Curly

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

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. 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 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 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. 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 It gives the muzzle for the M2 AP from the 36 inch aircraft machine guns as 2845 fps 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” 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. The 1945 Version of this same report gives the muzzle velocity as 2,835 fps. Including the data sheet. 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. 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" 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. 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. 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 https://archive.org/details/hypervelocitygun01bush/page/466/mode/1up And The effect burst length can have on accuracy. 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. And It continues to show up after the war too. 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. 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? 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.

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. 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. 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. 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 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 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 Blueprint M8 API Blueprint M20 APIT Blueprint M1 Incendiary Blueprint M1 Tracer 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. 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. 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. 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 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 . 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. 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 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 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. 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. 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%. 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. 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. And the radius of 50 % percent circle / Circle Error Probable for the default DCS World War 2 50 caliber Projectiles is 1.48 mils. 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. The thick steel sleeve and high muzzle velocity gave the M1 Incendiary the ability to penetrate armor up to 7/8 inches thick. This excerpt is from the US Army Air Forces Aircraft Evaluation Report of The Messerschmitt -109F 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.

I found the source for the DCS pattern. It's from the North American Aviation Version of the flight Manual. https://app.aircorpslibrary.com/document/viewer/fmp51na5914 The pattern. The DCS pattern is an almost exact fit of this pattern. The NAA manual pattern being the dashed lines. https://www.desmos.com/calculator/2dnjxa31ca It does look like someone from NAA may have miss interpreted the Air Force pattern. As the NAA pattern also mirrors the dispersion pattern. https://www.desmos.com/calculator/ngk08zcyuh And the NAA pattern Disappears from all the documents published after this manual. NAA Harmonization / Convergence Pattern K-14 Sight NAA Manual Azimuth Azimuth Degrees Elevation Elevation Degrees Gun 1 72.5 38.375 0.006623 0.3794699477 0.006348 0.3637136083 Gun 2 82.08823529 36 0.005002764706 0.2866373035 0.007493 0.4293172759 Gun 3 89.125 39 0.005951 0.3409671839 0.005002 0.2865934891

I know of two other official harmonization / convergence patterns for the P-51 D. The DCS P-51 does not match either of these. The two other harmonization / convergence patterns I know of, come from the P-51 maintenance manual. In the manual there is a 300 Yard and 250 Yard Harmonization / Convergence pattern. https://stephentaylorhistorian.files.wordpress.com/2020/04/p-51d-part-2.pdf I’ve plotted both patterns in Desmos so we can compare them to the DCS. Links to the graphs are provided as well 300 Yard Harmonization / Convergence at 0 mph https://www.desmos.com/calculator/hp4q0ry43j 300 Yard Harmonization / Convergence at 300 mph https://www.desmos.com/calculator/ygsuwf5tge Below is a table with the 300 yard 1000 inch boresight target data, gun azimuth and elevation settings. 300 Yard 1000 inch Card Horizontal Distance V Distance Azimuth Azimuth Degrees Elevation Degress Gun 1 70.25 38.125 0.008873 0.5083854516 0.006598 0.3780375532 Gun 2 77.5 37.5 0.009591 0.5495238213 0.005993 0.3433736066 Gun 3 83.375 37.125 0.011701 0.6704179161 0.006877 0.3940230757 The 250 Yard Harmonization / Convergence Pattern at 0 mph https://www.desmos.com/calculator/qkmq0qv6gi The 250 Yard Harmonization / Convergence Pattern at 300 mph. https://www.desmos.com/calculator/nfqmso8h1m Table for the 250 yard Harmonization / Converge settings. 250 Yard 1000 inch Card Horizontal Distance V Distance Azimuth Azimuth Degrees Elevation Elevation Degrees Gun 1 68.875 38.125 0.010248 0.5871671485 0.006598 0.3780375532 Gun 2 79.5 37.5 0.007591 0.4349322623 0.005993 0.3433736066 Gun 3 82.25 37.125 0.012826 0.734875668 0.006877 0.3940230757 DCS Harmonization / Convergence at 0 mph https://www.desmos.com/calculator/3ywwxznhdb DCS Harmonization / Convergence at 300 mph. https://www.desmos.com/calculator/yvfsqh0yim The current DCS P-51 harmonization pattern seems to be configured to match the depiction of the 75% 4 mil dispersion of the 50 cal. In the graphing program we can compute the and plot the 4 mil dispersion zone. https://www.desmos.com/calculator/wlsqlyaxtj Note that the convergence pattern of the DCS P-51 matches the plot of the dispersion zones almost perfectly. Maybe someone changed the azimuth to match the dispersion zone? However the current configuration of the DCS harmonization pattern does not seem to match anything I can find. Following the instructions in the Harmonization manual, we can create a 1000 inch boresight card for the DCS P-51 Harmonization / Convergence settings. Presenting the data in a table. DCS P-51 Harmonization H Distance V Distance Azimuth Azimuth Degrees Elevation Elevation Degrees Gun 1 72.50820213 38.37000152 0.006615 0.379 0.006352998477 0.364 Gun 2 82.09935834 35.49939203 0.004992 0.286 0.007993607974 0.458 Gun 3 89.12442725 39.51650382 0.005952 0.341 0.004485496178 0.257

