Data on World War II Tank Engagements Involving the U.S. Third and Fourth Armored Divisions

An M4 medium tank passes by knocked out PzKpfw. IV medium tanks, St. Lo, France, 9 July 1944.

by David C. Hardison

Editor’s Note

This article is a reprint of BRL Memorandum Report No. 798, published by the Ballistic Research Laboratories (BRL), Aberdeen Proving Ground, Maryland, in June 1954. The report was unclassified on 29 August 1972 under Department of Defense Directive 5200.10 (which actually stipulates that the material was to be downgraded at three year intervals and declassified after twelve years, although such is usually not accomplished until someone actually requests such to be able to utilize or copy the document).

I am indebted to Abe Flatau for providing a copy of this report so that it could be reprinted and make it available to all who are interested in such matters.

Merriam Press originally published this in book form in 1988 and went through seven editions, the last edition released in 2012 with ISBN 978-1470079062.

Abstract

A study of some tank engagements of World War II involving units of the U.S. 3rd and 4th Armored Divisions has been made. The numbers of Allied and enemy weapons used and lost, the combat range, advantage of the defender, the advantage of initiating the aimed fire engagement, and the engagement termination are discussed. An appendix contains the known details with explanatory remarks of the above factors and with particular remarks for each of 129 individual actions.

It is observed that, in the considered engagements, a great advantage was enjoyed by the force which initiated aimed fire and that small numbers of tanks were generally involved in the tank engagement. It is shown that there is no evidence in the data that the number of weapons used by the Allied force was dependent on the number used by the enemy force, and that a majority of engagements terminated with neither force being annihilated. The limited scope of the present study precludes attempts to estimate the relative combat effectiveness of the Allied and enemy weapons.

It is suggested that the tanks studied would have been greatly improved by:

a more effective method of detection of opposing weapons and

reduced time to obtain a killing hit once a target was identified.

Introduction

To estimate the combat effectiveness of a weapon, the evaluator generally needs some information as to the contemplated condition of its employment. The exact conditions of employment of weapons in tomorrow’s combat are unknown today. Their anticipation, it would appear, should contain a liberal portion of informed tactical imagination but should not fail to consider the combat experience of yesterday. It is clear that there exist no shortage of tank combat experiences. However, there is a shortage of tank combat experiences reduced to a form readily usable to the evaluator. It is the purpose of this report to present an analysis of a small portion of the available World War II combat data.

In an exploratory attempt to express tank combat experiences in a usable numerical form, a study was begun at the Ballistic Research Laboratories of historical records of tank engagements of World War II. The study indicates to date that the available information is extensive, that it is scattered throughout vast volumes of records, and that its extraction is neither rapid, direct, nor impossible. The present report is a result of the first efforts of the BRL to obtain tank combat data from these historical documents. The limited scope of the study demands caution in making observations based thereupon. The reliability of the data is at best no greater than that of the materials from which they were obtained.

It is noted that the engagements studied were viewed from a detailed rather than a strategic point of view. Primary efforts were toward ascertaining what the tanks actually did in battle. No attempt has been made to study the engagements as segments of the overall strategy.

Source of Data

The data given in this report were extracted from official military documents, including After Action Reports, Combat Interviews, Journals and Files, and Unit Histories, obtained from the Departmental Records Branch of the Adjutant General’s Office. A detailed identification of these source materials is provided in the bibliography of this report.

The method employed in extracting data from the documents has been discussed in a previous paper, “Terrain and Ranges of Tank Engagements.” The problem was essentially one of historical research and consisted mainly of fitting together the available fragmentary details of a series of individual engagements. In the study it was found necessary to supplement descriptive narratives with appropriate maps and overlays of the battlefield situation.

Areas of Combat

The considered engagements occurred in several rather local areas of Northwest Europe. These areas, the Allied units involved, and the approximate dates of the engagements are shown in Table I. A brief summary of the details of each engagement is given in the Appendix of this report. The serial numbers shown in the second column are for reference purposes and may be used in conjunction with the Appendix.

A discussion of the general terrain and tactical situation of each of the considered areas is given in BRLM 702, “Terrain and Ranges of Tank Engagement.”

Table I: Combat Area, Allied Unit, and Dates of Engagements

Area	Engagement Serial Number	Allied Units	Date of Engagement
Vicinity Fromentel	1-5	3rd Armored Division	15-17 August 1944
Vicinity Stollberg	6-14	„	15-22 September 1944
Roer to Rhein	15-31	„	26 February-6 March 1945
Belgian Bulge	32-54	„	20 December 1944-15 January 1945
Vicinity Arracourt	55-67	4th Armored Division	19-25 September 1944
Sarre	68-88	„	9 November-6 December 1944
Relief of Bastogne	89-98	„	22-30 December 1944

The Tank Engagement

Definitive Concepts of the Tank Engagement

The “tank engagement” is not simply defined. The first requirement is clear: a tank must have been involved. By common usage an engagement is a hostile encounter which may be general, as between entire armies, or minor, as between outposts. Such a nebulous concept has obvious objections, for the beginning, ending, and interim actions of an engagement are all related to what is meant by the term. Although a concise definition of “tank engagement” is not yet evident, the following general principles are stated as those which were followed as closely as possible:

An engagement was a hostile encounter between tactical units whose elements participated in a direct fire fight. It included those weapons which potentially were, or engaged, targets of direct fire.

The engagement began when one force brought to bear aimed direct fire at its opponent.

The engagement ended when neither force continued to subject its opponent to aimed direct fire.

That force attempting to occupy a new position was called the attacker. His opponent, or the force attempting to prevent this attack was called the defender, thus, motion was frequently the criterion used to determine the “attacker” and the “defender.”

The tank engagements studied were a part of fluid front warfare where maneuver and movements of forces were routine. Consequently, it is not always possible to know when a battle “began” or when it ended, which force should be called the attacker, which should be called the defender, how many forces were employed or how many tanks were lost. Consider, for example, the following over-simplified summary of the battle for the Siegfried Line town of Singling.

The 4th U.S. Armored Division had assigned as a Combat Command B objective the town of Singling. Combat Command A was to bypass the town and take the town of Bining. In attempting to bypass Singling, CCA came under direct fire originating in the Singling area and “lost five tanks upon topping the crest of a ridge south of the town.” Convinced that it was unwise to ignore the threat on the flank posed by the enemy forces in Singling, CCA sent a tank company with accompanying infantry to reduce the resistance there. The tank-infantry team reached the outskirts of the town under cover of friendly artillery and was deployed in an envelopment formation of three platoons when it began to receive hostile high velocity fire. The Allied tanks took cover in a walled orchard and behind several buildings. Any movement of the tanks brought in fire from the unobserved gun positions. Infantry located within the town several enemy guns (self-propelled guns and anti-tank pill boxes) and engaged them with shoulder fired weapons. It was “learned” (by what means not determined) that additional enemy armored weapons were in position back of a ridge 1200 yards north of the town. The CCA tankers anticipated the enemy attempt to reinforce the town’s defenders and a platoon occupied positions blocking the route of expected attack. When the enemy attempted his reinforcement, the Allied tanks waiting in the selected positions were able to ambush and destroy two Mk. IV tanks at close range. The reinforcement attempt was thwarted.

      This action near Singling has been considered as two engagements:

the attempt of CCA to bypass the town (Serial 87 of the Appendix) and,

the assault of Singling by the tank-infantry team (Serial 88 of the Appendix).

In both cases the Allies were considered the attackers. The question remains unanswered as to whether it would have been more reasonable to consider the battle for the town as three engagements:

the attempt to bypass,

the tank-infantry assault and

the attempted reinforcement by the German forces.

