How much delta-v does the Orion spacecraft have?

Question

Orion is intended to transport astronauts around cis-lunar space. How much delta-v performance does it actually have?

Answer 1

The Answer

Orion (with service module) can use between 1346 m/s and 1587 m/s of delta-v.

Here is a solar system delta-v map to get a sense of how much that is:

(Delta-v map taken from wikipedia page on delta-v)

What follows is the math for determining those values.

Spacecraft Mass

Capsule Masses:

• Capsule Dry Mass: 9300 kg
• Capsule Wet Mass: 10400 kg
• Capsule Hydrazine Mass: 1100 kg

Service Module Masses:

• Service Module Dry Mass: 6185 kg
• Service Module Wet Mass: 15461 kg
• Service Module Propellant Mass: 9276 kg

Plus 659 kg integration mass? (Found by subtraction component masses from total injected mass on Wikipedia)

Total mass: 26520 kg

Total mass after expending service Module Fuel: 17244

Mass values from https://en.wikipedia.org/wiki/Orion_(spacecraft)

Engine Performance

Capsule thrusters:

• MR-104G thrusters
• Hydrazine
• Specific Impulse: 220s (I can't actually find the specific impulse of MR-104G but this value seems pretty typical of hydrazine monopropellants)

Service Module Main Engine:

• AJ10 Engine
• Nitrogen Tetroxide Oxidizer and Aerozine50 Fuel
• Specific impulse 319s

The Math

The rocket equation is:

$\Delta v = \ln(\frac{wet\;mass}{dry\;mass}) \times g \times specific\;impulse$

Delta-v from the service module, with capsule attached (This is by far the most impactful piece):

$\ln(\frac{26520\, kg}{17244\, kg}) \times 9.8\, m/s² \times 319\, s = 1346\, m/s$

Delta-v from the capsule alone:

$\ln(\frac{10400\, kg}{9300\, kg}) \times 9.8\, m/s² \times 220\, s = 241\, m/s$

Delta-v from the service module, then the capsule, staying attached:

$\ln(\frac{26520\, kg}{17244\, kg})\times 9.8\, m/s² \times 319\,s + \ln(\frac{17244\,kg}{16144\,kg}) \times 9.8\,m/s² \times 220\,s = 1488\, m/s $

Delta-v from the capsule, then the service module, staying attached:

$\ln(\frac{26520\,kg}{25420\,kg}) \times 9.8\,m/s² \times 220s + \ln(\frac{25420\,kg}{16144\,kg}) \times 9.8\,m/s² \times 319\,s = 1511\,m/s$

Delta-v from the service module, then ejecting the service module and firing the capsule by itself:

$\ln(\frac{26520\,kg}{17244\,kg}) \times 9.8\,m/s² \times 319\,s + \ln(\frac{10400\,kg}{9300\,kg}) \times 9.8\,m/s² \times 220\,s = 1587\,m/s$

Note that I have ignored cosine losses from the Orion thrusters firing slightly off axis (the capsule walls are at an angle, after all), but I doubt they are substantial.