/mode/1up

pAtqM0T_Afww-bC6KFRO5BBDRT28XrByOhBHEGVs

 

As does the P-47

 

K38o6oFSvxsvlqal5awhLVi2IvXUn7VPj7k_e-YE

 

And the P-40

V6NmZdtx404yOxYqAj6ERU798lDJXfbzr4wjN7uw

 

The P-38 is interesting because it notes the 75% dispersion is slightly smaller for the 20mm, 3mils

0LdOd3tZepy2dOlw0ul0lKTZIuu8OVUPkJMgWbIr

 

The gun camera observation overlay template also notes the 4 mil dispersion is where 75% of the bullets will land. I’ve only included the overlay for the P-47 as this post is all ready getting large.  

nJZPBRDFPrMK4F7RkeGZTixyDz8YBcYdESYxoKVO

Pages 40 - 51 describe the use.

Vj4GOxm-UkhDM9utVsYXpXnxkn7goNxsn76NCCKN

 

 

4 mil 75% / 8 mil 100% was still the standard in the 1950’s 

https://www.google.com/books/edition/AF_Manual/81krAQAAMAAJ?hl=en&gbpv=1&pg=PA155&printsec=frontcover

Spoiler

 

Fighter Weapon Air Force Manual 335 -25

1zFqjz24D-CMKWFHU9p21U0sLUK9hw3jf2DrZdGb

kZR2yzVMOY_T38weUQHYtq7e7wn_33tDLtXedEhv

 

All of this information seems to indicate the 100% dispersion circle for the 50 caliber is around 8 mils and therefore the value Da0 should be set closer to 0.001.

 

If you made it this far, thanks for taking the time to read all this. In the next few posts I’ll be adding some more information and building some ballistic tables for various aircraft weapons.  

 

Edited by Curly
formatting
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Posted

Muzzle Velocity Part 2: More Data.

 

There is also some secondary data on muzzle velocity that also agrees with the numbers provided in my first post.  We’ll consider some indirect evidence, particularly what is known as Instrument Velocity. Along with the methods that were used within the War and post war era to compute muzzle velocity.  


In many of the source documents bullet velocity values are given at a specific distance. From the Small Arms Development Report for example.  The velocity of the M2 AP from a 36 inch barrel at 78 feet is 2810 +- 30 fps.

 

WxIO6Pp8CZ0OrxA8sN8W8FbRi_xJnZCdRDqp1UqK 

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=13268  

 

The Ballistic Research Laboratory (BRL) calls the bullet velocity at 78 feet, the instrument velocity.

BKIvRHoJE0s0TByyLh4k1G2Xn_yduUKdqGq8J_No 

Ballistic Coefficients of Small Arms in Production 1944

https://apps.dtic.mil/sti/pdfs/AD0491936.pdf

 

The standard setup used by the BRL was to place the first chronograph 28 feet from the barrel, and the second 128 feet from the barrel. Thus the distance from the midpoint of the chronographs was 78 feet and the chronographs were 100 feet apart. 

Spoiler


 

 

 

VlTdA9FRrdxKWS-jjAL0JdU9QXYzaFFMUz9FNkYY



 

This paper also gives us 2 equations to compute the muzzle velocity from the instrument velocity. 
 

Spoiler


 

00s6DqxE9xyRQ6HjaNKMniVXP47Rb-QMdrzPlO9x


 

Muzzle Velocity V0^.5 = v^.5 + (.059 rho/C5 Ballistic Coefficient)*Distance(78* 0.5)

 

We can simplify this a bit and just get the muzzle velocity by squaring the right side of the equation.

 

Muzzle Velocity = (Instrument Velocity ^.5 +((.059 * 0.07513/ Ballistic Coefficient) * ( 78 *05))^2.

 

Note, that rho is the ballistic sea level air density in lbs per foot^2. 

 

The report also gives us this equation. 

 

Ywwjxn8qGwVYhqLExh24eZrY-atwznYeQ-9SVhbh

 

The muzzle velocity - the instrument velocity = 4.3* (78^2/1000)

 

Mathematically this formula tells us to add about 26 fps to the instrument velocity. For example the instrument velocity of the .50 caliber  M2 AP is given as 2810 fps. The muzzle velocity is 2836 fps. Which is the figure quoted in many of the post 1944 reports. 

 

Such as the 1945 version of manual “Terminal Ballistics Data”.

https://cgsc.contentdm.oclc.org/digital/collection/p4013coll8/id/2373/rec/8

 

Jd6_looVFNtyAnZ2oOe5BopWoCV5tYIjjIAHpE6w

 

There is yet another way we can compute the muzzle velocity from instrument velocity. Since we have the ballistic coefficients of these bullets it’s possible to work backwards through the Siacci tables and compute the muzzle velocity. I’ll spare you the details of integration of the Siacci tables. However the approach is validated within Ballistic Coefficients of Small Arms in Production 1944, and by McCoy in Modern Exterior Ballistics. 

 

https://apps.dtic.mil/sti/pdfs/AD0491936.pdf

Spoiler


 

n79tST8DtTKIErNp6kSsJTFgbYZf0Mu2JEDT7RYB


 


 

So let's apply our 3 equations to compute the muzzle velocity from the Instrument Velocity. Then will  compare the results to the values given in th 19.   Well use ballistic coefficients given in 1944 report, The Instrument velocities from the Ordendance Department’s Small Arms Development Report and the post war report Form Factor of Projectiles BRL Report 564 1951.  


 

Value:

M2 AP

API M8

M1 Incendiary

BC C5

0.458

0.439

0.414

Instrument Velocity at 78 Feet

2810

2910

2950

Instrument Velocity At 78 Feet: mps

856.446

886.925

899.116

Muzzle Velocity BRL C5 Method

2850.160

2952.641

2995.534

Instrument Velocity + 26 fps

2836

2946

2976

Muzzle Velocity Siacci

2843.341

2945.325

2987.641

Muzzle Velocity 50 Cal Manual 1946

2840

2950

2990

 

All three methods used to compute the muzzle velocity from the instrument velocity show good agreement with the muzzle velocity cited in various source materials.  

 

This all just amounts to another piece of evidence indicating that muzzle velocities for the 50 calibers in game are a bit too low. 

 

Data Sources and links in the spoiler

 

 


 

Spoiler


eXKJ5qvxIUtuUrqwALn3wRlN6fL6uMBXy2RPccx6

 

 

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Posted (edited)

I realize the formatting of some of the tables is not ideal. If you wish to read this document in google docs, a link is provided below.  The tables can also be viewed from within the spreadsheet.

 

Link to the google doc version of this post.

 

https://docs.google.com/document/d/1LCRhctj31-tdp9ehzIFUILtF0OhItK6ROC2AhEopWXA/edit?usp=sharing

 

Link to spreadsheet.

 

https://docs.google.com/spreadsheets/d/1h3fCvpvdc7j2f3iyASP3ft4ogz3koOjQksYY3i7Bjd8/edit?usp=sharing

 

Ballistic Tables and Ballistic Calculators

 

Firing Tables for many of the bullets used in the war is particularly difficult to find. Especially for aircraft weapons. The aircraft version of the 50 caliber Browning has a 36 inch barrel. Thus has slightly reduced muzzle velocity when compared to the Heavy barrel version of the gun used in ground applications. Therefore, what data is available, for the various 50 caliber ammunition, may not be applicable to an aircraft machine gun. However we can recreate the firing / ballistic tables for various bullets by using the methods and equations from the world war 2 era..  

 

The ballistic tables of this era were computed based on ballistic coefficients and a few different methods of integrating through the appropriate ballistic table. This process is often called the Siacci Method of integration. 

 

US military manuals and academic papers of this era indicate the use of Siacci Tables integration methods was the standard process of computing ballistic and firing tables. See The spoiler for examples.

Spoiler

[spoiler]

From Technical Manual 9-2200

https://archive.org/details/TM9-2200/page/n266/mode/1up

 

 ZqWN1cxDZAkpL9LKFMrepfzepUudau_DfaBFqom5 

 

This example is specific to firing tables for Aircraft data. 

Ballistic Data For Flat Fire:

https://apps.dtic.mil/sti/pdfs/AD0491946.pdf

2a5BARysUm8we2VCaa_9nBLLcKqK6xjknUSJHGwJ

qeKydMDt7LwHYat4izpKEq_mK2ZkKydXUUYE1YvR

 

The Production of Firing Tables For Cannon Artillery 

https://apps.dtic.mil/sti/pdfs/AD0826735.pdf

 

4yd_3fsS6SUjaHMAUin05Wb_S031uEl_34wncer5

 

The Siacci method and tables were also in use in the 1980’s too.

 

https://apps.dtic.mil/sti/pdfs/ADA171476.pdf

 

ETUb_KsvLCXOEYlBQ6Sw9-gdSj5pjwzhgb1BqJdD

 

Ballistic Coefficients of Small Arms Bullets Of Current Production

 

https://apps.dtic.mil/sti/pdfs/AD0491936.pdf

NQmUJmN68Vv4I8c2EdkIfaiZVQy9OGW5VVtSLxr_

 

FT 0.50AA-T-1 1946 Firing tables of Gun Machine, Cal 0.050 Browning M2, firing Cartridge Armor Piercing Incendiary Cal 0.50 M8

 

Notes the firing tables were computed using a ballistic coefficient of 0.359 

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=3561

f6QEClA4Cp9sFAyuw2BL1uhzdOhWJoc5OZ6I7Spx

 

A custom drag function / projectile type was created for the M8. Where the M2 AP was given the ballistic coefficient of C5/ G5 0.458. The Equivalent nomenclature for the M8 would be, M8 0.359. The Drag Function is given in the report Aerodynamic Data For Spinning Projectiles.   

https://apps.dtic.mil/sti/pdfs/AD0800469.pdf 

tdjKmtYTBm7lNkPIMG84siA_H6s_2n9l4eFis4Fu

Based on the M8 drag function, a set of Siacci tables was created by the BRL for the M8 projectile type.

fzT4A7AVfEhMCJ0WZM-JsYec5RcOvFBqHwuUSwOS

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=5020

 

The Siacci Table along with the BC of 0.359 would then be used to create the firing table,  FT 0.50AA-T-1 1946 Firing tables of Gun Machine.

