TL;DR The Guardian FSD booster increases your FSD's fuel multiplier stat by a factor which would yield the listed range increase to your ship's maximum laden range.
When the Guardian FSD booster was originally made available I started a thread describing how it applied to the known FSD range formula. However the booster was removed from the game shortly after it was added and I never got the chance to unlock one myself. Now that I have unlocked it I have been able to revise the formula and correct the mistakes in the original thread.
[size=+2]Overview[/size]
The revised Guardian FSD booster advertises itself as "increasing the distance travelled per unit of fuel and enabling single jumps of a greater size". The range increase scales with the class of the module. For example a class 3 booster gives an increase of 7.75Ly. Unlike the original implementation, the new booster does not have a penalty to fuel cost, drawing additional power instead.
[size=+1]Experimentation[/size]
I fitted several different ships with various FSDs. Some with engineer modifications and some without. I then performed jumps back and forth between pairs of systems with scoopable stars (so I could refuel to maximum and keep my ship's total mass more-or-less constant for each test) both with and without a Guardian FSD booster activated. I made a note of the fuel cost for the jump with the booster and without it. The experiments were repeated for different classes of booster.
The following table lists a subset of the data I collected.
Here the Mass is the total mass of the hull and modules excluding fuel, Fuel is the amount of fuel carried, the two cost values are the fuel costs without the booster and with it activated. Factor is result of dividing the boosted cost by the regular cost.
You can see that factor is almost identical in each column. Further experimentation revealed that for identical combinations of FSD, total mass and fuel the factor would be more-or-less the same regardless of distance jumped. Different combinations of FSD and total mass would have different factors but as long as the only change in conditions was the distance jumped, the factor would not change.
That led me to devise the following hypothesis.
[size=+1]Formula[/size]
Let's look again at the jump range equation.
Rearranging for cost:
Let bonus range be the amount of additional range available from fitting a particular Guardian FSD booster. If the ship can jump that new range for the same fuel cost by applying a scaling factor to the fuel multiplier, it follows that
In other words
[size=+2]Conclusion[/size]
If max range is the range a ship can jump by expending max fuel per jump then the cost to jump an arbitary distance would be
[size=+2]Example[/size]
For an example, consider a Diamondback Explorer with a A2 power plant, D4 thrusters, A5 frame shift drive, D3 life support, D3 power distributor, D3 sensors and C4 fuel tank. The total mass of the ship when fully fueled is 307.82T assuming a fully filled reserve fuel tank of 0.52T. Given that an A5 FSD has optimised mass 1050T and max fuel per jump 5T, the ship's laden range is thus:
Now suppose the ship is fitted with a class 3 Guardian FSD booster with a mass of 1.3T and a bonus range of 7.75Ly.
The ship's new maximum range is
The booster's scaling factor can be calculated from the unboosted max range which is 39.8441.
The fuel cost to jump 30Ly with the booster deactivated would be
With the booster activated the cost falls
The jump that took 2.495T without the booster can be achieved with only 1.622T using the booster.
[size=+2]Benefits[/size]
Jumps that are in range of an unboosted drive will be more fuel efficient with a boosted drive.
More interestingly, a drive's maximum range given the same loadout will be increased by the amount listed in the booster's description.
Note that the booster itself has a mass, which is why the examples above describe it as being either activated or deactivated rather than fitted or not fitted. A ship's regular maximum range will be slightly more when it is not carrying the extra mass of the booster.
[size=+2]Idiosyncracies[/size]
Fuel cost
The original implementation of the Guardian FSD booster added a fuel cost penalty. That was bugged and has now been removed entirely.
Supercharging and injection
There was a bug in the implementation of the new FSD booster related to supercharging and injection, which was fixed in patch 3.1.1. Applying an injection or a neutron/white dwarf supercharge will increase your ship's range by a given percentage; 400% for neutron star boosts.
