SOVIET VOROSHILOV ACADEMY LECTURES
TACTICAL CALCULATONS

This is a series of typ;ical calculations made by tactical commanders.

(1) BASIC TIME AND DISTANCE CALCULATION

This simple formula is used for determining the approximate time required to move a unit from one area to another, not counting the time required to move out of the initial area and reach the start line. The information required is the length of the march as measured from the initial starting line (SL) (at a distance outside the original assembly area) to the nearest point of the new assembly area; the average rate of march of the column, the length of time spent in halts, and the time required to deploy from the road into the new area.


The formula is:






where:
t_Bt=is computed if the depth of new area is less than depth of the march formation.
t=total time of march;
D=length of route;
V=average speed of column on march in kph;
t_p=overall time for halts during march;
t_Bt=time required to deploy into new area;

(2) CALCULATION OF TIME TO BEGIN MOVE TO START LINE

This calculation is used to determine when a unit should begin moving out of its assembly area in order for the head of the column to cross the start line (SL) at the prescribed time. The given data are the distance from the assembly area to the start line and the rate of march. The formula is:

where:
D_n=distance to SL;
t_N=time column starts to move;
V_v=rate of movement to SL;
60=conversion factor Hr to min;
T=time head of column passes SL;

(3) CALCULATION OF TIME TO DEPLOY INTO NEW ASSEMBLY AREA

As noted in formula (1), this only must be calculated when the depth of the new area is less than the length of the mobile column. This is because in this case the head of the column will have stopped at the far end before the tail reaches the near side of the area. The formula gives the time it takes to deploy, once the head of the column has reached the new area.The formula is:

where:
T_d=time for deployment;
G_K=length of column;
G_R=depth of area;
V_d=speed during deployment;
60=convert hr to min;

(4) CALCULATION OF TIME A UNIT WILL BE IN A NEW AREA

This calculation combines the previous formulas in order to determine the clock time a unit will be deployed in the new area. It takes into consideration the time required for a unit to deploy into an area when the depth of that area is less than the length of the marching column. It also includes time for halts en route. Formula of calculation:

where:
t=clock time a unit will be regrouped in new area in hrs;
T=time (astronomical) of passing start point (line) by front of column in hrs/mins;
D=length of route and distance away of new concentration area in km;
V=average speed of movement;
G_K=length of column;
G_R=depth of new concentration area in km (considered only when the depth is less than the length of column);
0.6=coefficient, which takes into account the lowering of the average march speed while deploying into the new assembly area.
t_p=duration of halts en route in hrs.

This calculation may be conveniently performed by entering the data into a table.

(5) CALCULATION OF MARCH DURATION FROM ONE AREA TO ANOTHER

This is a more sophisticated version of the basic march formula to take account of possible reductions in the capacity of the road or other influences on the achievable rate of movement of the columns. The formula is:

when G_K > G_r

where:
t=duration of march in hours;
D=length of march in km;
K=coefficient for reduction in average rate of march of moving columns during entering and leaving the route of march;
D_i=distance of start point from original assembly area in km;
G_K=depth of column in km;
G_r=depth of the new assembly area in km;
V=average rate of movement of column in km/hr;
t_p=duration of halts or delays during movement in hrs.

(6) DETERMINE THE REQUIRED MOVEMENT RATE FOR A UNIT TO REGROUP IN A NEW AREA

This is a more elaborate version of the basic movement formulas to take into account more variables and possible interactions during the movement. The formula is:

(7) CALCULATION OF LENGTH OF ROUTE, AVERAGE SPEED AND DURATION OF MOVEMENT OF MOVING COLUMN

This calculation combines the basic equations. It is used when the total distance to be traveled is composed of segments having different route characteristics. The different characteristics result in different possible movement rates over the individual sectors. The initial data is the length of each sector, the movement rate over each sector, the length of the column and the depth of the new assembly area. Formulas for calculation:

where:

D=length of route in km;
L_i=length of each sector of different types of road each allowing V_i speed of movement of columns in km;
t_d=overall time on the route in hrs;
V_i=speed of movement on a type of sector of the route in kph;
V=average speed of movement in kph.
G_K=length of column in km;
G_P=depth of concentration area in km;
0.6=coefficient of reduction in speed of the column while deploying into the new area or depending on local conditions;
t_n=overall time of halts.

(8) CALCULATION OF OVERALL DEPTH OF COLUMN CONSISTING OF SEVERAL SUB-COLUMNS

This technique is for calculating the total length of a moving formation on a route given the number of vehicles in the moving columns and the distances between them is known. It is also used to determine the required distances between vehicles. The formula is:

where:
G_k=formation depth in km;
N_m=number of vehicles;
d_m=distance between vehicles;
N_K=number of columns;
d_K=distance between columns;
1000=convert meter to km.