null The azimuth Angle on the P-51 guns seems off a bit. Per this post https://forum.dcs.world/topic/79688-convergance-and-gun-options/page/2/#comment-1725050 The expected convergence pattern should mirror the one in Air Forces Manual No. 64 Fighter Gunnery https://archive.org/details/air-forces-manual-no.-64-fighter-gunnery-firing-rockets-dive-bombing-1-may-1945/page/110/mode/1up Which is the pattern as depicted in the manual Fighter Gun Harmonization. https://archive.org/details/aaf-manual-200-1-fighter-gun-harmonization/page/37/mode/1up From the DCS P-51 lua file we have the azimuth for the all 6 of the guns. DCS Gun 3, Outboard: gun azimuth_initial = 0.341, DCS Gun 2, Middle Gun: gun azimuth_initial =0.286 DCS Gun 1, Interior Gun: azimuth_initial = 0.379, The unit is likely degrees. Converting to radians gives us. DCS Gun 3, Outboard: gun azimuth_initial = 0.005951, DCS Gun 2, Middle Gun: gun azimuth_initial =0.004991 DCS Gun 1, Interior Gun: azimuth_initial = 0.0066147, The position of the gun is also given in meters within the lua file. With this data we can compute at which range the guns will converge. Using the graphing application Desmos, we can overlay the and compare the harmonization pattern of the DCS P-51 to the one depicted within the manual. We’ll straighten this up a bit and import it into Desmos and scale it. Link to the Desmos Convergence Calculator. https://www.desmos.com/calculator/ujiueojjjp Using azimuth angles and gun positions from the lua file. We plot the convergence pattern of the DCS P-51 at 0 mph. Note that interior guns, Gun 1, the red lines, Converge At 1007. Feet The middle Guns, Gun 2 ,the green line, converge at 1466 feet The exterior guns, Gun 3, the blue line, converge at 1337 feet. Let’s remove the graphic for a clear look at the DCS pattern. It’s important to note that the Harmonization Pattern and settings depicted in the manual are configured for an airspeed of 300 mph. At 300 mph in the real P-51 The Interior Guns, Gun 1, Converge at 1000 feet The Middle Guns, Gun 2, Converge at 1100 feet The Exterior Guns Gun 3, Converge ar 1200 feet. Removing the Graphic for a clear view. However the azimuth of the guns is actually set to a larger angle than is depicted. This is because the forward velocity of the aircraft alters the velocity vector of the projectile. This reduces the effective azimuth angle of the trajectory. The change in the effective azimuth angle can easily be calculated; The Fighter Gun Harmonization Manual and AAF Manual 335-25 both provide the relevant equation. Which I will call the trajectory correction function. The Manual Fighter Gun Harmonization https://archive.org/details/aaf-manual-200-1-fighter-gun-harmonization/page/7/mode/1up And AAF Manual 335-25 https://books.google.com/books/content?id=81krAQAAMAAJ&pg=PA331&img=1&zoom=3&hl=en&bul=1&sig=ACfU3U1BRdZA_vO5KY8Ylk_Y-i3WWQQ4mQ&ci=4%2C1%2C993%2C1326&edge=0 The trajectory correction function is ((Vias in FPS) * the basic azimuth angle of the gun) / the muzzle velocity of the gun. If we apply this correction factor to the DCS P-51 guns at 300 mph, the harmonization pattern moves well beyond what is depicted in the manuals. The Interior Guns, Gun 1 Converges at 1200 feet at 300 mph. The Middle Guns, Gun 2, Converges at 1751 feet at 300 mph The Exterior Guns, Gun 3, Converges at 1598 feet at 300 mph A more clear view with the graphic removed. The basic Azimuth angle for the real P-51 can easily be computed with the information provided in the Harmonization manuals. All we need is the position of the guns and the data from the 1000 inch boresight target. The basic azimuth angle of the gun is (Horizontal position of the Gun from the Center line - The position of the gun on the 1000 inch boresight card) / (range to the card 1000 inches). This gives the basic azimuth angle of the gun. For Gun 1 the equation is ( 79.123-71.25)/ 1000 = 0.007873 Which is the basic azimuth angle for the Gun 1. Lets Create a virtual boresight target in graph and plot the trajectory / basic angle of the guns. The line of sight of the guns does pass through the boresight target, however the convergence pattern of the gun is short of the chart. If we fired the guns at 0 mph with this pattern. Gun 1 Interior would Converge at 837 feet. Gun 2 Middle would Converge at 925 feet Gun 3 Exterior would Converge at 1012 feet. Let compute the trajectory correction for Gun 1 at 300 mph and plot the convergence pattern again. The Trajectory correction for Gun 1 is. ((Vias in FPS) * the basic azimuth angle of the gun) / the muzzle velocity of the gun. ((300 mph *1.467) * (0.007873)) / 2700 = .001283299. We then subtract the trajectory correction factor from our computation of the azimuth angle of the gun. Lets compute the effective azimuth angle of Gun at 300 mph (( 79.123-71.25)/ 1000)- 0.001283299. = .006589701= The effective azimuth angle of Gun 1 at 300 MPH Lets plot the effective line of sight of gun 1 with the trajectory correction for 300 mph With the trajectory correction Gun 1 matches the harmonization pattern as depicted in the manual. And Converges at ~ 1000 feet. Let's do the same for the other guns now. And without the graphic for clarity. All we have done is use the data and equations from the manuals, and computed the trajectory. The basic azimuth angle will always be greater than the effective azimuth angle, if the convergence pattern is configured for an airspeed greater than 0. In the P-51 maintenance manual there are settings for a 300 yard and 250 yard convergence pattern. This patterns are also based on a air speed of 300 mph. Above we depict the basic azimuth with a sold line and the effective azimuth angle at 300 mph with the dashed line. Note that the effective azimuth angle with trajectory correction converges at 300 yards, where it should. While the basic azimuth angle passes through the center of the boresight target, but converges well short of 300 yards. Therefore the azimuth angle for the guns should be set to basic azimuth angle as computed from the 1000 inch boresight target.

