Three Dimensional Interstellar Distance Charts
We live in a four-dimensional universe. It is one that consists of three dimensions such as height, width and depth, but also one of time.
Our maps though, such as the traditional Alpha Dawn map of the Frontier or the Zebulon map and various spin-offs are only two dimensional representations of space. This has caused some consternation among those who think the Frontier has become “filled up” because of all the added corporate worlds in the Zeb’s Guide. 
But perhaps we can start imagining the Frontier as a 3D space. This idea came up in the discussion “Beyond the Frontier, star nations and independent worlds” (http://www.starfrontiers.us/node/9099). Iggy (Eric Winsor) created a 3D map using a program called Celestia and posted it to YouTube (https://www.youtube.com/watch?v=rlKNlCY4BxY&feature=youtu.be). But, what can a referee do if he or she doesn’t have Celestia and isn’t running a campaign using a computer?
The GDW game Traveller: 2300 (later known as 2300 AD) provided the game master with a two dimensional map but also a star chart of every known star within 50 light years of Sol. This could serve as a bit of inspiration to handling 3D travel in Star Frontiers.
Knight Hawks provides the referee with a cheat sheet for figuring out interstellar distances with its 2D chart, represents the horizontal (Y-Axis) and vertical (X-Axis), but rounding any fractions to the nearest whole number. If you want a little more variety to your campaign, I’ve whipped up some 3D interstellar distance charts – your own cheat sheets so you don’t have to whip out your scientific calculator or use a computer spreadsheet (which is what I did to create the following charts).
The first chart represents the classic 2D Knight Hawks game, but I rounded the figures to the first decimal point rather than the nearest whole number. 
Chart 2 shows the minute changes in distance if the star you are traveling to is one light year above or below your starting point and so on. I’ve taken the calculations along the Z-Axis up to 10 light years and you can see it does start making a significant difference. 
One thing to consider is: how long does it take a Frontier ship to accelerate to 0.1 percent of the speed of light (0.1c)? Knight Hawks doesn’t make that clear, but Tom Stephens (TerlObar) did these calculations. 
At a normal 1g acceleration, it will take a ship 4.5 days to accelerate from an at rest speed up to what it needs to enter the Void. Then it takes another 4.5 days at 1g to decelerate to an at rest speed. So those seemingly short hops on the Frontier map are rather lengthy. To me, it provides a good reason for the existence of the storage class for passengers. For more information, see the discussion on “Misjumps Table” (http://www.starfrontiers.us/node/9454).