(9) CALCULATION OF DURATION OF PASSAGE OF NARROW POINTS AND DIFFICULT SEGMENTS

This calculation is the basic one for determining the time it will take a column of given length to pass through a constriction in the route. It does not take into consideration the issue of vehicle bunching up at the halt before the constriction nor the time to regain column vehicle separation distances after the passage. Therefore more elaborate formulas are used to determine the overall effect of a constriction on a full march. The formula for short obstacles is:

where:
N_m=number of vehicles;
d_m=distance between vehicles;
t=time required to overcome obstacle in minutes;
V=speed of column through obstacle;
0.06=conversion factor km/hr to meters/min.

The formula for major obstacles:

where:
G_k=length of column;
D=length negotiated segment;
t=duration to overcome obstacle in hours;
v=speed through obstacle.

(10) CALCULATION FOR PASSAGE TIMES ACROSS START POINT (SL) BY THE HEAD AND TAIL OF THE COLUMN

This calculation also determines the time for a column to pass a given point, however, since there is no delay as with an obstacle, the time interval is governed by the length of the column and its velocity. Since we are not interested in the length of time the column requires, but the clock times the head and tail cross, the equations yield time in military time. The formula is:

where:
ti=SL crossing time of the head of the march column i in hours and minutes;
T_i-1=the time for passing the line by the tail of the leading march column in hours and minutes; for the head of the first column this time is the time specified for passing the line by the head of the entire formation, for instance, by the column of the leading unit on a route;
d_i=the specified distance between the lead and the i march column in km;
60=factor for converting hours into minutes;
V=average speed in km per hr;
t'_i=the time for passing the line by the tail of the i route column in hours and minutes;
D_i=depth of the i column in km.

(11) CALCULATION OF EXPECTED TIME AND DISTANCE OF PROBABLE POINT OF CONTACT WITH ADVANCING ENEMY

Clearly this is one of the most important calculations Soviet commander's make regularly during the course of combat. As the discussion of meeting engagements in Chapters One and Two indicates, the commander's effort to control the flow of battle focuses heavily on the relative times and place of introduction of his second echelon versus the enemy's reserves, both of which are moving forward.

The formula is:

where:
t_e=expected tome of meeting in hours;
D=initial distance between opposing groupings in km;
V_f=movement rate of friendly troops in km per hr;
V_e=movement rate of enemy forces in km per hr;
d_l=distance from friendly initial position to expected point of contact in km;

(12) CALCULATION OF TIME REQUIRED FOR ADVANCING AND DEPLOYING SUB-UNITS TO CHANGE FROM LINE OF MARCH INTO THE ATTACK

Determination of the time a unit should begin to move for the advance from its assembly area to the line of commitment into battle and assault on the enemy position is a complex application of the basic time and distance formula. All times are measured backwards from "CHE" hour, the moment the troops hit the first line of the defending enemy's position. The total time from beginning of movement in the assembly area is composed of the segments of time while moving in each type of deployment, that is: line of attack, company column, battalion column, and regimental column. It also includes the time it takes to shift from one formation to the other and any time for halts and delays en route. This is one of the most important and fundamental of tactical calculations. The times for sub-unit movement are tied exactly into the times for the artillery preparatory fire and air strikes.

The required given data are the distances between each of the deployment and regulating lines, distance of the attack line from the enemy's forward line of defense, distance of the start line from the unit assembly area, the average speed of movement while mounted in the columns, the coefficient for speed reduction during deployment actions, the speed of movement in attack formation, the depth of the columns, and distance between first and second echelons of the units.

(12) CALCULATION OF TIME REQUIRED FOR ADVANCING AND DEPLOYING SUB-UNITS TO CHANGE FROM LINE OF MARCH INTO THE ATTACK

The set of formulas are:

where:
t_a=time for crossing final deployment into line of attack - "Che" hour -in minutes;
D_a=distance of line for going into attack formation from the forward edge of the enemy position in km;
V_a=rate of movement in attack formation in kph;
t_r=time for crossing the line of deployment into company columns at ("Che" - minutes)
D_r=distance of line of deployment into company columns from the line of deployment into attack formation in km;
V=average rate of movement of subunits in mounted formation during march;
t_b=time for crossing line of deployment into battalion columns at ("Che" - minutes);
D_b=distance of line for deployment into battalion columns from line of deployment into company columns in km;
t_rr=time for crossing the last regulation line or point prior to the deployment into battalion columns;
D_rr=distance of last regulation line from the line for deployment into battalion columns;
t_i=time for passing the start line at ("Che" - minutes)
D_i=distance of start line from last regulating line in km;
t_vit=time to begin movement of subunits in assembly area;
D=distance of start line from the last unit assembly area;
t^'_i=time for crossing the start line by the 2nd echelon of units at ("Che" - minutes);
G_k=depth of the mounted column of first echelon of units in km;
d_k=distance between the tail of the first echelon and head of the 2nd echelon of the units in km;

The numbers 60 and 90 are coefficients for conversion of time in minutes for the average speed of movement during the deployment of the units at each of the lines. For example, the 90 shows that the average maneuver speed of the unit during the actual deployment on a line decreases by a factor of 1.5 in comparison with the speed of forward movement between the lines. Depending on the concrete conditions and situation for movement on the terrain, this could be some other factor.