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

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

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

The gun heating due bullets fired model is incorrect. TLDR Version: The gun heating model has the wrong barrel and body mass. Resulting in a rapid rise in gun temps. The mass of the barrel in the game is 2.7 Kg. The mass of the real gun barrel is 10.6Lbs or 4.8kg. The mass of the body in the game is 14.3 Kg. The mass of the real gun minus the barrel is 58.09 lbs or 26.34 Kg There is too much heat per shot. The thermal energy input into the guns in the game is 7.823 Joules per bullet. Tests indicate the variable “shot_heat” should be from 4.62 to 4.023 Joules per bullet. The reduction in accuracy and velocity due to gun heating are too large. Tests of the Real gun barrel indicate that a burst of 365 bullets can be fired without a reduction in accuracy or muzzle velocity. And, that the accuracy and velocity life of the M3 gun barrels are 8 times greater than that of the regular steel barrels. https://www.loc.gov/resource/dcmsiabooks.hypervelocitygun01bush/?sp=499 An accurate model for gun heating would look like: { name = "HeatEffectExt" , shot_heat = 4.62, barrel_k = 0.462 * 4.94, body_k = 0.462 * 26.34 }, With a 20% reduction in accuracy and reduction in muzzle velocity 200 fps being applied at a barrel Temperature of 800c or the equivalent of 350 consecutive shots. Having the guns fire uncontrolled ( a Cook Off model) after a 200 round burst or a body temperature of 900 C would be realistic too. For comparison the current gun heat model in the code is: { name = "HeatEffectExt" , shot_heat = 7.823, barrel_k = 0.462 * 2.7, body_k = 0.462 * 14.3 }, Elsewhere in the code, the values of gun heating model are explained for the 50 cal M2: function M2_heat_effect() --[[ 7.823 kJ - one shot energy , 462 (steel specific heat), 6 kg - barrels mass ]] { name = "HeatEffectExt", shot_heat = 7.823, barrel_k = 0.462 * 6.0, body_k = 0.462 * 32.0} The heat effect model contains 3 variables which describe the thermal dynamics of the gun. The First variable is,. shot_heat = 7.823, This energy input into per bullet fired. It’s set to 7.823 Joules per bullet fired. The variables barrel_k and body_k are the thermal capacity of the gun barrel and body. This variable consists of two numbers: the specific heat of the material and its mass. For the F-86 Barrel, the thermal capacity is, barrel_k = 0.462 * 2.7 .426 is the specific heat of steel and 2.7 is the mass of the DCS F-86’s gun barrel. The specific heat of a material is the energy, in joules, required to raise the temperature of a kilogram of that material, by 1 degree C.The specific heat of steel is.462 joules per gram. Therefore, the energy (Joules) required to raise the temperature of the gun barrel 1 degree C is Joules Need to raise temp by 1c = mass of material * the specific heat of the material. 1.2474 =2.7*.462 Since the code gives the heat input per bullet, 7.823 Joules, we can compute the change in barrel temp after 1 shot is fired. As the change in temp is = (Joules per Shot * Number of bullets fired) / (the specific heating of steel * the barrel Mass) In terms of the Gun heat variables the change in barrel temp = (shot_heat = 7.823 * the number of shots) / (barrel_k = 0.462 * 2.7) For one bullet the temperature of the guns increase by 6.27C 7.823/(0.462 * 2.7)= 6.271C The code tells us, The DCS F-86 is modeling a barrel with a mass of 2.7 kg which is about 5 lbs. The manual for the 50 Cal M3 machine gun. . https://www.scribd.com/document/38654349/TM-9-2190-M3-Browning Notes, the barrel weight is 10.91 lbs which is 4.94 kg. The DCS M3 machine gun barrel has half as much mass as the real one. It seems trivial, but the reduced mass has important implications due to the heat modeling. If we model the gun with the correct barrel mass; the gun temperature increases 3.47C per shot. 7.823/(0.462 * 4.94) = 3.4377C. This is just about half as much heat as is currently modeled 6.7C per shot. The code shows the weight of the body of the gun as 14.3 Kg which is also incorrect. body_k = 0.462 * 14.3 The weight of the gun body in DCS is 14.3 Kg or 31.5 Lbs, The M3 manual gives the weight of total Gun as 64 1/2 lbs + 4 1/2 lbs for the recoil adapter. So 69 lbs total. The total mass - barrel should give us the “body mass” 69-10.91. Or 58.09 lbs / 26.34 Kg. Again about half the mass of the actual gun is in the thermal model. So the body of the gun heats up twice as much as it should too. In DCS, the temperature of the gun body increases 1.184C for every shot. 7.823/(0.462 * 14.3) = 1.184C increase in temp If we model the gun with real weight - barrel. The temperature of the body increases by .6428 C 7.823/(0.462 * 26.34) = .6428c. With the correct body weight that shot per heat is reduced by half. If you’re ready for a deep dive on the metallurgy and performance of 50 caliber gun barrels, read on. We’re going to compare the heat modeling of the DCS M3 to some real tests.The tests indicate that the loss of accuracy and the drop in muzzle velocity as a result of barrel heat are too high in the DCS F-86. The construction of the gun barrel used on the M3 machine gun is different from a standard steel barrel. The properties of the materials used in the barrel of the M3 machine gun increase the number of bullets which can be fired before the accuracy or the muzzle velocity of the gun drops when compared to the plain steel barrel. https://www.loc.gov/resource/dcmsiabooks.hypervelocitygun01bush/?sp=499 This chart shows how many M2 AP bullets can be fired on a severe firing schedule, before the muzzle velocity drops by either 200 fps or 20% of bullets impact yawed. The chart shows that a steel barrel can only fire a single 170 burst. The lined and plated barrels, Which are on the F-86’s machine guns, did a 350 round burst and two 500 round burst cycles, for a total of 1350 bullets before the accuracy of the weapon dropped. The test consisted of an initial burst of 350 rounds. The gun is then allowed to cool to room temperature. After the gun is cooled, a burst of 100 rounds are fired. The gun is allowed to cool for 2 mins and then another 100 round burst is fired. This cycle is repeated until 500 bullets have been fired. After the 500 round burst, the gun is allowed to cool to room temperature. The 500 bullet burst cycle is then repeated until either the muzzle velocity drops by 200 fps or the accuracy is degraded by 20%.The accuracy and muzzle velocity of the gun are measured periodically through the test. The model barrel of the M3 machine gun on the F-86, is the same design as the one tested in the chart. Stellite lined with chromium plating. From the M3 weapons manual. The model of M3 barrel is 7265156 and it has the same type of lining and plating as the barrel tested in the chart. Page 23 of manual notes, the barrel has a 9 inch liner and is plated with chromium. A cross section of the barrel is available in the M3’s weapon’s inspectors manual. https://www.