Thanks. I read a fair bit about mass flow rate (and understood about half well, about another 20-30% sort of, and there was some I need to go revisit). There were listings in the article of photonic rockets and some other drives that would have very high Isp (some well above the Expanse' Epstein drive).

One last question:

You gave me some ideas of a 30 day trip and a 210 day trip without worrying about the 'to earth orbit' fuel load.

I assume the time-to-mars vs. amount of fuel curve (on which these two points would live) is not a linear growth in fuel (or maybe it is?). I'm thinking because not only do you need to shove yourself further/harder at the start, but you also then need fuel (aerocapture won't do it) for decelerating into mars orbit and so you have to shove it up to speed at the start.

Is there an easy way to sort of characterize that curve? At some point, you need to start having deceleration fuel and then the curve would start to escalate faster/differently.

(Either a few more data points that would give a good sense, or a rough graph or equation of fuel use vs. trip duration?)

I'm curious from a game utility PoV to say

Take the 600 Isp rocket...

210 days looked like roughly a 1:1 ratio of vehicle mass to fuel mass (if lift from Earth ignored and aerocapture possible)

30 days looked like a 10 or 11 : 1 ratio of vehicle mass to fuel mass (if lift from Earth ignored, but one has to decelerate into aerocapture)

What might it look like at 140 days (2/3rds of 210), 110 days (1/2 of 210), 55 days (1/4 of 210)..... 30 days would fit at about 1/7th of 210 days

If you had to tinker a lot to get the 210 day and 30 day orbits to work, don't worry about it. I'm not sure if your equations were formulated in such a way as to take the travel time as an input (vs. just trying different cases until you got close to the desired travel time of 30 days... for example.

On Thu, Jul 30, 2020 at 7:59 PM Vareck Bostrom <xxxxxx@gmail.com> wrote:

Inline responses

On Thu, Jul 30, 2020 at 12:57 PM <xxxxxx@gmail.com> wrote:
What I'm taking from this (please correct me if I am incorrect):

a) Flights of 200+ days vs. a flight of 30 days could easily differ by two orders of magnitude in fuel requirements

Correct.

b) SpaceX is using about 18x as much fuel weight to escape earth relative to the weight of their vehicle

I was basing that on 600s Isp, which is better than what SpaceX currently has.

c) If we could ignore the earth escape fuel, 210 day flight would require about 0.95x the weight of fuel as compared to the weight of the vehicle.

Again, presuming 600s Isp

d) If we could ignore the earth escape fuel, 130 day flight would require about 1.1x the weight of fuel as compared to the weight of the vehicle.

as above

e) The 30 day run without earth escape looks like about 150x the weight of the vehicle.

as above

I did lose you in two places (assuming the above is roughly right):

Using SpaceX starship as an example with a 210 day flight to Mars launched from the earth's surface now, for the 120t (dry mass) starship you need 2246.4t of propellant for earth launch and escape and then 64.5t propellant for mars velocity match. However, spacex plans on aerocapture at mars so we can disregard the propellant at the end of the flight but we must limit ourselves to a 7.5 km/sec entry velocity at mars. This all presuming Isp of 600s.

What's 600s of Isp?

"Specific impulse" which is directly related to the exhaust velocity or the velocity of the expelled propellant. The higher the exhaust velocity, the more change in ship velocity you get for a given amount of propellant. Modern day rocket engines generally have specific impulses of 300-400s and that is related to how much energy is extracted via the chemical process of burning the fuel or whatever other process you use to accelerate the propellant. 600 seconds of Isp gives an exhaust velocity of 600 seconds * 9.806 meters * seconds^-2 = 5884 meters/second.

A hall effect thruster might have a specific impulse of more like 1500-3000s, meaning the use of propellant is much more efficient and you need less propellant for a given change of velocity. The "almost magical" epstein drives from the Expanse have a specific impulse of about 1.1 million seconds. With those kinds of drives much, much less propellant is needed.

Given that we are fine, velocity difference at mars is 2.5 km/sec (at infinity) which ends up being about 5.56 km/sec at 100 km altitude over Mars, so that would work, and we don't need to carry the propellant for deceleration with us which improves the situation so that we only need 1419t propellant for launch and TMI.

We delete the 64.5t for velocity match due to aerocapture.
But how do we get from the remaining 2246.4t for launch and escape to 1419t? It looks like you removed about 830-ish tons... why? Can you clarify why?

64.5t for velocity match and aerocapture and 830-ish tons for the acceleration of that 64.5t needed for velocity match and aerocapture. Every ton of fuel you don't need at the end of the journey saves a lot more propellant at the beginning of the journey as you don't need to accelerate the end of journey fuel in the first place.

Thanks (for what I understood already however well I did that, and for my follow up questions here).

As a follow on comment, unless there is a clear reason to make the trip time as short as possible, it's likely that every mission to mars that we conduct during our lifetimes will always use a minimum propellant-used approach as the amount of payload a given mission can carry will vary quite significantly and most missions would prefer to transport 200 tons over 210 days vs 1 ton over 30 days. When transporting humans though there may be a clear advantage to a, say, 110 day mission over a 210 day mission to the point that it would be worth the extra propellant. It does feel like we're able to roam all over the solar system (robotically, at least) at will but in practical terms we are still very limited at orbits that we can reach and timeframes that we can reach them (and this is a little why Traveller does as bit of a disservice to space fans who don't otherwise know, it dramatically minimizes the challenge of space flight)

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