 

We will use similar Siacci tables to compute time of flight and the vertical deflection ( bullet drop) for various other bullets in this post. 

 

 

Before ENIAC is also a good read on the computation of ballistic and firing tables before the computer age.

https://sci-hub.se/10.1109/85.586069

 

[/spoiler]

 

 

 

The ballistic performance data of the bullets from the World War 2 era is written in terms of a ballistic coefficient.  Through the use methods and mathematics of this era, it is possible to create and recreate accurate ballistic and firing tables for the various 50 caliber bullets. Even if the data is lost or missing from the historical record. 

 

First, it’s helpful to define the meaning of the term ballistic coefficient. The ballistic coefficient of this era is a way of relating the drag of the bullet in question to an idealized version of a bullet of similar shape.  Therefore the ballistic coefficient consists of two variables, a  type and a factor.

 

For example in the BRL report. “Ballistic Coefficients of Small Arms Bullets Of Current Production”

https://apps.dtic.mil/sti/pdfs/AD0491936.pdf

All of the 50 caliber bullets have a type of C5 / G5. While the factor varies 0.414 for the M1 Incendiary to 0.460 for the M2 Ball.

 

Spoiler

[spoiler]

 

EG451TEtOeltD6JaJ_gRVNsAqCaitXdZ8X-6k72X

[/spoiler]    

 

We would say the Ballistic Coefficient of the M1 incendiary is C5 / G5 0.414. The projectile type is as important as the factor. As the bullet is matched to a projectile type with a similar drag coefficient. 

 

The Equation for the ballistic coefficient as given by Mc Coy is 

Cj = (mass (lbs)/ form factor (i_j)  * diameter (inches)^2) 

 

Where j is is of projectile type and the 

form factor, i, = (CD of projectile) / ( CD of the projectile type.. Ie G5, G6, ect)

https://archive.org/details/ModernExteriorBallisticsTheLaunchAndFlightDynamicsOfSymmetricProjectiles2ndEd.R.McCoy/page/n98/mode/1up

 

If we take the weight and form factor data for the M1 incendiary from “Aerodynamic Data for Spinning Projectiles. We can compute the ballistic coefficient of this bullet. 

Projectile Name:

Projectile Weight Grains

Projectile Diameter

Projectile Type

Form Factor

M1 Incendiary

625

0.5

5

.86

The first step is to convert the projectile weight from Grains to lbs. We do this by dividing the weight by 7000, which gives us 0.08928 lbs. The ballistic coefficient is then computed as 

0.08928 / (.86 * 0.5^2) = 0.41525

Thus the ballistic coefficient of the M1 Incendiary is C5 / G5 0.41525. The test of the production gave a BC of .414 to this same bullet.

 

The ballistic coefficient and form factor are determined either through firing tests or in from a wind tunnel test. The drag of the projectile is then matched to the appropriate projectile type and the ballistic coefficient is determined. 

 

The standard Projectile types are  G/C 1 through 8. Drag profiles in the for KD are given Hitchcock's work Aerodynamic Data for Spinning Projectiles. 

 

https://apps.dtic.mil/sti/pdfs/AD0800469.pdf

Pics of both in the spoiler below

 

Spoiler

[spoiler]

aBaquOVpXI1mbg8LEY1YtGeitNS08L3pLNPoTVaY

 

Mach Vs Drag C5 / G5 

 

QxXe-hp26d2016nY3aLiVyHa7OmUL3VmxcrbgzFe

 

[/spoiler]

 

 

 

Data from the BRL on the ballistic coefficients and form factors of a variety of projectiles is readily available. Most of the data is from the World War Two era also. Two of the best sources for this type of data are the reports “Aerodynamic Data for Spinning Projectiles” and “Form Factors of Projectiles”. Excerpts and links to both reports are contained in the spoiler below along with a few other sources. 

Spoiler

[spoiler]

https://apps.dtic.mil/sti/pdfs/AD0800469.pdf

From Aerodynamic For Spinning Projectiles Data

 EVrxJE9H_XO3cWTIiysd83VnakG4EGq_RGGCsk6q 

 

 

From Form Factors of Projectiles

https://apps.dtic.mil/sti/pdfs/AD0802080.pdf

 

D85PHF251vOwvSy_Le9eNxTBCn2jfMFDz7ZLPU4i

Ballistic Coefficients of Small Arms In Production 1944

https://apps.dtic.mil/sti/pdfs/AD0491936.pdf

 

EG451TEtOeltD6JaJ_gRVNsAqCaitXdZ8X-6k72X

 

NDRC Analytical Studies in Aerial Warfare 

https://www.loc.gov/resource/gdcmassbookdig.analyticalstudie02bush/?sp=28

 

opQigSwHqU33_B1XUJzFqde5dGbXcEwmUOfz369E

 

[/spoiler]

 

 

We will use this data to create a ballistic table similar to the ones in the Air Force Manuals of the era. 

https://www.google.com/books/edition/AF_Manual/81krAQAAMAAJ?hl=en&gbpv=1 

 

Spoiler

[spoiler]

 

380A5hJITQgSJaq2_FclI8ZW_JPvLj7QVlb7o4UQ

[/spoiler]

 

 

We’ll use two methods to create our tables. The full long form of Siacci Method for Flat Fire Trajectories as described by McCoy, Hitchcock and Kent, and a simpler method that was developed specifically by the BRL to produce firing tables for aircraft weapons. 

 

The methodology for the Siacci method is described in detail with examples. In Modern Exterior Ballistics

https://archive.org/details/ModernExteriorBallisticsTheLaunchAndFlightDynamicsOfSymmetricProjectiles2ndEd.R.McCoy/page/n97/mode/2up?view=theater 

 

This method involves looking up data in a table of figures for our bullet type. Then modifying these values based on the ballistic coefficient of the bullet. 

 

For example, In the report “Form Factors of Projectiles”. The BRL gives the 50 Caliber M1 Incendiary   

A ballistic Coefficient of C/G 6 .387. If we assume a muzzle Velocity of 2990 our Siacci operations look a bit like this.

 

Spoiler

[spoiler]

 

The Table Below Uses The G6 / C6 Drag Function

 

Range Feet

                 

Ballistic Table M1 Incendiary MV 2990 BC: C6 .387 Computed with G6 /C6 BRL Siacci Table

 

200.0000

300.0000

328.1000

400.0000

600.0000

656.2000

800.0000

984.3000

1000.0000

1200.0000

Time of Flight

 

0.0678

0.1022

0.1121

0.1376

0.2097

0.2304

0.2842

0.3549

0.3611

0.4408

Drop in Inches

 

0.8856

1.9948

2.3990

3.6131

8.2769

9.9639

14.9660

23.1578

23.9429

35.2380

Impact Velocity: mps, M1 Incendiary Mv 2990 G6 BC .387 BRL C6 Siacci Table

911.3075

884.8761

871.6654

867.9596

858.4580

831.9619

824.5504

805.6376

781.3026

779.2401

752.9579

Impact Velocity: M1 Incendiary Mv 2990 G6 BC .387 BRL C6 Siacci Table

2990.0000

2903.2786

2859.9340

2847.7753

2816.6007

2729.6671

2705.3500

2643.2969

2563.4539

2556.6868

2470.4549

S(V)

8884.7000

9401.4959

9659.8938

9732.5036

9918.2917

10435.0876

10580.3072

10951.8835

11428.1109

11468.6793

11985.4752

S(V) High

8884.7000

9421.2000

9719.2000

9779.0000

9957.5000

10492.8000

10612.3000

10971.5000

11448.8000

11508.8000

11988.2000

S(V) Low

8884.7000

9361.1000

9659.5000

9719.2000

9898.1000

10433.1000

10552.5000

10912.0000

11388.9000

11448.8000

11928.3000

VFPS S(V) high

2990.0000

2900.0000

2850.0000

2840.0000

2810.0000

2720.0000

2700.0000

2640.0000

2560.0000

2550.0000

2470.0000

VFPS S(V) Low

2990.0000

2910.0000

2860.0000

2850.0000

2820.0000

2730.0000

2710.0000

2650.0000

2570.0000

2560.0000

2480.0000

T(V) High

2.4090

2.591

2.694

2.715

2.779

2.972

3.016

3.151

3.334

3.358

3.549

T(V) Low

2.4090

2.570

2.673

2.694

2.757

2.950

2.994

3.128

3.311

3.334

3.525

TV(V)

2.4090

2.584

2.673

2.699

2.764

2.951

3.004

3.143

3.326

3.342

3.548

A(V) High

163.6200

187.5200

201.7500

204.6800

213.6600

242.0500

248.7300

269.4900

299.0500

302.9100

335.1000

A(V) Low

163.6200

184.7700

198.8400

201.7500

210.6400

238.7600

245.3700

265.9600

295.2200

299.0500

330.9500

A(V)

163.6200

186.6184

198.8592

202.4018

211.6666

238.8695

246.9324

268.3262

297.7271

300.3289

334.9112

I(V)High

0.0426

0.0466

0.0489

0.0494

0.0508

0.0553

0.0564

0.0596

0.0642

0.0647

0.0696

I(V)Low

0.0426

0.0461

0.0484

0.0489

0.0503

0.0548

0.0558

0.0591

0.0636

0.0642

0.0690

I(V)

0.0426

0.0464

0.0484

0.0490

0.0505

0.0548

0.0561

0.0594

0.0640

0.0643

0.0696

Drop in Feet

 

0.0738

0.1662

0.1999

0.3011

0.6897

0.8303

1.2472

1.9298

1.9952

2.9365

BC

0.3870

                   

Y = (5*BC*X)*((((Av-Av0)/(Sv-Sv0))-Iv0)

                     

[/spoiler]

 

By interpolating through the G6 Siacci Table and applying the appropriate equations we are able to compute the bullet drop, the time of flight, and the impact velocity of the bullet at any range. 