In the outfitting and the galaxy map the formula used to calculate the final range for a neutron boost was 4 * (range + bonus range) but the fuel cost calculations used when you actually jumped used (4 * range) + bonus range. Players plotting a route using neutron boosts or FSD injection would be presented with a jump that they couldn't make, though if they manually chose a closer destination they were able to make the jump.
In 3.1.1 the bug is fixed and a ship's maximum range with a Guardian booster is indeed supercharge bonus * (range + bonus range).
Deep charge vs Mass manager
Because the range increase is a flat benefit applied after other calculations, it does not affect your choice of Deep charge or Mass manager experimental effect.
JonathanBurnage and VerticalBlank demonstrated that the cutoff point for picking Mass manager (optimised mass +4%) vs Deep charge (max fuel per jump +10%) is when
Fuel multiplier does not play any part in the calculation. Adding the range increase, eg 7.75, to both sides of the equation will not change the result.
When the Guardian FSD booster was originally made available I started a thread describing how it applied to the known FSD range formula. However the booster was removed from the game shortly after it was added and I never got the chance to unlock one myself. Now that I have unlocked it I have been able to revise the formula and correct the mistakes in the original thread.
[size=+2]Overview[/size]
The revised Guardian FSD booster advertises itself as "increasing the distance travelled per unit of fuel and enabling single jumps of a greater size". The range increase scales with the class of the module. For example a class 3 booster gives an increase of 7.75Ly. Unlike the original implementation, the new booster does not have a penalty to fuel cost, drawing additional power instead.
[size=+1]Experimentation[/size]
I fitted several different ships with various FSDs. Some with engineer modifications and some without. I then performed jumps back and forth between pairs of systems with scoopable stars (so I could refuel to maximum and keep my ship's total mass more-or-less constant for each test) both with and without a Guardian FSD booster activated. I made a note of the fuel cost for the jump with the booster and without it. The experiments were repeated for different classes of booster.
The following table lists a subset of the data I collected.
| FSD | Mass | Fuel | Distance | Regular cost | Boosted cost | Factor |
|---|---|---|---|---|---|---|
| 2A | 38.3 | 2 | 5.916 | 0.08045 | 0.04738 | 0.588336 |
| 2A | 38.3 | 2 | 13.4 | 0.413038 | 0.243005 | 0.588616 |
| 2A | 38.3 | 2 | 13.4 | 0.797907 | 0.469661 | 0.588337 |
You can see that factor is almost identical in each column. Further experimentation revealed that for identical combinations of FSD, total mass and fuel the factor would be more-or-less the same regardless of distance jumped. Different combinations of FSD and total mass would have different factors but as long as the only change in conditions was the distance jumped, the factor would not change.
That led me to devise the following hypothesis.
Suppose the ship's normal laden maximum range is r and the fitted Guardian FSD booster's bonus range is b.
When the Guardian FSD booster is active, the fuel multiplier stat in all fuel cost calculation is scaled by an amount which would allow the ship to jump r + b lightyears by expending the FSD's max fuel per jump amount of fuel.
When the Guardian FSD booster is active, the fuel multiplier stat in all fuel cost calculation is scaled by an amount which would allow the ship to jump r + b lightyears by expending the FSD's max fuel per jump amount of fuel.
[size=+1]Formula[/size]
Let's look again at the jump range equation.