The above discussion should re-emphasize the fact that while the concepts of the tank engagement appear logically simple, their numerical descriptions, due to the individuality of battlefield situations, require arbitrary qualitative decisions.

Engagement Variables

The number of variables in a single or series of tank engagements is large. Some factors, if determined, may be easily tabulated: the number of opposing weapons, the weapons type, the identity of the attacker, the identity of the force which fires first, the identity of the force which disengages, the number of weapons casualties. Other variables are more difficult to evaluate or to tabulate. The advantage enjoyed by a force due to its better terrain or tactical situation, the value of morale and training, the effects of weather, the adequacy of communication facilities, the intelligence information, effects of supporting weapons such as aircraft—all factors which can be decisive in an engagement are not as easily evaluated. It seems unwise to defer all considerations until such a time when every variable can be described by its mathematical equivalent. Accordingly, attention is focused toward factors which are readily expressible.

A summary of the engagement studied, grouped according to the weapons type, attacker and the force which fired the first aimed rounds is shown in Table II. It contains for each group of engagements the number of such engagements considered, the numbers of weapons which the Allied and enemy forces committed to the battle, and the number of weapon casualties suffered by each force. In columns 3 and 4 identification of the force firing first and of the attacking force is made. The Allied force is denoted by A, the enemy force is denoted by E.

It may be seen in Table II that the Allied weapons have been placed in three groups:

M4: The “Sherman” tank. Usually not known whether gun was 75-mm or 76-mm.

TD: The tank destroyer; generally an M10, mounting a 90-mm gun.

Others: Any force composed of weapons other than one of the above. This includes any combination of the above as well as the 37-mm gun tank M5 and the 75-mm gun tank M24.

The enemy weapons have been grouped as follows:

Mk. V: The 75-mm gun tank, “Panther”

A/T: Towed anti-tank guns. Caliber and gun type usually unknown

SP: The self-propelled gun. Model not always known. It appears that a majority were 75-mm Stu.K. 40 mounted on Mk. III and Mk. IV chassis.

Others: Any force composed of weapons other than one of the above. Usually some combination of above weapons with the 88-mm gun tank Mk. VI “Tiger” and/or the 75-mm Mk. IV.

In the first line of Table II it may be seen that five engagements have been considered in which the Allies used M4 Sherman tanks, the enemy employed Mk. V Panthers, the Allies were attacking, and the Allies fired the first round. In the five engagements the Allies employed forty-one tanks, suffered two tank casualties. The enemy used seventeen tanks, had twelve destroyed.

In the eighty-six engagements in which the numbers of weapons and casualties are known, the Allies employed a total of 797 weapons, lost 149. The enemy used 327 weapons, lost 158.

 Table II: Engagements Grouped According to Allied and Enemy Weapons Type

Allied Weapon	Enemy Weapon	Who Fired First	Attacker	Number Engagements	Number Allied Weapons	Number Allied Casualties	Number Enemy Weapons	Number Enemy Casualties
M4	Mk. V	A	A	5	41	2	17	12
M4	Mk. V	A	E	19	104	5	93	57
M4	Mk. V	E	A	2	10	3	4	1
M4	Mk. V	E	E	1	11	1	5	2
M4	Mk. V	E	?	1	5	5	4	0
M4	Mk. V	?	A	2	17	5	24	0
TD	Mk. V	A	E	11	61	1	19	19
TD	Mk. V	E	A	1	4	0	3	1
TD	Mk. V	?	E	2	4	2	4	2
Others	Mk. V	A	A	2	13	1	9	9
Others	Mk. V	A	E	1	3	2	2	2
Others	Mk. V	E	A	1	2	2	1	0
Others	Mk. V	E	E	1	6	2	4	0
Others	Mk. V	?	A	1	9	9	3	0
M4	A/T	E	A	9	107	25	19	3
M4	A/T	?	?	1	32	9	3	1
M4	A/T	?	E	1	1	1	1	0
Others	A/T	E	A	3	38	7	8	0
M4	SP	E	A	2	33	4	2	2
M4	SP	?	A	2	32	1	4	1
Others	SP	E	A	1	5	4	2	0
Others	SP	?	?	2	37	2	3	2
M4	Others	A	A	1	15	6	6	6
M4	Others	E	A	3	40	12	12	3
M4	Others	?	?	3	70	9	36	21
M4	Others	E	E	1	15	0	10	1
Others	Others	A	A	1	14	0	3	3
Others	Others	E	A	4	44	19	19	4
Others	Others	?	?	2	24	10	7	6
Total				86	797	149	327	158

The Local Advantage of the Defense

The “advantage” of the defender is used in the sense of lower expected loss rate and does not consider the success or failure in accomplishing the mission of the engagement or the practicability of its extensive use in mobile warfare.

Shown in Table III is a breakdown of the considered engagements with respect to the attacker, defender, and weapon type. In the forty considered engagements in which they were on the attack, the Allies lost 100 of 437 employed weapons while the defending enemy lost forty-five of 135. In the thirty-seven engagements in which the enemy were attacking, they lost eighty-three of 138 weapons while the Allied defenders lost fourteen of 205.

The figures in Table III indicate that both the Allies and enemy had fewer casualties when used in the defensive role. This simply reaffirms that it was more costly in terms of local losses to take a position than to hold it once it was obtained.

Table III: Losses of Attacking and Defending Forces

Allied Weapons	Enemy Weapons	Number of Engagements	Attack Weapons	Attack Losses	Defend Weapons	Defend Losses	Attacker
M4	Mk. V	9	68	10	47	13	A
TD	Mk. V	1	4	0	3	1	A
Mixed	Mk. V	4	24	12	13	9	A
M4	A/T	9	107	25	19	3	A
Mixed	A/T	3	38	7	8	0	A
M4	SP	4	65	5	6	3	A
Mixed	SP	1	5	4	2	0	A
M4	Mixed	4	55	18	18	9	A
Mixed	Mixed	5	58	19	22	7	A
All Weapons	All Weapons	40	437	100	135	45	A
M4	Mk. V	20	98	59	115	6	E
TD	Mk. V	13	23	21	65	3	E
Mixed	Mk. V	2	6	2	9	4	E
M4	A/T	1	1	0	1	1	E
M4	Mk. IV	1	10	1	15	0	E
All Weapons	All Weapons	37	138	83	205	14	E
Total		77	575	183	340	59

The defenders generally chose positions which provided protective cover and visibility advantages in excess of those available to the attacking force. Well covered tanks, used in the defensive role, were able to survive artillery, air strikes, and even area tank fire. Then, in the selected positions, they were able in a majority of the cases, to initiate the actual aimed-at-target direct fire tank engagement. Study of the engagements suggest that the advantages enjoyed by the defender were a consequence of his greater likelihood of choosing the time, choosing the exact position, and initiating the direct fire engagement.

If the advantage of the defender was in part due to the greater probability of initiating the aimed-at-target-direct-fire engagement, it is not surprising that in engagements in which the attacker was able to first fire, it too enjoyed fewer casualties. That this occurred in the studied engagements may be seen in Table IV which contains a breakdown of forces and casualties as a function of the side which fired first for the sixty-eight engagements in which the facts were determined.