 

 

In order to determine the accuracy of this method, Let’s compare a Siacci Calculation for 50 cal AP M2 to the ballistic table in Air Force Manual AFM 335-25 Fighter Weapons. We’ll compare the time of flight and vertical deflection in inches, which is also known as the bullet drop. At sea level with a true air speed of 0 mph. 

 

For our Siacci Calculations we’ll set the muzzle velocity to match the chart, 2700 fps, and use the a Ballistic coefficient of C5 / G5 0.458. As this matches the BRL data for a world war 2 version of the M2 AP. 

 

In the spoiler below we have the Air Force Firing Table for the 50 Caliber M2 AP.

 

https://www.google.com/books/edition/AF_Manual/81krAQAAMAAJ?hl=en&gbpv=1 

Spoiler

[spoiler]

 

380A5hJITQgSJaq2_FclI8ZW_JPvLj7QVlb7o4UQ

[/spoiler]

 

 

I’ve added the Air Force firing table for the 50 Caliber M2 AP  to a spreadsheet in order to compare it to the results of the Siacci method of calculating firing tables. 

 

Below is the Air Force Firing Table for the 50 cal AP M2 in table form from the spreadsheet. Note that gaps in data reflect those in the actual firing table. 

 

Spoiler

[spoiler]

 

Fighter Gun Harmonization 1945:

                                                   

Range Meters

0.0000

60.96

91.44

100.00

121.914

182.871

200.00

243.828

300.00

304.79

365.74

400.00

426.70

487.66

500.00

548.61

600.00

609.57

670.53

700.00

731.48

792.44

800.00

853.40

900.00

914.36

Range Feet

0.0000

200.00

300.00

328.10

400.000

600.000

656.20

800.000

984.30

1000.00

1200.00

1312.40

1400.00

1600.00

1640.50

1800.00

1968.60

2000.00

2200.00

2296.70

2400.00

2600.00

2624.80

2800.00

2952.90

3000.00

Time of Flight

0.0000

0.0700

   

0.150

0.230

 

0.310

 

0.4

0.49

 

0.58

0.67

 

0.77

 

0.87

0.98

 

1.09

1.2

 

1.32

 

1.44

Vertical Deflection Inches

 

1.0000

   

4.000

10.000

 

18.000

 

29

43

 

60

80

 

104

 

132

164

 

200

241

 

287

 

339

 

[/spoiler]

 

 

In the spoiler below we have A Similar Table with Values computed with the Siacci method.

Spoiler

[spoiler]

 

Range Feet

 

200

300

328.1

400

600

656.2

800

984.3

1000

1200

1312.4

1400

1600

1640.5

1800

1968.6

2000

2200

2296.7

2400

2600

2624.8

2800

2952.9

3000

3281

50 CAL AP M2 Time Of Flight Mv 2700 Fps BC C5 .458 Siacci Method

 

0.0752

0.1136

0.1245

0.1529

0.2331

0.2561

0.3157

0.3946

0.4015

0.4905

0.5417

0.5824

0.6779

0.6977

0.7768

0.8634

0.8798

0.9865

1.0398

1.0976

1.2132

1.2278

1.3335

1.4285

1.4586

1.6432

50 CAL AP M2 MV 2700 C5 .458 Vertical Deflection Inches Siacci Method

 

1.097

2.472

2.957

4.403

10.132

12.205

18.461

28.546

29.518

43.499

52.723

60.682

81.213

85.827

105.414

128.850

133.533

165.909

183.160

202.853

244.768

250.311

291.992

332.060

345.135

430.492

 

 

[/spoiler]

 

Spoiler

By plotting the vertical deflection ( bullet drop) Vs Range. We can compare the trajectory of the bullet from the Air Force Table and from the one computed from the Siacci Calculations. 

 

[spoiler]

Kz9sUKDwZKF8D6K4SwNys4Ywji2MQZ04b2efTudE

[/spoiler] 

We can also compare the Time of Flight Vs Range of the Air Force Table and the Siacci Method. As this will also give us a sense of the drag coefficient of both bullets. 

Spoiler

 

 

[spoiler]

poSMthLiRLRXiJNMeiv5fmdchIsGNvmd-sOtL0Qb

[/spoiler]

 

 

The results of the Siacci table are very similar to the Air Force Firing Tables. The average difference in time of flight between the two firing tables is 0.007 second.  Some of the difference being a  function of the original tables using a limited number of decimal places. 

 

The slight difference between the two data sets, indicates the Siacci Method, when using the appropriate tables, can produce results which effectively match the tables in the primary sources. Thus providing us with a valid means to create ballistic tables for projectiles where no such data exists. 

 

While the Siacci method is accurate and flexible. The manual calculations of firing tables using the Siacci method was still very time consuming. During the war the demand for firing tables was at an all time high. Therefore the BRL and the National Defense Research Council (NDRC) developed a faster method to calculate firing tables. The application being primarily limited to aircraft weapons.  

 

The method is described in the Report, “NDRC Analytical Studies In Aerial Warfare: “Pages 28 to 30. 

 

https://www.loc.gov/resource/gdcmassbookdig.analyticalstudie02bush/?sp=28

Spoiler

[spoiler]

NDRC Analytical Studies In Aerial Warfare: Pages 28 to 30

 

fbuK-fjOYGNhAh8WPKhb78aokPzpiVXwLrvfFObf

7L3CQSYMtJjsrfCQ7ULsXV1MXVRw-OFtYTc9xA_6

 

https://www.loc.gov/resource/gdcmassbookdig.analyticalstudie02bush/?sp=59&st=image

2IT2FEXh9Mgd0dbi54YthuAOPdqv2oYWtKEPweAV

btCXLboCoD0-_Y8TshX6kuBr5SENY5-IMtOjn8nU

[/spoiler]

 

 

The NDRC report provides two derivations of a time flight equation and one equation which computes the vertical deflection /  drop of bullet (Q) as function of Time of Flight (t)

 

The short version of the time of flight equation is

 

tof= (range / sqrt v0)/((sqrt(v0)-(((.00186*rho)/bc)*range

 

And the longer version of this equation is

 

tof= (1/((V0/Range)-((k_star*rho)/(2*BC)*Sqrt(v0))

 

Where k_star = 0.00372 for feet per second  

 

Both TOF functions return the same value given the same input. The second version is a bit more flexible as the constant k star can be altered based on the desired unit of measure.  

 

The equation for the bullet drop at a given range is given as:

 

Vertical Deflection Feet: Drop = .5*g*t^2*(1-((rho *.00372)/(3*BC))*(Range/(sqrt(V0)))

 

Where v0 = the muzzle velocity + the aircraft velocity in fps

 

Range is the down range distance to the target in feet.

 

Rho is the relative Ballistic Air Density 

 

And bc is the C5 ballistic coefficient of the projectile.

 

Thus we come to the major limitation of this equation. It is valid for projectiles with a C5 / G5 ballistic coefficient. Which may not always be the best drag function for a projectile. We’ll circle back to this in the end. For now, let's just compare these equations to the Air Force ballistic / firing table For the 50 Cal AP M2. 

 

In the spoiler below is a ballistic / firing table computed using the NDRC method. It is in the same format as the Air Force Firing Table. 

Spoiler

[spoiler]

 

Ballistic Table 50 Cal AP M2: MV 2700, BC: C5 .458, Computed by NDRC method

                   
 

Range Feet:

200.0000

300.0000

328.1000

400.0000

600.0000

656.2000

800.0000

984.3000

1000.0000

NDRC Method: TOF: 50 Cal AP Mv 2700 BC: C5 .458

 

0.07525

0.11378

0.12472

0.15293

0.23316

0.25618

0.31606

0.39494

0.40177

NDRC Method Vertical Deflection Inches Mv 2700 fps BC.458

 

1.0817

2.4600

2.9513

4.4207

10.1661

12.2355

18.4799

28.5660

29.5376

NDRC Method Vertical Deflection Feet Mv 2700 fps, BC .458

 

0.0901

0.2050

0.2459

0.3684

0.8472

1.0196

1.5400

2.3805

2.4615

[/spoiler]

 

 

In the spoiler below is a graph comparing the bullet drop Vs range, aka the trajectory,  of the Air Force Table and the trajectory of the bullet we computed via the NDRC method. Along with the time of Vs Range.