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=2758 And a color picture of the liner. https://apps.dtic.mil/sti/pdfs/ADA472711.pdf The Manufacturing process of the Stellite / Cobalt liner. The 9 inch liner in the F-86’s gun barrel is made of Stellite 21. An Air National Guard memo regarding the recycling of these barrels and liners verifies this. https://www.google.com/books/edition/National_Guard_Bureau_Bulletin/cYhat3J3bmUC?hl=en&gbpv=1&pg=RA7-PA7&printsec=frontcover Note the same barrel model, 7265156, as indicated in the Manual for the M3 machine gun posted above. The lining and plating of these barrels was developed during World War 2 to improve the accuracy and velocity of the 50 caliber aircraft machine gun. The development, metallurgy, construction and testing of these barrels are discussed in detail in the National Defense Research Committee Report. https://www.loc.gov/item/2007498072/ Let’s look at the 9 inch Stellite line and see how this improves the performance of the M3 machine gun barrel. The 9 inch liner is made of a cobalt alloy called Stellite 21. The Stellite / cobalt liner provides two primary advantages over the plain steel barrel. The cobalt liner has a higher heat hardness and is less prone to chemical erosion than the plain steel barrel. The properties of the Stellite / Cobalt liner reduces wear inside the barrel and keeps the grooves (rifling) in the barrel intact. This increases the velocity life of the weapon. Meaning long bursts can be fired through a Stellite /Cobalt lined gun without a reduction in muzzle velocity. The Stellite / cobalt barrel liner is so effective that it actually increased the muzzle velocity of the weapon. The Stellite / cobalt liner is so effective at preventing a drop in muzzle velocity during burst firing, that the limiting factor for burst length is the reduction in accuracy. Since the F-86’s gun barrels have this type of liner. There should be no drop in muzzle velocity for bursts shorter than 350 bullets. The second benefit of the cobalt / Stellite liner was that it reduced the heat input into the barrel. Which helped to prolong the accuracy life of the weapon. Meaning more bullets could be fired through the barrel before the accuracy drops. A 295 continuous burst could be fired through a Stellite / Cobalt lined barrel compared to 167 from a plain steel barrel, for the same loss in accuracy. This is because the cobalt liner is a worse conductor of heat than plain gun steel. Less thermal energy per second is transferred from the Stellite / Cobalt liner into the gun barrel. The Cobalt / Stellite liner reduces the heat transfer into the barrel per bullet fired when compared to the plain steel barrel. A 350 round burst test, on a 50 cal 36 inch aircraft barrel with just the 9 inch liner. Illustrates how effective the Stellite / cobalt liner is in reducing heat input into the steel barrel. The mean barrel temperature was measured to be 750 C after the firing. If we assume an ambient temp of 20c. The temperature of the barrel rose 730C after a 350 round burst. For a 350 burst, The DCS thermal model for the F-86 gun barrel predicts a temperature increase of 2195c. (7.823* 350) / (0.462 * 2.7) =2195C. That’s 3 times more than the test firing of a barrel the cobalt liner. Based on the test data we can compute the thermal energy input into the barrel per shot for a 50 caliber machine gun with a Stellite / Cobalt liner. In game terms we can find the real value for the variable “shot_heat =” Assuming 20 c ambient temperature. The temperature of the lined barrel increased by 730 degrees. Each shot increases barrel temp 2.0857C. Temperature increase per Shot 730/350 = 2.085714 c per shot The energy input into the barrel per shot works out to: Change in Temp =( Joules per shot *Shots fired) /( Barrel Mass * The Specific Heat of the barrel.) Joules per shot = (Temp * ( Barrel Mass * The Specific Heat of the barrel))/ Number of bullets fired. 730=x*350/4.808*.462 730=350x/2.219 x=(730*2.219)/350 = 4.6282 Joules Per shot Testing of the aircraft barrel shows that the energy input into the barrel with the Stellite / cobalt liner is 4.6282 Joules per bullet. The DCS model adds 7.823 Joules per bullet, 1.69 times more than the testing indicates. The reduction in heat transfer to the gun barrel is important because, reducing the temperature input into the barrel improves the accuracy during burst firing. As the gun barrel heats up, it expands. The expansion of the gun bore caused by heating is proportional to the linear coefficient of thermal expansion of the barrel material. Once the temperature of the gun barrel reaches 750c, The barrel expands to the point where the grooves (rifling) in the barrel do not engage the bullet. This causes the bullets to yaw and tumble in flight. Which reduces the accuracy of the weapon. The lack of grooves cut into the bullets 4, 5 and 6, indicate the barrel has expanded to the point where it no longer produces accurate fire. In this test of a plain steel barrel a 100 burst was fired, followed by 2 minutes of cooling. Then a 100 round burst was fired. After the second 100 burst all the bullets from the standard steel barrel begin to impact yawed / tumbled. In a burst test of the Stellite / cobalt lined barrel, the trigger is held down until the bullets begin to tumble and yaw in flight and impact, thus impacting sideways. The Stellite lined gun barrel can fire 350 round before all the bullets impact yawed. In this next series burst tests belts of combat mix ammo were fired. The C-1 schedule is a continuous burst fired until 100 % impact sideways / yawed. The Stellite lined barrel can fire a continuous burst of 295 bullets before the accuracy is degraded. Compared to only 167 bullets for the plain steel barrel. In another set of tests, a Settilte / Cobalt lined barrel was fired until the accuracy was reduced to the same point as the combat mix tests, 100% of the bullets tumbled / “keyholed”. The temperature of the barrel was measured to be 750C when all the bullets tumbled. We’ll use the temperature data from this test and the burst length from the combat ammo test to calculate the heat input per bullet into the plain steel gun and the Stellite / Cobalt lined barrel when belts of combat ammo are being fired. From the temperature monitored heating tests, we get the coefficient of linear thermal expansion of the gun barrel. 16*10^-6 or 0.000016 The coefficient of linear thermal expansion = The change in barrel diameter /( the initial barrel diameter * the change in temperature). This tells us how much the gun has to heat up to expand to the point where all the bullets tumble. The coefficient of linear thermal expansion of gun steel (0.000016) = The increase in barrel diameter due to heating (.006)/ the initial diameter of the barrel(.5) * The change in temperature (750). 