Hit Probability, Rate of Fire Muzzle Velocity

[Jabberwocky]

Jabberwokcy,not sure what planet your are one

from:8th Air Force Combat Losses in World War II ETO Against the AXIS Powers
Other losses occurred too. Collisions, training accidents and so on. The table below summarizes all losses in the ETO during the war:

Aircraft Type Number Lost
B-17 4,754
B-24 2,112
P-47 1,043
P-38 451
P-51 2,201
Total 10,561

RoFL

The war consisted of more than the USAAF, and more than the 8th AF, or did you forget the 15th AF, 9th AF and the entirety of the RAF?

US losses in ETO and MTO:

Heavy Bombers:
ETO: 5,548
MTO: 2,755

Light/Medium Bombers:
ETO: 815
MTO: 808

Fighters (just for fun):
ETO: 5,324
MTO: 3,157

Total of 18,418 losses in combat missions in theatres vs Germany, of which 7250 are directly attributed to action by enemy aircraft.

RAF bomber losses: 10,734, of which 9,130 were attributed to enemy action (fighter/flak) or lost on operations.
Heavy bomber losses: 6,150

 

[bruno_]

The rule "the higher the MV the lower the dispersion" (that is the same of "lower MV = higher dispersion") is not general, I guess. Once the bullet has leaved the barrel, the higher MV the lower the influence of any external factor: no point. But, if an higher MV is gained by increasing the launch charge, then the bullet momentum (m*MV where m is the bullet mass) is greater. This implies the same for the gun recoil. This stuff cannot have a nice impact on the dispersion since the greater recoil, the greater the dispersion, "all other factors being equal".
Therefore, if and only if the MV increase doesn't imply an increase of the recoil (bullet momentum), both internal and external ballistics work together for reducing dispersion. But this can be obtained by reducing (significantly maybe) the bullet mass and this adversely affects other important ballistic performances of the bullet: effective range, rate of energy bleeding, residual momentum on target, etc. etc.
In all remaining situations (MV and m*MV increase), since a greater recoil implies a greater "at the muzzle" dispersion, it is hard to say if the overall effect of a greater MV is, actually, a lower dispersion. It could easily happen just the opposite. IMHO, of course.

 

[tomo pauk]

ROF has no real affect. MV does, lower MV = higher dispersion

Any sources that could back the two claims?

 

[Shortround6]

There may be some confusion of terms or bad translation.

Muzzle velocity has very little to do with dispersion IF by dispersion we mean the group size or area we can expect the vast majority of projectiles fired from a single gun ( or group of guns? ).

Getting that group or target area to coincide (overlap) the desired target ( aircraft, vehicle, road, gun emplacement, etc) is where a higher Muzzle velocity helps. There will be much much less time for external forces (like cross winds, target movement or bad range estimation) to push the group/impact area to one side or up/down in relation to the target.

For example saw we have two guns, both will place 75% of rounds fired in a 6.6 ft ( 2 meter) circle at 400 meters but Gun "A" has enough velocity that it's time of flight to 400 meters is 1/2 that of gun "B". Both guns had the same dispersion but obviously have rather different abilities to hit a moving target at 400 meters. Say, for arguments sake, there is a 30mph cross wind. Gun "B"s projectiles will be blown much further to one side of the target than gun "A"s projectiles BUT 75% of gun "B"s projectiles will still impact in an area 6.6ft (2 meters) across. Obviously against a moving target gun "B" will require a much greater lead (aim off) in order to hit.

Low Muzzle Velocity can increase miss distances for a number of reasons but miss distance is NOT dispersion.

 

[Glider]

ROF has no real affect. MV does, lower MV = higher dispersion

Not according to my instructors
MV for a weapon has no effect as all the procectiles ae subject to the same forces for the same amount of time. It will make a difference if you are comparing two different weapons, but the other forces such as drag also have a significant impact. A higher MV does not guarantee a lower dispersion or a longer range.

ROF can have an efffect depending on how well the gun and its mounting are designed. Its possible for some of the forces to still be in the weapon/mounting if they are not dampened. There are other factors such as heat build up/dissipation. The higher the ROF the higher the chances of these factors coming into play agaiin depending on the design.

If you could point me in the direction of some supporting paperwork it would be appreciated. I hate to think that what I have been teaching is so wrong.