Spoiler

[spoiler]

Trajectory

EPouQKgOgMDmDSd3cZ38HoEoNpiCvvLA55kci2oT

 

Time of Flight

 

GY1QUTZJwMBDFWKAfuNZyD3NEBTB3mtUIIBtsmoz

 

 

[/spoiler]

 

  

 

The NDRC Method actually matches the Air Force Ballistic Table more closely then the Siacci Method. The average difference in time of flight between the NDRC method and Air Force Firing Table is only 0.0052 seconds. The NDRC method also provides an accurate means of computing firing tables. Which shouldn’t be a surprise as according to the NDRC study many of the aircraft ballistic tables of the era were generated with this method.

 

Let's look at one more case. The Aircraft is moving at 300 mph TAS, the density ratio is .6, which corresponds to an altitude of about 15,0000 feet. This altitude was chosen because the density ratio of both the Ballistic and NACA atmospheric models are about the same and it's the altitude for which all the convergence patterns are configured too.

 

In the spoiler We Have the firing table from the Air Force Firing Table and a set of values computed with the NDRC method.

 

Spoiler

[spoiler]

bYcHNJlgDRtqSAtaMCAjKGc4hCV71qeaF6iZJtvx

 

On top is the Air Force Data in the spreadsheet.

 

Table from Fighter Gun Harmonization M2 AP, Rho .6, TAS 300, MPh MV 2700

                                   

Range Feet

Range Feet

200

300

328

400

600

656

800

984

1000

1200

1312

1400

1600

1641

1800

1969

2000

TOF

 

0.070000

   

0.130000

0.200000

 

0.270000

 

0.330000

0.400000

 

0.470000

0.540000

 

0.620000

 

0.700000

Drop

 

1.000000

   

4.000000

8.000000

 

14.000000

 

22.000000

31.000000

 

42.000000

56.000000

 

71.000000

 

89.000000

                                     

Ballistic Table 50 Cal AP M2: MV 2700, BC: C5 .458, Air 

density .6 True Air Speed 300 mph Computed by NDRC method

                                   

TOF

 

0.064251

0.096801

0.105999

0.129639

0.196196

0.215112

0.263951

0.327478

0.332939

0.403192

0.443244

0.474747

0.547639

0.562566

0.621907

0.685613

0.697590

Vertical Deflection Inches

 

0.792302

1.793180

2.148388

3.206747

7.301533

8.762854

13.137493

20.111640

20.778238

30.290310

36.483433

41.743348

55.210258

58.189264

70.767403

85.564619

88.494801

Absolute value of Table drop - computed drop.

 

0.207698

   

0.793253

0.698467

 

0.862507

 

1.221762

0.709690

 

0.256652

0.789742

 

0.232597

 

0.505199

On the bottom, in blue, we have the data computed with the NDRC equations.

[/spoiler]

 

 

In the spoiler below there is a graph comparing the Bullet Drop (Trajectory) and time of flight of the NDRC Method to the Air Force Firing table under the same conditions.

Spoiler

[spoiler]

Trajectory

WS8mTCwt05wADcZcw5d3O5FLtJDY4trIXA37U9SO

Time of Flight

Dz534fOq5Xt379p8KJTm24WpPuLiRzmOesppQe5e

[/spoiler]

 

 

 

On average ,the NDRC method’s time of flight is within .0038 seconds of the chart. Even under flight conditions at altitude, the NDRC method can accurately reproduce the Air Force Firing Tables. 

 

 

Using the Siacci Method we can also compute the trajectory and time of flight under the same conditions. Density Alt .6, TAS 300 MPH. If we overlay all 3 data sets. The results are nearly identical.

Spoiler

[spoiler]

Trajectory.

oC7S3W-rtGaqhCf7wDYig-ixvnXDFeB8QPAvgxtS

Time Of Flight:

 

N3GLozd7B93Oey4pw-GJDsR9lrUb3J3pE_XSQu0U

 

 

[/spoiler] 

 

 

The marginal differences from the NDRC method, Siacci method and the Air Force Table. May also be the  result of some other ways error may have been introduced into the Air Force firing table. These sources of discrepancy may be a result of the earlier version of M2 AP having a higher ballistic coefficient then bullets produced after 1943. 

 

If we recompute the ballistic table using the NDRC method and change the BC to .471, to match BRL data for the pre 1943 version of the M2 AP. The average difference in TOF between the NDRC ballistic table and the Air Force firing table. Is the lowest of all the computations presented thus far at 0.002447 second. The same is true for the calculations of the bullet drop. Using a BC of 0.471, the average difference between the NDRC method and the chart is 0.373 inches. These results seem to indicate that the Air Force Ballistic Table for the M2 AP may have been computed for a heavier version of the M2 AP with a slightly higher (better) ballistic coefficient than the production bullets.  

 

There may also be some discrepancy between the results due to the fact that a graphic method of interpolation was used in parts of the original Air Force Firing Table. There are also reports from BRL which indicate that the Aberdeen Proving Grounds was having troubles with their measuring equipment .The equipment error caused the institution to issue lower ballistic coefficients to projectiles prior to August 1’st of 1944. Given that the Air Force Firing Table is based on Aberdeen data from prior to August 1’st it’s possible    

Spoiler

[spoiler]

BUL36tlC_WEVPzerFz1_RmQla7f2WlwohOWg9iL6

 

The Air Forces Firing tables are based on firing tables given to them by Aberdeen before the error in their equipment was detected. 

 

94oc1zlk4t-jTf3VeE2t40EUNVa0wwEPO1laDaC1

 

 

lSSeHwkpwMs457nMKCnFii04DI4XmvGuW96Y9bW5

WC_I8f5ZUnR4Yx-aPbOCB7Fyjg_g8gNY-hqle2HA

 

[/spoiler]

 

 

 

 

 

Both the NDRC and Siacci method show good agreement with the Air Force firing tables across a range of circumstances.  Therefore, utilizing either the NRDC  method with the appropriate  ballistic coefficients from period data is a valid way to generate the type of ballistic data needed to implement any of the 50 caliber bullets within DCS.

 

Below is a link to my spreadsheet where I have performed these computations. Most of the work haiving been performed in the Ballistic Calculator tab. Most of the functions and computations should be readable. The idea being that anyone can take a look at the math behind these calculations. There is also a page containing various images and links to the source data. Much of the document however is a work in progress. While parts of the spreadsheet can be useful, it may not be particularly user friendly. It’s easy to mess up a computation. 

https://docs.google.com/spreadsheets/d/1h3fCvpvdc7j2f3iyASP3ft4ogz3koOjQksYY3i7Bjd8/edit?usp=sharing

 

Thanks for reading this far. I hope this exercise has been insightful as it has been for me.  Below are some additional thoughts on the accuracy of these methods. It got a bit longer than I would have hoped, but if you’re interested in this kind of thing you may find it worth reading.  

 

As final thought I want to discuss some limitations of approaches presented in this post.  While the NDRC function is very useful there are some very real limitations to it. The model is based on the 3/2 drag power law. Meaning below half the muzzle velocity the data becomes unreliable. However there are also very useful ways to use the data generated from the NDRC tables. For example the impact velocity  can be computed through a derivation of the 3/2 drag law.

 

Impact Velocity = (Range^2) / (TOF^2) * V0

Which can provide for a more accurate basis of drag coefficient computation. The same information can also be obtained from the Siacci Methods however the process is more tedious. 

 

Both the NDRC and Siacci methods may also not be as accurate as more modern numerical techniques. Both methods depend on how well the projectile matches the drag coefficient of its associated type. The war time paper “Ballistic Coefficients of Small Arms Bullets Of Current Production”

https://apps.dtic.mil/sti/pdfs/AD0491936.pdf

 

Assigned almost every projectile a C5 / G5 ballistic coefficient. A few years after the war, the projectile types and form factors of some of the more common 50 caliber bullets changed. The M1 incendiary goes from a G5 0.414 in 1944 to a G6 0.387 in 1951. If we compute the impact velocity for both bullets with the Siacci method, On average the G6 0.0387 version impacts 35 to 45 fps faster than the G5 0.414 Ballistic coefficient. Which indicates that the BRL thought the C5 / G5 ballistic coefficient resulted in to much drag. 

In the spoiler below is chart comparing the impact Velocity Vs Range of the M1 incendiary with both ballistic coefficients.

 

Spoiler

[spoiler]

 

7GZkYz5s3mJQAjB8oClZjaDFb4K6z0QjIqzZuhHd

 

[/spoiler]

 

 

The story is similar for the M8 API, which is considered one of the most effective 50 caliber bullets. During the course of the War the bullet was given 3 different G5 ballistic coefficients. None of the G5 ballistic coefficients were accurate enough as there was considerable variation in the form factor as function of mach. Thus a custom drag function / bullet type was created for the M8 API.   

 

Image of custom drag function and conversion to modern CD notation in spoiler

Spoiler

[spoiler]

Va_3TbfdL5ql0axdQp2oDQPTHYkvhSQ0heBttyco

Note the equation which defines the KD, drag coeffiecent as a function of Mach. Utilizing the function we can plot this drag function in the modern term CD. As CD = 8/(pi * KD).

 

w8l0fSkSksnyFmgG27JvyNWBAn1VnM3EC8c3fZV1

 

[/spoiler]

 

 

A set of Siacci tables was created for the M8 drag function. There A 1996 report by the BRL indicates that the CDO of the M8 drag function is 4% lower in the supersonic regime. However examining data in detail also raises some questions. 

 

Plotting the old drag function on top of the 1996 data, shows that the old drag function actually has a higher supersonic drag coefficient than the author says. It is possible to match the data by reducing the old drag profile by 4% though. 

Spoiler

[spoiler]

Plotting the Hitchcock Drag Function over the McCoy Report. The Drag Function does not match the data presented. 

