Hit Probability, Rate of Fire Muzzle Velocity

[bruno_]

Just a remark: the bomber gunner perspective is, imho, different from the crosswind. In the gunner case, any azimuth and elevation of the gun (barrel axis) with respect to the velocity vector of the gunner aircraft implies that, at the very moment the bullet leaves the gun, it has already a direction which is different from the barrel axis. This asks for an extra correction with respect to the "fighter" deflection shooting, where, generally, fixed guns are aligned (more or less) to the aircraft axis and, thus, they were aligned (more or less) to the own aircraft velocity vector. This effect would be there even without atmosphere (and therefore no atmospheric wind).

To cope with the general case of the "own speed" problem, special aiming devices where developed since the WWI (the weathercock approach) and some guns of some WWII bombers still featured these devices. Later on, more sophisticated reflector gunsights (gyro etc mainly in Allied air forces) were able to correctly indicate the aiming point even in the general case of a bomber turret or waist action stations.

Anyway if we prefer to refer to the own speed as crosswind, then it is clear that this crosswind has an effect and then, the higher the "intrinsic" MV, the lower the correction for the own speed with respect to the weapon line of sight (barrel axis).

 

[bruno_]

I'd like to submit here something "odd" just to check if you consider it worth to be worked out or not. Please be patient for some math, I tried to keep it to the minimum.
Imagine you are a perfect marksman (no aiming errors) and, for the sake of simplicity, you are in the perfect position behind the target (dead six). Both target and your plane fly at the same constant speed along a straight path. The distance between the two planes is D. Finally let us neglect the effect of drag and gravity so that once fired, the bullet moves along a straight line at a constant MV relative speed with respect to the target.
If all this stuff is true, the time the bullet takes to reach the target is TOF=D/MV. If ROF is the rate of fire (bullets per seconds) the time between two successive bullets on the target is Delta_T=1/ROF.
Imagine now that, in the very moment you start firing, the target starts maneuvering to avoid your bullet stream. That is, the target starts to move away (horizontal, vertical, a combination, in a word, "lateral" move) from the impact point. If we assume that the "lateral" acceleration is A m/sec^2, then, according to the basic law of motion of a "body" under the action of a constant acceleration, the distance of the target from the impact point at the time T is given by S=0,5*A*T^2.
The lateral spacing between the aimed impact point and the target, after TOF seconds will be S=0,5*A*(D/MV)^2 and, after each further Delta_T seconds, the spacing from the stream of bullets will be increased by Delta_S=0,5*A*(1/ROF)^2 meters (while firing your "short" burst you don't change the aiming point).
What is, IMHO, worth noting now is the fact that both MV and ROF are "squared". Therefore, for the same maneuvering capability of the target, an higher MV (and or ROF) seems to play a "more than proportional" role in the Hit Probability game. That is, if we compare two guns with two different MV (MV1 vs MV2) and or ROF (ROF1 vs ROF2) , the ratios between the corresponding target " escape" spacings S2 and S1 are proportional to (MV1/MV2)^2 or (ROF1/ ROF2)^2. If " the lower the spacing the higher the Hit Probability" assumption holds (*), then the square of the ratios between different MVs or ROFs should play a role.

(*) Bullet dispersion distribution is not uniform. For the same target "cross-section", as its distance (lateral displacement) from the aiming line increases, the bullet density decreases thus the cumulative probability of hitting the target decreases. Imagine this cumulative probability (HP actually) changes, more or less, as the inverse of the distance from the aiming point. Stating that HP is proportional to 1/S (the inverse of lateral spacing) means HP is proportional to (2/A)*(MV/D)^2: if the target is moving away with a constant lateral acceleration, then, doubling the MV will imply a ¼ factor for the displacement and a factor 4 for HP. Finally Aircraft aren't spherical or ellipsoidal objects. Thus maybe the geometry could play a role in decreasing the HP more "quickly" than assumed, as distance of target from the aiming point increases. If this is true, then increasing the MV could have an higher than "quadratic" effect in increasing HP. By the way, if this last assumption holds, even for targets moving away at a constant speed (typical of deflection shooting against unaware targets), the MV increase would have a more than a proportional impact.
Some remarks on target acceleration/size and shooting distances:

Obviously the amount of acceleration plays a key role: an heavy bomber is quite slow both in terms of speed and acceleration. Shooting at these big and slow things is a job were MV could not be the primary feature to improve if HP were the point. Small&nimble fighters are a totally different affair. This suggests that "actual" quantitative links between HP and MV and/or RoF may depend on target features so that war reports/studies and weapon design guidelines could have been influenced accordingly.