Table IV: Tank Losses of Force Firing First and Second

	Attacking Weapon	Defending Weapon	Number Engagements	Number First Fire Weapons	Number First Fire Losses	Number Second Fire Weapons	Number Second Fire Losses
Attacker Fired First	M4	Mk. V	5	41	2	17	12
	Others	Mk. V	2	13	1	9	9
	M4	Others	1	15	6	6	6
	Mk. V	M4	1	5	2	11	1
	Mk. IV	M4	1	10	1	15	0
	Mk. V	Others	1	4	0	6	2
Total			11	88	12	64	30
Defender Fired First	M4	Mk. V	19	104	5	93	57
	TD	Mk. V	11	61	1	19	19
	Others	Mk. V	1	3	2	2	2
	Mk. V	M4	2	4	1	10	3
	Mk. V	TD	1	3	1	4	0
	Mk. V	Others	1	1	0	2	2
	A/T	M4	9	19	3	107	25
	A/T	Others	3	8	0	38	7
	SP	M4	2	2	2	33	4
	SP	Others	1	2	0	5	4
	Others	M4	3	12	3	40	12
	Others	Others	4	19	4	44	19
Total			57	238	22	397	154
Grand Total			68	326	34	461	184

Of eleven engagements in which they fired first, the attackers lost twelve of eighty-eight weapons while destroying thirty of sixty-four defending weapons. Of fifty-seven engagements in which they fired first, the defenders lost twenty-two of 238 weapons while destroying 154 of 397 weapons. Thus in sixty-eight engagements thirty-four of 326 weapons were lost by the side which fired first while destroying 184 of 461 opposing weapons.

The numbers of tanks lost in the engagement as a function of the numbers used and their respective characteristics has important implications in weapons design. In BRLM 724, “Some Mathematical Models of Tank Combat,” H. K. Weiss considered certain tank versus tank engagements described in British reports (M.O.R.U. No. 33, “Tank Battle Analysis,” and AORG M-C6, “A Summary of Tank Warfare from D-Day to 12 August 1944”) and the appendix to the present report. He excluded from consideration any battle where it was not known who initiated the action (“fired first”) as well as, for purely mathematical reasons, engagements in which the side firing second had only one tank. Weiss showed that the outcome of the remaining engagements can be predicted by the use of formulae based on simple mathematical models of the engagement. Using the notation,

m  =   number of tanks on side firing first

mc      =   number of casualties on side firing first

n, nc   =   number of tanks and casualties on side firing second

Ln =   average number of rounds fired by each “m” tank multiplied by its single shot probability of a kill

 (a - 1)     =         maximum “effective” number of “m” tanks attacking an “n” as m/n increases without limit

Weiss developed the following expressions for the losses as a function of the employed forces:

For the side firing second,

nc/n = 1 - e-L(m/n)/(1 + am/n)

and for the side firing first,

mc/m = LmLn[ (n/nc) - 1 ]

For the BRL data, Weiss, ignoring differences amongst the employed weapons, estimated the appropriate values of L = 2 and a = .8.

Curves of the above functions and the data which they approximate were in BRLM 724 and are, for the convenience of the reader, shown in Figures 1 and 1a of the present report. In Figures 1 and 1a the Weiss curves are shown by the solid lines; the triangular symbols represent data points obtained by computing the average outcome of several engagements in which the ratios of engaged forces were not very different and finally the circular symbols indicate the observed results of the individual engagements. It is clear that while the Weiss curves are a close approximation to the average of the observed results, there was, as would be expected, considerable variation in the individual outcomes.

The implications of the Weiss curves are themselves of interest. For example, they predict that if two forces A and B of different size such that A > B were to meet equal enemies C and C, the larger force A would inflict greater damage upon the enemy than would its lesser counterpart B, but that in so doing would, on the average, suffer greater casualties. Thus the real advantage of a numerically superior force would not be realized in fewer immediate casualties, but rather in terms of its ability to cause the enemy through casualties or withdrawal to lose the battle. Economy of force would then be achieved by overmatching the enemy merely enough to “win” the battle.

The advantage enjoyed by one side in the majority of the tank engagements makes it important to know just what were its fundamental sources. One receives the impression from study of the individual actions that the source was composite. To the writer, three factors seem to stand out:

Information—exactly where the enemy was located;

Tactical mobility—the ability or inability to take advantage of the natural terrain features;

Rate of kills—the ability to capitalize rapidly on whatever advantage had been obtained.

Not to be ignored is the fact that engagements occurred in which the concept of defender and attacker broke down completely, engagements in which each side was in motion and presumably became simultaneously aware of the other’s immediate presence. Under these conditions, cover and surprise would appear less important and the rapidity with which killing rounds could be delivered could become decisive.

It is of interest to note that final victory can come only through advance but that immediate local advantage lies with the defender. It thus appears reasonable that a general advance might be a series of engagements in which each force would attempt to secure positions placing the enemy in such untenable situations as to force the opponent to attack or withdraw. Thus, in effect, an advance would be a series of local advances to positions capable of being inexpensively defended.

The Disengagement

Since anti-tank weapons, including tanks, generally were capable of rapidly causing tank kills, one might suspect that tank engagements were usually fought to the annihilation of one of the contending forces. The studied engagements do not indicate this to be accurate provided a force had at least about three tanks engaged. In six of the eighty-six engagements, the Allied force was annihilated, in forty-one of the eighty-six engagements, all enemy weapons believed to be present were destroyed. Of the eighty-one cases where a force of three or less weapons was employed, that force, in thirty-seven cases, was annihilated. Of ninety-one cases in which a force of over three weapons was used, the force was annihilated in only ten cases. It thus appears as if roughly half the engagements ended with the two forces, each with surviving weapons, effecting a disengagement.

Annihilation was less likely when large numbers of weapons were employed. This would be expected because of its greater ability to absorb losses and retain the wherewithal to destroy that which caused them or to withdraw.

It is of interest to note that in 100 of the considered 129 engagements, one force had no losses. This, it would appear, is a further indication of the fact that in a majority of engagements, one force tended to possess an overwhelming immediate advantage.

Ranges of Combat

A detailed discussion of the ranges of tank engagements of Northwest Europe, including the engagements considered in the present paper, is given in a previous BRL publication, “Terrain and Ranges of Tank Engagements.” A summary of the ranges at which the Allied and enemy tanks were destroyed in the areas of combat presently considered is shown in Table V.

Table V: Summary of Ranges at Which Allied and Enemy Tanks Were Destroyed in Various Areas of Northwest Europe

Area	Number of Allied Casualties	Average Allied Casualty Range in Yards	Number of Enemy Casualties	Average Enemy Casualty Range in Yards
Vicinity Stollberg	26	476	0	–
Roer to Rhein	37	959	6	733
Belgian Bulge	60	1000	9	833
Vicinity Arracourt	20	1260	74	936
Sarre	37	1116	35	831
Relief of Bastogne	19	731	16	915
Totals	199	946	140	893

It was shown in the referenced report that the distribution of combat ranges is approximately represented by a Pearson III distribution function of the form:

It was concluded that an approximate index to the combat casualty range of an area is given by the distances, measured in a random direction, between terrain objects capable of concealing the tanks. For further details of the ranges of the engagements, including ranges at defended points, ranges at which the opposing weapons first became intervisible, and a summary of a “sighting range” study of Northwest Europe, BRLM 702 should be consulted.

Numbers and Ratios of Weapons Employed

In the “mass” tank engagement it would appear that such factors as surprise, concealment, and the ability to initiate the fire fight would assume a minor role in the outcome of the engagement. In a series of engagements each with relatively few participating weapons and of short duration, it would appear that the above mentioned factors would be of major importance. Thus the degree of concentration of weapons is of interest.

The advantages of weapons concentration were discussed previously, however, always present are factors which tend to limit concentration, among which are: available weapons, sector responsibility, potential destruction by opposing weapons having favorable exchange value (viz. aircraft), compartmentalization of battlefield by terrain features, and imperfectly coordinated tactical units. Because of such factors it would appear that the number of weapons participating in the tank engagement was the result of several considerations. The implications of number of weapons in the tank engagement to weapon design assures that interest in it is not academic.