9c7Vh5ih-L3J7JdyDenG732_FG3adaavSj3P46GR   

 

Reducing the Hitchcock Drag Function results in the Data matching the 1996 Report.

OFM3MVEI90hzB5Mo5AVZl49Y70cAzZeqJ1aRshy-

[/spoiler]

 

 

Given total drag on the projectile is a function of the CD0, the quadratic yaw drag coefficient and the angle of attack of the bullet. McCoy’s plot of CDO does not represent the total drag coefficient of the bullet in flight. The older drag function however computes the drag as a function of trajectory angle. Which may provide a more accurate assessment of the total drag on the M8 API during flight condtions.

 

 A comparison of both methods would require a full 6 dof simulation with McCoy’s data and a similar calculation using the Siacci Tables for the M8. However both sets of data would need to be checked against some type of test data. The best set of data publicly available are either the Air Force Firing tables, or the 1946 copy of the M8 firing table for the heavy barrel machine gun. Which puts us back to square 1. 

 

This has led to some reluctance on my part to take the time to implement M8 Siacci Tables into my spreadsheet. It’s a lot of data entry and I’ve already spent way too much time on this. The World 2 Data G5 data is probably accurate enough for the purpose of video games. 

     

 

 

 


 

Edited by Curly
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Posted

Thanks for posting this.  I hope, like the armor plating, this gets the attention it deserves.

  • Like 1

Hardware: T-50 Mongoose, VKB STECS, Saitek 3 Throttle Quadrant, Homemade 32-function Leo Bodnar Button Box, MFG Crosswind Pedals Oculus Rift S

System Specs: MSI MPG X570 GAMING PLUS, RTX 3090, Ryzen 7 5800X3D, 32GB DDR4-3200, Samsung 860 EVO, Samsung 970 EVO 250GB

Modules: AH-64D, Ka-50, Mi-8MTV2, F-16C, F-15E, F/A-18C, F-14B, F-5E, P-51D, Spitfire Mk LF Mk. IXc, Bf-109K-4, Fw-190A-8

Maps: Normandy, Nevada, Persian Gulf, Syria

 

Posted

Quality posts :thumbup:

  • Thanks 1

Modules I own: F-14A/B, F-4E, Mi-24P, AJS 37, AV-8B N/A, F-5E-3, MiG-21bis, F-16CM, F/A-18C, Supercarrier, Mi-8MTV2, UH-1H, Mirage 2000C, FC3, MiG-15bis, Ka-50, A-10C (+ A-10C II), P-47D, P-51D, C-101, Yak-52, WWII Assets, CA, NS430, Hawk.

Terrains I own: South Atlantic, Syria, The Channel, SoH/PG, Marianas.

System:

GIGABYTE B650 AORUS ELITE AX, AMD Ryzen 5 7600, Corsair Vengeance DDR5-5200 32 GB, NVIDIA GeForce RTX 4070S FE, Western Digital Black SN850X 1 TB (DCS dedicated) & 2 TB NVMe SSDs, Corsair RM850X 850 W, NZXT H7 Flow, MSI G274CV.

Peripherals: VKB Gunfighter Mk.II w. MCG Pro, MFG Crosswind V3 Graphite, Logitech Extreme 3D Pro.

  • 6 months later...
Posted

Having read over this, it looks like the parts of immediate relevance (assuming the game engine is accurate and the derivations of velocity aren't needed to further validate ingame performance after the bullet leaves the muzzle) are the first and third tables in the first post.

These clearly show:

  1. The DCS M2 muzzle velocity is 34m/s too slow
  2. The DCS M8 MV is 39m/s too slow
  3. M20 MV is 25m/s too slow
  4. The M8 bullet is too light by 0.017kg
  5. The M20 is 0.0014kg too heavy
  6. The 100% dispersion cone is 1.2 mils too small for the DCS bullets.

Cumulatively, it seems our 50-cal guns are all firing too low because of increased bullet drop with too low MV, and that they're also grouping tighter (more accurately) than they should be.

DCS WWII player. I run the mission design team behind 4YA WWII, the most popular DCS World War 2 server.

https://www.ProjectOverlord.co.uk - for 4YA WW2 mission stats, mission information, historical research blogs and more.

  • 4 weeks later...
Posted

We've been trying to get this fixed for years now. It just ain't happening, ED doesn't want to for reasons that are yet to be clarified in any manner.

Reformers hate him! This one weird trick found by a bush pilot will make gunfighter obsessed old farts angry at your multi-role carrier deck line up!

  • 3 months later...
Posted (edited)

In the hope of creating further discussion on this topic. I’ve created a “Historically Accurate 50 Cals Mod”. The mod changes the 50 caliber the muzzle velocity, projectile weight, filler weight, dispersion rating and tracer off times where appropriate, to match the historical data.

This mod will only affect the aircraft and vehicles which use the WW2 50 caliber ammunition. So the P-51, P-47, ect. Aircraft, like the F-86, which use their own unique implementation of the Browning 50 caliber will not be affected by this Mod

The mod is provided in a format that is compatible with the mod managers JSGME, OVGME. Using a mod manager allows you to easily toggle the mods on and off without ruining the base DCS install. Link to the Mod Below.

https://drive.google.com/file/d/1dAMiOFVFmrIZQq_LtjGD-S9PsMn3z9Uz/view?usp=sharing

Below is a table comparing the characteristics of the various DCS 50 caliber projectiles and those in the mod.

image.png

 

The Mod In Detail:

Due to my previous research, I’ve been able to create a mod which accurately simulates the various  50 caliber projectiles to  an incredible level of detail and  historical accuracy. Everything down to the tracer burn time is based on primary source materials.

Below I’ll discuss all of the changes this mod makes to the various 50 caliber projectiles and provide source materials and links justifying those changes.  Fair warning, things get a math heavy at the end, the dispersion section in particular.  If you have any questions or comments feel free to reach out, I’m always happy to explain something.  

With that out of the way, let’s begin going through the changes this mod makes to the 50 caliber projectiles

Muzzle Velocity:

The muzzle velocity of the modded projectiles are  from the 1947 version of the 50 Caliber Aircraft Machine Gun technical manual. “War Department Technical Manual, TM-9-225 Machine Gun technical manual for the Browning Machine Gun Caliber .50 AN-M2 Aircraft, Basic.” January 1947.

 

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The Manual is available on Google Books.
https://books.google.com/books?id=nXySRue3QAYC&pg=PA170#v=onepage&q&f=false

The muzzle velocities within this manual are the most commonly occurring values throughout the technical literature. These values are also representative of the true muzzle velocity of the bullets when being fired from the cold bore of a new gun. Therefore the muzzle velocities within the Weapon’s Technical Manual are reasonable to use as the DCS variable v0 which is equivalent to cold bore muzzle velocity in meters per second.

Projectile Weight and Filler Weights:

The  mod changes projectile weights and payload weights of the DCS projectiles to match  the weights from the projectile blueprints / schematics as presented in the Ordnance Departments Official Research Record of  Small Arms and Small Arms Bullets Research and Development Report.  

The Official Ordnance Department’s Report is the best source for this type of information. The Ordnance Department oversaw not only weapons R and D, but also supervised the manufacture and testing of these projectiles throughout the war. The drawings / schematics of the projectiles were updated throughout the war to reflect various changes in design that occurred during the war.  For example The M1 incendiary design was submitted in 1941 and was revised 10 times by 1945, the schematic was updated accordingly.

l4rpgdz1-zLjuNdtE21l2pXc35RCuzOfFe0vvqod

Given the origin of these schematics and their continual reversion. The Ordnance Department's Report and drawings are the best source for projectile and payload weight.

If you skipped down to look at the schematics, some of you may have noticed that Some of the projectile drawings have two weights listed. The M8 API for example

vJi_tMxb5eboRoHGFUUE5OeL6HKUH02qPOqZupBI

 

During the war, the Tungsten Chromium core was replaced with a lower weight hardened steel core.

page 190 of the Army Ordnance Research and Development Report for Small Arms Ammunition. 1946.

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=13268

aklVKiouakjgFMxZN_2XtMBNk9r8B5xrhbswwlM1

Therefore the weights of the Modded projectiles are equal to those of Alternate core versions. As the alternate core 50 caliber ammunition would have been in use during World War 2.  

Below, In the spoilers, are the blueprints for the 50 Caliber Projectiles effected by this mod.  The design drawings all come from various parts of the “Army Ordnance Small Arms Ammunition Development Report”  The only link I can provide to this document is from The Archive of the Small Arms Review. The report is split into 6 parts, all of which can be downloaded for free.

Link to Part 1:

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=13265

 

 

Blueprint M2 AP

Spoiler

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Blueprint M8 API

Spoiler

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Blueprint M20 APIT

Spoiler

Zt9HxfjhfyzZqnmTJ_nY1Op0QREHS9hEW6aaMMtX

 

Blueprint M1 Incendiary

Spoiler

kO2o3eohzxFIpYEelKPUqBdXDXsCFoTqDVoIYwlv

 

Blueprint M1 Tracer

Spoiler

VS9n42-YIEGQwbSq3GYW9HhJr0GfvZTkCzKRovhl

 

The weight of the incendiary payload in the mod, is equal to the weight of the incendiary payload + half the weight of tracer composition.  The M 20 APIT has a payload of 18 grains of incendiary and contains 14 grains of tracer. Thus the payload of the M 20 APIT in the mod is 25 grains, as 18 + (14*0.5) = 25 grains or 0.0016 kilograms.