To perform the calculation the required data may be entered into the table. The result will be the planning data for start of forward movement and deployment times for each shift of sub-unit columns. Since all times are measured backward from "Che", the planner must remember to subtract the values indicated in lines 12, 15, 18, 21, 24, and 27 from Che; and add the value for time in line 30 to the time in 24 to obtain line 31.

(13) CALCULATION OF THE TIME AND DISTANCE TO THE LINE OF CONTACT

This method takes into consideration the many situational factors that are ignored in the simpler formula and nomogram. In fact, there are so many possible influences on the time the two sides will meet and hence the location of meeting that a nomogram can only give a crude approximation of the answer. With the use of computers or even hand calculators and an established procedure such as that shown in this table it is possible to assess the influence of many more factors.

The set of formulas is:

t_v={D + [(t_n x V_n) + (t_p x V_p)]} ÷ (V_n + V_p)

T_n=t₁ + t₂ t₃; T_P=t₁' + t₂' + t₃'

where:
t_v=expected time if contact with enemy in hours;
D=distance between forces of the two sides in km;
t_n=total delay time for own force in hrs;
V_n=speed movement of own forces in km per hr;
t_p=total delay time of enemy in hrs;
V_p=speed movement of enemy in km per hr;
l_p=distance to expected line of meeting with enemy;
t₁ (t^'₁)=delay - (time difference) start of movement of one side versus other in hrs;
t₂ (t^'₂=duration of halts of forces of each side in hrs;
t₃ (t^'₃)=duration of delay of forces due to strikes by opponent en route in hrs;

(14) CALCULATION OF EXPECTED TIME AND RATE OF OVERTAKING WHEN PURSUING THE ENEMY

Naturally the commander hopes to use this calculation often! The initial data are the distance between the enemy and friendly forces, the average travel speed of friendly and enemy forces, or the ordered time to overtake him. The formula is:

where:

t_o=time to overtake enemy in hours;
D=distance to the enemy in km;
V_n=friendly speed in pursuit in km per hr;
V_p=enemy speed in retreat in km per hr;

(15) CALCULATION OF THE WORK TIME AVAILABLE TO THE COMMANDER AND STAFF FOR ORGANIZING REPULSE OF ADVANCING ENEMY FORCES

This is obviously a critical issue in meeting engagements and encounter battle. It is also relevant to defensive situations when preparing fire on the attacker. The method is designed to determine the time the commander and staff will have to organize the enemy's defeat by firing on the advancing forces relative to the distance to the enemy, the speed of his advance, the effective range of friendly weapons and the time required to prepare the sub-units to fire. In this example it is assumed that the enemy will be taken under fire beginning at the maximum range of the firing weapons. The formula is:

where:

t=time available for commander and his staff to organize repelling the advancing force in minutes;
D=distance to advancing enemy km;
d=max range of friendly weapons km;
60=conversion factor hours to minutes;
V_e=rate of enemy advance kph;
t_p=time required to prepare subunits to destroy enemy with fire in minutes;

(17) DETERMINATION OF QUANTITY OF VARIOUS WEAPONS, RECONNAISSANCE, SUPPORT, COMMUNICATIONS ETC. FOR TASK PERFORMANCE

This general technique is applicable to a wide variety of activities in which it is desired to know what the overall effectiveness of a group of agents will be when the probability of success of an individual agent is known. First one calculates the action of the number of identical equipments, and then determines the total effectiveness or total requirement for the systems. the initial data for the calculations are information about the number of available systems, the assigned degree of success for each, the effectiveness of the systems (which is expressed in probability of mission fulfillment or by the mean value of the applied damage to a particular target.) A single system also means a complex of systems combined into a whole unit. Such data, for instance, are the probability of target destruction, the man damage applied to an enemy target, the reliability of a communications channel, the probability of enemy target detection, the probability of the flawless operation of a water crossing for a specific time interval, the probability of overcoming the anti-air forces of the enemy and so on. These data may be obtained on the basis of the results of studies, from statistical data nd from tactical and technical characteristics.


The formulas for calculating the degree of mission fulfillment by a designated number of systems is expressed through mission fulfillment probability:

and through the mathematical expectation (mean value) of damage:

where:
P_n=probability of mission accomplished by a homogenous group of weapons;
P₁=same by a single system;
M_n=average (mean) value of damage inflicted on the enemy by a group of systems;
M₁=average value of damage inflicted on the enemy by one system;
n=quantity of available systems.

The formulas for computing the required number of systems when the effectiveness of the systems is expressed by probability of task performance is:

when P_n > P₁

when it is expressed by the mathematical expectation (the mean value) of the inflicted damage, the formula is:

when M_n > M₁

The formula for calculating the effectiveness of different systems fulfilling a common mission is :

where P_n is the overall effectiveness of systems used or in other words the likelihood of fulfilling the mission, and the individual "P"'s are the effectiveness measures of each system being summed for the task.

From these examples it is evident that the technique may be used for calculating a wide range of direct and inverse problems associated with the use of various forces and means. With proper additional factors this method may also be used to calculate rapidly the effectiveness and required number of forces and systems when taking into account also probable enemy countermeasures.