The number of participating weapons depends upon the decision as to what constitutes an engagement. With the previously stated engagement concept, the distributions of the number of Allied, enemy, and total participating weapons have been determined for the 88 engagements in which these facts were known. These are shown in Figure 2.

As can be seen in Figure 2, the numbers of participating weapons in the considered engagements were small. The average number of Allied weapons was 9.1, the average number of enemy weapons was 3.7, the average number of total weapons was 12.8. In fifty percent of the engagements the enemy used three or less weapons. In fifty percent of the engagements the Allies used six or less weapons. In fifty percent of the engagements the total participating weapons numbered fewer than twelve.

It is of interest to compare the number of Allied weapons used in a particular engagement to the number of employed enemy weapons. Table VI contains the frequency with which Ao Allied weapons engaged Eo enemy weapons.

It is apparent from Table VI that little, if any, evidence is present to support what might have been presupposed—that a large force tended to meet a large force and that a small force tended to meet a small force. On the contrary, the frequency table suggests the numbers of opposing weapons were completely independent.

The hypothesis of independence of numbers of Allied and enemy weapons in the individual engagements may be statistically tested. Employing a contingency table a grouping of the data is made such that the number of occurrences in each category be not smaller than, say five. The used contingency table is at Table VII.

The value of the D² statistic for the above table, using the well-known definition,

has been computed as 2.82. The D² value, having three degrees of freedom, of 2.82 indicates a value of P = .40. But the “critical region” of P is usually given as .05 > P > .95. Since P is not in the critical region, the hypothesis of independence of the number of Allied and enemy weapons involved in each engagement would not be rejected.

The hypothesis of independence can also be tested using the correlation coefficient approach. This may be preferable if the data are first transformed that they may reasonably be assumed to be approximately normally distributed. A square root transformation appears suitable. Using this transformation the computed correlation coefficient is .12 which is well below the five percent correlation value of .21 that would be required to reject the hypothesis of independence at the five percent level of significance.

Table VI: Frequency With Which Ao Allied Weapons Engaged Eo Enemy Weapons

		Eo – Number Enemy Weapons
		1	2	3	4	5	6	7	Over 7	Total
Ao – Number Allied Weapons	1	1	1	1						3
	2	3								3
	3	2	2	1						5
	4	6	5	1	5			1	1	19
	5	2	5	5	1			1		14
	6				1	1	1			3
	7
	8		1						1	2
	9	3	1	2						6
	10						1	2	1	4
	11			3		1				4
	12					1		1		2
	13		1							1
	14	2		1						3
	15		2	2		1	1		1	7
	16	1	2	1					1	5
	17		1							1
	18
	19
	20	2								2
	Over 20	1	1	1					1	4
Total		23	21	19	7	4	3	5	6	88

The hypothesis of independence of numbers of participating weapons receives further support from the distribution of the total number of weapons in the individual engagements.

An engagement involving n weapons would have resulted had the Allies used 1, 2, … n-1 weapons in the same engagement in which the enemy used n-1, n-2 … 1 weapons respectively. Let P(Ai) indicate the fraction of engagements in which the Allies employed just i weapons; P(Ej) indicate the fraction of engagements in which the enemy employed just j weapons, and the fraction of engagements having a total of n weapons denoted by P(n). With the assumption of independence, the probability that the Allies used i weapons in the same engagement in which the enemy used j weapons is computed as the product of the probabilities of their individual occurrence. Thus

P(Ai, En-i) = [P (Ai) ] & [&P (En-i)]

Now an engagement involving n weapons could have resulted from each of n - 1 combinations of numbers of opposing weapons. The probability that an engagement would include just n weapons is, assuming independence, given by the following formula:

Table VII: Frequency of Occurrence: Number Allied Versus Number Enemy Weapons

Number of Allied Weapons	Number of Enemy Weapons		Total
	1-3	Over 3
1-4	23	7	30
5-8	13	6	19
9-12	9	7	16
Over 12	18	5	23
Total	63	25	88

Using the above relation, the probabilities of the occurrence of engagements involving 2, 3 … weapons have been computed. The cumulative distribution of the percent engagements in which n or more weapons would have been expected to be involved has been obtained from these probabilities. This hypothetical distribution is shown in Figure 2 by the crosses. The close agreement between the observed distribution of total numbers of engaged weapons and the predicted distribution assuming independence appears to give added support to the hypothesis of independence of numbers of Allied and enemy weapons.

It has been previously stated that the Allies used 799 weapons in the eighty-eight engagements and that the enemy used 328 weapons. Therefore the expected number of Allied weapons per battle was 9.1, the expected number of enemy weapons was 3.7. Thus, the ratio of the expected numbers was 9.1/3.7 or about 2.5/1. Since the numbers of weapons engaged appear to have been independent, and in any case the forces would not have repeatedly engaged at a fixed ratio, it is of interest to note that the nature of the distribution of ratios of Allied to enemy weapons.

The cumulative distribution of the ratio of Allied weapons to enemy weapons is shown in Figure 3 by the circular symbols. Values of the ratio R where R = Ao/Eo are shown in the upper horizontal scale for .25 < R < 25.0. The lower scale gives the value of the ratio of the involved weapons in units of Q, the expected ratio, where Q = Ao/Eo = 2.5/1. Thus a value on the R scale of five indicates that the Allies outnumbered the enemy by a factor of five. This, it may be seen from the Q scale is greater than the expected ratio of 2.5/1 by a factor of two. On the vertical scale which shows the percent engagements having the ratio of forces less than R, it may be seen that an Allied numerical superiority this great or greater occurred in about one of five engagements.

Actually, the ratios in Figure 3 are plotted on logarithmic paper. On this paper the cumulative distribution of force ratios is seen to be nearly symmetric about the ratio of the number of weapons each force employed on the average. This is equivalent to stating that the Allied and enemy forces were equally likely to engage the opponent at a force ratio differing from the ratio of expected forces by any constant factor. Secondly it appears as if the logarithm of the ratios are approximately normally distributed, as is indicated by the closeness of the data points to the solid curve of Figure 2 which is a cumulative Logarithmic—Normal distribution. This distribution is defined as

        

where F(R) is the fraction of engagements having ratio less than R. The fit is indeed rough and any distribution of ratios based on only eighty-eight engagements is of limited reliability. However, the function has been checked against a sample of over 250 engagements the details of which are given in British publications M.O.R.U. No. 33 and AORG M-C6 and the distribution form above was seen to be a reasonable approximation. Thus, although nothing has been finally established concerning the distribution of ratios of engaged weapons, the logarithmic normal distribution is suggested as a first estimate. The advantage of such a distribution is that it provides the evaluator with some information as to the frequencies with which forces engaged at various ratios, given that the overall ratio of forces committed, is known. This, it appears, is at least one step better than previous assumptions that forces always engage in the ratio of their total strength.

Summary and Conclusions

Some tank engagements of World War II have been studied. No attempt was made to evaluate many of the influential factors. Efforts were made to separate the facts from the confusion, heroics, and the claims of the participants. Tentative observations have been made with reference to several aspects of the tank engagement-observations not indisputably proved but which have some quantitative support. Among the observations are the following:

A great advantage was had by a force which initiated the aimed-at-target direct fire action. The ability to initiate the action was associated with the tactical employment of the weapons, the “de­fenders” possessing a marked advantage.

The number of tanks involved in the actual direct-fire fight was generally small. The number of potential tank targets for a given tank was limited. Concentration was as much a concept of time as space.

The number of weapons employed in the Allied force was independent of the number of enemy weapons. The distribution of the ratio of forces is roughly approximated by a logarithmic-normal distribution.

Roughly half of the tank engagements ended by one force disengaging. Annihilation of a force of over three tanks was rare, occurring in about one of nine engagements.