Tracer Burn Times:

For the M1 Tracer, burn time is directly from from The Ordnance  R and D report.

oGfwiW4QwTDVyNooCLMYOoLSW5o5eGcAcwwfxNGk

 

The M1 Tracer burns for 3.8 seconds. Therefore, the mod sets the  tracer off time to 3.8 seconds for the M1 Tracer.

Determining the appropriate trace off time for the M20 APIT is a bit more complicated. As I could not find an exact tracer burn out time for the M20 APIT, only the specified burn distance. So we’ll have to compute the time of flight to burn out distance. Warning there be maths below!

The Ordnance Department’s Research And Development Report on Small Arms Ammunition Tracers does give the length of  tracer burn. The Tracer is expected to burn over 1800 yards.

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Qhyu4uty-AFvbZYEAHqVkNgrw21cb_WttwTz3AUc

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=13266

A footnote in M2 50 Caliber Machine Gun’s technical manual gives a similar burn out distance.

ph9Uhu2iIu4YA5zG6sV0VyEj8Z9njf2CloSi-9Ii

 

In DCS we specify the burn out time of the tracer. If we want the mod  to match the historical data, we just have to compute the TOF of M20 APIT to 1800 yards. Then set the tracer on M20 APIT  to turn off when the bullet has flown 1800 yards.

As the goal of this mod is historical accuracy.  When we compute the time of flight to 1800 yards, We’ll use the same methodology the Ballistic Research Laboratory employed to compute firing tables during World War 2. This  computed TOF to 1800 yards will be the number of seconds DCS waits before turning off the tracer effect.

The analytical technique used to compute firing  / ballistic tables is explained in detail within the National Defense Research Committee report “Analytical Studies in Aerial Warfare”.

https://archive.org/details/analyticalstudie02bush/page/12/mode/1up

f81fwwyBJsSHwGnQ5rHClXG6KFo8wCNVNaI9FYbH

Putting the time of flight equation into something a bit more manageable we get.

TOF= (1/((V0/Range)-((.00372*rho)/(2*BC)*Sqrt(V0)))

Where V0 = The Bullets Muzzle Velocity + The Aircraft Speed (TAS) In FPS, We’ll set V0 to the muzzle velocity of M20 APIT, when being fired from a stationary position on the ground, from an M2 machine gun with a 36 inch aircraft barrel.

The Technical Manual for the 50 Caliber M2 Caliber Aircraft Machine gives the muzzle velocity of M20 APIT as 2950 fps.

V0= 2950 (fps)

C5 is the C5 ballistic coefficient of 50 Caliber M20 APIT, This value is = 0.437
As is stated in BRL Report Form Factors of Projectiles.  
https://apps.dtic.mil/sti/pdfs/AD0802080.pdf

C5 = 0.437

Rho is the relative air density to the sea level standard ballistic density 0.07513 lb / feet^3. This is also called the density ratio. At sea level, on a standard day, this value is 1.  
Rho =1

The Range is 1800 yards, however this equation uses feet as the format for the range input. So we just convert yards to feet and Range is set to.

Range = (1800*3)

The NDRC equation configured to compute the TOF to 1800 yards for the M20 APIT now looks like:

TOF = (1/((2950/(1800*3))-((.00372*1)/(2*0.437)*Sqrt(2950)))

Thus

TOF To 1800 Yards = 3.173390047 Seconds.

Let's compare our computed TOF to some historical data and see if the NDRC time of flight equation we used is accurate.

We’ll look at a Ballistic table for the M8 API from 1946. Given that, the M8 API is a ballistic match to the M20 APIT .

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if we correctly set up the NDRC TOF equation and  compute the TOF of the M8 API to 1800. And, the computed TOF is equal to the TOF data within the real Ballistic / Firing table. We can reasonably assume that the computed TOF of the M20 APIT is accurate.

 

NrK47Btidh0bVGRjQtL50QIOGrdUwWPqcIDrX-Q6

This Firing table is for an M8 API fired from a 45 inch heavy barrel version of the 50 Caliber Browning, with a muzzle velocity of 3000 fps

 

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The ballistic table says the time of flight to 1800 yards is 3.08 seconds.  

Now we just have to configure the NDRC TOF equation with the proper variables for the M8 API.  
If the computed time of flight to 1800 yards is close to 3.08 we can assume this equation is accurate enough for our mod.

 To configure the TOF equation to compute the TOF of M8 API to 1800 yards.

We change the muzzle velocity to be equal to the muzzle velocity in the ballistic table. Meaning we set V0, to 3000 fps
V0 =3000,

We also have to change the C5 ballistic coefficient the correct value for the M8 API, which is 0.439

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https://apps.dtic.mil/sti/pdfs/AD0491936.pdf

BC M8 API = 0.439

The range is still = (1800*3) feet

The time of flight equation for the M8 API to 1800 yards is now:

TOF Computed M8 API = (1/((3000/(1800*3))-((0.00372*1)/(2*0.439)*Sqrt(3000))))

TOF Computed M8 API = 3.091277324 Seconds

The computed TOF to 1800 yards is 3.09127 seconds.

The TOF for M8 API using the NDRC equation is 3.09 seconds. In the real ballistic table the TOF to 1800 yards is 3.08 seconds. The computed TOF is 0.01 seconds longer. A difference of +0.0032%. The high level of accuracy of the NDRC method means that it can be relied upon to compute the TOF M20 APIT to 1800 yards.

Based upon the accuracy of NDRC method I’ve set the tracer off time  of the M20 APIT to 3.1 seconds.

 

Dispersion Data:

The variable DCS uses to describe the weapon dispersion is Da0. In the Western technical literature this variable is equivalent to Deflection Error Probable or Range Error Probable. Error Probable is equal to 0.6745 * the standard deviation of dispersion from the aim point in  the x or y axis alone.

oU5QQYQ-0P_OVbWABeyDz26yozwyTGhCS1U5rwz8

 

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https://apps.dtic.mil/sti/tr/pdf/AD1009077.pdf

 

Error Probable as a measure of accuracy is more commonly used in Soviet and Russian sources.

The Image in the spoiler Below is from a manual on Soviet Aircraft Ammunition from the 1950’s.

Spoiler

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The Manual gives the error probable for few Soviet Cold War Era aircraft cannons in meters.

On the other hand, Western Sources often depict accuracy as the radius or diameter of a circle and a percentage. For example, the  1945 “Air Force Gunnery Manual 64” states the dispersion of the 50 Caliber Browning is a diameter of 4 mils 75%.

5mIzS_aAK98xA_WHRh8g25FxrswP4Us8MfrhfC2Y

https://archive.org/details/air-forces-manual-no.-64-fighter-gunnery-firing-rockets-dive-bombing-1-may-1945/page/67/mode/1up

To convert the Western accuracy measurement, a diameter of 4 mil 75%,  to the same format as DCS uses (Error Probable) we have to do some math.

First, We’re going to use the 4 mil 75% accuracy rating  of the 50 Caliber and determine the standard deviation of the dispersion, also known as sigma.  After, we have determined sigma. It’s relatively easy to convert sigma to Error Probable, then convert Error probable from mils to radians, which is the format DCS uses for the accuracy rating  Da0.

The value 4 Mil 75% is a function of a circular bivariate normal distribution.
The diameter of a circle containing a given probability  is =
The standard deviation of the distribution of the dispersion (sigma) * sqrt(-8*ln(1-the probability of the circle).

Therefore, the diameter of 75% circle is equal to:
 
Sigma * sqrt(-8*ln(1-0.75) = The Diameter of 75% Circle

Which simplifies to:

Sigma * 3.33021 = The Diameter of 75% Circle

Since the document gives us the diameter of the circle (4 mils). We know that:

Sigma * 3.33021 = 4

With some simple algebra, we can now determine sigma.  By dividing 4 mils /  3.33021 we get sigma  

4/3.33021 = sigma = 1.2011 mils

Our computed value of sigma agrees with other values of sigma present in the technical literature.

DfU7u7BGjT-E51BqtlD0xHSR0MUR1E1Iq2qmuUGJ

Standard Deviation Source.
From “Analytical Studies in Aerial Warfare”

https://archive.org/details/analyticalstudie02bush/page/105/mode/1up

Now that we have sigma,  all we have to do is convert sigma to Error Probable. Which is pretty straight forward.

Sigma * 0.6745 = Error Probable (Mils)

1.2011*0.6745 = 0.810 Error Probable (Mils)

The variable for dispersion in DCS, Da0, is in radians,  To convert mils to radians. Multiply by 0.001

Thus Da0 50 Cal Mod = 0.810 *0.001

Da0 50 Cal Mod = 0.00081.

The current value of Da0 for the 50 Cal is = 0.00085, Which equates to a standard deviation of 1.26 Mils. The standard deviation of the 50 Cal Mod is 1.2 mils.

The net result of the mod is a 10% reduction in area of Circle Error Probable.

In the web based graphing application Desmos.  I’ve created a simulation that randomly places some random normally distributed "bullet impacts." While plotting the Circle Error Probable aka the 50% impact circle of dispersion.

Link to the Dispersion Sim

https://www.desmos.com/calculator/srjak2emph

With this tool we can easily create an accurate depiction of the Modded Dispersion, which has a 1.41 Mils 50% radius. Thus the radius of Circle Error Probable for the Mod is 1.41 Mils.

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And the  radius  of 50 % percent circle  / Circle Error Probable for the default DCS World War 2 50 caliber Projectiles is 1.48 mils.

l3rsW4z7NlMl5aD8d33bPnKjmFnfH5Txv3a02Qrq

Yeah that was a lot of math for not much of a change in dispersion. The size of the dispersion in DCS before barrel heat effects are applied is only slightly off.