range = (optimised mass / total mass) * (fuel cost / multiplier)[color=#cb7e07](1 / fuel power)[/color]
Rearranging for cost:
range = (optimised mass / total mass) * (fuel cost / multiplier)[color=#cb7e07](1 / fuel power)[/color]
range / (optimised mass / total mass) = (fuel cost / multiplier)[color=#cb7e07](1 / fuel power)[/color]
(range / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color] = (fuel cost / multiplier)
multiplier * (range / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color] = fuel cost
range / (optimised mass / total mass) = (fuel cost / multiplier)[color=#cb7e07](1 / fuel power)[/color]
(range / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color] = (fuel cost / multiplier)
multiplier * (range / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color] = fuel cost
Let bonus range be the amount of additional range available from fitting a particular Guardian FSD booster. If the ship can jump that new range for the same fuel cost by applying a scaling factor to the fuel multiplier, it follows that
fuel cost = factor * multiplier * ((range + bonus range) / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color]
In other words
multiplier * (range / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color] = factor * multiplier * ((range + bonus range) / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color]
(range / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color] = factor * ((range + bonus range) / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color]
range * total mass = log[sub](fuel power)[/sub] factor * (range + bonus range) * total mass
range = log[sub](fuel power)[/sub] factor * (range + bonus range)
range / (range + bonus range) = log[sub](fuel power)[/sub] factor
(range / (range + bonus range))[color=#cb7e07](fuel power)[/color] = factor
(range / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color] = factor * ((range + bonus range) / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color]
range * total mass = log[sub](fuel power)[/sub] factor * (range + bonus range) * total mass
range = log[sub](fuel power)[/sub] factor * (range + bonus range)
range / (range + bonus range) = log[sub](fuel power)[/sub] factor
(range / (range + bonus range))[color=#cb7e07](fuel power)[/color] = factor
[size=+2]Conclusion[/size]
If max range is the range a ship can jump by expending max fuel per jump then the cost to jump an arbitary distance would be
fuel cost = factor * multiplier * (range / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color]
= (max range / (max range + bonus range))[color=#cb7e07](fuel power)[/color] * multiplier * (range / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color]
= multiplier * ((range * max range * total mass) / ((max range + bonus range) * optimised mass))[color=#cb7e07](fuel power)[/color]
= (max range / (max range + bonus range))[color=#cb7e07](fuel power)[/color] * multiplier * (range / (optimised mass / total mass))[color=#cb7e07](fuel power)[/color]
= multiplier * ((range * max range * total mass) / ((max range + bonus range) * optimised mass))[color=#cb7e07](fuel power)[/color]
[size=+2]Example[/size]
For an example, consider a Diamondback Explorer with a A2 power plant, D4 thrusters, A5 frame shift drive, D3 life support, D3 power distributor, D3 sensors and C4 fuel tank. The total mass of the ship when fully fueled is 307.82T assuming a fully filled reserve fuel tank of 0.52T. Given that an A5 FSD has optimised mass 1050T and max fuel per jump 5T, the ship's laden range is thus:
range = (optimised mass / total mass) * (fuel cost / multiplier)(1 / fuel power)
= (1050 / 307.82) * (5 / 0.012)(1 / 2.45)
= 3.4110 * 416.6667 0.4082
= 3.4110 * 11.7301
= 40.0123
= (1050 / 307.82) * (5 / 0.012)(1 / 2.45)
= 3.4110 * 416.6667 0.4082
= 3.4110 * 11.7301
= 40.0123
Now suppose the ship is fitted with a class 3 Guardian FSD booster with a mass of 1.3T and a bonus range of 7.75Ly.
The ship's new maximum range is
range = ((1050 / 309.12) * (5 / 0.012)(1 / 2.45)) + 7.75
= (3.3967 * 416.6667 0.4082) + 7.75
= (3.3967 * 11.7301) + 7.75
= 39.8441 + 7.75
= 47.5941
= (3.3967 * 416.6667 0.4082) + 7.75
= (3.3967 * 11.7301) + 7.75
= 39.8441 + 7.75
= 47.5941
The booster's scaling factor can be calculated from the unboosted max range which is 39.8441.