The tank when used in the anti-tank, or defensive role, knocked out more tanks than it suffered casualties. On the other hand, the tank casualties were high when attacking positions defended by any of the various anti-tank weapons.

The difference in combat effectiveness of the various weapons is not apparent from the present study. The smallness of the sample size, the large number of variables, and the relative insensitivity of the engagement outcome to minor differences in weapons characteristic combine to conceal any existent differences. Whatever major differences in weapons effectiveness were existent have not been ascertained.

If a single conclusion be permitted on the basis of the present study it is that a critical weakness of both the Allied and enemy tank was the inability of its crew to obtain information as the exact location and nature of the hostile weapons. The records repeatedly indicated that the tank engagements generally developed suddenly, often unexpectedly, and usually ended quickly. The advantage of firing the first aimed rounds, the relatively small numbers of casualties per battle, the independence of numbers of opposing weapons, the fact that one force suffered no casualties in seventy-seven percent of the engagements—all suggest that at least one force generally was engaged with an enemy whose immediate location was not previously recognized. Unless they can be made relatively invulnerable to opposing fire (and this, with conventional armor, seems improbable without crippling mobility) it appears that tanks might be profitably improved by

providing the crew with the means for more quickly detecting the location of opposing weapons, and

lessening the time required to obtain a killing hit once the target is identified.

Bibliography

Documents obtained from the Departmental Records Branch, The Adjutant General’s Office, Washington, D.C.:

Combat Interviews:

      261-269, 272-275

 Journals:

	Log	Envelope
	8	1, 2, 4
	49	1
	61	1, 2, 4, 5, 8, 9, 15, 19
	158	1
	461	11, 12, 13
	470	1, 35, 36, 38
	508	1, 27
	546	31, 33, 34
	564	1, 32, 33
	601	1, 26, 27, 28
	666	1, 39, 40, 41
	688	1, 35, 36, 37
	736	1

Unit Histories:

      603-0      (27613)       -           Third Armored Div.

      604-0      (276111)    -           Fourth Armored Div.

BRLM 702, “Terrain and Ranges of Tank Engagements,” D. C. Hardison, R. H. Peterson, A. A. Benvenuto.

BRL 724, “Some Mathematical Models of Tank Combat,” H. K. Weiss.

M.O.R.U. No. 33, “Tank Battle Analysis.”

AORG M-C6, “A Summary of Tank Warfare from D-Day to 12 August 1944,” H. G. Gee.

Appendix

The following appendix contains a brief summary of each considered engagement. The following notations are used:

