[Space, Spaceships] Total ΔV for Interplanetary Travel

[RyanW]

Originally Posted by Fred Brackin

Just to be exhaustive there's the possibility of an change or orbital plane maneuver. It was part of the effect of launching from Cape Canaveral for the Moon that on the right days no change of plane was needed.

Russia's got it even worse, with their even further north launch site, and the most sensible trajectory passing through unfriendly Chinese airspace during assent. The need to be accessible from Baikonur is a big part of why the ISS is placed in such a highly inclined orbit.

[DaltonS]

Originally Posted by PTTG

You can run it in linux, you just need to use grape-based ethanol fuel.

Perhaps if it's made from Grand Fenwick grapes. ;)

Dalton “what sort of ΔV can we get from Pinot Grand Fenwick?” Spence

[DaltonS]

Originally Posted by Anthony

Realistically, the Oberth Effect means that the total ΔV is less than their sum; how much less depends on your thrust.

The limit case for infinite thrust is ΔV = sqrt( escape velocity ^ 2 + transfer velocity ^ 2 ) - orbital velocity, to either enter or leave orbit. For example, from low earth orbit (escape velocity = 11.2 km/sec, velocity = 7.92 km/s) to a Mars transfer orbit (2.9 km/s) requires sqrt( 11.2^2 + 2.9^2) - 7.92 = 3.65 km/s, which is barely more than the 3.28 km/s required to break orbit.

Okay, let's translate this to "mps" (the speed unit of choice for GURPS Spaceships). The Halfway to Anywhere “Mission to Mars" profile on page 33 of Pyramid #3/79: Space Atlas breaks the 3.4 mps ΔV of the Hohmann transfer orbit into two burns (1.8 mps at Earth orbit and 1.6 mps at Mars) and adds a 0.6 mps burn “to account for a 1.85° difference in orbital planes”. Ve = 6.96 mps (SS1 p.37) making Vo = Ve /sqrt(2) = 4.92 mps. So ΔV = sqrt(6.96^2 + 1.8^2) - 4.92 = 2.27 mps. (I could have directly converted the numbers, but I like using official sources.) Now for the tricky bit; would there be a reverse Oberth effect when making Mars orbit?

Dalton “just when I think I'm getting it, what I get is confused” Spence

[Ulzgoroth]

Originally Posted by DaltonS

Okay, let's translate this to "mps" (the speed unit of choice for GURPS Spaceships). The Halfway to Anywhere “Mission to Mars" profile on page 33 of Pyramid #3/79: Space Atlas breaks the 3.4 mps ΔV of the Hohmann transfer orbit into two burns (1.8 mps at Earth orbit and 1.6 mps at Mars) and adds a 0.6 mps burn “to account for a 1.85° difference in orbital planes”. Ve = 6.96 mps (SS1 p.37) making Vo = Ve /sqrt(2) = 4.92 mps. So ΔV = sqrt(6.96^2 + 1.8^2) - 4.92 = 2.27 mps. (I could have directly converted the numbers, but I like using official sources.) Now for the tricky bit; would there be a reverse Oberth effect when making Mars orbit?

Dalton “just when I think I'm getting it, what I get is confused” Spence

There's no 'reverse Oberth effect'. The Oberth effect helps you make your transfer burn and helps you make your orbital insertion burn.

[Anthony]

Originally Posted by DaltonS

Now for the tricky bit; would there be a reverse Oberth effect when making Mars orbit?

The Oberth effect applies at both ends (it's not reverse).

[DaltonS]

Originally Posted by Anthony

The Oberth effect applies at both ends (it's not reverse).

Mars Ve is 3.1 mps making Vo = 2.19, so ΔV = sqrt(3.1^2 + 1.6^2) - 2.19 = 1.3 mps. That makes the total ΔV for the trip = 2.27 + 0.6 + 1.3 = 4.17 mps, which according to my ΔV calculator spreadsheet would take 10 tanks of fuel with a TL8 NTR.

Dalton “did I get this right?” Spence

[Anthony]

Originally Posted by DaltonS

Mars Ve is 3.1 mps making Vo = 2.19, so ΔV = sqrt(3.1^2 + 1.6^2) - 2.19 = 1.3 mps. That makes the total ΔV for the trip = 2.27 + 0.6 + 1.3 = 4.17 mps, which according to my ΔV calculator spreadsheet would take 10 tanks of fuel with a TL8 NTR.

Note that the thrust of a TL 8 NTR is low enough that the limit case approximation isn't correct. I'm not aware of a simple solution for the moderate thrust case.

[Humabout]

Originally Posted by DaltonS

Thanks. This will help.
I think areobraking would require a certain level of armor to withstand aerodynamic heating depending on the ΔV you want to shed.
That's where a One-Tangent Burn orbit calculator comes into play. Unlike a Hohmann transfer, you can adjust the launch windows by adjusting the ΔV used. The second burn has to be done at an angle to the flight path, requiring more ΔV.


There is even a spreadsheet to go with the article. :) For some reason they missed One-Tangent Burns though.

Dalton “still working on his Mars Semi-Cycler” Spence

One-Tangent Burns weren't overlooked so much as intentionally omitted. The primary focus of the article was to give GMs reasonable bounds on realistic transfer times. That's why it covers the longest, most fuel-efficient transfers and the fastest, least fuel-efficient transfer. Enough variables exist in between these two senarios that it becomes unrealistic to provide a simple explaination of planning such voyages. I drew a pretty hard line at the GM having to track the motion of celestial bodies on a calendar, and you start to need that sort of thing to determine just how fast of a one-tangent burn is possible at a given time. If you gloss over that and arrive at the speed of plot, the article gives that speed upper and lower bounds, as it does for dV requirements.

After next spring, I may reprise the article with something more detailed, but I won't attempt this before I do more in depth study of the material. I probably won't present it through Pyramid unless Steven asks for it or there appears to be enough demand for something more math-heavy than the original.

[DaltonS]

Originally Posted by Anthony

Note that the thrust of a TL 8 NTR is low enough that the limit case approximation isn't correct. I'm not aware of a simple solution for the moderate thrust case.

What is sufficient thrust for this to work?

Dalton “who missed the limit number somewhere” Spence

[Anthony]

Originally Posted by DaltonS

What is sufficient thrust for this to work?

Dalton “who missed the limit number somewhere” Spence

It's generally a reasonable approximation as long as thrust exceeds local gravity, and gets gradually worse. I wrote a simulator for a simple constant thrust spiral away from a planet a few years back, I can't promise as to its accuracy, but rough results I got were:
10 Gs: 3.6 km/s ΔV for a transfer orbit (less than 3.65 because I assumed an initial 200 altitude)
1 G: 3.65 km/s ΔV for a transfer orbit.
0.1G: 4.6 km/s ΔV for a transfer orbit.
0.01G: 6.9 km/s ΔV for a transfer orbit.
0.001G: 8.4 km/s ΔV for a transfer orbit.
0.0001G: 9.4 km/s ΔV for a transfer orbit.