Operating Time: Math Implications and issues to be aware of
Posted: Sun Sep 27, 2020 10:54 am
The 2E RPG asserts that the VF-1 can operate for 48hrs, and the ASC VTs for 168hrs and the UEEF VFs for 336hrs (for those still using 1E, this is still an issue). If we take this to the implied conclusion that they can generate full thrust for that time one ends up with some ridiculous (and contradictory) space propulsion performance. We can also safely assume that all the VFs in the 2E (and 1E) RPG have T/W ratios of greater than 1, and sense T/W Ratio = acceleration measured in Earth Gravity we can do some simple math to work out what the "Delta-V" capacity of various veritechs (and other units) would be depending on their specific T/W Ratio and stated operating time. For simplicity I am only going to calculate the figures at 1G (to get a specific unit then multiply these numbers by whatever value the T/W is for specific units, for example the VF-1 T/W ratio is 3.47 so multiply the 48hr result by 3.47, though keep in mind this is the empty value and not loaded).
@1G for:
-048hrs = ~01,694.5kps
-168hrs = ~05,930.7kps
-336hrs = ~11,861.3kps
For comparison you only need ~9.4kps to launch into Earth orbit from the surface, with basically twice that you could IINM duplicate every propulsive maneuver of an Apollo Lunar Mission (by the Service Module, both Lander stages, and the 3 stages from the Saturn-V combined). Clearly some limits need to be placed on operating time in space form a propulsion standpoint or you end up with contradictions (SSTO) or game breaking features (and Life Support Endurance just will not cut it) that I don't think anyone really intended. I looked at 6minutes, 15minutes, 30 minutes (and did a 1G baseline as before, multiple the resulting figure as above based on the VF's T/W ratio) and this represents operating at FULL THRUST for the stated time (longer duration at lower thrust settings are possible, but the end delta-v is not going to change).
@1G for
-06min = ~03.5kps
-15min = ~08.8kps
-30min = ~17.7kps
All the Math done here is basically solving for a variable in the classic Acceleration = (Velocity-end - Velocity-start)/ Time formula (and if need be substituting in Velocity = Distance / Time) with Velocity-start being Zero. All figures are rounded to nearest 10th. I leave it to GMs to choose what they think works best for them (if you want to use a custom time you'll have to do the math).
On a side note, to give you an idea of how game breaking the propulsion system is as described, at 1G of constant Acceleration for 48hrs depending on planetary position you could travel from Earth to either Venus or Mars (with a wider window if you just want to fly by or have some other external means to "stop"). This doesn't change much aside from the window of planetary positions with either the standard VF-1 or any Alpha (two VFs with well known T/W ratios) based on their T/W ratio at full thrust for the duration. If the UEEF VFs had sufficient Life Support to operate at only 1G of acceleration for the duration of their operating time, they pretty much could range out to Pluto (not quite its max distance from Earth, but with 5% more acceleration, which they should all be able to do they could reach Pluto). If I did the T/W ratio right a VF-1 w/FAST Packs has a T/W Ratio of ~15, at that amount for 48hrs Earth-Saturn is covered (a bit short for Earth-Uranus actually, the main draw back here is if a person could sustain those G levels for the required time).
On a second side note I also calculated the acceleration of the big ships display per the 2E RPG. All figures should be viewed as approximate for several reasons: these are presented as rounded and the acceleration time may or may not be precise (but was taken as such, ex. of what I mean the writers could have rounded 46hrs or 50hrs to 2 days for simplicity).