However, this small change does make the bullets more historically accurate, which is the intent of this mod.

While we did not end up with large change to the dispersion. I did learn a lot from research that went into determining the appropriate value of Da0.

 I ended up with a much better understanding of how the accuracy values of the weapons in DCS relate to the real world accuracy ratings. This knowledge will end up helping me with a few other projects I have in mind too.

With the dispersion taken care of, we have just about covered all the changes this mod makes to the 50 caliber projectiles. However we do have a few miscellaneous changes to cover

Other Changes and Final  Notes:

DCS also has a variable which randomizes the muzzle velocity of the project, Dv0.  This is set to 0 in the mod during test and validation and has been left off.

The duration of the smoke effect has been reduced. In DCS the  Smoke effect of the tracer effect doesn’t match the trajectory of the bullet. The smoke effect just travels straight out from the gun barrel. Thus the smoke tends to hinder aiming. The thickness and amount of smoke produced by the effect also obscures the visual signature of the tracer glow. Which also greatly reduces the effectiveness of the tracer as an aiming aid.  Thus the smoke time has been reduced from 0.5 Seconds to 0.1 Seconds.

I’ve also changed the projectile type of the M1 Incendiary from Ball to AP. The M1 Incendiary was manufactured around a tubular steel dowel / frame.

MkfAZLGc9fiW5Fta7FIyXfBAQIPt8i_I_EFMHpuZ

 

 

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The thick steel sleeve and high muzzle velocity gave the M1 Incendiary the ability to penetrate armor up to 7/8 inches thick.

 

 

o4C_dS17Wz0nqKN5odbYl4jmfzjoi1yM2oPJLmmq

This excerpt is from the US Army Air Forces Aircraft Evaluation Report of The Messerschmitt -109F

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Link to the 109F report:

https://stephentaylorhistorian.files.wordpress.com/2020/04/bf-109f-evaluation.pdf

Given the M1-Inc’s ability to penetrate fairly thick armor, the change in projectile type is reasonable.

That covers all the changes this mod makes to DCS 50 caliber projectiles. If you have read this far down I want to thank you for taking the time to do so. If you have any questions please feel free to ask. I’m always happy to help.

 

 

 

Edited by Curly
I word good?
  • Like 3
  • Thanks 2
Posted

Once again a truly incredible post! :thumbup:

Modules I own: F-14A/B, F-4E, Mi-24P, AJS 37, AV-8B N/A, F-5E-3, MiG-21bis, F-16CM, F/A-18C, Supercarrier, Mi-8MTV2, UH-1H, Mirage 2000C, FC3, MiG-15bis, Ka-50, A-10C (+ A-10C II), P-47D, P-51D, C-101, Yak-52, WWII Assets, CA, NS430, Hawk.

Terrains I own: South Atlantic, Syria, The Channel, SoH/PG, Marianas.

System:

GIGABYTE B650 AORUS ELITE AX, AMD Ryzen 5 7600, Corsair Vengeance DDR5-5200 32 GB, NVIDIA GeForce RTX 4070S FE, Western Digital Black SN850X 1 TB (DCS dedicated) & 2 TB NVMe SSDs, Corsair RM850X 850 W, NZXT H7 Flow, MSI G274CV.

Peripherals: VKB Gunfighter Mk.II w. MCG Pro, MFG Crosswind V3 Graphite, Logitech Extreme 3D Pro.

Posted

Holy crap!

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Hardware: T-50 Mongoose, VKB STECS, Saitek 3 Throttle Quadrant, Homemade 32-function Leo Bodnar Button Box, MFG Crosswind Pedals Oculus Rift S

System Specs: MSI MPG X570 GAMING PLUS, RTX 3090, Ryzen 7 5800X3D, 32GB DDR4-3200, Samsung 860 EVO, Samsung 970 EVO 250GB

Modules: AH-64D, Ka-50, Mi-8MTV2, F-16C, F-15E, F/A-18C, F-14B, F-5E, P-51D, Spitfire Mk LF Mk. IXc, Bf-109K-4, Fw-190A-8

Maps: Normandy, Nevada, Persian Gulf, Syria

 

  • ED Team
Posted

I have to add some engineer's birch tar to this barrel of honey...
First of all, I always wonder how people use the results of measurements in their calculations :). For example, one can measure a diameter with a plain ruler with 1 mm scale (23 mm, for example), put it to a calculator and after a while (after using Pi constant) write down an area of 415.47562 mm2.
If we take a look at the source that was used
nullwe clearly can see the original data 74" and 37" at 750 feet, that gives 8.22 and 4.11 mils. In the text these values were rounded to 8 and 4.  Why was it done? Because if you try to count 100% and 75% of hits performing test by test, each of 100 rounds, you will see that the values for D100% and D75% will noticeable vary from test to test. So, the values (D100% or D75%) we want to have as a constant for a random dispersion values ARE NOT THE CONSTANTS  and have their own dispersion. And for 100 rounds it quite big.
Everyone can check: generate the series of 200 random Gaussian numbers in pairs (X, Y) with the certain dispersion using a valued generator and find diameters for circles of 100% and 75% hits.
Performing these tests 1-20 times and recording these numbers test by test you can find the average and std deviation for the test result. And the next step is to increase test size up to 1000-2000 tryings and calculate the same values for it. 

If the same math is applied to 8.22 and 4.11 from the original data it gives 0.00083 for Error Probable (EP). What is more accurate? Frankly, I can not say exactly, because the accuracy of even 100 rounds test is way low: the second test could show 8.57 and 4.05, for example. So, DCS EP=0.00086 was calculated from other source using different test results. In practice for probability calculations, for example, EP can be taken as 1/8 of D100% that gives circa 0.001 of EP. That's why 8.22 and 4.11 were easily transformed to 8 and 4 in the text.

But there are some bright things at this dark picture: nobody can notice these small changes in EP during real air firing, because they can be statistically significant only if you managed to keep absolutely accurate aiming for a unrealistic time period. 
The second note:  if somebody thinks that low dispersion gives him an advantage in hit probability, he is deeply wrong. It is a different item to talk about, but I can only say that there were a lot of scientific study between WWI and WWII to find the right decision about it.

So, having zero muzzle velocity deviation will not make you happy. 

 

image.png

Ніщо так сильно не ранить мозок, як уламки скла від розбитих рожевих окулярів

There is nothing so hurtful for the brain as splinters of broken rose-coloured spectacles.

Ничто так сильно не ранит мозг, как осколки стекла от разбитых розовых очков (С) Me

  • ED Team
Posted

Regarding the "right" muzzle velocities. 
There is an AAF manual 200-1 that stated muzzle velocities for M2 guns for aircraft. The manual issued on 30 Jan 1945, so the data there is relevant to WWII period.
M2 - 2700 ft/s
M8 - 2870 ft/s

and what we see in the table from 1947 year?
M2 - 2840 ft/s
M8 - 2950 ft/s

Because both manuals are official but the first one is a special AAF manual we can be sure that the first one is more historically accurate for aircraft guns of WWII period.
 




 null 

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Ніщо так сильно не ранить мозок, як уламки скла від розбитих рожевих окулярів

There is nothing so hurtful for the brain as splinters of broken rose-coloured spectacles.

Ничто так сильно не ранит мозг, как осколки стекла от разбитых розовых очков (С) Me

Posted (edited)
9 hours ago, Yo-Yo said:

Regarding the "right" muzzle velocities. 
There is an AAF manual 200-1 that stated muzzle velocities for M2 guns for aircraft. The manual issued on 30 Jan 1945, so the data there is relevant to WWII period.
M2 - 2700 ft/s
M8 - 2870 ft/s

and what we see in the table from 1947 year?
M2 - 2840 ft/s
M8 - 2950 ft/s

Because both manuals are official but the first one is a special AAF manual we can be sure that the first one is more historically accurate for aircraft guns of WWII period.
 




 null 

The firing tables for field use, like  AAF manual 200-1, use reduced muzzle velocities for their tabulations because they are accounting for wear and the average velocity of the bullets in a burst.

 

This is plainly stated in M8 API ballistic table.

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The ballistic data in those AAF field manuals. Often comes from firing tables like the one above, FT 0.5AA-T1.

In “AAF-200-1 Fighter Gun Harmonization” The data comes from Aberdeen Firing Table FT. 50 AC M-1

4TW2l14koq9dhzPspE1J1fclY0kJJbxNcLTKM5kj

https://archive.org/details/aaf-manual-200-1-fighter-gun-harmonization/page/9/mode/1up

 

The ballistic data in “Air Force Manual 64 Fighter Gunnery”

Comes from FT. 50 AC-M-1-8

ORhIWuQ6m3uu14RhlIPJ-N6oKdp6g3nSS4-Atqyn

https://archive.org/details/air-forces-manual-no.-64-fighter-gunnery-firing-rockets-dive-bombing-1-may-1945/page/111/mode/1up

 

The reduced muzzle velocity (2700 FPS) used in AAF-200-1 is representative of a gun halfway through its service life.

The Army Air Force considered a 50 caliber machine gun barrel worn out when the cold gun muzzle velocity of  the weapon dropped by 200 fps.

ZAXQLoEDOgioAagA0b3Ffujx2YDp_-eg-a31kOMd

https://archive.org/details/hypervelocitygun01bush/page/466/mode/1up

 

However, If you want some more sources with higher muzzle velocities from the war with. I can provide a few more.