Of course, shooting distance plays a fundamental role. At very close shooting distance from big targets, the above mentioned effects are negligible and for a wide range of MV the HP doesn't change at all: most of the bullets would hit the target anyway. At very high shooting distances, the bullet density is so low that even doubling or tripling the HP means doubling or tripling something that is desperately close to zero. But, if the basics I described have some ground, practical values of HP could reasonably depends more than proportionally on MV (and ROF), for an "intermediate" range of shooting distances.

"Conclusions"
The proposed scenario is definitely basic and relies on several hypotheses. No "claim" to accurately model the actual combat scenario by too simple relations; just the attempt to inject some new elements and see if they have some chance to survive the criticism.

 

[zjtins]

I am back.

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.

Negative, wind sped vectors are relative to the moving object, ground speed is irrelevant (to flight). Hence the terms true sir speed vs ground speed in aviation.

Bruno you are a better man than I your writeup is spot on.


ROF has no impact on flight and it only affect is distance between bullets can be calculated for any ROF (assuming a rigid enough mount). Or said any other way vary the fire rate you have the same dispersion and average if the mount is rigid enough. Some aircraft in WWI did not have sufficiently rigid mounts and were modified at times to rectify this problem.

 

[tyrodtom]

Bruno, I think that is the best bunch of gooblygook i've ever read in a long time.

You need to get a job with one of the political parties.

 

[bruno_]

Dear tyrodtom, in spite of my limits, Politcs doesn't attract me. So, I'm sorry, but my destiny is to go on with my posts here. At least for a while.
That said, I'm sorry but I've not understood if, after the painful reading of my last post, you think that the side move of the target and its dependence on the square of the bullet time of flight is or not a good basis for a more than proportional contribution of MV to the Hit Probability.

 

[bruno_]

Dear tyrodtom, in spite of my limits, Politcs doesn't attract me. So, I'm sorry, but my destiny is to go on with my posts here. At least for a while.
Beside this, I've not understood if, after the painful reading of my last post, you think that the side move of the target and its dependence on the square of the bullet time of flight is or not a good basis for a more than proportional contribution of MV to the Hit Probability.

 

[tyrodtom]

Really, you're missing out on your true calling.

 

[DerAdlerIstGelandet]

Keep it civil...

 

[bruno_]

Dear DerAdlerIstGelandet if someone will kindly tell me if and where I'm wrong about my hypotesis, I'll be very happy since I'm looking for contructive discussion and criticism. If I wrote something unpolite, please tell me. Maybe I've missed some point. Thanks in advance.
By the way, sorry for my previous "double posting"

 

[DerAdlerIstGelandet]

Did I say you wrote something unpolite? It was a general statement to both of you.

 

[zjtins]

What Bruno wrote could be straight from a text book.

 

[tyrodtom]

It was me that was being impolite.
I think you've complicated needlessly something that's no that hard to understand.

The more bullets you shoot at the target when he's manuvering, the more likely you are to hit him.

There can be no equation for it because there's endless varibles.

Some weapons have a greater ROF, but have a lower muzzle velocity, or fire lighter bullets sometimes depending only on their stored kinetic energy to destroy. But sometimes the projectiles have explosive energy, and depend less on just impact for destruction.

Sometimes one bullet might just pass thru the fuselage, but between structual members, so all the ground crew does later is cut out the ragged metal and rivet on a patch.
Or that one bullet might pass thru the fuselage and go thru the pilots brain.

Just two bullets with radically different results.
You can't reduce combat to equations.

 

[zjtins]

Just two bullets with radically different results.
You can't reduce combat to equations.

My first job was with the DoD and they do it all the time but it is classified.

What is missing are things like pilot training affects, human factors, target hardness and weak point, individual round effectiveness (not just HE size), range affects for AP.

The Blackhawk and Apache Helicopters are both impervious to .30cal and resistant to .50 cal AP rounds. While a UH-1 was taken down by a crossbow in Vietnam.
The IL-2 was armored as is the A-10. Both were found be very difficult to kill.

What needs to be understood is there is a range of factors/actions that need to be considered and the results are not a single number but a range.

 

[tyrodtom]

Please don't try the " If I told you, i'd have to kill you " bs.
I'm a 8 year Army and USAF veteran, with 2 tours in Southeast Asia.
Us guys in the field would have loved nothing better than to get our hands on some of those idiots in the DOD.

Even the Hueys had armor, not a lot, but armor for the pilots, gearbox, etc.
I heard too many different vatiations on the UH-1 brought down by a arrow tale, to believe it.
I think that should be listed in the section of what we used to call, "latrine rumors ".