Another item of interest, though it is tangential to the interstellar distance chart discussion, is that the hex size for the Knight Hawks map should be changed from a distance of 10,000 kilometers to 3,600 km if 1 ADF is supposed to equal 1g of acceleration. See “See ADF/MR question” at http://www.starfrontiers.us/node/4816.
Now for the charts:
 	 	 	X-Axis	 	 	 	 	 	 	 	 	 	 	 	 	 	 	
Z-Axis	Y-Axis	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	
0	0	0.0	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0	11.0	12.0	13.0	14.0	15.0	16.0	
0	1	1.0	1.4	2.2	3.2	4.1	5.1	6.1	7.1	8.1	9.1	10.0	11.0	12.0	13.0	14.0	15.0	16.0	
0	2	2.0	2.2	2.8	3.6	4.5	5.4	6.3	7.3	8.2	9.2	10.2	11.2	12.2	13.2	14.1	15.1	16.1	
0	3	3.0	3.2	3.6	4.2	5.0	5.8	6.7	7.6	8.5	9.5	10.4	11.4	12.4	13.3	14.3	15.3	16.3	
0	4	4.0	4.1	4.5	5.0	5.7	6.4	7.2	8.1	8.9	9.8	10.8	11.7	12.6	13.6	14.6	15.5	16.5	
0	5	5.0	5.1	5.4	5.8	6.4	7.1	7.8	8.6	9.4	10.3	11.2	12.1	13.0	13.9	14.9	15.8	16.8	
0	6	6.0	6.1	6.3	6.7	7.2	7.8	8.5	9.2	10.0	10.8	11.7	12.5	13.4	14.3	15.2	16.2	17.1	
0	7	7.0	7.1	7.3	7.6	8.1	8.6	9.2	9.9	10.6	11.4	12.2	13.0	13.9	14.8	15.7	16.6	17.5	
0	8	8.0	8.1	8.2	8.5	8.9	9.4	10.0	10.6	11.3	12.0	12.8	13.6	14.4	15.3	16.1	17.0	17.9	
0	9	9.0	9.1	9.2	9.5	9.8	10.3	10.8	11.4	12.0	12.7	13.5	14.2	15.0	15.8	16.6	17.5	18.4	
0	10	10.0	10.0	10.2	10.4	10.8	11.2	11.7	12.2	12.8	13.5	14.1	14.9	15.6	16.4	17.2	18.0	18.9	
0	11	11.0	11.0	11.2	11.4	11.7	12.1	12.5	13.0	13.6	14.2	14.9	15.6	16.3	17.0	17.8	18.6	19.4	
0	12	12.0	12.0	12.2	12.4	12.6	13.0	13.4	13.9	14.4	15.0	15.6	16.3	17.0	17.7	18.4	19.2	20.0	
0	13	13.0	13.0	13.2	13.3	13.6	13.9	14.3	14.8	15.3	15.8	16.4	17.0	17.7	18.4	19.1	19.8	20.6	
0	14	14.0	14.0	14.1	14.3	14.6	14.9	15.2	15.7	16.1	16.6	17.2	17.8	18.4	19.1	19.8	20.5	21.3	
0	15	15.0	15.0	15.1	15.3	15.5	15.8	16.2	16.6	17.0	17.5	18.0	18.6	19.2	19.8	20.5	21.2	21.9	
0	16	16.0	16.0	16.1	16.3	16.5	16.8	17.1	17.5	17.9	18.4	18.9	19.4	20.0	20.6	21.3	21.9	22.6	
0	17	17.0	17.0	17.1	17.3	17.5	17.7	18.0	18.4	18.8	19.2	19.7	20.2	20.8	21.4	22.0	22.7	23.3	
0	18	18.0	18.0	18.1	18.2	18.4	18.7	19.0	19.3	19.7	20.1	20.6	21.1	21.6	22.2	22.8	23.4	24.1	

			X-Axis															
Z-Axis	Y-Axis	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	
1	0	1.0	1.4	2.2	3.2	4.1	5.1	6.1	7.1	8.1	9.1	10.0	11.0	12.0	13.0	14.0	15.0	16.0	
1	1	1.4	1.7	2.4	3.3	4.2	5.2	6.2	7.1	8.1	9.1	10.1	11.1	12.1	13.1	14.1	15.1	16.1	
1	2	2.2	2.4	3.0	3.7	4.6	5.5	6.4	7.3	8.3	9.3	10.2	11.2	12.2	13.2	14.2	15.2	16.2	
1	3	3.2	3.3	3.7	4.4	5.1	5.9	6.8	7.7	8.6	9.5	10.5	11.4	12.4	13.4	14.4	15.3	16.3	
1	4	4.1	4.2	4.6	5.1	5.7	6.5	7.3	8.1	9.0	9.9	10.8	11.7	12.7	13.6	14.6	15.6	16.5	
1	5	5.1	5.2	5.5	5.9	6.5	7.1	7.9	8.7	9.5	10.3	11.2	12.1	13.0	14.0	14.9	15.8	16.8	
1	6	6.1	6.2	6.4	6.8	7.3	7.9	8.5	9.3	10.0	10.9	11.7	12.6	13.5	14.4	15.3	16.2	17.1	