      Ao = number of Allied weapons at outset of engagement

      AL  = Number of Allied casualties

      Eo = Number of enemy weapons at outset of engagement

      EL = Number of enemy casualties

      Rc = Combat range at which tanks were destroyed

      RI = Range of Intervisibility of weapons

      WFF = Which force initiated the aimed fire engagement

Serial	Ao	AL		Eo	EL	Rc	RI	WFF	Type Weapon		Attacker	Who Withdrew	Remarks
									Allied	Enemy
2a	10	1		?	0	150	?	E	M4	A/T		A	The A/T was concealed in woods, tanks in column on road. After first loss, tanks deployed, called artillery.
4a	?	3		?	6	1200-800	?	?	M4	A/T	A
6b	?	2		1	0	350	?	E	M4	A/T	A	A	Tanks attacking across gentle rolling open valley. No mention of returning A/T fire.
6c	?		2	1	0	600	?	E	M4	A/T	A	A	A/T concealed at edge of woods, Allies unaware of its presence until tanks were destroyed.
15	5		1	2	0	1600	?	E	M4	A/T	A	–	The destroyed M4 was part of a reconnaissance force. It “forgot its objective and stopped to shoot up a haystack. Once it thus presented a stationary target it was destroyed.”
16	24		4	2	2	1000	2200	E	M4	A/T	A	–	Terrain very flat and open—visibility up to 3600 yards along axis of attack. The A/T guns were “captured,” the objective was taken.
20	15		3	2	0	1000	1100	E	M4	A/T	A	?	“The leading three tanks were destroyed.” The attack continued, bypassing the A/T.
21	15		4	3	0	1200	1900	E	M4	A/T	A	A	A/T guns in four positions, possibly only three fired. The tanks had traveled 1500 yards while in view of at least one A/T before the A/T opened fire. Two M4 had mechanical difficulties and were abandoned.
24	9		4	3	0	1200	1400	E	M4	A/T	A	–	The Allied tanks were traveling to what they believed to be a cleared town when suddenly hit by fire from A/T. These guns had been previously engaged by other Allied forces who had, by employing smoke, temporarily isolated the A/T guns.
25	15		2	2	0	1300	1300	E	M4	A/T (88-mm)	A	A “delayed”	The tanks were destroyed just as they left the concealment of the town which was to have been line of departure. The attack was delayed until air and artillery hit the defense.
29	5		3	3	0	800	1200	E	M4	A/T	A	A	The tank platoon was leading an attack across open field between Berrendorf and Graven—villages 1200 yards apart. When 400 yards from line of departure they drew fire—the two survivors returned to Line of Departure.
33	?		4	2	0	300	1000	E	M4	A/T	A	–	As the Task Force marched down the road in column it was hit by fire from concealed A/T who were in ideal position on wooded hillside across stream from the column. Not clear what action task force took.
53a	6		4	?	0	1000	1800	E	M4	A/T	A	A	Tanks confined to road in bottom of valley. Two survivors took cover of nearby houses.
53d	1		1	?	0	1200	1800	E	M4	A/T	A	–	Tank hit as it left concealment of a house—A/T fire originated at edge of woods.
54	32		9	3	1	?	?	?	M4	A/T	?	?
67d	1		1	1	0	1500	1500	?	M4	A/T	E		The M4 was moving to take up a defensive position when hit by A/T which was covering German attack.
94	14		3	1	1	1400	1400	E	M4	A/T	A	–	The A/T guns were on wooded hillside covering the sole route of attack—a road in valley.
95	5		1	1	0	1500	1500	E	M4	A/T	A	G	Tank destroyed as it topped crest of a hill. The A/T withdrew quickly upon receiving counterfire.
6a	?		2	1	0	500	500	E	M4	SP	A	A	Allied force probably a platoon—did not return fire until they had cover.
8	30		5	?	0	500	500	E	M4	SP	A	A	“The second pair of companies lost five tanks immediately on jumping off”—objective was a patch of woods 500 yards across an open field from the line of departure.
30	16		1	3	0	400	400	?	M4	SP (88)	A	E	Allies used smoke to isolate the SPs, continued overrun the objective. The SP abandoned the defense.
31	16		0	1	1	?	?	?	M4	SP	A	–	The single SP was at an outpost position. Only one Allied tank fired and “with 9-11 rapid shots—set it on fire.”
85	3		1	1	1	1300	1300	E	M4	SP	A	–
96	30		3	1	1	900	900	E	M4	SP	A	–	The SP was also hit by a P-47 aircraft.
71	15		0	10	1	2000	2200	E	M4	Mk. IV	E	E	Soggy terrain confined tanks to roadways. Apparently a lot of long range shooting. Fire fight continued for six hours with only the single casualty.
72	20		3	?	0	1800	1800	E	M4	Mk. V	A	A	Two additional M4s destroyed by Allies as they bogged in mud attempting to deploy. Allies withdrew because mud too restricted maneuverability of tanks.
17	5		1	1	1	200	200	E	M4	Mk. V	A	–	Battle fought on the streets of Cologne.
32b	5		5	4	0	1400	1400	E	M4	Mk. V	?	–	Allied tanks were in march to what they believed to be the front when ambushed by the Panthers who had a commanding hill position overlooking the road.
73	17		0	3	2	1000	1000	A	M4	Mk. V	A	E	M4s used cover of houses of a village for protection while hitting the Panthers which were confined to roads by mud.
74	5		1	3	3	700	700	A	M4	Mk. V	A	–	Both forces were in motion, neither had cover. Appears that forces “stumbled across each other.”
76	5		2	3	0	1800	1800	E	M4	Mk. V	A	E	Artillery was used to dislodge the Panthers at long range. The destroyed M4s were bogged in mud before hit.
78	5		0	?	2	500	1000	A	M4	Mk. V	E	A	Enemy used artillery to cover attack of tanks, abandoned attack when mud and losses became too great.
79	5		1	3	2	2 500 1 300	500 1200	A	M4	Mk. V	A	E
81	5		1	?	0	1000	1000	E	M4	Mk. V	A	E
82	11		1	5	2	50	50	A	M4	Mk. V	E	E	Attack launched during very dark night—visibility about 50 yards. Allies held fire to not reveal positions, assure a hit when first round was fired.
83	10		0	7	4	900	900	A	M4	Mk. V	A	E	Enemy tank in woods commanding best route of approach to Allied objective. Artillery barrage and tank fire concentrated on enemy positions. Not positively ascertained what weapon inflicted damage.
84	10		0	?	4	800	800	A	M4	Mk. V	A	E	Essentially a static battle. Both forces in woods exchanging shots. Artillery used by both forces.
86	10		0	10	2	1000	2100	A	M4	Mk. V	E	E	Allied on wooded hill position. Met enemy attack with artillery but destroyed tanks were hit by AP rounds.
91	16		4	21	0	200	200	?	M4	Mk. V	A	A	Allies began attack on town of Chaumant with 22 M4s. Six became bogged so only 16 continued attack. Upon entering town the M4s met an enemy counterattack. Eleven M4s were abandoned in the town which was then shelled by artillery. The following day seven of the abandoned tanks were recovered.
97	4		0	1	1	1300	1300	A	M4	Mk. V	A	–
98a	6		0	5	5	1000	1000	A	M4	Mk. V	E	–	Allies had hull defilade positions in open field.
35	3		2	1	1	600	600	A	M4	Mk. V	E	–	Allied tanks at roadblock positions, opened fire on Panther who returned fire to destroy two M4s. The Panther was destroyed by an infantry bazooka.
53c	1		1	3	0	200	200	?	M4	Mk. V	A	–	City engagement.
53e	4		3	?	0	2000, 1700	2000	E	M4	Mk. V	A	?
57a	4		0	2	2	75	75	A	M4	Mk. V	E	–	Extreme range due to heavy fog.
57b	4		0	1	1	600	600	A	M4	Mk. V	E	–	Allied tank platoon in outpost position, single enemy tank apparently on patrol mission.
57c	4		0	12	5	900	900	A	M4	Mk. V	E	See remark	The attack was continued with a changed axis.
57d	4		0	7	3	1300	1300	A	M4	Mk. V	E	See remark	This engagement involved seven enemy survivors of engagement 57c but different Allied forces. The attack continued.
57e	4		0	4	3	500	500	A	M4	Mk. V	E	See remark	Forces are the survivors of 57d who had moved to new positions. Allied platoon got to commanding hill and waited for enemy force to arrive. And then there was one…
57f	4		0	1	1	2000	2000	A	M4	Mk. V	E	–
63	8		1	22	17	3 700 14 2000-400 1 2000							Enemy attacked from woods across open valley commanded by Allied positions. Assault dissipated at 400 yards, enemy withdrew to woods. At end of fight Allied tanks possessed only 12 rounds of ammo.
64a	4		0	4	2	900	1300	A	M4	Mk. V	E	E	Allied tanks at defensive hill positions repulsed enemy thrust.
64b	4		0	4	1	600	1400	A	M4	Mk. V	E	E
66	2		2	?	0	800	1500	E	M4	Mk. V	E	–
67a	5		0	2	2	600	2400	A	M4	Mk. V	E		Might possibly be better described as a single engagement. The Allies employed only nine tanks, the enemy used ten. These actions were a series of thrusts by the enemy in an attempt to take hill positions held by the two Allied platoons.
67b	5		0	2	2	900	2000	A	M4	Mk. V	E	–	See above remark.
67c	5		1	2	0	1500	1800	A	M4	Mk. V	E		See above remark.
67d	4		1	2	0	1500	2200	A	M4	Mk. V	E		See above remark.
67e	4		0	4	2	1500	1500	A	M4	Mk. V	E	E	See above remark.
67f	4		0	2	2	1300	1300	A	M4	Mk. V	E	–	See above remark.
98b	6		0	6	6	100	1000	A	M4	Mk. V	E	–	Same Allied tanks and positions as 98a. Enemy used different route of attack, was again annihilated.
69	? ”(Bn)”		0	?	1	1500		A	M4	Mk. VI	E	–
2b	?		5	?	0	?	?	?	M4	?	A	A
9	5		1	?	0	600		E	M4	?	A	A
93	5		1	?	0	?	?	?	M4	?	A	?