0.000016=.006/(.5* 750) This says for the barrel to expand .006 inches the temperature of the barrel has to be 750C. When the diameter of the gun bore expands .006 inches, The bore diameter is greater than the depth of the rifling, the grooves in the barrel. When the bore diameter increases by .006 inches, The groves in the rifling no longer make contact with the bullet. No spin is imparted to the bullet and it tumbles in flight, resulting in a drop in accuracy. Since we know the barrel has to be 750c to expand enough for 100% keyholing to happen: The burst test conducted to 100% keyholing, provides us with a means to make a direct comparison of the two gun barrels. Since we can assume the barrel Temperature of both guns barrels was 750C when the test was stopped. *note the lower burst length in these tests is a result of the ammunition used. These bullets have a larger powder charges / higher muzzle velocity when compared to 50 Cal M2 AP ammunition We’ll compute the energy input per shot for the steel barrel and Stellite / Cobalt lined barrel. Based on the law of linear thermal expansion and the previous testing. We can assume Both barrels were 750c when 100% keyholing / tumbling occured. The coefficient of linear thermal expansion of gun steel (0.000016) = The increase in barrel diameter due to heating (.006)/ the initial diameter of the barrel(.5) * The change in temperature (750). 0.000016=.006/(.5* 750) If we assume that the ambient temperature of the guns was 20 C, We can solve the specific heat equation, to determine the energy per bullet needed to raise the barrel temperature 730c to 750C. Let's look at the steel barrel first and compute the energy input per shot. Barrel Temperature = ( Joules Per Shot * The number of shots)/ (Specific heat * The barrel Mass. 730 =( x * 167) / (.462 * 4.807) Joules per shot = (Temp * ( Barrel Mass * The Specific Heat of the barrel))/ Number of bullets fired. 9.707 = (730 * 2.220834)/ 167 9.707 Joules per bullet are transferred into the barrel when fired from the plain steel gun. The Stellite / Cobalt lined barrel reaches 750c after firing a 295 round burst. Therefore the energy input per shot is (730 * 2.220834) / 295 =5.495 Joules per shot. The Stellite / Cobalt liner reduces the thermal energy transferred into the barrel by 56%. On a per shot basis, the barrel of a Stellite / Cobalt does not heat up as much as a regular steel gun. Therefore the barrel of the Stellite barrel expands less than the regular barrel per shot. Thus over a large burst, the Stellite barrel is more accurate than the plain steel barrel. While the accuracy and velocity life improvements resulting from the Stellite/ Cobalt liner to gun are impressive. The performance of barrels of the M3 machine gun were also improved by their Chromium plating. The development and testing of the Chromium plating is covered in the same NDRC report. The Chromium plating also improved the velocity life and accuracy life of the gun barrel. However Chromium plating primarily improved accuracy of the gun. The Chromium plating of the barrel chokes the bore. Meaning the plating reduces the bore of the gun near the muzzle. The bore of the Chromium plated barrels is reduced from .5 inches near the breech to .492 inches at the muzzle. This reduces the loss accuracy due to heating. Going back to our calculations of the linear thermal expansion of the gun. We can calculate the temperature need to increase the narrow barrel diameter to the original diameter .5 Since the linear coefficient of expansion is intrinsic to the gun barrel material. algebraically we can compute the temperature needed to make the Chromium barrel expanded from .462 to .5 inches or .006 inches Coefficient = material expansion/(Bore of the Gun * temperature of the gun.) 0.000016=.006/(.492* x) Temp = ( expansion / Coefficient * Bore) 762.1951 =.006/(0.000016*.492). In the report it’s noted that the temperature required to increase the muzzle diameter of the plated barrel to .5 inches is 800C Tests of the Chromium plated barrel indicate that 319 consecutive bullets can be fired before the accuracy is degraded. If we assume 800 C is the critical temperature for this accuracy reduction and 319 bullets are fired we can compute the number if Joules per shot fired were fired to reach 800C. Well assume the ambient temperature is 20C and compute the Joules per bullet based on a 780 C rise in barrel temp. Joules per Bullet = ((Barrel Mass * Spec Heat) * Change in Temperature) / The Number of Bullets fired. 5.42 = ((4.807 * .462)* 780) / 319 The accuracy of the Chromium plated barrels was remarkable when compared to the accuracy life of the plain steel barrels. On the same 100 round burst 2 min of cooling schedule. The line barrels can fore over 1000 rounds without a reduction in accuracy. The plain steel barrel, on the same firing schedule, loses accuracy halfway into the second 100 round burst. The chromium plating also helps to reduce the heat input to the barrel, While not as effective as the Stellite / Cobalt liner, it still helps. Temperature monitored tests of the barrel give an indication of the effect. The plated barrel was seen primarily as an accuracy enhancement, While the Stellite / Cobalt lined barrel was seen as velocity enhancement. Since the two improvements were complementary, The Stellite liner was combined with Chromium plated barrel to provide a gun with the best features of both materials. When the Stellite / Cobalt liner and Chromium plated were combine, the barrel was known as a “combination” barrel. The performance of the combination barrels was remarkable. The guns equipped with these barrels, could be fired without a loss of accuracy and minimal velocity drop until the barrel melted. Given the increased performance of these barrels, why does the 50 Cal M3 have a 200 round burst limit? The burst limit is not the result of decreased velocity or accuracy. The burst limit is pure a function of the cook temperature of the ammunition. The manual for the 50 caliber M3, actually notes ``The treatment of the barrel gives it exceptional velocity and accuracy life, but does not affect the cook off point.” A cook off is an uncontrolled firing of a bullet inside of the gun. https://www.smallarmsreview.com/archive/detail.arc.entry.cfm?arcid=13265 The cook off point is temperature in the breach which will cause the bullet to fire on its own, without a trigger pull. The M3 weapons Manual notes that a 200 burst is the cook off limit. The NDRC report gives the temperature above which a misfire / cook off can occur. 900 F = 482C the cook off temp. Using the specific heating capacity of the real gun we can calculate how many bullets in a burst it would take to heat the gun up to 482 C. We’ll assume the ambient temperature of Barrel is 20 C. The barrel reaches the cook off / misfire temperature after a burst of 221 bullets have been fired. As the number of shots fired = ((Barrel Mass * Specific Heat) * delta Temp) / Joules Per shot Assuming the ambient temp of the gun is 20 c. The temp has to rise 462C to reach 482C, the cook off temp. 221.6 = ((4.807 * .462) * 462) / 4.63 By using the test data, we can compute the burst limit within 21 rounds of the limit given within the manual. When we compare the burst limit to the performance tests of the real gun barrels, it is obvious that the burst limit of the F-86’s are not reflective of a performance drop of the guns. f86 gun heat .trk