 

[zjtins]

Read Chickenhawk

 

[tyrodtom]

I've read Chickenhawk, many years ago, but I don't remember that.
I was a crewchief/doorgunner, and like I said heard too many varitions on the tale. From a arrow with a string and a rock fowling the main rotor, to a arrow shaft in the tailrotor gearbox.
The Montagnards had crossbows, but were used for small game, not going to penetrate even a unarmored gearbox.

 

[zjtins]

I believe it was a fuel line but that was many years ago. Point is the un-armored vs armored target are vastly different. Not just hiding behind armor but placement of critical systems/component behind less critical systems, redundancy, material choices etc.

 

[DerAdlerIstGelandet]

The Blackhawk and Apache Helicopters are both impervious to .30cal and resistant to .50 cal AP rounds.

BS.

You know how I know? I crewed Blackhawks in the Army for 6 years. 1600+ flight hours including over 600 Combat flight hours. The Blackhawk is made out of regular Aircraft Aluminum. When we flew into Iraq, we had to "uparmor" our Aircraft because they don't stop anything. The Armor was just bass blankets anyhow that covered the floor and the sides to protect the crew. The only armor that was standard on the aircraft is the pilots and copilots sliding armored plates on the seats. We even had an Apache brought down by a 7.62 round to the oil cooler.

Don't talk about something you don't know about. There is always someone around who knows the truth.

 

[zjtins]

Had an ex boss who was on the development team. Armor is only one component. Placement of components, redundancy, material, selection etc. The hub was spec'd for 30 minutes emergency no lub, Engine were split so there should be armor or something between them so 1 round cant take both out

From Defense Journal

The Apache has been designed for high survivability in combat. the helicopter can continue fight for a further 30 minutes following impact by 12.7 mm rounds directed from the ground. Some sections of the helicopter, such as the main rotor blades, are also tolerant to hits by 23 mm rounds. The crew stations are fitted with Kevlar seats. The cockpits are protected by boron armour shielding rated to provide protection against 12.7 mm rounds. The four blades of the main rotor can be folded or removed for transportation, and are specified to be tolerant to 23 mm shell impact.

The Apache is equipped with two turboshaft engines each providing 1265 kW. The American Apache has the type T700-GE-701 from General Electric and the engine chosen for the UK Apache is the type RTM322 from Rolls-Royce/Turbomeca. The engines mounted above the fins on either side of the fuselage are armour protected. The thermal signature of the helicopter has been reduced by incorporating a system of exhaust nozzles to reduce the temperature of the gases from the engine exhaust and the temperature of the external metal surfaces.

Another quote

The book: "In the Company of Soldiers" by Rick Atkinson details an amazing account of Apaches used in the Iraq invasion in 2003.

A whole flight of over 30 Apaches were flying at night toward a town when all of the sudden all the towns lights went off. As they flew over the lights went back on and whole streets were lined by hundreds of men with AK's firing straight up into the air. The flight was had to return to base and the choppers were turned into Swiss Cheese with each one having and average of 27 odd bullet holes in it.

There were a few minor injuries but it really shook them up, they had previously overflown towns at night thinking nothing could touch them. General Petraeus (who was the commander of the 101st at the time and was planning a similiar attack with his own Apaches) took great pains to talk to all the pilots involved and analysed the ambush and made sure his own pilots adjusted their operating procedures in order not to have them fall into the same trap.

Whoever the guy was who organized the ambush was a tactical genius who changed the whole theater of combat for attack choppers simply with AK bullets.

 

[zjtins]

From AviationExplorer

(Apache) Armor
The first line of defense the Apache helicopter has is keeping out of range. It is specifically designed at flying low to the ground and hiding behind cover. The Apache also has a radar jammer to confuse the enemy's radar. To hide itself form heat-seeking missiles it reduces its infrared signature. The Black Hold infrared suppression system dissipates the heat of the engine exhaust by missing it with air flowing around the helicopter. The cooled exhaust then passes through a special filter, which absorbs more heat. The Apache Longbow is also equipped with an infrared jammer, which generates infrared energy of varying frequencies to confuse heat-seeking missiles. The Apache is heavily armored on all sides. Some areas are also surrounded by Kevlar. The cockpit is surrounded by bulletproof glass. According to Boeing, every section of the Helicopter can survive 12.7-mm rounds and vital engine and rotor components can withstand 23-mm fire. The cockpit uses crumple zones, like in a car to protect the crew if there is a crash.