1	7	7.1	7.1	7.3	7.7	8.1	8.7	9.3	9.9	10.7	11.4	12.2	13.1	13.9	14.8	15.7	16.6	17.5	
1	8	8.1	8.1	8.3	8.6	9.0	9.5	10.0	10.7	11.4	12.1	12.8	13.6	14.5	15.3	16.2	17.0	17.9	
1	9	9.1	9.1	9.3	9.5	9.9	10.3	10.9	11.4	12.1	12.8	13.5	14.2	15.0	15.8	16.7	17.5	18.4	
1	10	10.0	10.1	10.2	10.5	10.8	11.2	11.7	12.2	12.8	13.5	14.2	14.9	15.7	16.4	17.2	18.1	18.9	
1	11	11.0	11.1	11.2	11.4	11.7	12.1	12.6	13.1	13.6	14.2	14.9	15.6	16.3	17.1	17.8	18.6	19.4	
1	12	12.0	12.1	12.2	12.4	12.7	13.0	13.5	13.9	14.5	15.0	15.7	16.3	17.0	17.7	18.5	19.2	20.0	
1	13	13.0	13.1	13.2	13.4	13.6	14.0	14.4	14.8	15.3	15.8	16.4	17.1	17.7	18.4	19.1	19.9	20.6	
1	14	14.0	14.1	14.2	14.4	14.6	14.9	15.3	15.7	16.2	16.7	17.2	17.8	18.5	19.1	19.8	20.5	21.3	
1	15	15.0	15.1	15.2	15.3	15.6	15.8	16.2	16.6	17.0	17.5	18.1	18.6	19.2	19.9	20.5	21.2	22.0	
1	16	16.0	16.1	16.2	16.3	16.5	16.8	17.1	17.5	17.9	18.4	18.9	19.4	20.0	20.6	21.3	22.0	22.6	
1	17	17.0	17.1	17.1	17.3	17.5	17.7	18.1	18.4	18.8	19.3	19.7	20.3	20.8	21.4	22.0	22.7	23.4	
1	18	18.0	18.1	18.1	18.3	18.5	18.7	19.0	19.3	19.7	20.1	20.6	21.1	21.7	22.2	22.8	23.5	24.1	

			X-Axis															
Z-Axis	Y-Axis	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	
2	0	2.0	2.2	2.8	3.6	4.5	5.4	6.3	7.3	8.2	9.2	10.2	11.2	12.2	13.2	14.1	15.1	16.1	
2	1	2.2	2.4	3.0	3.7	4.6	5.5	6.4	7.3	8.3	9.3	10.2	11.2	12.2	13.2	14.2	15.2	16.2	
2	2	2.8	3.0	3.5	4.1	4.9	5.7	6.6	7.5	8.5	9.4	10.4	11.4	12.3	13.3	14.3	15.3	16.2	
2	3	3.6	3.7	4.1	4.7	5.4	6.2	7.0	7.9	8.8	9.7	10.6	11.6	12.5	13.5	14.5	15.4	16.4	
2	4	4.5	4.6	4.9	5.4	6.0	6.7	7.5	8.3	9.2	10.0	11.0	11.9	12.8	13.7	14.7	15.7	16.6	
2	5	5.4	5.5	5.7	6.2	6.7	7.3	8.1	8.8	9.6	10.5	11.4	12.2	13.2	14.1	15.0	15.9	16.9	
2	6	6.3	6.4	6.6	7.0	7.5	8.1	8.7	9.4	10.2	11.0	11.8	12.7	13.6	14.5	15.4	16.3	17.2	
2	7	7.3	7.3	7.5	7.9	8.3	8.8	9.4	10.1	10.8	11.6	12.4	13.2	14.0	14.9	15.8	16.7	17.6	
2	8	8.2	8.3	8.5	8.8	9.2	9.6	10.2	10.8	11.5	12.2	13.0	13.7	14.6	15.4	16.2	17.1	18.0	
2	9	9.2	9.3	9.4	9.7	10.0	10.5	11.0	11.6	12.2	12.9	13.6	14.4	15.1	15.9	16.8	17.6	18.5	
2	10	10.2	10.2	10.4	10.6	11.0	11.4	11.8	12.4	13.0	13.6	14.3	15.0	15.7	16.5	17.3	18.1	19.0	
2	11	11.2	11.2	11.4	11.6	11.9	12.2	12.7	13.2	13.7	14.4	15.0	15.7	16.4	17.1	17.9	18.7	19.5	
2	12	12.2	12.2	12.3	12.5	12.8	13.2	13.6	14.0	14.6	15.1	15.7	16.4	17.1	17.8	18.5	19.3	20.1	
2	13	13.2	13.2	13.3	13.5	13.7	14.1	14.5	14.9	15.4	15.9	16.5	17.1	17.8	18.5	19.2	19.9	20.7	
2	14	14.1	14.2	14.3	14.5	14.7	15.0	15.4	15.8	16.2	16.8	17.3	17.9	18.5	19.2	19.9	20.6	21.4	
2	15	15.1	15.2	15.3	15.4	15.7	15.9	16.3	16.7	17.1	17.6	18.1	18.7	19.3	19.9	20.6	21.3	22.0	
2	16	16.1	16.2	16.2	16.4	16.6	16.9	17.2	17.6	18.0	18.5	19.0	19.5	20.1	20.7	21.4	22.0	22.7	
2	17	17.1	17.1	17.2	17.4	17.6	17.8	18.1	18.5	18.9	19.3	19.8	20.3	20.9	21.5	22.1	22.8	23.4	
2	18	18.1	18.1	18.2	18.4	18.5	18.8	19.1	19.4	19.8	20.2	20.7	21.2	21.7	22.3	22.9	23.5	24.2	

			X-Axis															