19	5		0	3	3	1000	?	A	M4	1 Mk. VI 2 Mk. IV	?	–	Enemy tanks attempting to escape other Allied forces, inadvertently passed by the platoon which destroyed them.
22	15		6	5	0	300	1100	E	M4	2 tanks 3 A/T	A	A	The attacking Allied tanks were allowed to cross about 800 yards of open field before the enemy defenses opened fire. “The attacking tank company became disorganized and pulled back to the line of departure.”
23	15		6	6	6	200	?	A	M4	1 tank 3 A/T	A	–	Same defenders as in 22. Allied attack was preceded by liberal use of smoke. The enemy weapons were “captured.”
26	13		2	2+	0	2200	2200	E	M4	2 Mk. V 7 A/T	A	Allies “delayed”	The Allied tanks were hit upon jumping off. The attack was delayed and re-routed along a more covered approach.
59	50 (approx.)		.5	30 (approx.)	15	1 Mk. IV 1600 1 Mk. IV 500 1 Mk. IV 1400 12 Mk. IV 700 1 M4 700 3 M4 2200	1600     500   2000     700   1000   2200	?     ?   ?     ?   ?   ?	M4     M4   M4     M4   M4   M4	Mk. IV     Mk. IV   Mk. IV     Mk. IV   Mk. IV   A/T	A	E	This engagement waged over a period of three hours. Possibly was a series of discreet actions but incomplete records make more detailed analysis impossible.
61	? (Bn)		1	2	1	2200, 800	2200	E	M4	1 Mk. V 1 A/T	A	–
68	12		2 to A/T 2 to Mk. V	5	3	1000	1000	E	M4	3 Mk. V 2 A/T	A	A	Tanks were confined to roads. Part of Allied tanks could not get in position to engage enemy forces.
80	15		1	?	0	3500	3500	E	M4	Arty	A	A
70	15		4	?	1	3 M5 1200 1 M4 1500		E	M4, M5	Mk. V	E	A	Allies had moved on road to an untenable position between railroad and river. Muddy terrain presented even restricted maneuver. It appears as if the German attack was aided by 88-mm dual-purpose guns.
75	5		0	7	7	5 200 2 100	See re­marks   Open field of 2000 yards	A	M4, ba­zooka	Mk. V	A	–	A classic engagement. Allied artillery pinned down enemy tanks, when Allied tanks within 200 yards of enemy tanks, artillery lifted, tanks opened up from flanks. Bazookas knocked out two Mk. Vs.
89	10		1	?	1	200	?	?	M4, M5	Mk. V	A	A
11	2		2	1	0	400, 800	400, 800	E	M5, TD	Mk. VI	A	–
5	11		1	3+	3	1 M4 400 by Mk. IV; 1 Mk. IV 400 by TD; 1 Mk. IV 75 by TD; 1 75-mm SP 25 by TD		E	9 M4; 2 TD	Mk. IV; SP	A	E	Exact number of enemy not known. Fight included infantry and continued all day.
13	14		7	?	0	200	200	E	M4; M5	“Fortress”	A	A	The “fortress” consisted of AT pillboxes, tanks, A/T and SP. It never was successfully assaulted, only bypassed and “captured” a month later.
14b	21		0	?	0	700	700	E	M4; M5	“tanks”	A	–
14d	21		0	1	0	100	neither side fired		M4; M5	“tanks”	–	–
14e	21		0	?	0	200-800		E	M4; M5	“tanks”	see remarks	–	Allies attempting  to return to original positions. Had been on a night patrol, encountered several enemy tanks, refused to fire on some, escaped fire from others.
27	? (Co)		3	?	0	200	200	E	M26; M4 (75); M4 (76)	?	A	?	Company in open field in city of Cologne. Defense in a factory area. Details of engagement unavailable.
41	14		0	3	3	See re-marks	See re-marks	A	M5; bazooka	Mk. IV; A/T	A	–	Second attack on objective (see 40). Mk. IV destroyed by bazooka, A/T guns “overrun.” It is probable that crews abandoned them.
7	? (task force)		8	?	0	1000, 400		E	M4; TD	SP	Allies marching	A	The task force was stretched over eight miles of road. Only the forward elements were actually engaged. The enemy SPs were in position on ridges on both sides of road—waited for lead elements to get past them. Opened up on flanks of columns. Column was “caught unprepared for attack.”
14c	21		0	1	0	50		no shot fired	M4; M5	SP
51	16		2	2	2	400	400	?	M4; M5	SP (88)	A	–	One Allied tank hit mine, a second one was hit by SP. The remaining 14 attacked the SP positions, hit one and forced crew to abandon the other. It was captured.
90	5		4	2	0	200	200	E	M5	SP	A	A	SPs located in town. Allied light tanks unable to dislodge SPs from cover of buildings.
18	2		2	1	0	200	200	E	1 M26; 1 M4	Mk. V	A	–	Enemy hit the M26 in machine gun part disabling it. Then continued to destroy the M4 which had had AP bounce off the front glacis plate of the Panther.
28	31 Bn		0	5	4	1000, 400, 100	See re-marks	A	M24; TD; bazooka	Mk. V	A	E	Battle started before dawn, continued until early morning. The enemy tanks were surprised by the Allied column. Enemy attempted to escape only to run into another company of tanks.
32a	6		2	4	0	2000	2000	E	M4; TD	Mk. V	E	See remarks	Allied position at a roadblock. Enemy brought fire from edge of woods across a valley, continued on attack bypassing defended road junction.
37	3		2	2	2	M4 by Mk. V, 75; M5 by Mk. V, 75; Mk. V by bazooka 75; Mk. V by M4, 400		A	M4; M5; bazooka	Mk. V	E	–
52	8		1	2	2	200	200	A	M4; TD	Mk. V; mine	A	–
53b	9		9	3	0	200	200	?	M5	Mk. V	A	–	Two platoons of Allied attempting to take Sterpigry. Reached town and were then destroyed by the Panthers “just like a milk run—one at each house.”
58f	?		0	2	2	200		A	arty	Mk. V	E	–
87	30		14	?	0	1100	1100	E	M4	Arty; pill-boxes	A	A	As the Allied column topped the crest of a small ridge it drew fire from a heavy defensive unit placed on ridge. Five tanks were destroyed immediately. Nine others became bogged in attempt to deploy and were later destroyed by artillery.
88	14		5	?	2	1 M4, 200; 1 M4, 1200; 1 M4, 200; 1 M4, 300; 1 M4, 1200; 1 Mk. V, 150; 1 Mk. V, 800	200   1200   200   300   1200   150     800	see re­marks	M4	Mk. V; SP			Might more accurately be described as a series of incidents in the taking of a small town. Although Allies had 14 tanks they were employed as platoons which attacked different parts of the town. Good records show that tanks used cover of buildings, that losses occurred when they betrayed (by movement) their concealment.
92	15		4	3	3	400 or less	?	See re­marks	M4	2 Mk. V; 1 SP; bazooka	A	E	Company attack of a small town. Fought as three platoons. Range not greater than 400 yards. First platoon lost three M4 to a single SP. Second platoon lost an M4 to bazooka, knocked out a Mk. V. Third platoon lost M4 to SP, then destroyed it.
6b	?		2	?	0	150	?	E	M4	bazooka	A
10	2		1	?	0	?	?	E	M4	bazooka	A	A
57g	4		1	1	0	100	?	E	M4	bazooka	E	?
14a	21		0	?	0	600		E	M4; M5	A/T	A	A
39	7		4	2	1	650	?	E	M4; M5	A/T; mines	A	?	Two M5, one M4 hit mine field. A third M4 hit by A/T gun which was covering mine field.
40	16		2	2	0	650	650	E	M5	A/T (88)	A	See remarks	The task force was marching on road through woods. Met fire just as it left edge of woods to assault town. Delayed attack (see 41).
47	11		2	3	0	800	800	E	7 M4; 4 TD	A/T	A	A
48	11		3	3+	0	1300, 2500	1300, 2500	E	7 M4; 4 TD	A/T	A	?
49	? (task force)		3	?	0	1500, 1700	2500	?	–	A/T	A	A
43	12		6	7	0	2, 1000; 2, 300; 2, 1800	1600   3000   1600	E	M4; M5	TK; A/T; mortar	A	A	A perfect ambush. Enemy had ridge positions on both sides of road leading to town. Also had tanks in town. Allied column allowed to march within 300 yards of town, then received fire from both flanks as well as frontal sector.
44	10		10	7	0	300, 1000, 1200		E	M4; M5	A/T; TK5	A	–	Same town as Engagement 43. This was second unsuccessful effort to take the town. Not apparent that this attack plan was any different from the first which had failed.
46	?		0	?	2	500		?	M4; M5; TD; bazooka	SP; Mk. IV	A	E	Allied and enemy weapons both in same woods. Enemy weapons driven out.
1a	10		6	6	6	?	?	?	?	?	?	?
1b	5		0	?	4	?	?	?	?	?	?	?
3	?		?	?	0	1000		E	M4; TD	?	E	A
42	14		4	1	0	1000	100	?	M4; M5	?	A	A	The Allied tanks hit a mine field which immobilized two M4s. Two others hit by anti-tank fire which was covering the mine field.
55a	4		1	2	2	100	100	A	TD	Mk. V	E	–
55b	3		0	3	3	1900	1900	A	TD	Mk. V	E	–	Neither force moving. Exchange of long range shots.
55c	3		2	2	0	600	600	?	TD	Mk. V	E	A	Ditto, shorter range.
55d	1		0	2	2	600	600	?	TD	Mk. V	E	–
56a	4		0	4	4	1000	1600	A	TD	Mk. V	E	–	This is a series of attacks on a single position held by four TDs. Each time a Panther appeared it was destroyed by TD fire. The TDs were  place in “an ideal TD position.” A depression on the reverse slope of a ridge overlooking a broad gentle open valley.
56b	4		0	1	1	800	800	A	TD	Mk. V	E	–	See above remark.
56c	4		0	1	1	1100	1100	A	TD	Mk. V	E	–	See above remark.
56d	4		0	2	2	1200	1300	A	TD	Mk. V	E	–	See above remark.
58a	9		0	2	2	400	400	A	TD	Mk. V	E	–	Terrain much more open though range indicate very foggy morning.
58b	9		0	1	1	300	300	A	TD	Mk. V	E	–
58c	2		0	1	1	1600	1600	A	TD	Mk. V	E	–	Second TD adjusted range by observing first round of first TD. Later found that crew abandoned Panther prior to first hit.
58d	9		0	1	1	1800	1800	A	TD	Mk. V	E	–	Neither force was moving.
58e	9		0	1	1	3000	3000	A	TD	Mk. V	E	–	Required three rounds to get a hit. Neither force moving.
77	4		0	3	1	2200	2200	E	TD	Mk. V	A	E