The formulas for calculating the effectiveness of forces and means with consideration for probable enemy countermeasures are:

where:
P_n=the probability of mission fulfillment by a group of systems;
P₁=the probability of mission fulfillment by a single system of this type;
Q=the probability indicator of the enemy countermeasure ;
n=the number of forces and means of the given type;
M_n=the mathematical expectation of the damage inflicted by a single system of this type'

(18) Modeling battle

There is much discussion in the Soviet literature about the theory of development of coefficients of comensurability. The coefficient is designed to make it possible to aggregate the effective contribution of various weapons to a combined arms battle into a composite score for each side. This makes the measurement of the correlation of forces relatively simple, ie. only one number for each side rather than the long list of individual types of weapons found in the standard tables of correlation of forces. However, what sounds simple in theory is quite difficult in practice. Soviet authors point out that even within types of weapons such as tanks or artillery the "proving ground scores" assigned on the basis of technical/tactical characteristics may not be true reflections of the actual value of the weapon to the commander in all the diverse conditions of real combat. When it comes to establishing a uniform score that will place tanks, artillery, aircraft, and small arms, etc on one scale; a lot of judgment is involved. There is some argument for two different methods, one would develop a "average" score for each weapon reflecting its varied value in different circumstances, and the other method would establish a single theoretical value number and then provide situation modifiers to be applied to account for each actual set of combat conditions. We do not have available an actual set of Soviet "utils" as they call their weapons scores. The following table is taken from a Soviet article, but the scores are purely hypothetical for educational purposes. Nevertheless, the following method represents a typical Soviet approach which may be used by American officers with an appropriate set of "utils".

The mathematical expectation of the level of destruction of a side from fire and strikes of artillery and aviation (M) in the experience of the Great Fatherland War could reach on defense to 40-60% and on the offense to 20-30%. The losses of combat effectiveness due to destruction in various types of combat is shown in the table of expected losses. Another Soviet source gives 30% loss as the critical break point for attackers and 40% loss as the typical break point for defenders. Of course the effect of losses on unit combat effectiveness depends heavily on the rate of loss and the size of the unit.

One more indicator is the coefficient of superiority (K_p) of the defenders over the attackers, which in the experience of combat typically is three times.

MODELING BATTLE

The possibility of sub-units for destruction of the enemy during the course of accomplishing their combat missions is calculated according to the following formulas:

a) in offense:

b) in defense:

where:
K_s1, K_s2, K_sp=coefficients of comensurability of combat means of units of country A;
K_b1, K_b2, K_bp=coefficients of comensurability of combat means of units of country B or V;
i=quantity of combat means of given type;
Z₁, Z₂=level of destruction at which the unit loses combat effectiveness;
M=mathematical expectation of the level of destruction due to artillery and aviation fire;
K_p=coefficient of superiority of defender over attacker;
S=combat capability of the sub-unit.


For calculations of combat capability during meeting engagement (battle) use formula (1) but for the coefficient of superiority of defender over attacker use 1.

Example calculation: The tactical situation; a tank platoon of country A (with tanks 7) with motor rifle section in a APC has the mission of attacking from the march to destroy defending section of country B.

Initial data for the calculation:
a. type of combat action is attack;

b. model of combat means of the sides, their quantity and coefficient of comensurability calculated qualitative indices, are shown in table of comensurability.

The attackers:
tanks "7" K_s1=1.5, and quantity, i=3;
APC, K_s2=0.8, and quantity, i=1.

Defenders:
APC, K_b1=1.4, and quantity i=1;
AT gun, K_b2=0.3, and quantity i=3;

c. the mathematical expectation of the level of destruction of the defenders in the time of artillery preparatory fire and attack support fire is M=0.4;

d. losses of the sub-unit during the time of approach to the line of going over to the attack must not exceed Z₁=0.3;

e. level of destruction of the defenders at which they loose combat effectiveness is found in the table of expected loss of effectiveness, Table 2, Z₂=0.55;


Taking the initial data and using formula 1 to create a mathematical model of the battle gives the following:
S_n={[(1.5 x 3) + (0.8 x 1)] x [1 - (0.3 + 0.55 - 0.4)]} ÷ {3 [(1.4 x 1) + (0.3 x 3)] x (1 - 0.4)=0.7


Analysis: If S_n is greater than or equal to 1, then the sub-unit will fulfill its mission, if (as in this example) the S_n is less than 1, then the defender with his forces will be superior. This means that it is necessary to raise the capability if the force to achieve likelihood of accomplishing the mission.

Decision: Reenforce by fire the platoon on the march from a range of 2000 meters to destroy the enemy APC, and after that conduct fire on the AT gun.

The problem may be decided by means of mathematical modeling of battle:

S_n1={[(1.5 x 3) + (0.8 x 1)] x (0.3 + 0.55 - 0.4)} ÷ (3 x 1.4 x (1 - 0.4))=1.19;

In other words, the APC will be destroyed.

S_n2={(1.5 x 3 + 0.8 x 1) x (1 - (0.3 + 0.55 - 0.4)} ÷ {3 x 0.3 x 3 x (1 - 0.4)}=1.9.