Z-Axis	Y-Axis	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	
3	0	3.0	3.2	3.6	4.2	5.0	5.8	6.7	7.6	8.5	9.5	10.4	11.4	12.4	13.3	14.3	15.3	16.3	
3	1	3.2	3.3	3.7	4.4	5.1	5.9	6.8	7.7	8.6	9.5	10.5	11.4	12.4	13.4	14.4	15.3	16.3	
3	2	3.6	3.7	4.1	4.7	5.4	6.2	7.0	7.9	8.8	9.7	10.6	11.6	12.5	13.5	14.5	15.4	16.4	
3	3	4.2	4.4	4.7	5.2	5.8	6.6	7.3	8.2	9.1	9.9	10.9	11.8	12.7	13.7	14.6	15.6	16.6	
3	4	5.0	5.1	5.4	5.8	6.4	7.1	7.8	8.6	9.4	10.3	11.2	12.1	13.0	13.9	14.9	15.8	16.8	
3	5	5.8	5.9	6.2	6.6	7.1	7.7	8.4	9.1	9.9	10.7	11.6	12.4	13.3	14.2	15.2	16.1	17.0	
3	6	6.7	6.8	7.0	7.3	7.8	8.4	9.0	9.7	10.4	11.2	12.0	12.9	13.7	14.6	15.5	16.4	17.3	
3	7	7.6	7.7	7.9	8.2	8.6	9.1	9.7	10.3	11.0	11.8	12.6	13.4	14.2	15.1	15.9	16.8	17.7	
3	8	8.5	8.6	8.8	9.1	9.4	9.9	10.4	11.0	11.7	12.4	13.2	13.9	14.7	15.6	16.4	17.3	18.1	
3	9	9.5	9.5	9.7	9.9	10.3	10.7	11.2	11.8	12.4	13.1	13.8	14.5	15.3	16.1	16.9	17.7	18.6	
3	10	10.4	10.5	10.6	10.9	11.2	11.6	12.0	12.6	13.2	13.8	14.5	15.2	15.9	16.7	17.5	18.3	19.1	
3	11	11.4	11.4	11.6	11.8	12.1	12.4	12.9	13.4	13.9	14.5	15.2	15.8	16.6	17.3	18.1	18.8	19.6	
3	12	12.4	12.4	12.5	12.7	13.0	13.3	13.7	14.2	14.7	15.3	15.9	16.6	17.2	17.9	18.7	19.4	20.2	
3	13	13.3	13.4	13.5	13.7	13.9	14.2	14.6	15.1	15.6	16.1	16.7	17.3	17.9	18.6	19.3	20.1	20.8	
3	14	14.3	14.4	14.5	14.6	14.9	15.2	15.5	15.9	16.4	16.9	17.5	18.1	18.7	19.3	20.0	20.7	21.5	
3	15	15.3	15.3	15.4	15.6	15.8	16.1	16.4	16.8	17.3	17.7	18.3	18.8	19.4	20.1	20.7	21.4	22.1	
3	16	16.3	16.3	16.4	16.6	16.8	17.0	17.3	17.7	18.1	18.6	19.1	19.6	20.2	20.8	21.5	22.1	22.8	
3	17	17.3	17.3	17.4	17.5	17.7	18.0	18.3	18.6	19.0	19.5	19.9	20.5	21.0	21.6	22.2	22.9	23.5	
3	18	18.2	18.3	18.4	18.5	18.7	18.9	19.2	19.5	19.9	20.3	20.8	21.3	21.8	22.4	23.0	23.6	24.3	

			X-Axis															
Z-Axis	Y-Axis	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	
4	0	4.0	4.1	4.5	5.0	5.7	6.4	7.2	8.1	8.9	9.8	10.8	11.7	12.6	13.6	14.6	15.5	16.5	
4	1	4.1	4.2	4.6	5.1	5.7	6.5	7.3	8.1	9.0	9.9	10.8	11.7	12.7	13.6	14.6	15.6	16.5	
4	2	4.5	4.6	4.9	5.4	6.0	6.7	7.5	8.3	9.2	10.0	11.0	11.9	12.8	13.7	14.7	15.7	16.6	
4	3	5.0	5.1	5.4	5.8	6.4	7.1	7.8	8.6	9.4	10.3	11.2	12.1	13.0	13.9	14.9	15.8	16.8	
4	4	5.7	5.7	6.0	6.4	6.9	7.5	8.2	9.0	9.8	10.6	11.5	12.4	13.3	14.2	15.1	16.0	17.0	
4	5	6.4	6.5	6.7	7.1	7.5	8.1	8.8	9.5	10.2	11.0	11.9	12.7	13.6	14.5	15.4	16.3	17.2	
4	6	7.2	7.3	7.5	7.8	8.2	8.8	9.4	10.0	10.8	11.5	12.3	13.2	14.0	14.9	15.7	16.6	17.5	
4	7	8.1	8.1	8.3	8.6	9.0	9.5	10.0	10.7	11.4	12.1	12.8	13.6	14.5	15.3	16.2	17.0	17.9	
4	8	8.9	9.0	9.2	9.4	9.8	10.2	10.8	11.4	12.0	12.7	13.4	14.2	15.0	15.8	16.6	17.5	18.3	
4	9	9.8	9.9	10.0	10.3	10.6	11.0	11.5	12.1	12.7	13.3	14.0	14.8	15.5	16.3	17.1	17.9	18.8	
4	10	10.8	10.8	11.0	11.2	11.5	11.9	12.3	12.8	13.4	14.0	14.7	15.4	16.1	16.9	17.7	18.5	19.3	
4	11	11.7	11.7	11.9	12.1	12.4	12.7	13.2	13.6	14.2	14.8	15.4	16.1	16.8	17.5	18.2	19.0	19.8	