Macross Saga Source Book:
-Orberth: 0.0900G
-ARMD: 0.0819G
-SDF-1: 0.0098G
-Zentreadi Flagship: 0.0158G
-Zentreadi Destroyer: 0.0211G
Masters Saga Source Book:
-Master Transport: 0.1629G
-Master City Ship: 0.0977G
-Tri-Star: 0.0791G
Genesis Pits Source Book:
-SDF-4: 0.0983G
-Icarus: 0.0733G
Average Acceleration Time is 0.0730G between these 10 ships (AFAIK these are the only ships in the 2E RPG with those ratings). IIRC Dialogue cues in TRM saga for a ship journey to the Moon, and assuming it is using constant thrust (ie acceleration) at 100% output the Tri-Star would need to be ~7x the existing value (which puts a trip at 12+ hrs, IIRC dialogue it is more like 5hrs) so the ship (and others potentially) might be able to sustain higher rates for shorter periods of time (as a possible explanation).
@1G for:
-048hrs = ~01,694.5kps
-168hrs = ~05,930.7kps
-336hrs = ~11,861.3kps
For comparison you only need ~9.4kps to launch into Earth orbit from the surface, with basically twice that you could IINM duplicate every propulsive maneuver of an Apollo Lunar Mission (by the Service Module, both Lander stages, and the 3 stages from the Saturn-V combined). Clearly some limits need to be placed on operating time in space form a propulsion standpoint or you end up with contradictions (SSTO) or game breaking features (and Life Support Endurance just will not cut it) that I don't think anyone really intended. I looked at 6minutes, 15minutes, 30 minutes (and did a 1G baseline as before, multiple the resulting figure as above based on the VF's T/W ratio) and this represents operating at FULL THRUST for the stated time (longer duration at lower thrust settings are possible, but the end delta-v is not going to change).
@1G for
-06min = ~03.5kps
-15min = ~08.8kps
-30min = ~17.7kps
All the Math done here is basically solving for a variable in the classic Acceleration = (Velocity-end - Velocity-start)/ Time formula (and if need be substituting in Velocity = Distance / Time) with Velocity-start being Zero. All figures are rounded to nearest 10th. I leave it to GMs to choose what they think works best for them (if you want to use a custom time you'll have to do the math).
On a side note, to give you an idea of how game breaking the propulsion system is as described, at 1G of constant Acceleration for 48hrs depending on planetary position you could travel from Earth to either Venus or Mars (with a wider window if you just want to fly by or have some other external means to "stop"). This doesn't change much aside from the window of planetary positions with either the standard VF-1 or any Alpha (two VFs with well known T/W ratios) based on their T/W ratio at full thrust for the duration. If the UEEF VFs had sufficient Life Support to operate at only 1G of acceleration for the duration of their operating time, they pretty much could range out to Pluto (not quite its max distance from Earth, but with 5% more acceleration, which they should all be able to do they could reach Pluto). If I did the T/W ratio right a VF-1 w/FAST Packs has a T/W Ratio of ~15, at that amount for 48hrs Earth-Saturn is covered (a bit short for Earth-Uranus actually, the main draw back here is if a person could sustain those G levels for the required time).
On a second side note I also calculated the acceleration of the big ships display per the 2E RPG. All figures should be viewed as approximate for several reasons: these are presented as rounded and the acceleration time may or may not be precise (but was taken as such, ex. of what I mean the writers could have rounded 46hrs or 50hrs to 2 days for simplicity).
Macross Saga Source Book:
-Orberth: 0.0900G
-ARMD: 0.0819G
-SDF-1: 0.0098G
-Zentreadi Flagship: 0.0158G
-Zentreadi Destroyer: 0.0211G
Masters Saga Source Book:
-Master Transport: 0.1629G
-Master City Ship: 0.0977G
-Tri-Star: 0.0791G
Genesis Pits Source Book:
-SDF-4: 0.0983G
-Icarus: 0.0733G
Average Acceleration Time is 0.0730G between these 10 ships (AFAIK these are the only ships in the 2E RPG with those ratings). IIRC Dialogue cues in TRM saga for a ship journey to the Moon, and assuming it is using constant thrust (ie acceleration) at 100% output the Tri-Star would need to be ~7x the existing value (which puts a trip at 12+ hrs, IIRC dialogue it is more like 5hrs) so the ship (and others potentially) might be able to sustain higher rates for shorter periods of time (as a possible explanation).