Outcome: Attacking from the march with forces of three tanks and APC to destroy an APC and then a AT gun. The line of going over to the attack is designated in accordance with the characteristics of the terrain, but not closer than 2000 meters from the forward edge of the enemy defenses.

As is evident from the example, the conduct of the calculation is difficult work demanding a significant amount of time and corresponding conditions. If the commander has an electronic calculator he could work out the answer quickly.

What is not evident is to what level of aggregation this method and these formulas may be taken without loosing validity. The given example illustrates duels and very small unit combat. With the use of computers it would be possible to calculate combat at the level of a full regiment or even division but so many other factors enter in and effect combat outcomes at that level that a simple formula is no longer valid.

(19) CALCULATION OF STRIKE CAPABILITY OF SUB-UNITS

This method is designed to calculate the expected depth of penetration of a unit on the offensive as a measure of its strike capability, or, in reverse, to forecast the ability of a unit of given combat capability to achieve the depth of penetration required in its mission. The initial data for the calculation includes the composition of the attacking and defending units, the conditions of combat and combat potentials with calculated losses of the sides and also the designated critical level of losses necessary to cause unit failure.

The critical figure is considered to be the loss at which the sub-unit losses its combat capability and cannot continue the kind of action it was performing without re-enforcement. The calculation is made over the width of the front of the attacker and the designated area of the defense. See the section on modeling battle for more discussion of the theory and use of the critical level of loss as an indicator in forecasting and modeling combat. Together these formulas may be used to determine the initial data on the three measures of effectiveness described in Chapter One as those deemed critical for assessing and forecasting battle outcomes.

(19) CALCULATION OF STRIKE CAPABILITY OF SUB-UNITS

The formula for calculating the expected depth of penetration follows:

when:
Y_N (1 - P_N ) > (1 - P_N^K) and Y_o (1 - P_o) > P_o^K)

where:
N_N, N_o=number of units of attackers and defenders, measured in combat potentials ("utils");
P_N, P_o=expected losses of the units of each side up to the arrival at the immediate mission line;
P_N^K, P_o^K=critical loss of a unit of attacker and defender;
F_N=width of front of attack in km;
F_o, G_o=width of front and depth of the defender's area in km.
Y_N, Y_o=composition of the units of each side as a percentage of unity 100%.
K=coefficient of combat effectiveness of the defending side. (This is the same as K_p in the formulas for modeling battle.

(20) CALCULATION OF THE WIDTH OF MAIN ATTACK SECTOR

There are several different ways to determine the possible, desired, or required width of the main attack sector depending on the purposes and criteria. The following is one quick way to calculate the relationship between the width of a strike sector and the total width of zone in relation to the correlation of forces in the strike sector and the total correlation. For these calculations the correlation of forces may be calculated in terms of "utils" or in terms of some other aggregate measure based on the quantities of forces and means of the two sides. The following formula applies:

where:
W_m=width of strike sector;
W_o=total width of zone;
C_o=overall correlation of forces;
C_m=correlation of forces in strike sector;
C_s=minimum desired correlation of forces in rest of zone excluding strike sector.

(21) CALCULATION OF REQUIRED DESTRUCTION OF ENEMY

Another calculation related to the preceding is to determine what damage should be inflicted on the defender prior to the attack in order to bring the correlation of forces into the desired range, considering that there will be a given amount of loss on the friendly side as well. The formula is as follows:

where:
M=required level of destruction of enemy in percent;
C_N=beginning correlation of forces;
C_T=required correlation of forces;
P=forecast friendly losses from enemy action in percent.

(22) Calculation of Rate of Advance in Relation to Correlation of Forces

Various Soviet articles have discussed the concept of the relation of advance rates to the correlation of forces of the sides. The relationship is complex and also depends on several other variables. Evaluation and analysis of the actual correlations of forces achieved in various operations of World War II and recent local wars shows that a single norm for the correlation of forces and means does not exist, but it all depends on the concrete conditions. Nevertheless sufficient figures to make approximate calculations can be developed, especially for academic and training purposes. The actual rate of advance, V, in km per day may be related to a coefficient reflecting the influence of the correlation of forces, K_C, in an equation such as V=140 x K_C. In this the number 140 represents the collected resulting effect of variables acting in the area, for instance the Western TVD to give a practical maximum technically possible speed of movement for mechanized forces in km per day and also an indicator characterized by the influence of terrain, engineer obstacles, time of year, length of daylight, etc. The factor K_C is a coefficient depending on the correlation of forces of the sides. This approximate relationship can be shown in a graph. Analogous graphs can be made for other theaters and conditions. The formula together with the graph is used to evaluate the formation and determine the correlation of forces required to achieve a required rate of advance or in reverse the expected rate of advance for a given correlation of forces.