4	12	12.6	12.7	12.8	13.0	13.3	13.6	14.0	14.5	15.0	15.5	16.1	16.8	17.4	18.1	18.9	19.6	20.4	
4	13	13.6	13.6	13.7	13.9	14.2	14.5	14.9	15.3	15.8	16.3	16.9	17.5	18.1	18.8	19.5	20.2	21.0	
4	14	14.6	14.6	14.7	14.9	15.1	15.4	15.7	16.2	16.6	17.1	17.7	18.2	18.9	19.5	20.2	20.9	21.6	
4	15	15.5	15.6	15.7	15.8	16.0	16.3	16.6	17.0	17.5	17.9	18.5	19.0	19.6	20.2	20.9	21.6	22.3	
4	16	16.5	16.5	16.6	16.8	17.0	17.2	17.5	17.9	18.3	18.8	19.3	19.8	20.4	21.0	21.6	22.3	23.0	
4	17	17.5	17.5	17.6	17.7	17.9	18.2	18.5	18.8	19.2	19.6	20.1	20.6	21.2	21.8	22.4	23.0	23.7	
4	18	18.4	18.5	18.5	18.7	18.9	19.1	19.4	19.7	20.1	20.5	21.0	21.5	22.0	22.6	23.2	23.8	24.4	

			X-Axis															
Z-Axis	Y-Axis	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	
5	0	5.0	5.1	5.4	5.8	6.4	7.1	7.8	8.6	9.4	10.3	11.2	12.1	13.0	13.9	14.9	15.8	16.8	
5	1	5.1	5.2	5.5	5.9	6.5	7.1	7.9	8.7	9.5	10.3	11.2	12.1	13.0	14.0	14.9	15.8	16.8	
5	2	5.4	5.5	5.7	6.2	6.7	7.3	8.1	8.8	9.6	10.5	11.4	12.2	13.2	14.1	15.0	15.9	16.9	
5	3	5.8	5.9	6.2	6.6	7.1	7.7	8.4	9.1	9.9	10.7	11.6	12.4	13.3	14.2	15.2	16.1	17.0	
5	4	6.4	6.5	6.7	7.1	7.5	8.1	8.8	9.5	10.2	11.0	11.9	12.7	13.6	14.5	15.4	16.3	17.2	
5	5	7.1	7.1	7.3	7.7	8.1	8.7	9.3	9.9	10.7	11.4	12.2	13.1	13.9	14.8	15.7	16.6	17.5	
5	6	7.8	7.9	8.1	8.4	8.8	9.3	9.8	10.5	11.2	11.9	12.7	13.5	14.3	15.2	16.0	16.9	17.8	
5	7	8.6	8.7	8.8	9.1	9.5	9.9	10.5	11.1	11.7	12.4	13.2	14.0	14.8	15.6	16.4	17.3	18.2	
5	8	9.4	9.5	9.6	9.9	10.2	10.7	11.2	11.7	12.4	13.0	13.7	14.5	15.3	16.1	16.9	17.7	18.6	
5	9	10.3	10.3	10.5	10.7	11.0	11.4	11.9	12.4	13.0	13.7	14.4	15.1	15.8	16.6	17.4	18.2	19.0	
5	10	11.2	11.2	11.4	11.6	11.9	12.2	12.7	13.2	13.7	14.4	15.0	15.7	16.4	17.1	17.9	18.7	19.5	
5	11	12.1	12.1	12.2	12.4	12.7	13.1	13.5	14.0	14.5	15.1	15.7	16.3	17.0	17.7	18.5	19.3	20.0	
5	12	13.0	13.0	13.2	13.3	13.6	13.9	14.3	14.8	15.3	15.8	16.4	17.0	17.7	18.4	19.1	19.8	20.6	
5	13	13.9	14.0	14.1	14.2	14.5	14.8	15.2	15.6	16.1	16.6	17.1	17.7	18.4	19.1	19.7	20.5	21.2	
5	14	14.9	14.9	15.0	15.2	15.4	15.7	16.0	16.4	16.9	17.4	17.9	18.5	19.1	19.7	20.4	21.1	21.8	
5	15	15.8	15.8	15.9	16.1	16.3	16.6	16.9	17.3	17.7	18.2	18.7	19.3	19.8	20.5	21.1	21.8	22.5	
5	16	16.8	16.8	16.9	17.0	17.2	17.5	17.8	18.2	18.6	19.0	19.5	20.0	20.6	21.2	21.8	22.5	23.2	
5	17	17.7	17.7	17.8	18.0	18.2	18.4	18.7	19.1	19.4	19.9	20.3	20.9	21.4	22.0	22.6	23.2	23.9	
5	18	18.7	18.7	18.8	18.9	19.1	19.3	19.6	19.9	20.3	20.7	21.2	21.7	22.2	22.8	23.3	24.0	24.6	

			X-Axis															
Z-Axis	Y-Axis	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	
6	0	6.0	6.1	6.3	6.7	7.2	7.8	8.5	9.2	10.0	10.8	11.7	12.5	13.4	14.3	15.2	16.2	17.1	
6	1	6.1	6.2	6.4	6.8	7.3	7.9	8.5	9.3	10.0	10.9	11.7	12.6	13.5	14.4	15.3	16.2	17.1	
6	2	6.3	6.4	6.6	7.0	7.5	8.1	8.7	9.4	10.2	11.0	11.8	12.7	13.6	14.5	15.4	16.3	17.2	
6	3	6.7	6.8	7.0	7.3	7.8	8.4	9.0	9.7	10.4	11.2	12.0	12.9	13.7	14.6	15.5	16.4	17.3	
6	4	7.2	7.3	7.5	7.8	8.2	8.8	9.4	10.0	10.8	11.5	12.3	13.2	14.0	14.9	15.7	16.6	17.5	
