# How many pulse units would be required to reach 1% and 10% the speed of light?

For an unmanned probe which can theoretically withstand 100G acceleration, from Lunar orbit, in regards to Project Orion.

• Aaand how many tonnes is your payload mass? Dec 28, 2015 at 10:17
– John
Dec 29, 2015 at 18:19
• For about 0.1c the ship kinetic energy would be equal to annihilating ship's 10% of own mass in antimatter. That is neglecting the rocket equation - fuel needed to accelerate the fuel; just the payload. Nuclear devices have efficiency of below 3% of antimatter, then the Orion project wastes great most of the explosion energy, taking in only a small portion of the blast, and then we still need the rocket equation, number of nukes to accelerate all these nukes,,,
– SF.
Dec 30, 2015 at 5:26
• As effect, I don't have the calculation but I can say already it wanders into territory of victims of tyranny of rocket equation. As you want to increase craft speed using a certain propellant, you need to add exponentially more of the propellant to achieve linear growth of delta-V. And quite fast that results in rockets bigger than the solar system. I'm not entirely sure about 1%c but 10%c+Orion certainly seems to land into that territory.
– SF.
Dec 30, 2015 at 5:31

Is that possible at all? Given the relatively low accuracy of all estimates, 1% or 10% of the speed of light would experience only minor relativistic effects. I will therefore treat them as 3.000.000 m/s and 30.000.000 m/srespectively. Given those extreme velocities, the fact that you start in lunar orbit is not important. Also, the exact number of pulse units is highly dependent on the payload mass and the implementation of the system.

The paper on project Orion state a maximum ISP of 1.3 * 10⁶ s. Plugging this, and the target velocity into the inverse rocket equation, gives a mass ratio of 10 for the 1% of speed of light spacecraft, and aprox. 10 billions for the 10% spacecraft.

But, the paper also gives ISP values several orders of magnitudes lower for any actual implementation of a nuclear pulse rocket. So fractions of the speed of light are even inaccessible for the Orion.

Of course this is hard to estimate accurately, but a few percent of the speed of light is achievable. The actual number of pulse units is more difficult to answer, as their decided size is a bit arbitrary. As bigger nuclear charges are more effective, I choose pulse units giving your stated 100g of acceleration. Then the number is around 10000 for 1% of the speed of light.

• Later studies indicate that the top cruise velocity that can theoretically be achieved by a Teller-Ulam thermonuclear unit powered Orion starship, assuming no fuel is saved for slowing back down, is about 8% to 10% of the speed of light (0.08-0.1c).[2] An atomic (fission) Orion can achieve perhaps 3%-5% of the speed of light. A nuclear pulse drive starship powered by Fusion-antimatter catalyzed nuclear pulse propulsion units would be similarly in the 10% range and pure Matter-antimatter annihilation rockets would be theoretically capable of obtaining a velocity between 50 to 80% of the speed.
– John
Dec 29, 2015 at 18:23
• @John - there is a lot of material in your comment above that would be good to add to your question. In particular, links to the documents you are quoting would be great. Dec 29, 2015 at 19:52
• @kim holder - that was from the wiki page of project orion, at the end of the interstellar missions chapter.
– John
Dec 31, 2015 at 0:36