Another approach is to use the following formula to calculate a factor corresponding to the K factor in the previous method. In the following nomogram the rate of advance is related also to movement distance, terrain type, length of the operation and a theoretical maximum movement speed. These variables are joined into a single factor according to the equation: F=D ÷ KTV_max

where:
D=distance (depth) of operation;
K=terrain coefficient (1.25 - level; 1.00 - rough-level; .75 - rugged hills; .75 - urban; .50 - mtns.)
T=time required for operation in days and fractions of days;
V_max=theoretical speed in km per day.

According to this nomogram, to achieve a depth of advance of 30 km on level terrain in one day with a theoretical maximum speed of 60 km per day requires a superiority in correlation of forces of 4:1. With a correlation of forces of 3:1 on rough-level terrain and a theoretical maximum speed of 50 km per day in two days the force may advance 20 km.

(23) Determine the Possible Friendly and Enemy Losses in Relation to the Correlation of Forces and Rate of Advance

A simplified expression of the relationship between attrition and the correlation of forces may be shown with a nomogram. In actuality many factors influence this relation, however, for general planning at front level the averages shown in the nomogram may be sufficient. This nomogram is built with the following assumptions.
1. The attacker needs a 3:1 advantage represented by the line at 45 degrees to break even and have the same loss rate as the defender.

2. The losses to each side are related to the force ratio in a relatively simple and direct way, but the greater the force ratio advantage and the longer the time interval the larger the difference in attrition will be. So losses accumulate faster for the side with the disadvantage in forces;

3. For an army size force the losses are about .5% per day when the correlation of forces in 1:1

(24) DETERMINE THE REQUIRED AMOUNT OF MANPOWER AND WEAPONS TO RESTORE THE COMBAT CAPABILITY OF SUB-UNITS

The formulas for the calculation are:

M_i=C_i - A_i ÷ B_i ; A_i=(n_f P_f) x N_f ;

B_i=(n_e -N_e P_e) x N_e ; m_i=B_i x M_i

where.

M=index of the reduction of combat capability in terms of the required ratio of manpower and weapons for the execution of the mission;

C_i=required degree of superiority ratio for a particular type of the i type of weapon;

A_i=availability remaining on hand quantity of weapons of a particular type i of own forces;

B_i=availability of remaining number of weapons of a particular type i for enemy forces;

n_f (n_e)=initial full strength of own troops (enemy troops) by type i of weapons pers/ proportions;

P_f (P_e )=losses of own troops (enemy troops) pers/proportions;

N_f (N_e )=TOE number of weapons of a particular type i of own forces (enemy forces);

m_i=number of weapons of a particular type which are required for the restoration of own troops combat capability.

If M is less than 0 then the calculation is no longer performed since the filling out of the forces and means is not required to restore combat capability.

Form for the Calculation of the Required Amount of Personnel

Form for the Calculation of the Required Amount of Personnel

(25) DETERMINE THE EXPECTED RADIATION DOSE

The initial data for this calculation are the length of travel route within the zone of radioactive contamination, the average radiation level on the travel route and the speed and direction of travel of the sub-units.

The degree of shielding of the personnel is assigned by a coefficient of radiation reduction by the transport equipment.The formula is:

where:

D=the expected radiation dose of personnel in roentgens;

L_i=the length of the route within the i zone of radioactive contamination in km;

N_i=factor which considers the direction of zone relative to the axis of the radioactive pattern. (If travel is along the axis of the pattern N equals 1, and if perpendicular to the axis N equals 0.25, and at an angle to the axis N equals 0.375);

R_i=mean radiation level on the travel route in roentgens per hour;

V_i=the speed of travel in km per hr;

K=the coefficient of reduction of radiation by the protection of the transport equipment;

n=the number of zones to be crossed.

DETERMINE THE EXPECTED RADIATION DOSE (CONT)

The formula and method for calculation may be simplified by considering the entire zone as a whole and using average values for the above variables. In this case the expected dose of radiation may be expressed as:

D=(R x L) ÷ (K x V);

and the required speed of movement is:

V=(R x L) ÷ (K x D);

This relationship is shown on the nomogram.

Example calculations using the formulas: Determine the anticipated dose of radiation of personnel crossing a sector of radio-active contamination with a level of 78 R/hr, if the length of route is 18 km, the sub-unit speed is 25 km/hr, and the coefficient of protection is 7. The solution is 8 roentgens.

Determine what is the required speed to negotiate a contaminated zone 17 km deep when the mean radiation level is 95 R/hr, the protection coefficient is 4 and the allowable radiation level for personnel is less than 20 R. Solution is approximately 20 km/hr.

Example calculations using the nomogram: Determine the expected personnel radiation dose from passing through a sector of radio-active contamination of 60 R/hr, when the length of route is 12 km, the unit travel speed is 15 km/hr and the protection coefficient is 2. Solution: (Variant A) From the "12" mark on the "Length of sector of contaminated route" scale draw a perpendicular line to the intersection with the "Average level of radiation - 60" line. From that point draw a horizontal line through the obtained point to the intersection with the "Speed of movement 15" line and then draw a vertical line to the "Coefficient of degradation 2" line." From that point draw a horizontal line to the "Dose of radiation of personnel scale, on which read the result=24 roentgens.