6	5	7.8	7.9	8.1	8.4	8.8	9.3	9.8	10.5	11.2	11.9	12.7	13.5	14.3	15.2	16.0	16.9	17.8	
6	6	8.5	8.5	8.7	9.0	9.4	9.8	10.4	11.0	11.7	12.4	13.1	13.9	14.7	15.5	16.4	17.2	18.1	
6	7	9.2	9.3	9.4	9.7	10.0	10.5	11.0	11.6	12.2	12.9	13.6	14.4	15.1	15.9	16.8	17.6	18.5	
6	8	10.0	10.0	10.2	10.4	10.8	11.2	11.7	12.2	12.8	13.5	14.1	14.9	15.6	16.4	17.2	18.0	18.9	
6	9	10.8	10.9	11.0	11.2	11.5	11.9	12.4	12.9	13.5	14.1	14.7	15.4	16.2	16.9	17.7	18.5	19.3	
6	10	11.7	11.7	11.8	12.0	12.3	12.7	13.1	13.6	14.1	14.7	15.4	16.0	16.7	17.5	18.2	19.0	19.8	
6	11	12.5	12.6	12.7	12.9	13.2	13.5	13.9	14.4	14.9	15.4	16.0	16.7	17.3	18.1	18.8	19.5	20.3	
6	12	13.4	13.5	13.6	13.7	14.0	14.3	14.7	15.1	15.6	16.2	16.7	17.3	18.0	18.7	19.4	20.1	20.9	
6	13	14.3	14.4	14.5	14.6	14.9	15.2	15.5	15.9	16.4	16.9	17.5	18.1	18.7	19.3	20.0	20.7	21.5	
6	14	15.2	15.3	15.4	15.5	15.7	16.0	16.4	16.8	17.2	17.7	18.2	18.8	19.4	20.0	20.7	21.4	22.1	
6	15	16.2	16.2	16.3	16.4	16.6	16.9	17.2	17.6	18.0	18.5	19.0	19.5	20.1	20.7	21.4	22.0	22.7	
6	16	17.1	17.1	17.2	17.3	17.5	17.8	18.1	18.5	18.9	19.3	19.8	20.3	20.9	21.5	22.1	22.7	23.4	
6	17	18.0	18.1	18.1	18.3	18.5	18.7	19.0	19.3	19.7	20.1	20.6	21.1	21.7	22.2	22.8	23.5	24.1	
6	18	19.0	19.0	19.1	19.2	19.4	19.6	19.9	20.2	20.6	21.0	21.4	21.9	22.4	23.0	23.6	24.2	24.8	

			X-Axis															
Z-Axis	Y-Axis	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	
7	0	7.0	7.1	7.3	7.6	8.1	8.6	9.2	9.9	10.6	11.4	12.2	13.0	13.9	14.8	15.7	16.6	17.5	
7	1	7.1	7.1	7.3	7.7	8.1	8.7	9.3	9.9	10.7	11.4	12.2	13.1	13.9	14.8	15.7	16.6	17.5	
7	2	7.3	7.3	7.5	7.9	8.3	8.8	9.4	10.1	10.8	11.6	12.4	13.2	14.0	14.9	15.8	16.7	17.6	
7	3	7.6	7.7	7.9	8.2	8.6	9.1	9.7	10.3	11.0	11.8	12.6	13.4	14.2	15.1	15.9	16.8	17.7	
7	4	8.1	8.1	8.3	8.6	9.0	9.5	10.0	10.7	11.4	12.1	12.8	13.6	14.5	15.3	16.2	17.0	17.9	
7	5	8.6	8.7	8.8	9.1	9.5	9.9	10.5	11.1	11.7	12.4	13.2	14.0	14.8	15.6	16.4	17.3	18.2	
7	6	9.2	9.3	9.4	9.7	10.0	10.5	11.0	11.6	12.2	12.9	13.6	14.4	15.1	15.9	16.8	17.6	18.5	
7	7	9.9	9.9	10.1	10.3	10.7	11.1	11.6	12.1	12.7	13.4	14.1	14.8	15.6	16.3	17.1	18.0	18.8	
7	8	10.6	10.7	10.8	11.0	11.4	11.7	12.2	12.7	13.3	13.9	14.6	15.3	16.0	16.8	17.6	18.4	19.2	
7	9	11.4	11.4	11.6	11.8	12.1	12.4	12.9	13.4	13.9	14.5	15.2	15.8	16.6	17.3	18.1	18.8	19.6	
7	10	12.2	12.2	12.4	12.6	12.8	13.2	13.6	14.1	14.6	15.2	15.8	16.4	17.1	17.8	18.6	19.3	20.1	
7	11	13.0	13.1	13.2	13.4	13.6	14.0	14.4	14.8	15.3	15.8	16.4	17.1	17.7	18.4	19.1	19.9	20.6	
7	12	13.9	13.9	14.0	14.2	14.5	14.8	15.1	15.6	16.0	16.6	17.1	17.7	18.4	19.0	19.7	20.4	21.2	
7	13	14.8	14.8	14.9	15.1	15.3	15.6	15.9	16.3	16.8	17.3	17.8	18.4	19.0	19.7	20.3	21.0	21.8	
7	14	15.7	15.7	15.8	15.9	16.2	16.4	16.8	17.1	17.6	18.1	18.6	19.1	19.7	20.3	21.0	21.7	22.4	
7	15	16.6	16.6	16.7	16.8	17.0	17.3	17.6	18.0	18.4	18.8	19.3	19.9	20.4	21.0	21.7	22.3	23.0	