 

There’s TM 9220

image.png

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It gives the muzzle for the M2 AP from the 36 inch aircraft machine guns as 2845 fps

S3p2TA6tgMQrOp8ogNnSxxAn_gpdTjeSVrXOfPla

 

The same document gives the muzzle velocity for the M1 Incendiary when fired from the 36 inch aircraft barrel as 3,100 fps

https://archive.org/details/TM9-2200/page/n209/mode/2up

Or the 1944 version of “Terminal Ballistic Data”

5aIFjVDl8tJP48o6cAhgA6KAn2LEPA7CGLThIVOr

Which contains the Range, impact velocity and armor penetration values for the 50 Caliber AP M2. The test from the Ballistic Test Section was conducted on December 20 1943. This report gives the muzzle velocity of the 50 Caliber M2 AP as fired from a 36 inch aircraft barrel as 2845 fps.

k8IH2In0eK-UU9-EaWPZKY2Yh5IYjEPNBH8MTgIz

The 1945 Version of this same report gives the muzzle velocity as 2,835 fps.

PkKhW5ULbeIZPfJ68Mh3xJ6jac51hVaO8UNkChI5

Including the data sheet.

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and The revised Velocity Penetration Graphic.

 

Or From the Small arms R and D report. Which states the muzzle velocity at 78 feet from the 36 inch barrel is 2810 fps.

Esq1gktXUohykKf6mpskYD7fo5WUIgiAjWM86gzM

When you take in the totality of all source materials and account for the practical application of the use of the firing table. I feel it safe to say that muzzle velocity of the 50 caliber projectiles,  fired from a cold barrel, is best represented by the values in the 1946 Technical Manual  for 50 Caliber aircraft Machine gun.

 

The 2700 fps value, used in the Air Force firing tables already accounts for reduction in muzzle velocity due to burst firing and wear. When the game applies additional reductions in muzzle velocity with the shot_heat effect, it's over modeling the drop in velocity. The drop in velocity due to burst firing is baked into the Air Force firing table. 

 

The procedure for accounting for the drop in muzzle velocity due to burst fire when the firing table is created,  is described by the Agency which creates those tables, The Ballistic Research  Lab. In BRL Report 889 "On The Computation Procedures for Firing and Bombing Tables"

image.png

https://apps.dtic.mil/sti/tr/pdf/AD0027123.pdf

 

 

 

 

I know that you can ruin the performance of a 50 caliber machine gun by burst firing it.  I’m not advocating for turning off shot heat for these weapons. I’m well aware that a continuous burst of 170 bullets will reduce the velocity life of a standard steel M2 50 Caliber Aircraft to zero.

zXBRlXGiUXjdIWRKcHfDXp4k51StYI5ZWQ2wh552

au5qBDhNEbE7zMNN4vOeBqWcdrFVyDfTWPZ7aR9g

https://archive.org/details/hypervelocitygun01bush/page/481/mode/1up

Meaning that weapon would fire 200 fps slower  than a new 50 caliber, EG a worn out barrels fires  around 2600 fps from a cold barrel. As this was the definition of the velocity life of the weapon.

zJiBJSrjVrTJs7wW-s8_gYjdnfzp1wQEcG5aPfuL

https://archive.org/details/hypervelocitygun01bush/page/466/mode/1up

Velocity drop and an increase in Dispersion should be in game. However the 50 caliber machine gun DCS models is  half worn out and and prone to  to delivering muzzle velocities for a weapon closer to the end of its service than the begging of it . 

 

I would make this same argument for why a small reduction in the dispersion value is important. When the heat effect is added to the slightly larger dispersion, the dispersion is too great and over modeled.  

 

Again, I’m not trying to argue that burst firing should should not increase the dispersion of the projectiles. I’ve read detailed reports on how long of a burst fire it takes to reduce the accuracy of this weapon

Biqnbb5ZV_vPA4EQLhznqMcx7FLA6e2gbEjA8YVv

https://archive.org/details/hypervelocitygun01bush/page/466/mode/1up

 

And The effect burst length can have on accuracy.

0_Aak_mKbYAtkaKLGC2xiy2wxEC5MXCQP4JKuFpy

 

tIjXLvPpI8J_797isHV6BZpn_18_dKpa4nQYJaYe

 

HQ34i4RHdIx4CROx-piZsVcyeIEnaegrbsEqPd6a

I chose to use the 1.2 milliradian std deviation as the basis for my mod because that value is so widely used in various manuals.  4 mil 75% Shows up over and over again in numerous Air Force Weapon manuals.

K38o6oFSvxsvlqal5awhLVi2IvXUn7VPj7k_e-YE

And It continues to show up after the war too.

1zFqjz24D-CMKWFHU9p21U0sLUK9hw3jf2DrZdGb

kZR2yzVMOY_T38weUQHYtq7e7wn_33tDLtXedEhv

4 mil 75% / 8 mil 100% was still the standard in the 1950’s 

https://www.google.com/books/edition/AF_Manual/81krAQAAMAAJ?hl=en&gbpv=1&pg=PA155&printsec=frontcove

The fact that this figure was used over and over again for as long it did gave reasonable assurance that this was a sound basis for an accurate assessment of the gun's accuracy.

 

There was also some other data in form of mean radius that I chose not to use because, if you computed a standard deviation for the mean radius given It was far below what the Air Force was using in their manuals. It looks like they may have had switch the notation of feet with inches when they wrote the mean radius.

 

The document also does not define mean radius. Is it CEP? Error Probable? the Mean Radial Miss distance?. There were just to many questions about the data in this table. So I did not use any of these figures as the basis for my mod.

 

KkaTizuLyAw7mZg9ndUUFVbFq_0BceTgoiNDQzG1

https://archive.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=13265

 

I just want to impress upon  you the level research and consideration that I put into developing this mod. I didn't just pick the best numbers. I selected numbers which would best represent the cold barrel performance of new 50 caliber M2 Aircraft Machine Gun.

 

Is this the report you based your accuracy data on?

3d9VLm0ea1kv5zI5PGgugMjojjW-Zi7qUKC0O-7c

 

4WxQG7mFHoVSR-nbEA6mpPZwJQes-J_WfJbBCxgh

Or was it that Russian P-40 firing test I've heard about but have never been able to get my hands on.

 

I appreciate that you looked at this and I  hope that I have convinced you to take another look at the data presented.

 

 

 

 

Edited by Curly
added BRL Firing Table Report
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  • ED Team
Posted

You stated too many things without any direct proof. For example "The firing tables for field use, like  AAF manual 200-1, use reduced muzzle velocities for their tabulations because they are accounting for wear and the average velocity of the bullets in a burst."
And after that you place  minus 45 ft/s correction made for very different department to state that for AAF somebody corrected not less than for 80-140 ft/s (why M8 has less due to barrel wearing?)


So, your logic is very strange " If source C states that data for object D was modified IT MEANS that in the source A the same was done for object B". It does not work this way even if you want it very much, until you find direct proofs.

Ніщо так сильно не ранить мозок, як уламки скла від розбитих рожевих окулярів

There is nothing so hurtful for the brain as splinters of broken rose-coloured spectacles.

Ничто так сильно не ранит мозг, как осколки стекла от разбитых розовых очков (С) Me

Posted
7 hours ago, Yo-Yo said:

why M8 has less due to barrel wearing?

So, your logic is very strange " If source C states that data for object D was modified IT MEANS that in the source A the same was done for object B". It does not work this way even if you want it very much, until you find direct proofs.

The firing table for the M8 AP is for the 28 lb 45 inch heavy barrel machine gun. 

The firing tables the Air Force manuals are based on the 10 lb 36 inch aircraft machine gun barrel.

the reason for the difference in between the two manuals is because heavy barrel is less prone a drop in muzzle velocity than the light M2 barrel.

Given the same burst length the barrel of the lighter 36 inch aircraft expands more and the overall temperature of the 36 inch barrel is greater. Resulting in a greater reduction in velocity and accuracy for the 36 inch barrel.

The 28 lbs heavy barrel can fire 8 times more rounds

Heavy Barrel Wear.png

Compared to 10 lbs 36 barrel used on aircraft machine guns.

Aircraft Barrel wear.png

The reason for the difference in between the two manuals is because heavy barrel is less prone a drop in muzzle velocity than the light M2 barrel.

If you want some direct proof that the cold barrel muzzle velocity of a 36 inch aircraft machine gun barrel firing M2 AP has a muzzle velocity of 2845 fps I'll point you to the firing tables in MIL STD 662.

MIL 662.png

 

 

  • Like 2
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Posted

I'm unclear as to why the M2HB gun enters the discussion at all in the context of WWII aircraft weapons. Both the P-51D and the P-47D carried the AN/M2 gun with the 36" (35.8") bbl. We should expect significantly lower MVs than for the 45" bbl M2HB, for the simple reason that the aircraft gun bbl is 9" shorter.

I'm on the move so don't have access to my ballistic calculator software, but any of the free online ones will return ballpark figures illustrating that point. You don't need a university course in thermodynamics or exterior/terminal ballistics for this one!

For Yo-Yo, I would caution that the mid/late 1940s was a huge period of data gathering and capture. Much of what we know about WWII tactics and equipment was written down in the years immediately after the end of the war as both British and American forces went on a spree of writing manuals and carrying out experiments to quantify "common knowledge" before too many soldiers were demobilised. A 1947 manual, in my view, just as likely to contain reliable data than a 1944 edition. Certainly much of what is known about British gun and ammunition performance today comes from post war trials.

DCS WWII player. I run the mission design team behind 4YA WWII, the most popular DCS World War 2 server.

https://www.ProjectOverlord.co.uk - for 4YA WW2 mission stats, mission information, historical research blogs and more.

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