(Variant B) is to calculate the speed for negotiating a contaminated zone so that the personnel will receive less than 48 roentgens when the route length is 18 km, the radiation level is 80 R/hr, and the coefficient for protection is 2. Draw a perpendicular line from the 18 mark on the "Length of sector" line to intersect with the "Average level of radiation - 80" line and draw a horizontal line to the left. Then draw a horizontal line from the "48" mark on the "Dose of radiation of personnel" line to the intersection with the "Coefficient of degradation - 2" line and from that point draw a vertical line to intersect with the previously drawn horizontal line. The intersection point on the "Speed of Movement" lines at the 15 line shows that 15 km/hr is the minimum acceptable speed for crossing the contamination.

Another method for calculating the expected radiation dose for personnel may be used with a nomogram by considering only averages over the entire width of the radiation zone. The initial data for this calculation are the length of the contaminated section of the route, the mean radiation level over the route, the unit travel speed during passage of the contaminated area, the degree of shielding of personnel by the vehicles. This method is used to calculate the speed required to pass the contaminated area so that personnel do not receive a larger radiation dose than allowed.

The formulas are: D=RL ÷ KV; and V=RL ÷ DK

where:

D=the expected radiation dose of personnel in roentgens;

L=the length of the route in km;

R=mean radiation level on the travel route in roentgens per hour;

V=the speed of travel in km per hr;

K=the coefficient of reduction of radiation by the protection of the transport equipment;

The mean radiation level is determined on the basis of radiation reconnaissance data by averaging the readings at various points along the route.

Example calculations using the formula: Determine the expected radiation dose for personnel in crossing a radioactive zone 18 km deep when the mean radiation level is 78 roentgens per hr, the sub-unit travel speed is 25 km/hr, and the reduction coefficient is 7.

The solution is D=78 x 18 ÷ 7 x 25=8 roentgens.

To determine the speed required to cross a contaminated area 17 km deep when the mean radiation level is 95 roentgens/hr, the reduction coefficient is 4, and the allowable radiation level is less than 20 roentgens.

The solution is: V=95 x 17 ÷ 4 x 20=20 km per hr.

Example calculations using the nomogram Figure 105: Variant A: Determine the expected personnel radiation dose in crossing a contaminated zone with radiation level of 60 Roentgens/hr when the length of route is 12 km, the travel speed is 15km/hr and the reduction coefficient is 2.

Solution: From the 112 mark on the "contaminated route length" scale draw a perpendicular line to the intersection with the "Mean radiation level - 60" line. From this point draw a horizontal line to the intersection with the "Travel speed - 15" line. Draw a vertical line through this point to the intersection with the "Reduction coefficient - 2" line and then draw a horizontal line to the "Personnel radiation dose" scale. At that point read the result=24 roentgens.

Variant B: Determine the speed for crossing a contaminated zone so that the personnel receive less than 48 roentgens, when the route length is 18 km, the mean radiation level is 80 roentgens per hr, and the radiation reduction coefficient is 2.

Solution: Draw a perpendicular line from the 18 mark on the "contaminated route length" scale to the intersection with the "Mean radiation level - 80" line and then draw a horizontal line to the left. Draw a horizontal line from the 48 mark on the "Personnel radiation dose" scale to the intersection with the "Reduction coefficient - 2" line and through this point draw a vertical line to the intersection with the previously draw horizontal line. The point of their intersection on the "Travel speed - 15" line shows the result is 15 km/hr. This is the minimum speed required.

(26) Calculation to Select the Optimal Travel Route

This is an extremely important and varied class of calculation. The example given here is only illustrative of the possibilities for employing the given method for solving problems of optimization from among a small set of possible variants.

The commander of a sub-unit has a mission to break out to an assigned line and assume the defense in the shortest possible time. There are five possible travel routes to reach the assigned position. All routes pass through a zone of radioactive contamination. Therefore, an additional condition of the advance is the expected dose of radiation received by sub-unit personnel. It is apparent that in this example there are five decision variants. The main criterion for evaluating their relative effectiveness is the travel time. The shorter the better. However, the commander must also strive to keep the received radiation dose at a minimum, or at least not allow it to exceed a set maximum per norms, for instance 50 roentgens.

The conditions for the sub-unit to advance to the assigned mission line may be expressed in a table showing quantitative characteristics. From the data it becomes obvious that the possible movement routes differ from each other in length, road quality, and mean level of radiation.

From the table we see that on route 1 in advance variant 1 there are four segments of 16 km of highway, (travel speed 40 km/hr) 10 km of improved dirt road (travel speed 25 km/hr), 9 km of dirt road (travel speed of 15 km/hr), and 5 km of damaged, nearly impassable road (travel speed < 5 km/hr). The mean radiation level on the entire first route is 100 roentgens per hr. From this information we can calculate the expected duration of travel time to reach the mission line, as follows:

t₁=(16 ÷ 40) + (10 ÷ 25) + (9 ÷ 15) + (5 ÷ 5)=2.4 hrs or 2 hrs, 24 min. The first route passes through a radiation zone of 100 roentgens per hr. Using the previous method for calculating radiation with a reduction factor of K=4 for equipment D=(100) (2.4) ÷ 4=60 roentgens.