 

[bruno_]

About the crosswind:
Just to be sure we are considering it in the same way, here are my observations:
If we refer to combat situations where the distance between the attacking aircraft, the bullett and the target aircraft are in the range of 500m, the attacking aircraft, the bullet and the target fly into the same "atmosphere". Therefore any wind is, reasonably, the same for any flying object in that bit of world. Therefore the only extra influence that can act on the bullet but not on the aircrafts is the wind velocity component that is transversal with respect to the bullet rotational axis. This component is responsible for the Magnus effect on the bullet that can change its flight path. The Magnus effect is a force and its effectiveness in changing the bullet path depends on bullet momentum (m*MV). The higher the bullet momentum, the lower such an influence. Thus, again, don't forget the role of the bullet mass m. The Magnus effect depends on the rotational speed of the bullet. For the same number of barrel rifles and for the same barrel length, the higher the MV, the higher the rotational speed and the higher the Magnus effect for the same wind.

About the ROF: Again, it is a matter of gun recoil, IMHO, and how good the gun mounting is. Thus, for the same gun position and mounting it is reasonable that "the higher the ROF, the higher the dispersion"

Finally, I confirm, that in my mind, dispersion is a measure of the area where we can find the large majority (some say 75%) of bullet shot from the same weapon, at a given distance. The greater this area the greater the dispersion.

 

[zjtins]

Lower MV = longer flight the time the longer the flight time the more other factors influence the flight. The closer the target the shorter flight the less dispersion, longer flight more hence MV matters.
It is flight duration that matters, distance is a component of duration, just like MV, drag, etc.


ROF only matters if the gun mount resonates (is compliant) to a significant degree.

 

[Glider]

Can I ask what your experience is of ballistics or what source you use to support this wild theory as its total rubbish.

You were talking about dispersion which from a weapon of the same type will not differ as all the shells will be subject to the same forces for the same length of time. Its a simple concept, what do you find difficult to understand about it.

 

[zjtins]

I am in an avionics systems engineer. I know flight paths, control laws. Other than rotation a round follows the same aerodynamic laws. They do not change just because it is a bullet. A ballistic path reacts to every force places on it, and every bullet does not experience the same set of forces. Dispersion measured on the ground on a stationary mount and stationary relative target is the not the same dispersion in a fighter. Also in the 80's I worked on Firefinder so yes I know something about ballistics.

 

[Glider]

Clearly you don't and you clearly don't have a source for that statement or you would have quoted it.

 

[Shortround6]

I am in an avionics systems engineer. I know flight paths, control laws. Other than rotation a round follows the same aerodynamic laws. They do not change just because it is a bullet. A ballistic path reacts to every force places on it, and every bullet does not experience the same set of forces. Dispersion measured on the ground on a stationary mount and stationary relative target is the not the same dispersion in a fighter. Also in the 80's I worked on Firefinder so yes I know something about ballistics.

It sure doesn't show.

Dispersion is the measure of how far the bullets/projectiles will stray from the intended ideal aiming point, as in Gun XX using ammo YY has a dispersion of 0.5 minutes of angle at 600yds. There are a number of things which can displace the center of such a group of shots or pattern of dispersion from the desired aiming point or desired impact point. Bullets fired 1/10 of second apart are going to have very similar forces acting on them once they leave they gun barrel. As in a strong cross wind dispacing ALL of the bullets 5-6 minutes of angle to the left or right but ALL the bullets will still be in that 0.5 minute area if the cross wind was constant for each bullet fired.

A high muzzle velocity can help minimize the effects of these external forces that are displacing the "group" but high MV doesn't do a thing either for or against the actual size of the "pattern of dispersion" (group size) with the type of guns we are talking about.
I have been a target shooter for over 40 years and have competed at in some matches at 1000 yds and observed shooters using black powder rifles at over 500 yds.

I have two rifles that require the cartridge cases to be formed from other cases ( you cannot buy them) so I think I have some idea of ballistics.

 

[bruno_]

It sure doesn't show.

Dispersion is the measure of how far the bullets/projectiles will stray from the intended ideal aiming point, as in Gun XX using ammo YY has a dispersion of 0.5 minutes of angle at 600yds. There are a number of things which can displace the center of such a group of shots or pattern of dispersion from the desired aiming point or desired impact point. Bullets fired 1/10 of second apart are going to have very similar forces acting on them once they leave they gun barrel. As in a strong cross wind dispacing ALL of the bullets 5-6 minutes of angle to the left or right but ALL the bullets will still be in that 0.5 minute area if the cross wind was constant for each bullet fired.

