chance of hit.pptx
TRANSCRIPT
Prof James K Varkey19 Dec 14
Chance of Hit Theory
Chance of Hit Theory
Procedure and Evaluation
Probability Distribution of Attack on the Tank from all the sides – Assumptions, Probability Distribution
Whittaker’s Directional Probability Variation Theory.
Analysis of DPV Theory
Calculation of Armour as per DPV Theory.
Chance of Hit Theory
Evaluation of tank design is very difficult without going to battle field
Possible approach is through probability theory
If the tanks are to be assessed on the basis of probabilities of success, we have to define what is success.
Generally we can say that the tank’s mission is to destroy all major battle field targets with in visual range.
The most difficult target the tank likely to face is the enemy tank
Chance of Hit TheoryThus the evaluation of tank design reduces to the determination of probabilities of success in destroying hostile tanks.
To determine probability of success, involving battle field is very difficult, one approach is to break it down to many independent events.
Consider a simple scenario in which success against a hostile tank consists of :
Arriving on time within striking distance of the target. Surviving to engage the target Inflicting lethal damage by engaging the target
Let the probabilities of occurring these are Pa, Ps and Pk, Then the overall probability of success,
Pss = Pa x Ps x Pk.
Chance of Hit Theory
Each of these events is made up of a sequence of many events. To achieve a KILL when a target is engaged involves-
Hitting the target - Probability of hit- Ph Got a hit, Perforating the armour – Probability of
perforating armour –Pp Achieved a perforation, Inflicting lethal damage.
– Probability of lethal damage –Pl
All the above depend on correct functioning of weapon system – Probability of weapon system functioning correctly - Pr
Chance of Hit Theory
Hence Probability of inflicting Lethal Damage,
Pk = Ph x Pp x Pl x Pr
Hit probability Ph depends on the points of impact of a number of projectiles fired from a tank and can be described by a probability density function of the distances (x,y) from the impact points to the centre of the target.
This function is generally assumed to be a bivariate normal distribution which when integrated over target area gives the probability hit.
Chance of Hit Theory
Where,Ph = Probability of hitA = Area of the targetXm = Mean horizontal error (horizontal distance between the aiming point and the MPIYm = Mean vertical errorσx = Standard deviation of the distribution of horizontal errorsσy = Standard deviation of the distribution of vertical errors (the vertical and horizontal errors are statistically independent)
Chance of Hit Theory
The above mathematical model clearly relates hit probability to four parameters of the distribution of impact points namely:
Two mean errors which define the position of MPI Two standard deviation which characterize the
dispersion of impact point about mean.
The magnitude of these four parameters is the result of a number of component errors and they increase with distance.
The most important of all the source of errors is the determination of range to the target which determines the elevation of gun. i.e. Ym, the mean vertical error, is the dominant parameter
Chance of Hit Theory
Aiming Point
Mean Point of Impact
Under ideal conditions with the distance to the target is known accurately a pattern of 10 hits scored is shown in the figure.
Chance of Hit Theory
The probability of perforating the armour (Pp)of a tank depends on the terminal performance of the projectile and the effectiveness of the armour at the point of impact. For calculation we can take average of vital area like front of hull and turret.
The probability of inflicting lethal damage (Pl) is most difficult to determine. The lethality of different types of armour piercing projectiles is still debatable and is matter of opinion.
The probability of performance of weapon system (Pr) has improved a lot and needs to be determined by direct observation and also by deduction from records.
Chance of Hit Theory
The complexity of weapon system is very high as it consists of a large number of components operating in series and the failure of one causes the whole system failure.
Thus the probability that the system will not fail is given by product of the probabilities of the components not failing, and if there are n components each with same probability Pc, then,
Pr = c
Chance of Hit Theory
Probability Gun- APDS %
Missile %
Probability of hit- Ph 70 80Probability of perforating armour -Pp
70 80
Probability of lethal damage -Pl 95 90Probability of weapon system functioning correctly - Pr
99 75
Kill Probability 47 43
A comparative study between high velocity APDS shot and Guides missile on probability of hit.
Chance of Hit Theory
The curves show the single shot probability of a 105 mm APDS projectile against a target of 2.3m (W) x 2.3 m (H) (Standard NATO stationary target) at various ranges.Conclusion: ACCURATE RANGE FINDING is the key to increase chance of hit.