After calculating the same data for the other four routes the information needed for the decision may be shown in another table of movement time and expected radiation dose.

These results may now be compared to determine the optimum decision of which route to choose. Displaying this data in the table makes it easy to see that the optimum solution is route number 5, having both the shortest travel time and lowest radiation dosage, however this might not always be the case. We can also see that the shortest route (no 2) is actually worse than the longest ( no 3). However, a more general technique for solution, when the answer is not evident is to prepare a graph to plot the information. In this example plot the radiation dose on the y axis and the travel time on the x axis. Then enter the coordinates for the given mission requirements, such as maximum travel time of 3 hrs and maximum radiation dose of 50 roentgens. Draw vertical and horizontal lines from the axes to the selected coordinates. Plot the data for all the possible variants. Those variants whose position falls within the rectangle formed by the axes and the lines to the decision point.

(27) Calculation to Determine Optimal Distribution of Weapons

One of the most important classes od decision for the commander is the optimal distribution of weapons against various targets. This is a more complex calculation that the previous example of optimum route given two decision criteria. As an example consider the distribution of weapons against a group of targets. The calculation technique shows the course and result of the calculation for optimization. Of course, the ideal solution technique is to use computers, and Soviet headquarters are certainly using this method. In the field, however, the commander may be required to make a rough calculation without having a computer available.

The following simple method produces sufficiently reliable results when a small number of forces and means and targets are being considered. The illustration, nevertheless, indicates the type of problem for which computer solutions may be developed.

In this example the commander must find the most effective distribution of five different groups of weapons against five strong points in order to inflict the maximum casualties on the enemy. having calculated the effectiveness of fire of each of the groups of weapons against each target, for instance, using the technique with the nomogram the commander may create a table of effectiveness of damage to each enemy target by each weapon.

The damage achieved by different weapons against various types of targets is not identical because of the difference in the quantity and quality of the weapons, the quality of the shells, and the relationship of the ballistic characteristics of the weapons (dispersion pattern etc) to the dimensions of the targets, and the degree of shelter of the enemy personnel.

According to the data in the table, the first group of weapons when hitting the first enemy target inflicts casualties to the personnel in an area of 8 hectares, the second weapons group against the same target damages 4 hectares, and so on.

If the commander assigns the first weapons group against the first target, the second group to the second target, etc., then the effectiveness of the distribution will be the total area damaged or 30 hectares. However, this solution will not be optimal, since the actual combat capabilities of the available weapons in these conditions are not used in the best way. In order to find the best distribution and solve the problem quickly, another method for calculation must be used. The initial data for this are shown in the next table; the weapons groups, the number of target groups and the firing effectiveness.

The calculation of the optimal distribution is performed directly on the table. First, select the two greatest values for the effectiveness values in each line. In the first line these are 9 and 8, and in the second they are 7 and 7, etc. Then subtract the lesser value from the greater and write the results in the right hand column, as shown. Perform the calculation first by each line and then by each column. Examine the differences by lines and columns, select the greatest value and mark it (*). In this example the result is the fifth line, but the maximum may also be in a column. Then in the line or column in the fields for which the greatest value shows, find the maximum indicator and underline it. (This is the 9 in line 5 column 1.) This indicates that the fifth weapons group should be targeted against the first target group. Eliminate this pair from further consideration.

The course of the further calculation is shown in the next table. The remaining weapons are in a similar manner distributed against the remaining target groups until all groups of weapons are distributed.. This shows that the first group should fire on the fourth target, the second on the second, the third against the fifth, and the fourth against the third. This results in the greatest damage to enemy personnel, a total area of 42 hectares. This is the maximum value of damage from the 120 possible combinations of weapons and targets in the example.

In this example the total area of damage was considered the indicator of effectiveness. Sometimes one must minimize the effectiveness indicator instead of maximizing it. For instance, the indicator might be the time required for fulfilling the mission, the expenditure of munitions or other materials, etc. Top optimize the distribution according to a minimum indicator value, use the same technique, only in calculating the differences in the lines and columns, select two minimum values instead of the two maximum ones and subtract the least from the greatest. Then find the minimum indicator in the appropriate line or column and fix it first.

This comparatively simple and practical technique for determining the optimum distribution of forces and means is useable in the field. The materials being distributed might be weapons, reconnaissance means, communications systems, water crossing equipment, etc.

(29) CALCULATION TO DETERMINE THE EFFECTIVENESS OF FIRE DESTRUCTION MEANS

This is a more elaborate version of the basic formula designed for use with calculators. The initial data is the number of fire targets, the number of weapons, rate of fire, and coefficient of effectiveness of fire, the length of time for conducting fire, and the coefficient of resistance (counteraction) of the enemy. The formula is:

where:
M=quantity of targets to be destroyed;
N_t=total number of targets;
P_i=probability of destruction of target from one weapon by one shot;
q=probability of destruction of weapon by fire of enemy;
N_w=number of weapons;
=rate of fire (number of rounds per min);
t=duration of fire in min.