What's the most efficient way to travel with your lamp lit?

I have applied SCIENCE! to this question. Now that you can sail around in a floating dinner table Steam Launch, I took my couple of thousand Echoes and tested how far you could get in various conditions, with different engines and ship weights.

The Bottom Line:

1. Steaming at full throttle is better even if your lamp is off, because there's no difference in fuel-per-mile between full throttle and half throttle.
2. Since your lamp and food costs depend on time, not speed, you're better off going faster so that you spend less on lamp-fuel and sailor-food.
3. The ship's weight barely affects fuel-per-distance. The change is so small that you're better off ignoring it when deciding whether to upgrade. The difference between the 500-weight Steam Launch and the 3000-weight Destroyer is around a 12% difference in distance.
4. The more crew you have, the more it makes sense to upgrade your engine. Having a better engine means spending more fuel-per-mile, but you're also spending less on supplies when you go faster. For low-crew ships like the Tramp Steamer and Corvette, the extra fuel costs are larger than the money you're saving on food. The bigger ships, though, definitely save money with bigger engines.

Cost difference when upgrading a ship from the 800-power engine to the 1500-power engine:

Ship             Lights     Cost difference
Steam Launch     Off        +64%
                 On         +20%
Tramp Steamer    Off        +20%
                 On         +14%
Corvette         Off        +14%
                 On         -5%
Destroyer        Off        -2%
                 On         -15%

The Method: I started in Fallen London with exactly one unit of fuel and 5 hunger, steamed east until I ran out of fuel, and measured how far I got. I used hunger as a stand-in for time, because 1) I was too lazy to use a stopwatch, and 2) the important question is how many supplies are consumed, not how long you have to wait.

The Raw Data: Distance Traveled on One Barrel of Fuel

The unit of measurement is the width of one vertical band on the in-game chart. I measured everything in inches on my monitor, but you won't find that useful unless you have my monitor. And you can't have my monitor, it's mine.

For costs, I used Fallen London's prices: 10 Echoes per barrel of Fuel, 20 Echoes per crate of Supplies.

The Steam Launch^†, weight 500:

800 Power Engine, Lights Off
                    Distance    Echoes per distance (Fuel only)
  Full Throttle:    1.61        6.2
  Half Throttle:    1.59        6.3

800 Power Engine, Lights On
                    Distance    Echoes per distance (Fuel only)
  Full Throttle:    .72         14
  Half Throttle:    .46         22

1500 Power Engine, Lights Off
                    Distance    Echoes per distance (Fuel only)
  Full Throttle:    .98         10
  Half Throttle:    .98         10

1500 Power Engine, Lights On
                    Distance    Echoes per distance (Fuel only)
  Full Throttle:    .60         16
  Half Throttle:    .43         23

2000 Power Engine, Lights Off
                    Distance    Echoes per distance (Fuel only)
  Full Throttle:    .84         12
  Half Throttle:    .84         12

2000 Power Engine, Lights On
                    Distance    Echoes per distance (Fuel only)
  Full Throttle:    .55         18
  Half Throttle:    .41         24

The Tramp Steamer, fully crewed (10), weight 1000:

800 Power Engine, Lights Off
                    Distance    Hunger   Echoes per distance (Fuel + Supplies)
  Full Throttle:    1.56        55       20
  Half Throttle:    1.58        125      38

800 Power Engine, Lights On
                    Distance    Hunger   Echoes per distance (Fuel + Supplies)
  Full Throttle:    .70         25       28
  Half Throttle:    .46         35       52

1500 Power Engine, Lights Off
                    Distance    Hunger   Echoes per distance (Fuel + Supplies)
  Full Throttle:    .98         35       24
  Half Throttle:    .99         70       38

1500 Power Engine, Lights On
                    Distance    Hunger   Echoes per distance (Fuel + Supplies)
  Full Throttle:    .57         25       32
  Half Throttle:    .43         30       51

The Corvette, fully crewed (15 crew), weight 2000:

800 Power Engine, Lights Off
                    Distance    Hunger   Echoes per distance (Fuel + Supplies)
  Full Throttle:    1.48        88       30

800 Power Engine, Lights On
                    Distance    Hunger   Echoes per distance (Fuel + Supplies)
  Full Throttle:    .66         46       43

1500 Power Engine, Lights Off
                    Distance    Hunger   Echoes per distance (Fuel + Supplies)
  Full Throttle:    .91         54       35

1500 Power Engine, Lights On
                    Distance    Hunger   Echoes per distance (Fuel + Supplies)
  Full Throttle:    .54         30       41

The Destroyer, fully crewed (25 crew), weight 3000:

800 Power Engine, Lights Off
                    Distance    Hunger   Echoes per distance (Fuel + Supplies)
  Full Throttle:    1.41        134      45

800 Power Engine, Lights On
                    Distance    Hunger   Echoes per distance (Fuel + Supplies)
  Full Throttle:    .62         70       61

1500 Power Engine, Lights Off
                    Distance    Hunger   Echoes per distance (Fuel + Supplies)
  Full Throttle:    .88         72       44

1500 Power Engine, Lights On
                    Distance    Hunger   Echoes per distance (Fuel + Supplies)
  Full Throttle:    .53         46       53

^† The Steam Launch does not consume hunger. Hooray for small blessings?

Caveats, flaws, and other reasons to distrust my data: There were a couple of islands in the way, so I ended up sailing mostly-east-and-a-hair-south. Over the full distance, the largest deflection was about 7 degrees, but on the longer trials I had to make a turn of up to 30 degrees for short periods to get around a rock. Also, you always start with your lamp turned on, so I burned some fragment of fuel before I turned it off. Plus, I'm measuring things on the screen with an engineering ruler; there's going to be a little inaccuracy there.

If you're on the starting boat, the lamp is your biggest fuel consumer. It consumes 1% per second. All lamps, all boats.

Engine power, on the other hand is somewhere between 0.05% and 0.1% of engine power per second. So with 800 starting, it's between 0.4% and 0.8%.

The lamp at 1% is obviously considerably more.

If you have 3500 engine power (and no fuel efficiency) the lamp is less impactful, but your fuel is a mess anyway at that point.

I don't have stats for you but based on my play to date...

• The lamp uses a considerable amount of fuel
• Early on, when fuel is scarce and you return to London often, running without the lamp can let you explore more, get more reports, make more money, etc.
• There are lots of ways to reduce terror but many of them are expensive/unreliable except in London.
• Later on, going back to London frequently interrupts trade routes/other activities. By this point, you've got enough money that it's more beneficial to stay out longer and waste a little fuel.

To give you an example... At the moment, I've got a 3-stop trading route that nets me ~2k/circuit. Every time I have to head back to London, I waste approx 1.5 circuits in time/fuel/sipplies. As such, a few hundred on fuel is easily worth the investment. I run lights all the time except when dodging enemies.