factor = (max range / (max range + bonus range))(fuel power)
= (39.8441 / 47.5941) 2.45
= 0.83716 2.45
= 0.6469
= (39.8441 / 47.5941) 2.45
= 0.83716 2.45
= 0.6469
The fuel cost to jump 30Ly with the booster deactivated would be
fuel cost = multiplier * (range / (optimised mass / total mass))(fuel power)
= 0.012 * (30.0 / (1050 / 309.12)) 2.45
= 0.012 * (30.0 / 3.3967) 2.45
= 0.012 * 8.8319 2.45
= 0.012 * 207.8953
= 2.495
= 0.012 * (30.0 / (1050 / 309.12)) 2.45
= 0.012 * (30.0 / 3.3967) 2.45
= 0.012 * 8.8319 2.45
= 0.012 * 207.8953
= 2.495
With the booster activated the cost falls
fuel cost = multiplier * ((range * max range * total mass) / ((max range + bonus range) * optimised mass))(fuel power)
= 0.012 * ((30.0 * 39.8441 * 309.12) / (47.5941 * 1050)) 2.45
= 0.012 * (369498.2457 / 49973.805) 2.45
= 0.012 * 7.4094 2.45
= 0.012 * 135.1977
= 1.622
Or alternatively
= 0.012 * ((30.0 * 39.8441 * 309.12) / (47.5941 * 1050)) 2.45
= 0.012 * (369498.2457 / 49973.805) 2.45
= 0.012 * 7.4094 2.45
= 0.012 * 135.1977
= 1.622
fuel cost = factor * multiplier * (range / (optimised mass / total mass))(fuel power)
= 0.6469 * 0.012 * (30.0 / (1050 / 309.12)) 2.45
= 0.6469 * 0.012 * (30.0 / 3.3967) 2.45
= 0.6469 * 0.012 * 8.8319 2.45
= 0.6469 * 0.012 * 207.8953
= 0.6469 * 2.495
= 1.622
= 0.6469 * 0.012 * (30.0 / (1050 / 309.12)) 2.45
= 0.6469 * 0.012 * (30.0 / 3.3967) 2.45
= 0.6469 * 0.012 * 8.8319 2.45
= 0.6469 * 0.012 * 207.8953
= 0.6469 * 2.495
= 1.622
[size=+2]Benefits[/size]
Jumps that are in range of an unboosted drive will be more fuel efficient with a boosted drive.
More interestingly, a drive's maximum range given the same loadout will be increased by the amount listed in the booster's description.
Note that the booster itself has a mass, which is why the examples above describe it as being either activated or deactivated rather than fitted or not fitted. A ship's regular maximum range will be slightly more when it is not carrying the extra mass of the booster.
[size=+2]Idiosyncracies[/size]
Fuel cost
The original implementation of the Guardian FSD booster added a fuel cost penalty. That was bugged and has now been removed entirely.
Supercharging and injection
There was a bug in the implementation of the new FSD booster related to supercharging and injection, which was fixed in patch 3.1.1. Applying an injection or a neutron/white dwarf supercharge will increase your ship's range by a given percentage; 400% for neutron star boosts.
In the outfitting and the galaxy map the formula used to calculate the final range for a neutron boost was 4 * (range + bonus range) but the fuel cost calculations used when you actually jumped used (4 * range) + bonus range. Players plotting a route using neutron boosts or FSD injection would be presented with a jump that they couldn't make, though if they manually chose a closer destination they were able to make the jump.
In 3.1.1 the bug is fixed and a ship's maximum range with a Guardian booster is indeed supercharge bonus * (range + bonus range).
Deep charge vs Mass manager
Because the range increase is a flat benefit applied after other calculations, it does not affect your choice of Deep charge or Mass manager experimental effect.
JonathanBurnage and VerticalBlank demonstrated that the cutoff point for picking Mass manager (optimised mass +4%) vs Deep charge (max fuel per jump +10%) is when
1.04 = 1.1(1 / fuel power)
(1 / fuel power) = log[sub]1.1[/sub] 1.04
(1 / fuel power) = ln 1.04 / ln 1.1
fuel power = ln 1.1 / ln 1.04
(1 / fuel power) = log[sub]1.1[/sub] 1.04
(1 / fuel power) = ln 1.04 / ln 1.1
fuel power = ln 1.1 / ln 1.04
Fuel multiplier does not play any part in the calculation. Adding the range increase, eg 7.75, to both sides of the equation will not change the result.
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