per the report cited in the OP. The peak power figures come from this Public Canadian radar assessment. https://www.collectionscanada.gc.ca/obj/s4/f2/dsk2/ftp04/mq22118.pdf

Problem : After the GAR-8 is launched, it takes about 2 seconds before the missile will begin to maneuver to intercept the target it is tracking. The GAR-8 in game may also not pull enough G. According to various official sources, The missile should begin to maneuver 0.5 seconds after it leaves the rail and pull up to 12 g. Details Below. The GAR-8 and the Sidewinder B are the same missile. Per the 1971 Air Force Data Sheet for the GAR-8. According to the Declassified 1966 Manual for Sidewinder B the missile should begin to maneuver 0.5 seconds after firing. https://archive.org/details/OP23093rdAIM9B The manual describes the operation of the missile: The Time line for the operation of the missile is as follows. 1. The Trigger is pulled, The seeker gyro / gimbal is unlocked. The seeker has +-30 degree FOV. null And will track the target through +-30 degrees. 2. 0.8 seconds after the trigger is pulled, the missile leaves the rail. The seeker is tracking the target. However maneuver commands are inhibited 3. 0.5 seconds after the missile has left the rail; Steering capabilities are initiated, as command signals are applied to the control servos. The missile will now pull up to 12g's to intercept the target. 21 seconds after launch; Guidance stops as the gas generator burns out. 24 seconds after launch; the missile self destructs. What I think is happening in game is, 1.the missile comes of the rail instantly, 2. maneuvering is prevented until the time of flight is +1.2 to 2 seconds. 3. After 1.2 to 2 seconds the missile begins to track the target. Meaning that, Either maneuvering is being inhibited for too long or the missile is not pulling enough G to intercept after it leaves the rail. The result of the current implementation is; Shots which are within parameters miss, because of the missile is prevented from maneuvering for to long, or wont pull enough to intercept it's target. Attached is a track which illustrates this. In this mission I've attached a 4000 foot zone to a non maneuvering MIG 15. Shooting from within 4000 feet will give the missile a time of flight of 1 to 2 seconds depending on the closure rate. When firing the GAR-8 with good tone, within 4000 feet, and within the seekers +-30 degree FOV, the missile will not track. Kills can be achieved but the missile has to be ballistically aimed. IE it functions like a rocket with a proximity fuse. In closing, the GAR-8 should be pulling up to 12 g's 0.5 seconds after it leaves the rail. Gar 8 test.trk

https://www.enginehistory.org/Turbochargers/TSCtrlSys/TSCtrlSys1.shtml The regulator has 2 pressure bellows. The top bellows is exhaust pressure + ambient pressure. The bottom is a vacuum or partial vacuum. With the boost lever forward , at sea level and the waste gate open, and therefore, zero tubro RPM. The force acting on the regulator to keep the waste gate open is ambient pressure . As ambient pressure drops, the waste gate closes and the tubro RPM increases. Maybe you can just 64 inches of manifold with water injection alone. Edit, Looks like the water injection system bias the tubro regulator to allowing the tubro to spool at low alt.

They in the encrypted Database files. https://github.com/Quaggles/dcs-lua-datamine/tree/master/_G/db/Units/Planes/Plane

There two drivers of the MiG 15's characteristics. The handling qualities and the basic aerodynamics. The Soviet Technical Manual for the MiG 15, linked above, notes some interesting handling qualities. Aspects of the handling qualities could make the aircraft dangerous for poorly trained pilots, who might be unaware of it's quirks. In the high transonic regime. Roll and pitch handling qualities change quite dramatically. At mach .82 alieron effectiveness drops rapidly to zero at mach .85. They then enter an area of reverse command until mach .95 Stability issues are noted above Mach .92. However they can be counteracted by ~5 degrees of alieron. Also, as mach increase the force to command more g increase above mach .86 Notably the amount of elevator per G required reduces from mach .72 to mach .88. Aerodynamically the MiG 15 is pretty well designed. The designers went to a fair bit of trouble to ensure the aircraft was stable and paid some performance penalties to do so. To compensate for the roll stability, the wing was given anhedral, angled down. This done to increase the roll rate of laterally stable aircraft. However, anhedral lowers the lift a wing generates. As the lift is a function of the cosine of the dihedreal angle ^2 times the angle of attack and the lift curve slope of the airfoil. The wing fences reduce spanwise flow as the angle of attack increases. This prevents the wing tips from stalling before the root. Which prevents adverse yaw at high angles of attack. It also increase alieron effectiveness at high angles of attack. This makes the aircraft much more stable and safe. However the fences reduce the over Cl max of the wing. The result was an aircraft that was not prone to spinning at high angles off attack. To get the aircraft to spin you have to apply opposing alieron and rudder inputs. just like in DCS. Lets go back to alieron handling and see how this could get deadly fast. First, entering high angles above mach .86 may cause the aircraft to spin, as uncommaned roll begins to occur. At the same time ailerons lose effectiveness and reverse at high mach. If you try and oppose inadvertent roll with alieron and rudder inputs, you are now inputting the only control combination which spins the jet. Which is why the spin and roll correction techniques call for stick neutral. The version of F-86 in DCS is also not without it's handling issues either. DCS models the non- slatted F-86 F with the "6-3" wing. The 6-3 wing was designed to increase the maximum lift coefficient of the aircraft while reducing the drag. However this version of the wing was noted for a rapid reduction in lift and being longitudinally unstable post stall. https://ntrs.nasa.gov/citations/19930087007 evidenced of this instability is noted in the pilots manual too. The 6-3 wing, without slats, also tended to roll at the stall. The small fence installed on the wing was an attempt to elevate this issue. https://ntrs.nasa.gov/citations/19930087699 However the fence also reduced Cl max of the aircraft from ~1.4 to ~1.2. https://hdl.handle.net/2027/mdp.39015086432781?urlappend=%3Bseq=8 The slatted version of the 6-3 wing gave the Sabre a higher Cl max than fenced non slatted, A gentler stall and reduced rolling tendencies at the stall. Which is why Sabre went to a slatted 6-3 wing. https://ntrs.nasa.gov/api/citations/19930089460/downloads/19930089460.pdf The F-86's pilots manual also seems to indicate this also reduced the stability issues.