7	16	17.5	17.5	17.6	17.7	17.9	18.2	18.5	18.8	19.2	19.6	20.1	20.6	21.2	21.8	22.4	23.0	23.7	
7	17	18.4	18.4	18.5	18.6	18.8	19.1	19.3	19.7	20.0	20.5	20.9	21.4	22.0	22.5	23.1	23.7	24.4	
7	18	19.3	19.3	19.4	19.5	19.7	19.9	20.2	20.5	20.9	21.3	21.7	22.2	22.7	23.3	23.9	24.5	25.1	

			X-Axis															
Z-Axis	Y-Axis	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	
8	0	8.0	8.1	8.2	8.5	8.9	9.4	10.0	10.6	11.3	12.0	12.8	13.6	14.4	15.3	16.1	17.0	17.9	
8	1	8.1	8.1	8.3	8.6	9.0	9.5	10.0	10.7	11.4	12.1	12.8	13.6	14.5	15.3	16.2	17.0	17.9	
8	2	8.2	8.3	8.5	8.8	9.2	9.6	10.2	10.8	11.5	12.2	13.0	13.7	14.6	15.4	16.2	17.1	18.0	
8	3	8.5	8.6	8.8	9.1	9.4	9.9	10.4	11.0	11.7	12.4	13.2	13.9	14.7	15.6	16.4	17.3	18.1	
8	4	8.9	9.0	9.2	9.4	9.8	10.2	10.8	11.4	12.0	12.7	13.4	14.2	15.0	15.8	16.6	17.5	18.3	
8	5	9.4	9.5	9.6	9.9	10.2	10.7	11.2	11.7	12.4	13.0	13.7	14.5	15.3	16.1	16.9	17.7	18.6	
8	6	10.0	10.0	10.2	10.4	10.8	11.2	11.7	12.2	12.8	13.5	14.1	14.9	15.6	16.4	17.2	18.0	18.9	
8	7	10.6	10.7	10.8	11.0	11.4	11.7	12.2	12.7	13.3	13.9	14.6	15.3	16.0	16.8	17.6	18.4	19.2	
8	8	11.3	11.4	11.5	11.7	12.0	12.4	12.8	13.3	13.9	14.5	15.1	15.8	16.5	17.2	18.0	18.8	19.6	
8	9	12.0	12.1	12.2	12.4	12.7	13.0	13.5	13.9	14.5	15.0	15.7	16.3	17.0	17.7	18.5	19.2	20.0	
8	10	12.8	12.8	13.0	13.2	13.4	13.7	14.1	14.6	15.1	15.7	16.2	16.9	17.5	18.2	19.0	19.7	20.5	
8	11	13.6	13.6	13.7	13.9	14.2	14.5	14.9	15.3	15.8	16.3	16.9	17.5	18.1	18.8	19.5	20.2	21.0	
8	12	14.4	14.5	14.6	14.7	15.0	15.3	15.6	16.0	16.5	17.0	17.5	18.1	18.8	19.4	20.1	20.8	21.5	
8	13	15.3	15.3	15.4	15.6	15.8	16.1	16.4	16.8	17.2	17.7	18.2	18.8	19.4	20.0	20.7	21.4	22.1	
8	14	16.1	16.2	16.2	16.4	16.6	16.9	17.2	17.6	18.0	18.5	19.0	19.5	20.1	20.7	21.4	22.0	22.7	
8	15	17.0	17.0	17.1	17.3	17.5	17.7	18.0	18.4	18.8	19.2	19.7	20.2	20.8	21.4	22.0	22.7	23.3	
8	16	17.9	17.9	18.0	18.1	18.3	18.6	18.9	19.2	19.6	20.0	20.5	21.0	21.5	22.1	22.7	23.3	24.0	
8	17	18.8	18.8	18.9	19.0	19.2	19.4	19.7	20.0	20.4	20.8	21.3	21.8	22.3	22.8	23.4	24.0	24.7	
8	18	19.7	19.7	19.8	19.9	20.1	20.3	20.6	20.9	21.3	21.7	22.1	22.6	23.1	23.6	24.2	24.8	25.4	

			X-Axis															
Z-Axis	Y-Axis	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	
9	0	9.0	9.1	9.2	9.5	9.8	10.3	10.8	11.4	12.0	12.7	13.5	14.2	15.0	15.8	16.6	17.5	18.4	
9	1	9.1	9.1	9.3	9.5	9.9	10.3	10.9	11.4	12.1	12.8	13.5	14.2	15.0	15.8	16.7	17.5	18.4	
9	2	9.2	9.3	9.4	9.7	10.0	10.5	11.0	11.6	12.2	12.9	13.6	14.4	15.1	15.9	16.8	17.6	18.5	
9	3	9.5	9.5	9.7	9.9	10.3	10.7	11.2	11.8	12.4	13.1	13.8	14.5	15.3	16.1	16.9	17.7	18.6	
9	4	9.8	9.9	10.0	10.3	10.6	11.0	11.5	12.1	12.7	13.3	14.0	14.8	15.5	16.3	17.1	17.9	18.8	
9	5	10.3	10.3	10.5	10.7	11.0	11.4	11.9	12.4	13.0	13.7	14.4	15.1	15.8	16.6	17.4	18.2	19.0	
9	6	10.8	10.9	11.0	11.2	11.5	11.9	12.4	12.9	13.5	14.1	14.7	15.4	16.2	16.9	17.7	18.5	19.3	
9	7	11.4	11.4	11.6	11.8	12.1	12.4	12.9	13.4	13.9	14.5	15.2	15.8	16.6	17.3	18.1	18.8	19.6	
