azimuth angle of guns seems off / convergence

[Curly]

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. 

Edited December 16, 2022 by Curly

[Yo-Yo]

There were several harmonisation patterns for P-51.  I see, you use 71.25/79.25/87.25 at 1000" boresight figure.
We used the different one.

 

[Nealius]

Which different one, specifically, was used?

[Curly]

On 12/16/2022 at 6:50 AM, Yo-Yo said:

There were several harmonisation patterns for P-51.  I see, you use 71.25/79.25/87.25 at 1000" boresight figure.
We used the different one.

 

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

Spoiler

 

 

 

 

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

 

Edited December 18, 2022 by Curly

[Curly]

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

Spoiler

The pattern.

Spoiler

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

 

Edited December 19, 2022 by Curly
formatting