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   Rules Design 1 - Time and Distance

It is possible in wargames to have real time and distance calculations underlying movement on the tabletop. Since this will seem shockingly like mathematics to some readers, I will try to keep the explanations clear and simple.

The following table shows miles per hour and the actual yards per hour and yards per minute that may be moved. The column at the end rounds up the yards per minute into multiples of three. (The rounded value at 1 mph actually equals 1.022727 mph. At 30 mph it equals 30.68182 mph, not quite a full mph over our rounded number, so the distortion is not too great.)

Miles per hour

Yards per hour

Yards per minute

Rounded

1

1760

29

30

2

3520

59

60

3

5280

88

90

4

7040

117

120

5

8800

147

150

10

17600

293

300

15

26400

440

450

20

35200

587

600

25

44000

733

750

30

52800

880

900

With this information it is very easy to relate time to distance moved. We will use the rounded numbers from the table above since they fall so conveniently into multiples of three. In 1 minute, a unit with a movement rate of 1 mile per hour can move 30 yards. A unit with a movement rate of 3 miles per hour can move 90 yards.

We now have a very practical and realistic time to movement relationship. How do we use these numbers on a wargame table? If an inch equals 10 yards in your wargame rules, a unit that can move at a rate of 30 yards per turn can move 3 inches in one turn. (Keep in mind that we are working with a 1 minute time frame.)

1 minute turn

Miles per hour

Inches of movement,

if 1 inch equals 10 yards

1

3

2

6

3

9

4

12

5

15

10

30

15

45

20

60

25

75

30

90

Probably very few rules use a scale of 1 inch equals 10 yards, so we will want to be able to change the scale. We will also want to be able to change the amount of time per turn. Before we go on to that letís look at some aspects of the current calculations. One thing that is not immediately apparent until you play with these calculations for a while is that you can maintain the convenient multiples of threes only if there is a 1 to 10 ratio between minutes and yards. If the scale is 1 inch equals 10 yards the time factor should be 1 minute. If the scale is 1 inch equals 50 yards the time factor should be 5 minutes. We can develop several examples to illustrate this:

1 minute turn

5 minute turn

10 minute turn

15 minute turn

Miles per hour

Inches, if 1 inch equals 10 yards

Inches, if 1 inch equals 50 yards

Inches, if 1 inch equals 100 yards

Inches, if 1 inch equals 150 yards

1

3

3

3

3

2

6

6

6

6

3

9

9

9

9

4

12

12

12

12

5

15

15

15

15

10

30

30

30

30

15

45

45

45

45

20

60

60

60

60

25

75

75

75

75

30

90

90

90

90

This could be perfectly fine if you are developing a set of new rules but, what if you are working with existing rules and you want a scale of 1 inch equals 50 yards and a turn that represents 15 minutes? The quickest way to resolve this problem is to multiply the distance moved by 3.

5 minute turn

15 minute turn

Miles per hour

Inches of movement,

if 1 inch equals 50 yards

Inches of movement,

if 1 inch equals 50 yards

1

3

9

2

6

18

3

9

27

4

12

36

5

15

45

10

30

90

15

45

135

20

60

180

25

75

225

30

90

270

Using the above table, if infantry in line formation moves at 2 miles per hour, the unit will move 6 inches in one turn. If infantry in column formation or open order moves at 3 miles per hour, the unit will move 9 inches in one turn. A tank destroyer with a movement rate of 25 miles per hour will move 75 inches in one turn.

This immediately raises a number of issues. First of all, realistic movement rates cause problems. While these movement rates might be fine for ancient, medieval or horse and musket era wargames, how many players have room on their tables for tank moves of 75 inches per turn? Secondly, these rates illustrate the fact that rules that set arbitrary movement rates for infantry and vehicles are not capturing the tremendous difference in speed of these units. The designers may juggle the numbers to "balance" the game, or to capture what "feels right," but they are not reflecting reality.

Fortunately, the tables allow for a lot of manipulation and diversity. The user can change the time per turn or change the yards per inch. Letís increase the distance that an inch represents.

1 minute turn

Miles per hour

Inches of movement,

if 1 inch equals 20 yards

Inches of movement,

if 1 inch equals 30 yards

1

1.5

1

2

3

2

3

4.5

3

4

6

4

5

7.5

5

10

15

10

15

22.5

15

20

30

20

25

37.5

25

30

45

30

The above process provides some flexibilities, and the last column suggests another approach. We can create a time and distance scale where a unit can move one inch per turn for every mile per hour of its movement rate. The following table provides the details for a number of different scales.

If the scale is:

It takes this amount of seconds to move the distance at 1 mph

1 inch = 1 yard [1/36]

2

1 inch = 48 inches [1/48]

2.67

1 inch = 72 inches [1/72]

4

1 inch = 86 inches [1/86]

4.78

1 inch = 100 inches [1/100]

5.56

1 inch = 144 inches [1/144]

8

1 inch = 285 inches [1/285]

15.83

1 inch = 10 yards

20

1 inch = 20 yards

40

1 inch = 30 yards

60 [1 minute]

1 inch = 100 feet [1/1200]

66.67 [1.1 minutes]

1 inch = 50 yards

100 [1.67 minutes]

1 inch = 100 yards

200 [3.33 minutes]

1 inch = 120 yards

240 [4 minutes]

1 inch = 200 yards

400 [6.67 minutes]

Based on the above table, if a wargamer using 1/285 scale vehicles sets the length of the turn at 16 seconds (15.83 rounded up) a tank with a speed of 25 mph will be able to move 25 inches per turn. Keep in mind that terrain has not been factored in, so these are maximum speeds.

Hopefully this brief review will provide food for thought and a tool for experimentation for those wargamers who want to move their games more in the direction of simulations. Setting realistic movement rates is a meaningful consideration for science fiction and fantasy games as well as historical games.

 

Finally, as a parting gift to the mathematicians, the following formula will allow you to determine the movement rate for one mile per hour for any combination of minutes per turn and yards per inch.

30/(y/m)      That is, divide y by m and then divide 30 by the result.

m = minutes per turn

y = yards per inch

30 is a constant based on 30 yards per minute at one mile per hour.

 

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