FA-18A.lua has the old Cl Max of 1.2 FA-18C.lua has the old Cl Max of 1.2 FA-18C_Hornet.lua has a Cl max of 2.4

The uncommanded roll is modeled. It's mentioned in the DCS MiG-15 Manual, section 9.1.5. However this is not present in the AI aircraft as they use the simple flight model. From the Manual. "The DCS: MiG-15bis model features a randomized wing rigidity calculation. As such, the specific airspeed, at which uncommanded roll occurs, and its intensity depend on flight conditions, however the direction of the roll condition (left or right) is randomized with each aircraft "spawn". "Uncommanded roll can occur at high flight speeds throughout the altitude envelope. At altitudes below 4000 m, this can occur at TAS greater than 1070- 1090 km/h (small needle on the airspeed indicator). As altitude increases, the true airspeed, at which uncommanded roll can occur, decreases. At altitudes above 11000 m, the true airspeed, at which uncommanded roll can occur, stabilizes in the 1010 - 1090 km/h range." "Applying opposite pedal during uncommanded roll at speeds of Mach 0.86 and greater in an attempt to correct the effect can lead to increased roll rate and significant lateral stick force. Roll can be reduced in this case by carefully applying pedal in the direction of the roll. For example, if uncommanded roll is to the left, apply slight left pedal or if uncommanded roll is to the right, apply slight right pedal. " The go to source for aerodynamic data on the MiG-15 seems to be. МиГ-15бис. Техническое описание. Книга I. https://www.digitalcombatsimulator.com/en/files/2365583/ It does show a loss of alieron effectiveness at high mach high angle of attack situations. At Mach .86 at 15 degrees of AOA the ailerons alone can not counter act the roll tendency. Some rudder would be needed. Just like the DCS manual says

It looks like a change to lift coefficient in the simple flight model also increased the drag 6 times. Resulting in degraded performance. In the last patch, the Cl max in Simple Flight Model for the F-18C was doubled. It went from 1.2 to 2.4. This also caused the drag to increase. In the SFM the drag is computed directly from the lift. The drag computation is given as: Cx = Cx_0 + Cy^2*B2 +Cy^4*B4. Where B2 and B4 are coefficients also defined in the SFM. Cx is the drag and Cy is lift coefficient. Previously Cl max was capped at 1.2. it is now 2.4 This meant the drag at Cl max with flaps was Cx = (Cx0 + Cx Flaps) + (Cy^2*B2) + (Cy^4* B4) The old SFM F-18C, at mach .2 at CL max, 1.2, with the flaps down, had a drag coefficient of .584 Cx .584 = (Cx0 .0154)+ .(Cx Flaps. 23) + (Cy Max 1.2)^2*(B2 .134) + (Cy max 1.2)^4* (B4 .056) The new SFM at Cl max, 2.4 with flaps down has a drag coefficient of 2.905 Cx 2.905= (Cx0 .0154)+ .(Cx Flaps .23) + (Cy Max 2.4)^2*(B2 .134) + (Cy max 2.4)^4* (B4 .056) The previous version, Cl max of the F-18C was capped at 1.2 it is now 2.4. Based on the the ratio of Cl to alpha as defined in the SFM; If the current SFM F-18C goes over 13.8 AOA with the flaps down, then it will have more drag than previous previous version of the SFM F-18C was capable of producing.

It's both. The bullets have to much drag and the barrel heating penalties (accuracy and velocity drop) are to high. However the MiG-15 also has issues with it's armament. The 23mm HEI shells don't fire. So the 23mm cannon only has half the ammo. 40 rounds not the 80 it's supposed to have. Also, the 23 mm AP rounds have their caliber set to 37 mm. Which I assume was a hack to get the 23 mm cannon to work.

I also noticed that the 23 MM HEI shells don't seem to be firing. Perhaps because their caliber is set to 23mm and there is some type of engine limit that prevents aircraft from having multiple caliber weapons. I tested it by placing a static on the runway and firing the 23mm guns only. No 23mm HEI shells show up in the logs. Only API Rounds.trk The 23 mm HEI should show up in the logs as user_name = "23mm HEI T", based on the shell table entry. The API do appear in the logs. They match their reporting name as defined in the shell table. user_name = "23mm API" However the 37 MM HEI shells seem to be working. Tested by firing on a static with only the 37mm firing. The HEI rounds show up in the logs. 37 MM API and HE Rounds.trk It may be, that the 23 mm shells need to have their caliber also set to 37mm for them to work too. Right now the 23 mm HEI have their caliber set to 23mm. In the files it looks like this. AP_cap_caliber = 23, Da0 = 0.0007, Da1 = 0, Dv0 = 0.005, _file = "./CoreMods/aircraft/MiG-15bis/MiG-15bis.lua", _origin = "MiG-15bis AI by Eagle Dynamics", _unique_resource_name = "weapons.shells.NR23_23x115_HEI_T", caliber = 23,

One of the shells that MIG 15 uses is the "NR23_23x115_API.LUA". Has the caliber is set to 37, not 23. Not sure if it effects any of the modeling. Just thought I would bring it your attention. First in the shell table. weapons_table/weapons/shells/NR23_23x115_API.lua NR23_23x115_API.lua ["weapons_table"]["weapons"]["shells"]["NR23_23x115_API"] = { AP_cap_caliber = 37, Da0 = 0.0007, Da1 = 0, Dv0 = 0.005, _file = "./CoreMods/aircraft/MiG-15bis/MiG-15bis.lua", _origin = "MiG-15bis AI by Eagle Dynamics", _unique_resource_name = "weapons.shells.NR23_23x115_API", caliber = 37, Then in db/Units/Planes/Plane/MiG-15bis.lua }, <6>{ AP_cap_caliber = 37, Da0 = 0.0007, Da1 = 0, Dv0 = 0.005, _file = "./CoreMods/aircraft/MiG-15bis/MiG-15bis.lua", _origin = "MiG-15bis AI by Eagle Dynamics", _unique_resource_name = "weapons.shells.NR23_23x115_API", caliber = 37, Also in Eagle Dynamics\DCS World\CoreMods\aircraft\MiG-15bis\MiG-15bis.lua declare_weapon({category = CAT_SHELLS,name = "NR23_23x115_API", user_name = _("NR23_23x115_API"), model_name = "tracer_bullet_crimson", v0 = 680, Dv0 = 0.0050, Da0 = 0.0007, Da1 = 0.0, mass = 0.199, round_mass = 0.340+0.071, -- round + link cartridge_mass = 0.0, -- 0.111+0.071, cartridges are ejected explosive = 0.000, life_time = 5.0, caliber = 37.0,