9	8	12.0	12.1	12.2	12.4	12.7	13.0	13.5	13.9	14.5	15.0	15.7	16.3	17.0	17.7	18.5	19.2	20.0	
9	9	12.7	12.8	12.9	13.1	13.3	13.7	14.1	14.5	15.0	15.6	16.2	16.8	17.5	18.2	18.9	19.7	20.4	
9	10	13.5	13.5	13.6	13.8	14.0	14.4	14.7	15.2	15.7	16.2	16.8	17.4	18.0	18.7	19.4	20.1	20.9	
9	11	14.2	14.2	14.4	14.5	14.8	15.1	15.4	15.8	16.3	16.8	17.4	18.0	18.6	19.3	19.9	20.7	21.4	
9	12	15.0	15.0	15.1	15.3	15.5	15.8	16.2	16.6	17.0	17.5	18.0	18.6	19.2	19.8	20.5	21.2	21.9	
9	13	15.8	15.8	15.9	16.1	16.3	16.6	16.9	17.3	17.7	18.2	18.7	19.3	19.8	20.5	21.1	21.8	22.5	
9	14	16.6	16.7	16.8	16.9	17.1	17.4	17.7	18.1	18.5	18.9	19.4	19.9	20.5	21.1	21.7	22.4	23.1	
9	15	17.5	17.5	17.6	17.7	17.9	18.2	18.5	18.8	19.2	19.7	20.1	20.7	21.2	21.8	22.4	23.0	23.7	
9	16	18.4	18.4	18.5	18.6	18.8	19.0	19.3	19.6	20.0	20.4	20.9	21.4	21.9	22.5	23.1	23.7	24.4	
9	17	19.2	19.3	19.3	19.5	19.6	19.9	20.1	20.5	20.8	21.2	21.7	22.2	22.7	23.2	23.8	24.4	25.0	
9	18	20.1	20.1	20.2	20.3	20.5	20.7	21.0	21.3	21.7	22.0	22.5	22.9	23.4	24.0	24.5	25.1	25.7	

			X-Axis															
Z-Axis	Y-Axis	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	
10	0	10.0	10.0	10.2	10.4	10.8	11.2	11.7	12.2	12.8	13.5	14.1	14.9	15.6	16.4	17.2	18.0	18.9	
10	1	10.0	10.1	10.2	10.5	10.8	11.2	11.7	12.2	12.8	13.5	14.2	14.9	15.7	16.4	17.2	18.1	18.9	
10	2	10.2	10.2	10.4	10.6	11.0	11.4	11.8	12.4	13.0	13.6	14.3	15.0	15.7	16.5	17.3	18.1	19.0	
10	3	10.4	10.5	10.6	10.9	11.2	11.6	12.0	12.6	13.2	13.8	14.5	15.2	15.9	16.7	17.5	18.3	19.1	
10	4	10.8	10.8	11.0	11.2	11.5	11.9	12.3	12.8	13.4	14.0	14.7	15.4	16.1	16.9	17.7	18.5	19.3	
10	5	11.2	11.2	11.4	11.6	11.9	12.2	12.7	13.2	13.7	14.4	15.0	15.7	16.4	17.1	17.9	18.7	19.5	
10	6	11.7	11.7	11.8	12.0	12.3	12.7	13.1	13.6	14.1	14.7	15.4	16.0	16.7	17.5	18.2	19.0	19.8	
10	7	12.2	12.2	12.4	12.6	12.8	13.2	13.6	14.1	14.6	15.2	15.8	16.4	17.1	17.8	18.6	19.3	20.1	
10	8	12.8	12.8	13.0	13.2	13.4	13.7	14.1	14.6	15.1	15.7	16.2	16.9	17.5	18.2	19.0	19.7	20.5	
10	9	13.5	13.5	13.6	13.8	14.0	14.4	14.7	15.2	15.7	16.2	16.8	17.4	18.0	18.7	19.4	20.1	20.9	
10	10	14.1	14.2	14.3	14.5	14.7	15.0	15.4	15.8	16.2	16.8	17.3	17.9	18.5	19.2	19.9	20.6	21.4	
10	11	14.9	14.9	15.0	15.2	15.4	15.7	16.0	16.4	16.9	17.4	17.9	18.5	19.1	19.7	20.4	21.1	21.8	
10	12	15.6	15.7	15.7	15.9	16.1	16.4	16.7	17.1	17.5	18.0	18.5	19.1	19.7	20.3	21.0	21.7	22.4	
10	13	16.4	16.4	16.5	16.7	16.9	17.1	17.5	17.8	18.2	18.7	19.2	19.7	20.3	20.9	21.6	22.2	22.9	
10	14	17.2	17.2	17.3	17.5	17.7	17.9	18.2	18.6	19.0	19.4	19.9	20.4	21.0	21.6	22.2	22.8	23.5	
10	15	18.0	18.1	18.1	18.3	18.5	18.7	19.0	19.3	19.7	20.1	20.6	21.1	21.7	22.2	22.8	23.5	24.1	
10	16	18.9	18.9	19.0	19.1	19.3	19.5	19.8	20.1	20.5	20.9	21.4	21.8	22.4	22.9	23.5	24.1	24.7	
10	17	19.7	19.7	19.8	19.9	20.1	20.3	20.6	20.9	21.3	21.7	22.1	22.6	23.1	23.6	24.2	24.8	25.4	
10	18	20.6	20.6	20.7	20.8	21.0	21.2	21.4	21.7	22.1	22.5	22.9	23.3	23.8	24.4	24.9	25.5	26.1