Chance of Hit TheoryProbability Distribution of Attack on the Tank from all the sides – Assumptions, Probability Distribution
The amount of protection which can be given to a tank is governed by weight.
The lowest level of attack a tank faces is from rifle calibre bullets and shell fragments.
This type of attack is likely to come from all directions and its probability distribution in the horizontal plane will be circular which calls for all round protection.
Light Armoured vehicles are likely to face such threats from 7.62 mm or 12.7 mm or 14.5 mm armour piercing bullets. Considering the weight consideration, generally front part is provided with protection against 14.5 mm bullets and sides against 7.62 mm bullets.
MBTs are likely to face much more threats from enemy tanks and missiles and require higher protection.
Chance of Hit Theory
Considering the weight and mobility requirements, all round protection against enemy tanks/missiles is not possible.
Pre world war tanks had armour distribution purely intuitive basis as no major study on distribution of armour was available.
Since second world war the Directional Variation of Probability of attack has been a subject of study by many countries.
Russia developed a Tactical Diagram based on the probability of attack directions to a tank. This covers all major parts of the tank.
Probability Distribution of Attack on the Tank from all the sides – Assumptions, Probability Distribution
Chance of Hit Theory
Tactical Diagram of Ballistic Strength
Chance of Hit Theory
Tactical Diagram
Objective is to estimate the tank vulnerability in the battle field.Closed curves shows the vulnerabilityFollowing details should be known:
Normal thickness of armour Angle of slope to vertical Course direction of the shell Method of manufacturing (casting / Rolling)
Enemy tank Gun Calibre Weight o f shell Muzzle velocity Ballistic coefficient
Curves constructed with course directions of 10, 20, 30,-----degrees and the corresponding angle of impact.
Chance of Hit Theory
Observations Absence of dangerous zone in front of the tank for 90 mm
gun Large dangerous zone on the sides with 120 mm gun 120 mm gun kill probability is very high in all directions
Disadvantages Ignored the different probability of shelling from different
directions and at different ranges. Differential armour plating not considered. Probability of detecting the target and hitting the tank not
considered.
Chance of Hit TheoryWHITTAKER’S
DIRECTIONAL PROBABILITY VARIATION (DPV) THEORY
The first known study to produce a distribution of the probability of attack has been carried out in Briton by JM Whittaker in 1943.
It was a theoretical study and was based on one tank advancing against a line of anti-tank guns.
Anti-tank Guns
Chance of Hit Theory
Whittaker's DPV Curve
Chance of Hit Theory
Analysis of DPV Theory It is an analysis of attack probability from any given direction.
Based on theoretical attack by anti-tank guns against a single straight advancing tank.
Curve plotted based on the finding of the study.
Findings confirmed during world war II and even subsequent operations such as 1973 Arab – Israel campaign.
Assumptions Anti-tank guns fire as soon as the target is observed at a range
possible to engage.
Anti-tank guns do not change their position and fire is not biased.
Tank drives forward at a steady speed, upto and through the enemy lines of anti-tank guns.
Anti-tank guns are located in line.
The anti-tank guns do not have any knowledge of the target tank armour
Chance of Hit Theory
Findings:- In the frontal 600 arc, number of expected attacks are 45%.
Beyond that the number of attacks reduced considerably.
In the frontal 450 arc, number of expected attacks are 33.3%.
Calculation of Armour as per DPV Theory
Used as a basis for distribution of armour during design
Armour distribution at 600 frontal arc to cater for 45% of attacks and further increase in 450arc wherein 33.3% attacks expected.
Designing an armoured fighting vehicle immune in 600 arc makes its probability of survivability to 45%.
Making the armoured fighting vehicle immune in 3600 arc is impractical due to exorbitant weight penalty.
High protection at 600 arc is preferred.
Chance of Hit TheoryDrawbacks
The directional probability variation is valid for main armament only.
The DPV theory is applicable to hull only. It does not caters for turret.
The attack from short range weapons is not catered for.
DPV theory does not cater for attacks from all directions.
The modern battle fields are fast, fluid and range is more.
In mobile warfare the distribution of probability of attack likely to be uniform.
In spite of the drawbacks, Whittaker’s theory is still valid as basic tactics remains same.
Recent analysis shows probability of attack with in 60° as 49%.
The Briton has now introduced the elliptical distribution. It follows the Whittaker’s distribution very closely and can be easily mathematically treated.
Chance of Hit Theory
Elliptical Distribution