.....

This is the very concept of dispersion! Totally agree.

As to the crosswind, if the shooter and the target don't move, the crosswind has an influence (beside the Magnus Effect) on bullet only. Even if shooter and target move with respect to the ground, crosswind is relevant. In an air toair duel, as I pointed out in my previous post, crosswind, that is the way a bit of atmosphere moves with respect to ground, has the same effect on shooter, target and bullet (beside the magnus effect) and, since all three elements have no relative crosswind, crosswind is ineffective (again, beside the magnus effect operating on the bullet). Shooter, target and bullet are simply immersed in the same "inertial reference frame" that is moving at the crosswind speed with respect to the ground.


Finally, about resonance of gun and its mounting: if resonace occurs then dispersion increase but, even with an infinitely stiff mount, dispersion is "on" since the gun itself has a number of "internal" oscillating modes.

 

[zjtins]

Wrong dispersion is the variance from the center of the distribution. If the aim is off you get the group mean at a point where the group dispersion is centered. Dispersion has nothing to do with aim. It is the measure of distribution around the center of the group.
1. 3 bullets fired form a perfect equilateral triangle around a target, but are a distance from it.
2. 3 more bullets form a perfect equilateral triangle but off the side of a target
3. 3 more bullets form a perfect equilateral triangle but 1/3 the size of the triangles in 1 and 2 and further away from the target.
4. Same as 3 but center on target.
Dispersion of 1 and 2 are equal, 3 is 1/9 of 1 and 2.
Accuracy of 2 and 4 are the same, their mean is both centered on the target.

As to the crosswind, if the shooter and the target don't move, the crosswind has an influence (beside the Magnus Effect) on bullet only. Even if shooter and target move with respect to the ground, crosswind is relevant. In an air toair duel, as I pointed out in my previous post, crosswind, that is the way a bit of atmosphere moves with respect to ground, has the same effect on shooter, target and bullet (beside the magnus effect) and, since all three elements have no relative crosswind, crosswind is ineffective (again, beside the magnus effect operating on the bullet). Shooter, target and bullet are simply immersed in the same "inertial reference frame" that is moving at the crosswind speed with respect to the ground.

So you say a crossing shot is not effected by wind.
The only time you hypothetical situation this would occur is ever there are no air currents, no clouds, no temperature inversion layers, no moisture changes and the planes were flying in straight lines and the trail plane is directly being on the same vector.

Dont believe me go and take around 4 college level courses of flight dynamics because I am not going to do the math for you.

http://asc.army.mil/docs/pubs/alt/2011/3_JulAugSep/articles/67_Accuracy_in_Armaments_201103.pdf

Go ahead have at it. Army arty dispersion calculations

 

[Shortround6]

http://asc.army.mil/docs/pubs/alt/2011/3_JulAugSep/articles/67_Accuracy_in_Armaments_201103.pdf

Go ahead have at it. Army arty dispersion calculations

Wrong, Army Small arms dispersion calculations, NOT "arty".

 

[Matt308]

Easy guys.

 

[zjtins]

Just giving a lesson to those who do not understand

 

[zjtins]

Wrong, Army Small arms dispersion calculations, NOT "arty".

You got me oh my hahahaha, and your point?

 

[bruno_]

My point is: wind is speed of air with respect to ground. Objects flying into a bit of atmosphere that is moving with respect to the ground don't feel any cross-wind. All of them are "displaced" with respect to the ground by the same amount of wind effect. This is why I say that crosswind has no influence in air to air combat when distances between the two aircrafts are so close to assume that atmospheric conditions are the same for both of them. IMHO, of course.

 

[Shortround6]

Sort of.

Once the bullet leaves the barrel it is on it's own. No course correction

Normal ground speed winds are going to have little effect at ranges of 200-300yds. At higher altitudes the air thinner but often faster.

Bomber gunners however had some real problems,a plane coming in from the beam presented a real challenge as the crosswind to the gun is now the forward speed of the bomber, at least for the first moments of flight. Granted the bullet leaves the barrel with the aircraft forward speed as a side velocity component but while the bomber and fighter both are adding energy from their engines to maintain their courses the bullet cannot and and falls 'behind' the relative positions of the two aircraft.

 

[tomo pauk]

The bigger the RoF, the movement/vibration of the gun, mount and airframe is increased, hence increasing the grouping? The greater muzzle energy, the greater recoil (in most of the practical examples) - the story from the 1st sentence repeats?