The correct Muzzle Velocity for the M2 AP should be 2,840 FPS, 865 MPS. The reduction in accuracy and velocity due to barrel heating should be reduced to reflect the qualities described in weapons manuals. Possibly replaced with either a cook off event or a jam. With regards to the correct muzzle velocity for these rounds. The manual for the AN-M2 and AN-M3 both give the same muzzle velocity for the various rounds. From the 1947 version of the AN-M2 manual, TM9-225 1947. http://www.nj7p.org/Manuals/PDFs/Military/TM 9-225 28-Jan-47 Google.pdf The AN-M3’s ammo table and muzzle velocity from the 1955 version of the AN-M3 manual, TM 9-2190 Both manuals also refer to the same document, which provides the ballistic profile of the ammunition. Ballistic Data Performance of Ammunition TM-9-1907 https://ia800909.us.archive.org/22/items/TM91907BalisticDataPreformaceOfAmmunition/TM%209-1907%20Balistic%20Data%20Preformace%20of%20Ammunition.pdf A cleaner version of this chart is available in https://cgsc.contentdm.oclc.org/digital/collection/p4013coll8/id/2374 TM 9-1907 also gives the muzzle velocity as 2,835 FPS. So this appears to be the correct muzzle velocity for M2 AP round. However, in some of the literature, the muzzle velocity is quoted as 2700 fps. This lower velocity 2700 fps comes from 1940 version of the AN-M2 manual -TM 9-225 https://ia601208.us.archive.org/21/items/TM9-225/TM9-225.pdf It gives the velocity of the M1 AP Round as 2700 fps at 78 feet. Then in 1942, the revised TM 9-225 manual states muzzle velocity for the M2 AP round is 2900 fps. https://digital.library.unt.edu/ark:/67531/metadc29988/m1/50/ It appears the correct muzzle velocity for the M2 AP rounds is 2840 FPS, As the most current sources list it. On burst length. The manuals for both guns, indicate barrel heat affects 4 aspects of the guns performance, velocity, accuracy, stoppage, and cook off. The 150 round limit cited before, a 11 second burst, is the stoppage limit (the gun locks up) of the AN-M2, due to overheating. There is also a burst limit due to the possibility of a ammunition cook off. That is, the rounds heating up to point where the powder charge ignites and causes inadvertent firing. For the AN/M3 the 200 rounds burst limit is due to the possibility of a cook off, not a reduction in accuracy or velocity. The reduction in accuracy or velocity due to barrel heat occurs at different temperatures. The accuracy reduction is referred to as Key-holing in the manual. The AN/M2 manual notes, the circumstance in which the accuracy is degraded separately from the conditions that result in a reduction of the bullet’s velocity. The conditions depend on the barrel type and the number of rounds fired.. The 50 Cal AN/M3 has a plated and lined barrel and the ammo is more likely to cook off, before the velocity and accuracy are reduced. As the cook off limit is 200 rounds and the accuracy degradation occurs at 300 rounds. The maximum burst length before there is a reduction accuracy, is 300 rounds. This should happen without a reduction in velocity. The AN/M3 manual also notes that the operating parameters described are for temperate conditions at low altitude. So perhaps the increase in barrel temp can be reduced to reflect operation at high altitude.

The drag on the bullets the Sabre uses are to high. The F-86 uses the bullets as defined in the lua files as. shells = {"M2_50_aero_AP","M20_50_aero_APIT"}, mixes = {{1,2,2,1,2,2}}, -- In the shell table the drag currently is defined as M20_50_aero_APIT.lua cx = { 0.5, 0.61, 0.8, 0.27, 2 }, M2_50_aero_AP.lua cx = { 0.5, 0.61, 0.8, 0.27, 2 } The variables are defined as. -- Drag (Сx) = { 0.5 , -- Cx_k0 Cd0 at low mach ( M << 1) 0.61 , -- Cx_k1 Peak Cd0 value 0.8 , -- Cx_k2 steepness of the drag curve before the transonic wave crisis 0.27, -- Cx_k3 Cd0 at high mach (M>>1) 2 , -- Cx_k4 steepness of the drag curve after the transonic wave crisis } Drag profiles for all the rounds are available from primary sources. Primarily, the US Ballistic Research Lab. The first two drag profiles are from the Ballistic Research Lab's 1990 range test. "The Aerodynamic Characteristics of .50 Ball, M33, API, M8, and APIT, M20 Ammunition. By Robert McCoy. https://apps.dtic.mil/dtic/tr/fulltext/u2/a219106.pdf Lets start with the API M8 Then The M20. Finally We have a drag profile for the M2 AP round. This chart is in older format Kd. However this can be converted to the standard notation for the Drag Coefficient Cd / Cx. The conversion is Cd = (8/Pi) * Kd The method is given in McCoy's work. The drag profile is from Report 620, Aerodynamic Data for Spinning Projectiles” H.P. Hitchcock Ballistic Research Laboratories, Aberdeen Maryland 1947. https://apps.dtic.mil/sti/pdfs/AD0800469.pdf From the chart, peak drag occurs at Mach 1.2 and the Kd is ~ .161 Converting using McCoy Cd = (8/Pi) * .161 Cd = .4099 At mach 2 the Kd is = .14, therefore the Cd = .35 The slope of drag curve at Mach > 1 is = .4 - .35 / .8 = .05 The drag at low Mach is ~.078 Kd = .1985 Cd The slope of the drag profile before area transonic appears flat. Therefore the drag for the rounds should look more like, M2_50_aero_AP.lua cx = { 0.198 0.4, 0.0, 0.4, .05 }

This is from 1995, I dont know if the accuracy has been increased since then. https://apps.dtic.mil/sti/pdfs/ADA299307.pdf

https://ndiastorage.blob.core.usgovcloudapi.net/ndia/2005/garm/tuesday/siewart.pdf https://www.academia.edu/32755624/Phalanx_Block_1B_CIWS_Ready_For_The_Fleet_