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Formula Error in Classic Traveller? http://sfrpgdiscussion.net/viewtopic.php?f=45&t=3289 
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Author:  HalC [ Thu Oct 04, 2018 2:10 pm ] 
Post subject:  Formula Error in Classic Traveller? 
Hi Guys, This quote from another thread, has me wondering if someone already caught this and is one of the reasons for the sentiment expressed... EDG wrote: I mean we're talking Traveller here (and T5 at that), it's not unknown for them to get calculations wrong... While not T5, it does make me wonder a bit about how something accepted early on without questioning, can maybe be a problem further down the road. I posted this question at SJGames in their Traveller section, hoping that someone there will catch the mistake that I SURELY must have made (and please, no comment along the lines of stop calling you Shirley)! Formula for Velocity = Acceleration * Time. So, if I accelerated at 1 G for 1,000 seconds (original unit of time for a turn in Classic Traveller's space combat pg 26 of book 2), and 1 G was rounded to 10 from 9.8, we'd have a value of 10 * 1,000 or 10,000 meters per second. When converting 10,000 meters into kilometers, we divide by 1,000, which brings us to 10 km per second right? At a scale of 1mm = 100 km, a single G of acceleration should only change the velocity by 0.1 mm instead of 100mm. Now, distance TRAVELLED on the other hand, is equal to 10/2 x 1000^2 (just for the distance covered in 1000 seconds over and above its initial velocity). So, that is equal to 5000 km. So, the problem here is that per the original rules, the built up velocity vector should be incrementing by .1mm per turn instead of 100mm per turn. Is this correct? Note: originally wrote in the values for Distance Traveled wrong. Corrected it above to read 5,000 km as it should have been. 
Author:  EDG [ Thu Oct 04, 2018 2:45 pm ] 
Post subject:  Re: Formula Error in Classic Traveller? 
Yeah... they say 10,000 km in the book, but G is 10 metres per second so after 1000 seconds the ship should be going at 10 km per second. 
Author:  HalC [ Fri Oct 05, 2018 12:03 am ] 
Post subject:  Re: Formula Error in Classic Traveller? 
I finally finished my "proof" of concept for VB.NET where I added vectors together. So, the first vector is "Where is the ship now relative to the Star Mass"  this gives us where the current position of the ship is. Second Vector is "What is the built up velocity relative to the Ship itself"  this gives us the next turn's future position should the ship not accelerate Third vector will be "What will the ship accelerate by and in what heading"  this will give us the final location of the ship when added to the future position. Now the problem becomes one of "What is the new built up velocity" as well as what is its bearing. My gut instinct is that if a ship accelerates at 10 m/sec for 400 turns, the BEST velocity it can achieve is if it heads on the same bearing for those 400 turns. Its built up velocity then, would be 10 km per turn x 400 turns or 4,000 km per turn. If I were to make a right turn against that built up Velocity of 4,000 km per turn, my new built up velocity will be (4000^2 + 10^2)^.5 or 4000.012499 km per second. That's not much of a change in built up velocity. If I'm making a mistake here, now is the time for me to catch it (hopefully you don't mind my asking for the help!!!). Ultimately? If I can accurately add all three vectors  I will have a virtual table top that spans the entire Star system  since units of measure can be miles (for 93,000,000 miles per AU) or Km (for 150,000,000 Km Per Au). It can track missile locations, it can track ship locations, and if it can determine distances between two objects being tracked, it can also determine range between the two items. I had looked for an algorithm for calculating the location of a planet on an elliptical orbit  but I'm not finding anything that I can use thus far. I think I saw a method that required the use of an actual circle inside of the elliptical, and the true location on the elliptical was based on the inside circle, but I am likely misremembering it. The thing is? Even if the method is "Slightly" flawed, the same level of flaw will apply to all ships trying to navigate to that present planet based upon where it will be in a given time frame. If I had the means to calculate planetary locations, ship locations, missile locations etc  then in theory? I could write a subroutine where it would have a range from the ship, and be able to display all "discovered" items within a circle radius of the ship. In theory? I could make a "radar blip" type screen showing where things are, what their observed built up velocity vector is, etc. Then, over the internet  or perhaps via FANTASY GROUNDS  I could run a ship to ship combat for the players on a mostly text based set up  but all computer generated. The "Basic' application would be "Game system neutral" as far as movement goes. It would be system dependent for sensor information (whether CT, MT, TNE, T4, GT, MgT or what have you. I am NOT going to try and figure out T5 rules. So technically? Being able to add vectors together was the primary hurdle. If I simply cheat and use strictly circular orbits, then I have planetary motion as well. 
Author:  Agemegos [ Fri Oct 05, 2018 10:56 am ] 
Post subject:  Re: Formula Error in Classic Traveller? 
HalC wrote: So, if I accelerated at 1 G for 1,000 seconds (original unit of time for a turn in Classic Traveller's space combat pg 26 of book 2), and 1 G was rounded to 10 from 9.8, we'd have a value of 10 * 1,000 or 10,000 meters per second. When converting 10,000 meters into kilometers, we divide by 1,000, which brings us to 10 km per second right? Yes, and 10 km/sec is 10,000 km/turn, where a turn is 1,000 seconds. 
Author:  HalC [ Mon Oct 08, 2018 3:01 am ] 
Post subject:  Re: Formula Error in Classic Traveller? 
Yeah  I went and dug deeper into the issue  even set up an excel sheet to compare both the real world formulas for displacement, velocity, etc  and compared it against the "displacement" that is apparent if one uses the methodology of 100mm of movement = 1 turn at 1 G accel. The net result? The first turn, the "approximation" of vector addition per the CT rules, resulted in a displacement that was twice what it should be. When I compared the actual velocity values per 100mm = 100mm x 100 km, and then converted that into meters per turn, dividing it by 1000 for the number of seconds  the values matched 100% So built up velocity matched as it should. Only the displacement failed to match properly. But then I simply extended the columns down. Originally I set up the analysis to compare the two methodologies (the CT rules and real equations) and I found myself surprised. I went so far as to extent the turns from 10, to 50, and even as far as 350 turns. The result? The vector movement rules were off by a factor of about 2% too large once you hit 40 turns, and by 350 turns, the inaccuracy was only .2% TO put it another way, "Good enough for government work". Well, at least I now have faith in the process, and am torn between using the real formulas versus the vector rules from CT. The reason why? Eventually  I'm going to want another set of eyes on this. I'm going to want to give the app to someone to test where they can know that if they start off at a given location, go for 5 turns on a given bearing with any given Acceleration they care to name  and choose any bearing they want to accelerate with at any given turn  they're going to need to be able to confirm that the values the program calculates matches the values they calculated themselves. That's just common sense  quality assurance testing 
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