Knocked out M4 medium tanks of the 4th Armored Division burn in a field near Avranches, France, 31 July 1944.

M4 medium tanks of the 8th Tank Battalion, 4th Armored Division, pass through Coutances, France, 31 July 1944.

M7 howitzer motor carriage of the 4th Armored Division moves through a French town.

An M4A1 medium tank (left) and an M4 (105mm) howitzer tank in a field near Chartres, France, 16 August 1944.

M4 medium tank of 8th Tank Battalion, 4th Armored Division, in action near the Marne River, 21 August 1944.

M4 medium tank of the 8th Tank Battalion, 4th Armored Division, in action near the Marne River near Rashecourt, 31 August 1944.

M4A1 medium tank with Cullin hedgerow cutter moves through Aubencheil-Aubac, near the French-Belgian border, 2 September 1944.

Tanks of the 4th Armored Division ford the National Canal near Bayon, France, after the Germans destroyed the bridges over the Moselle River. An M4A3(76)W climbs the bank of the canal and soon pulled out the M4A1 seen stuck in the mud. The capture of Nancy soon followed.

Crew of an M4 of the 37th Tank Battalion, 4th Armored Division, sets up camp for the night near Chateau Salinas.

Three knocked-out PzKpfw. V Panther medium tanks and an M4A3(76)W medium tank litter a portion of the battlefield near Arracourt where a battle between the 4th Armored Division and the German Fifth Panzer Army from 19 to 22 September 1944 resulted in German losses of 107 tanks and 30 StuGs against American losses of 14 M4 medium tanks and 7 M5A1 light tanks.

Captain J. Brady, commander of A Company, 35th Tank Battalion, 4th Armored Division, after the Arracourt battle.

An M4A1 medium tank of the 3rd Armored Division guarding a road near Manhay, Belgium, 23 December 1944.

An M4A3(76)W medium tank moves forward during the relief of Bastogne, 27 December 1944.

M4 medium tanks of the 4th Armored Division near Sainlex, Belgium, on the way to Bastogne.

“Block Buster 3rd”, an M4A3(W)76 HVSS of B Co., 37th Tank Bn., 4th Armored Division, after it arrived in Bastogne.

An M4 medium tank of the 4th Armored Division moves past a .30-cal. machine gun team of the 104th Infantry Regiment keeping open the corridor to Bastogne on 3 January 1945.

Track repair on an M4A1(76)W medium tank of the 32nd Armored Regiment, 3rd Armored Division, near Trou-de-Bra, Belgium, 3 January 1945.

A new M4A3(76)W HVSS medium tank of the 4th Armored Division covers the H-4 highway outside Bastogne on 8 January 1945. Note the painted out turret star.

Soldiers of the 75th Infantry Division move along a road into Basse, Belgium, past M4 medium tanks.

An M4 medium tank unit deployed for an attack in Belgium in January 1945.

An M4A3(76)W medium tank passes by an abandoned PzKpfw. IV medium tank along the Houffalize road outside Bastogne on 15 January 1945.

A task force of M36 gun motor carriages and M4 medium tanks prepare for an attack in Belgium, January 1945.

M4(105) howitzer tanks of the Headquarters Company, 774th Tank Battalion, providing fire support for the 3rd Armored Division, and 75th Infantry Division, 16 January 1945.

An M4A3(76)W medium tank of the 3rd Armored Division passes a knocked out PzKpfw. V Ausf. G Panther medium tank, 17 January 1945.

An M4A3(75)W medium tank knocked out by a German anti-tank gun in Belgium, 25 January 1945.

M4A1 medium tanks (and an M32 armored recovery vehicle, left) of the Third Army advance across the field towards Binsfield, Germany, in support of the 76th Infantry Division, 8 March 1945.

An M4A3E2 Jumbo assault tank (left) and an M4A3(76)W HVSS medium tank of the 37th Tank Battalion, 4th Armored  Division, in Alzey, Germany, 20 March 1945.

An M4A1 DD (Duplex Drive) amphibious medium tank of the Third Army moves through Braunshorn, Germany, on its way to the Rhine River, March 1945.

M4 medium tanks, including an M4A3E2 Jumbo in the lead, moves along a road littered with the smoldering remains of a German column, Germany, April 1945.

An M4A3(76)W medium tank moves up behind a burning M5A1 light tank in a town in Germany during an attack on 4 April 1945.

An M4A3(76)W medium tank leads a Third Army armored column into Austria near Lembeck, 3 May 1945.

M10 gun motor carriages (GMC) move across a stream, France, August 1944.

An M10 GMC and an M5A1 light tank guard a crossroads in a French village, August 1944.

An M10 GMC passes through a French town, August 1944

M10 GMCs firing on German positions near the German border, 14 September 1944.

An M18 GMC guards a street in a French town, 22 September 1944.

M10 GMCs advance into Aachen, Germany, 14 October 1944.

M36 GMCs during training in France before deployment in combat, 14 October 1944.

An M10 GMC during a night fire mission.

An M36 GMC dug-in at a crossroads near Manhay, Belgium, 27 December 1944.

An M18 GMC of the 704th Tank Destroyer Battalion and an M15A1 Multiple Gun Motor Carriage (MGMC) of the 4th Armored Division knocked out on the approaches to Bastogne, 29 December 1944.

An M10 GMC of the Third Army in Luxembourg, 3 January 1945.

An M36 GMC of the 703rd Tank Destroyer Battalion, 3rd Armored Division, passes a knocked out PzKpfw. IV of the 115th Panzer Abteilung, 15th Panzer Division, south of Langlir, Belgium, 13 January 1945.

An M10 GMC of the 703rd Tank Destroyer Battalion, 3rd Armored Division, guarding a road in Belgium, 6 January 1945.

An M10 GMC of the Third Army in action during the fighting along the Sauer River near Echternach, Luxembourg, 7 February 1945.

M10 GMCs in a village in France, 24 February 1945.

An M36 GMC guards half-tracks and jeeps of the 23rd Armored Engineers, 3rd Armored Division, in Duren, Germany, 26 February 1945.

An M18 GMC of the 704th Tank Destroyer Battalion, 4th Armored Division, crosses the Moselle River on a treadway bridge, 15 March 1945.

An M36 GMC provides cover for GIs of the 301st Infantry, 94th Infantry Division, Third Army, from German artillery in Schillingen, Germany, 15 March 1945.

An M36 GMC of the Third Army reloads near Sertig, Germany, 16 March 1945.

An M4 medium tank and supporting infantry fighting in France.

M10 GMCs in action in Aachen, Germany.

M4 medium tanks and M10 GMCs of the Third Army advance across a field.

Knocked out burning M4 medium tank.

Knocked out burning Panther during the Battle of the Bulge.

GIs examine the effect of German tank guns on an M4 medium tank. At least six large caliber rounds have pierced the vehicles frontal armor.

The crew of the M4 medium tank, “Berlin Bound”, of Company B, 37th Tank Battalion, 4th Armored Division, while at Devizes, Wiltshire, England, in May 1944.