GURPS Spaceships Design Spreadsheet

[Flyndaran]

Is there a reason my initial ship design doesn't reach 2500 mph from 1 g of jet engine accel, but only reaches 2000 mph?

[ericbsmith]

Top Air Speed for a Turbofan is 2000mph (SS7, p. 10)

[Flyndaran]

Originally Posted by ericbsmith

Top Air Speed for a Turbofan is 2000mph (SS7, p. 10)

D'oh. I figured it was something obvious. Thanks.

[Flyndaran]

Adjustments to delta V when getting relativistic?

As in Newton says I should get to 76,160 mps, but I know Einstein says that I would be going a bit slower.
As a viewer from the starting point would see it of course.

Is it just the time dilation ratio in velocity format, or something else entirely?

[Agemegos]

Originally Posted by Flyndaran

Adjustments to delta V when getting relativistic?

As in Newton says I should get to 76,160 mps, but I know Einstein says that I would be going a bit slower.
As a viewer from the starting point would see it of course.

Is it just the time dilation ratio in velocity format, or something else entirely?

You don't have to worry about relativistic exhaust velocities because the Lorenz factors of the propellant and spacecraft cancel out nicely — except when the vessel has an external source of propellant or energy, as in the case of a ramjet or light-sail. The Rocket Equation for relativistic values of delta-vee (well, actually it's the correct Rocket Equation, but the Tsiolkovsky Equation is a very good approximation when delta-vee is small compared with c) is:

Δv = c tanh(ve ln(m0/m1)/c)

Compare that with Tsiolkovsky's equation:

Δv = ve ln(m0/m1)

Note that the relativistic rocket equation really only applies to acceleration all in the same direction, because relativistic velocities don't add nicely. If you want to add the fuel requirement for accelerating to an interstellar coasting speed and then slowing down at the other end, or to add stages. you have to use rapidities rather than velocities. The formula for the delta or rapidity available to a relativistic rocket is a lot more like Tsiolkoksky's equations:

Δr = ve ln(m0/m1) / c

For your information, tanh(x) = (e^x -e^-x)/(e^x + e^-x)

[Flyndaran]

So no easy way to whip the Spaceships' rules into working just from classical delta V?

I can't quite see at what point the issue becomes big enough to reach its granularity.
Would slow acceleration up to 10% to 20% C be big enough, and ball park figure any idea what that adjustment would be?
My brain is not working so well to remember my math classes from 20 years ago.
I just realized how old that makes me. :)

Though, if I could remember enough, Rapidity seems to be what I was fumbling around for.

[Agemegos]

Originally Posted by Flyndaran

So no easy way to whip the Spaceships' rules into working just from classical delta V?

Use Rapidity. Delta-r is classical delta-v divided by c.

But in general, you can't do relativity without doing relativity.

[vierasmarius]

Originally Posted by Flyndaran

I can't quite see at what point the issue becomes big enough to reach its granularity.
Would slow acceleration up to 10% to 20% C be big enough, and ball park figure any idea what that adjustment would be?
My brain is not working so well to remember my math classes from 20 years ago.
I just realized how old that makes me. :)

According to the Time Dilation Calculator on Wolfram Alpha, 0.1c to 0.2c will result in a time dilation of 0.5% to 2% - not enough to be significant in most gaming contexts.

[Agemegos]

Originally Posted by vierasmarius

According to the Time Dilation Calculator on Wolfram Alpha, 0.1c to 0.2c will result in a time dilation of 0.5% to 2% - not enough to be significant in most gaming contexts.

That's right. Relativistic corrections are small enough to disregard for velocities under 0.2 c, especially when you are working with a system that ignores the mass of empty propellant tanks including anti-matter storage.

But for delta-v you really ought to use tanh(v/c) rather than gamma(v). There ought to be a tanh button on your scientific calculator.

tanh(0.1) is approximately 0.099667994625, so the correction at v = 0.1 c is -0.033% to delta-vee.

tanh(0.2) is approximately 0.197375320225, so the correction at v = 0.2 c is -1.312% to delta-gee.

Both negligible.

[Flyndaran]

Originally Posted by Agemegos

Use Rapidity. Delta-r is classical delta-v divided by c.

But in general, you can't do relativity without doing relativity.

Okay, sorry that I'm asking questions when my normally subpar brain is even less par.

But since rapidity for 0.200 C is 0.203, I should use (0.200)(0.200/0.203) to get its real cruising speed of 0.197, right?

Thanks for walking me through what's old hat to you.