Introduction I was going to call this article "How to Make a Circular Slide-Rule for Wargaming" but I was afraid I would frighten away half my readers before I had a chance to tell them that they did not have to be engravers, draftsman nor needed a knowledge of a higher mathematics than simple multiplying. The whole idea was born at a wargaming convention at which American wargamer Dave Wesely and myself were trying to come up with a simple device for calculating casualties in those games whose rules have a large number of multiplying correctives for numerous factors. After some discussion I decided to build a circular slide-rule out of Bristol Board. I was very pleasantly surprised to find that circular rules are very simple to make since the irregular scale does NOT depend on the size of the discs used nor therefore, the length of the circumference. In the one I made for use with Roman Campaigns I chose the maximum casualties to be 60 that being the number of men in a Century, hence I used a repeating scale of from 1 to 10 and for 10 to 100. I have since figured out that actually a single scale of from 1 to 10 will work for any number of casualties and is easier to make accurate although it is not difficult to make an accurate rule provided you start with a 1arge enough circle. Well so much for the yaking and lets get started. Materials 1 sheet of Bristol Board 1 pen 1 ruler (with good straight edge) 1 straight pin 1 strip of adhesive tape 1 table of logarithms (do not need to know how to use them). 1 drawing compass (a piece of string will do in a pinch). 1 protractor. Construction After obtaining the highly technical tools and strategically difficult to come by items in the above list we start our equally difficult task which will require the long period of about 1-2 hours. Cut out a square of Bristol Board (any stiff cardboard) a little more than 10" to a side. Draw in the diagonals on the under side to locate the centre. Using the compass or a length of string tied around a pen draw in a circle of 5" radius, this does not have to be accurate, but the bigger the circle the easier to work with it is. Now lay out the ruler from the centre of the circle to any point on the circumference (try to line up carefully on the centre, the only accuracy required) and draw a short line touching the edge of the circle. (See drawing). This starting point for each disc will be called the BASIC LINE. To the right of this line mark 1 and to the left mark it 10. We will lay out marks for all the digits 2, 3, 4 etc., to 9. To do this look up the number 2 (probably appear as 200) in the log tables and you will find the number 30103 in the first column. Now comes the deep maths: we multiply 360 degrees by .30103 or by plain old .3 will do. Now what do we get, kiddies? Why 108 degrees of course. So starting at the BASIC LINE we measure clockwise 108 degrees around and draw another short radial line at that point, and mark it 2. Next we do the number 3 in the same way - so we have 360 x .47712 or .48 giving 172.8 or 173 degrees. So, starting again from the BASIC LINE, we lay out clockwise 173 degrees draw in the short radial line and mark it 3. Continue in this way until you have all the numbers to 9. You will notice that the spaces get progressively smaller but this is natural for the logarithms of numbers. Now comes the sub-dividing of the spaces. Just how far you carry this depends on the total number of casualties you can have. For instance, a century having 60 men and fighting takes place between centuries, then of course you could not have more than 60 casualties and you need only sub-divide in this case up to 60. Anyway we next want the number 11. So looking up the log of 11 or (110) we see in the first column of the tables and get .04139 so we multiply 360 x .041 getting 14 3/4 degrees which we lay out clockwise from the basic line. Then we wish the number 12 (120) whose log we find is .07918 so 360 degrees at .079 gives 281 degrees which we lay off from the BASIC LINE. Continue in this fashion to 19. Now you will find that you are near the previous line you draw for 2, which now becomes 20. So next we want 21 and we repeat the above procedure, continuing till we reach 60 or whatever number we need. The maximum would be 100. The only other number scale comes next and it is much easier to make. Cut out a circle of Bristol Board about 1/4 inch less in radius then the first circle. Push your pin through its centre and the centre of large square piece laid underneath it and anchor it in place. Now merely extend the marks on the bottom circle up onto the upper circle and label them the same. This second circle should be labelled number of attackers. Now we cut another circle about 1/4 inch smaller still in radius and centre it by putting the pin through all three pieces of board. Draw in your BASIC LINE on this third layer. These BASIC LINES should be marked darker, or in colour or place an arrowhead on them so that they can be readily spotted. Let Us assume this third disc corrects for the position of the attack - that is FRONTAL, FLANK and REAR. Mark the basic line as FRONTAL. Now consult your rules to see how many times more effective the FLANK attack is. Suppose it is 14 times more so, that is 1.5 this means we want the digits 15. Looking up the log of 15 (150) in the first column we see .17609 so 360 x .18 gives 64.2 or 64 degrees. So starting from the BASIC LINE lay off clockwise this angle and rule in your short radial marker line. Label this line or mark FLANK. Now determine the number of times the REAR attack is more effective, say 2 times and lay out from the BASIC LINE that number of degrees and label REAR. You can now make another smaller disc to handle the effectiveness of various weapons. Say that the SWORD is at the BASIC LINE then work out for Spears Long Range and Spears Short Range, Arrows Long and Short Range, etc. You now have the idea and you keep adding discs for each new factor. There is one more important point to note. If the factor reduces casualties, say no armour, just shield, just armour, Shield and Armour then remember that these angles are laid out counter-clockwise, otherwise everything is done just the same. Finally after you have completed all the various discs you require (remember one for effectives of terrain or cover) you cut out the indicator as shown in the drawing. Just be sure that the edge marked straight must be a radius, that is, it travels straight out from the centre and long enough to reach the marks on the outer scale. Now insert the pin through the indicator and down through the pyramid of discs and the bottom square. Bend the pin at right angles underneath and anchor in place with the strip of tape. Operation Now let's see how it works. First you consult the rules to see at what rate the casualties occur under basic conditions. Here you only need one simple table showing two columns - the first the nunbers on the die and the other the number of casualties. If you want to eliminate the die then you need only decide one value of basic casualties. Let us take an example and follow it through. We want the basic casualty rate so 60 Legionaires using swords on men without protection standing in open flat ground frontal attack for a dice roll of 5 is 10 men. Now we find that in our problem we only have 42 men in our attacking force, that they shoot arrows at long range on men carrying shields on open ground and the attack is made from the flank. We line up 60 on the second bottom disc with 10 on the outer scale. Next we place the FRONTAL line opposite 42 on the second disc. Now we move the sword line opposite the FLANK line. Next we place the unarmoured line opposite ARROWS LONG RANGE, then the NO COVER line opposite the SHIELD LINE and finally the straight edge of the indicator with the NO COVER line and follow the indicator out to the outer scale and there read off the casualties. Multiple Use: Since the two bottom scales are always used and likely some of the others remove those discs that do not apply in other wargames and replace them with ones that do. If you make a record of your various games, letter your discs and record opposite the games the discs needed, you can readily put the thing together and in no time you have a ready computer. If it seems like work, remember it only has to be done once and think of the time it will save. Back to Table of Contents -- Wargamer's Newsletter # 113 To Wargamer's Newsletter List of Issues To MagWeb Master Magazine List © Copyright 1971 by Donald Featherstone. This article appears in MagWeb.com (Magazine Web) on the Internet World Wide Web. Other articles from military history and related magazines are available at http://www.magweb.com